research article joint bandwidth and power allocation for...
TRANSCRIPT
Research ArticleJoint Bandwidth and Power Allocation for LTE-BasedCognitive Radio Network Based on Buffer Occupancy
Alia Asheralieva and Yoshikazu Miyanaga
Laboratory of Information Communication Networks Hokkaido University Kita 14 Nishi 9 Kita-kuSapporo Hokkaido 060-0814 Japan
Correspondence should be addressed to Alia Asheralieva aasheralievagmailcom
Received 17 August 2015 Accepted 23 November 2015
Academic Editor Yuh-Shyan Chen
Copyright copy 2016 A Asheralieva and Y Miyanaga This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited
We investigate the problem of resource allocation in a cognitive long-term evolution (LTE) network where the available bandwidthresources are shared among the primary (licensed) users (PUs) and secondary (unlicensed) users (SUs) Under such spectrumsharing conditions the transmission of the SUs should have minimal impact on quality of service (QoS) and operating conditionsof the PUs To achieve this goal we propose to assign the network resources based on the buffer sizes of the PUs and SUs in theuplink (UL) and downlink (DL) directions To ensure that the QoS requirements of the PUs are satisfied we enforce some upperbound on the size of their buffers considering two network usage scenarios In the first scenario PUs pay full price for accessingthe spectrum and get full QoS protection the SUs access the network for free and are served on a best-effort basis In the secondscenario PUs pay less in exchange for sharing the bandwidth and get the reduced QoS guarantees SUs pay some price for theiraccess without any QoS guarantees Performance of the algorithms proposed in the paper is evaluated using simulations in OPNETenvironment The algorithms show superior performance when compared with other relevant techniques
1 Introduction
The traditional fixed spectrum allocation policy has beencharacterized by a very ineffective spectrum utilizationresulting in an artificial scarcity of the network resources[1] which stimulated a surge of interest to an alternativespectrumusage concept known as cognitive radio (CR) [2] Ina CR network (CRN) the available bandwidth resources canbe shared among the PUs (paying some price for accessingspectrum) and the SUs (who can get the wireless accessfor free) Needless to say under such spectrum sharingconditions the transmission of the SUs should have minimalimpact on QoS and operating conditions of the PUs [2]
Among existingwireless standards considered for deploy-ment in CRNs LTE is considered to be the most favourabledue to such appealing features as spectrum flexibility fastadaptation to time-varying channel conditions high spectralefficiency and robustness against interference [3] A detaileddescription of the LTE radio interface can be found forinstance in [4] In short LTE is based on the universal
terrestrial radio access (UTRA) and a high-speed downlinkpacket access (HSDPA) In the DL LTE uses an orthogonalfrequency division multiple access (OFDMA) which hashigh spectral efficiency and robustness against the interfer-ence A single carrier frequency divisionmultiple access (SC-FDMA) is applied in the UL direction due to its lower(compared to OFDM) peak-to-average power ratio (PAPR)[5] The numerology of LTE includes a subcarrier spacingof 15 kHz support for scalable bandwidth of up to 20MHzand a resource allocation granularity of 180 kHz times 1ms(called a resource block) Available transmission resourcesare distributed among the users by the medium accesscontrol (MAC) schedulers located in enhanced NodeBs(eNBs) Depending on the implementation the schedulingcan be done based on queuing delay instantaneous channelconditions fairness and so forth [6 7]
Due to existence of two types of users (primary andsecondary) with different QoS requirements the problems ofdynamic spectrum access (DSA) and resource allocation forCRNs are more complex than those considered in traditional
Hindawi Publishing CorporationMobile Information SystemsVolume 2016 Article ID 6306580 23 pageshttpdxdoiorg10115520166306580
2 Mobile Information Systems
wireless networks The majority of the works on resourceallocation in LTE-based CRNs focus on various lower layertechniques for spectrum sensing and spectrummobility (seeeg [8ndash10])These techniques are very effective in identifyingand reducing the interference in the physical channels butdo not improve the overall user-perceived QoS which ismainly expressed in terms of the packet end-to-end delay andloss for the network users Consequently the results of theseworks are applicable only in combination with the techniquesdesigned for MAC and higher layers [11]
The QoS protection for the PUs and the admissibility ofthe SUs have been studied using the theoretical analysis ofuser behaviour For instance in [12] the authors propose astatistical traffic control for the LTE-based CRNs To satisfythe timing constraints of all packets belonging to differentstreams (with diverse QoS characteristics and requirements)and achieve the statistical QoS guarantees the authorsdeploy admission control and coordinated transmissions ofthe constant-bit-rate (CBR) and the variable-bit-rate (VBR)streams Dynamic channel selection for autonomous wirelessusers transmitting delay-sensitive multimedia applicationsover a CRN has been studied in [13] Unlike prior workswhere the application-layer requirements of the users havenot been considered here the rate and delay requirements ofheterogeneous multimedia users are taken into account Theauthors propose a novel priority based virtual queue interfaceto efficiently manage the available spectrum resources Thisinterface is used to (i) determine the required informationexchanges (ii) evaluate the expected delays experiencedby various priority traffics (iii) design a dynamic strategylearning (DSL) algorithm deployed at each user that exploitsthe expected delay and (iv) adapt to the channel selectionstrategies to maximize the userrsquos utility function
The authors of [5] present a delay-power control (DPC)exploiting the trade-off between the transmission delayand transmission power in wireless networks In a pro-posed resource allocation procedure each wireless linkautonomously updates its power based on the interferenceobserved at its receiver (without any crosslink communi-cation) The DPC scheme has been proved to convergeto a unique equilibrium point and contrasted to the well-known Foschini-Miljanic (FM) formulation Some theoreti-cal underpinnings of DPC and their practical implications forefficient protocol design have also been established In [14]the problem of allocating the network resources (channelsand transmission power) in a multihop CRN is modeledas a multicommodity flow problem with the dynamic linkcapacity resulting from dynamic resource allocation Basedon such queue-balancing the authors propose a distributedscheme for optimal resource allocation without exchangingthe spectrum dynamics between remote nodes Consideringthe power masks each node makes resource allocationdecisions based on current or past local information fromneighboring nodes to satisfy the throughput requirement ofeach flow and maintain the network stability
In this paper we suggest an alternative strategy forresource allocation in a LTE-based CRN and propose toassign the network resources (bandwidth and transmissionpower) to the UL and DL of LTE system based on buffer
size of user equipment (UE) pieces Note that in manypreviously proposed algorithms (eg [8ndash13]) the bandwidthand transmission power are assigned without considering thebuffer occupancy of UE pieces which may lead to a ratherunfair resource allocation (when users with lower demandsare allocated larger bandwidth than the users with higherdemands)
To ensure that the QoS requirements of the PUs aresatisfied we put the constraints on the sizes of their buffersTwo network usage scenarios are considered In the firstscenario the PUs pay full price for accessing the spectrumand get the full QoS protection whereas the SUs access thenetwork for free and are served on a best-effort basis In thesecond scenario the PUs pay less in exchange for sharingthe bandwidth and get the reduced QoS guarantees SUs paysome price for their usage without any QoS guarantees Theproposed resource allocation algorithm is derived based on adiscrete spectrum assumption with the spectrum resourcescounted in terms of LTE resource blocks (RBs) Note thata continuous spectrum assumption (used in all past works)is not applicable for a practical LTE realization since thenumber of RBs comprising the bandwidth is relatively small(6 10 20 50 and 100 RBs corresponding to 14 3 5 10and 100MHzwidebands resp [15]) Unlike existing researchcontributions the transmission rates of SUs and DUs arecalculated using the modified Shannon expression whichaccounts for the adaptive modulation and coding (AMC)used in LTE
The rest of the paper is organized as follows In Section 2we describe the network model and formulate the resourceallocation problems in two network usage scenarios InSection 3 we provide the solution methodology and dis-cuss the implementation of a presented resource allocationapproach in a real LTE system In Section 4 we outline asimulation model and evaluate performance of the proposedresource allocation algorithms in two network usage scenar-ios The paper is finalized in Conclusion
2 Problem Statement
21 NetworkModel Assumptions and Notation In this workthe problem of joint power and bandwidth allocation forthe LTE-based CRN is investigated for both the UL and theDL directions Similarly the discussion through the rest ofthe paper is applicable (if not stated otherwise) to eitherdirection
Consider a basic LTE-based CRN architecture whichconsists of one eNB providing wireless access to 119899 PUs num-bered PU
1 PU
119899 and 119898 SUs numbered SU
1 SU
119898
Two spectrum usage scenarios are considered in this paperIn the first scenario PUs are the licensed network users whopay some price for accessing the spectrum and thereforemustbe provided with the certain guaranteed QoS levels SUs arethe unlicensed network users who can access the spectrumfor free and therefore they are served on a best-effort basis Inthe second scenario the PUs pay less in exchange for sharingthe spectrum the SUs have to pay some price for the sharedspectrum to compensate for the income losses of a serviceprovider
Mobile Information Systems 3
The considered network operates on a slotted-time basiswith the time axis partitioned into mutually disjoint timeintervals (slots) 119879
119904 (119905+1)119879
119904 119905 = 0 1 2 with 119879
119904denoting
the slot length and 119905 being the slot indexThenumber of activePUs and SUs can be tracked using an LTE random accesschannel (RACH) procedure [15] which is used for initialaccess to the network (ie for originating terminating orregistration calls)
In the UL direction the user-generated traffic (in bits perslot or bps) is enqueued in the buffers of UE pieces and thentransmitted to the eNB using a standard packet schedulingprocedure [15] In this procedure the information about theamount of data (in bps) enqueued in the buffers of UE piecesis constantly transmitted to the eNB so that the eNB ldquoknowsrdquothe exact amount of data generated by the users at any slot 119905This information is then used by the eNB to allocate the ULtransmission resources to UE pieces In the DL direction thetransmission resources are allocated based on the amount ofdata transmitted by eNB to the users
In LTE system the transmission resources are allocatedto the users in terms of RBs Each user can be allocatedonly the integer number of RBs and these RBs should notbe adjacent to each other [7 15] Another important featureof both the SC-FDMA (applied in the UL direction) andOFDMA (applied in the DL direction) is the orthogonal-ity of resource allocation which allows achieving minimallevel of cochannel interference between different transmitter-receiver pairs located within one cell (ie when no frequencyreuse is considered)
It is assumed that the bandwidth of the eNB is fixed andequal to 119861 RBs For any 119894 in I = 1 119899 and any 119895 in J =1 119898 consider the following
(i) The channel between the eNB and PU119894is character-
ized by the noise and interference coefficient 0 lt
ℎ119875119894
le 1 which is known to the eNB and PU119894 The
channel between the eNB and SU119895is characterized by
the noise and interference coefficient 0 lt ℎ119878119895le 1
which is known to the eNB and SU119895 The values of ℎ
119875119894
and ℎ119878119895in the UL and DL directions can be obtained
from the channel state information (CSI) through theuse of the LTE reference signals (RSs) [16 17]
(ii) The size of the buffers and the arrival rates (in bits) ofPU119894and SU
119895can be observed at any slot 119905 in the UL
and DL directions
The following notations are used throughout the paper
(i) 119887119875119894(119905) and 119887
119878119895(119905) denote the number of RBs allocated
at slot 119905 to PU119894and SU
119895 respectively
(ii) 119901119875119894(119905) and 119901
119878119895(119905) denote the transmission power
allocated at slot 119905 to PU119894and SU
119895 respectively
(iii) 119886119875119894(119905) and 119886
119878119895(119905) denote the arrival rate (in bps) at slot
119905 in PU119894and SU
119895 respectively
(iv) 119902119875119894(119905) and 119902
119878119895(119905) denote the buffer size (in bits) at slot
119905 of PU119894and SU
119895 respectively
(v) 119903119875119894(119905) and 119903
119878119895(119905) denote the transmission rate (in bps)
at slot t in the channels of PU119894and SU
119895 respectively
(vi) 119875eNB 119875119875119894 and 119875119878119895denote the maximal transmission
power of the eNB PU119894 and SU
119895 respectively
22 Scenario 1 The objective of this paper is to devise asustainable algorithm for joint bandwidth and transmissionpower allocation based on two goals
(1) QoS Protection for the PUs PUs should maintain theirtarget QoS irrespective of how many SUs enter thenetwork and how much load they are generating
(2) Admissibility of the SUs SUs should be able to utilizethe spare capacity of the eNB (if left) to maximizetheir QoS
These goals however cannot be achieved without pro-viding the quantified measures for the user-perceived QoSNote that because of the orthogonality of the RB allocationthe need for interference mitigation in a considered CRNis eliminated In this case the use of such physical layercharacteristics as signal-to-noise ratio (SNR) is not well-reasoned More practical QoS measures can be obtainedfrom the higher layers network information For instancesuch metrics as round-trip latency and loss are traditionallyused for performance evaluation in wireless networks [5]Unfortunately in LTE system the direct estimation of delayand loss is rather complex For instance the end-to-endlatency consists of various delay components includingtransmission and queuing delays propagation andprocessingdelays the UL delay due to scheduling and delay due tohybrid automatic repeat request (HARQ) [18] The accurateanalysis of these delay components requires knowledge ofmany system parameters which may be not available duringresource allocation
Consequently in this paper we argue in favour of usingthe buffer size of UE pieces as a QoS measure The buffersize of PUs and SUs can be easily estimated from the knownparameters 119902
119875119894(119905) 119886119875119894(119905) and 119902
119878119895(119905) 119886119878119895(119905) using well-known
Lindleyrsquos equation [19]
119902119875119894(119905 + 1) = lceil119902
119875119894(119905) + 119886
119875119894(119905) minus 119903
119875119894(119905)rceil+
forall119894 isin I (1a)
119902119878119895(119905 + 1) = lceil119902
119878119895(119905) + 119886
119878119895(119905) minus 119903
119878119895(119905)rceil
+
forall119895 isin J (1b)
where lceil119909rceil+ = max0 119909 whereas the transmission rates119903119875119894(119905) 119903119878119895(119905) depend on the unknown bandwidth and trans-
mission power allocation vectors given by (relationshipbetween the transmission rate transmission power and thebandwidth will be established in the next section)
p119875= [1199011198751(119905) 119901
119875119899(119905)]119879
b119875= [1198871198751(119905) 119887
119875119899(119905)]119879
(2a)
p119878= [1199011198781(119905) 119901
119878119898(119905)]119879
b119878= [1198871198781(119905) 119887
119878119898(119905)]119879
(2b)
Note that the average round-trip latency of any primaryUE can be retained below some upper bound level by
4 Mobile Information Systems
restricting its buffer size to be less than a certain target buffersize The only information which is necessary in this case isthe desired upper bound on delay and the average arrival ratein PUs during some interval 119879 gt 0 Then we can find thetarget buffer size by deploying Littlersquos formula [20]
119863119894sdot 119886119875119894(119905) = 119871
119894 forall119894 isin I (3a)
where119863119894is the upper bound on delay for PU
119894 119871119894is the target
buffer size for PU119894 119886119875119894(119905) is the average arrival in PU
119894during
time interval [119905 minus 119879 + 1 119905] given by
119886119875119894(119905) =
119905
sum
120591=119905minus119879+1
119886119875119894(119905) forall119894 isin I (3b)
To maintain the desired upper bound on the end-to-enddelay the buffer size of PUs should be constrained as follows
119902119875119894(119905 + 1) le 119871
119894 forall119894 isin I (4)
or equivalently using (1a)
119902119875119894(119905) + 119886
119875119894(119905) minus 119871
119894le 119903119875119894(119905) le 119902
119875119894(119905) + 119886
119875119894(119905)
forall119894 isin I(5)
If added to an optimization problem constraint (5) canguarantee the QoS protection for PUs Except some (veryrare) cases when constraint (5) is not feasible the buffersize will always stay below the target level irrespective ofhow many SUs are in the network and how much load theyare generating The setting of the parameters 119871
119894 as well as
the cases when constraint (5) is unfeasible is discussed inSection 3
Note that at any slot 119905 the number of RBs allocatedfor data transmissions of PUs and SUs in the UL and DLdirections should not exceed 119861 RBs That is
sum
119894isinI119887119875119894(119905) + sum
119895isinJ119887119878119895(119905) le 119861 (6a)
where
119887119875119894(119905) isin Z+
119887119878119895(119905) isin Z+
forall119894 isin I forall119895 isin J
(6b)
where Z+ represents the set of all nonnegative integersAdditionally the transmission power allocated to the
users at any slot 119905 should be nonnegative and cannot exceedthe maximal transmission power levels Hence
119901119875119894(119905) le 119875
119875119894
119901119878119895(119905) le 119875
119878119895
forall119894 isin I forall119895 isin J
(7a)
for the UL direction and
sum
119894isinI119901119875119894(119905) + sum
119895isinJ119901119878119895(119905) le 119875eNB (7b)
for the DL direction where119901119875119894(119905) ge 0
119901119878119895(119905) ge 0
forall119894 isin I forall119895 isin J
(7c)
We are now ready to show how to attain the second goalof resource allocation As in case with QoS protection of PUswe use the buffer sizes of SUs as ameasure of the SUsrsquoQoSWesay that the admissibility of SUs in the network is preserved ifthey are allocated the bandwidth that is not used by the PUsThis can be done for instance byminimizing the sum (or thelogarithmic sum) of the buffer sizes of SUs or minimizing themaximal buffer size of SUs subject to the constraints listedabove
For the UL direction this gives us the following problem(to simplify notation we skip the index t below)
minimize max119895isinJ
lceil119902119878119895+ 119886119878119895minus 119903119878119895rceil
+
(8a)
subject to 119902119875119894+ 119886119875119894minus 119871119894le 119903119875119894le 119902119875119894+ 119886119875119894 forall119894 isin I (8b)
sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (8c)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(8d)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(8e)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(8f)
For the DL direction constraint (8e) should be replaced by
sum
119894isinI119901119875119894+sum
119895isinJ119901119878119895le 119875eNB (8g)
In above formulation each PU is guaranteed a certaintarget QoS level and the optimal allocations for PUs are suchthat
119902119875119894+ 119886119875119894minus 119903119875119894= 119871119894 forall119894 isin I (9)
The spare bandwidth (if left) is distributed among the SUsto minimize the size of their buffer which means that thetwo goals of resource allocation are achieved However thisformulation works well only if the aggregated traffic demandof the SUs is greater than that of the PUs Otherwise theremight be a situationwhen the optimal solution for SUs is suchthat
max119895isinJ
lceil119902119878119895+ 119886119878119895minus 119903119878119895rceil
+
le 119871119894 forall119894 isin I (10)
Mobile Information Systems 5
which is apparently not fair since the PUs have larger buffersizes than the SUs and therefore they will experience longerdelays than the SUs
To avoid such situation we propose to modify problem(8a)ndash(8g) by replacing its objective (8a) with
minimize max119894isinI
lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+
+max119895isinJ
lceil119902119878119895+ 119886119878119895minus 119903119878119895rceil
+
(11)
Objective (11) guarantees that PUs are served with max-imal QoS even if the aggregated traffic demand of SUs isgreater than that of the PUs
23 Scenario 2 We now consider a different scenario inwhich the PUs will benefit (by paying less in exchange) fromsharing their bandwidth with the SUs Let us assume that inthe network without price benefits (ie in Scenario 1) theprice for accessing the licensed spectrum of the PUs equals1 In this case all the PUs get the full QoS protection (ieguaranteed target buffer size 119871
119894and the average end-to-end
latency 119863119894) Suppose that each PU can define the portion of
allocated spectrum that it is willing to share with the SUsThedelay in turn is related to lceil119902
119875119894+ 119886119875119894minus 119903119875119894rceil+
Let us denote by 120572119894 0 le 120572
119894lt 1 the price for the portion
of spectrum that PU119894is willing to share with the SUs So
120572119894represents the willingness of PU
119894to trade off its QoS for
money Subsequently the guaranteed QoS level of PU119894will
reduce and instead of the QoS protection constraint (8b) wewill have
119903119875119894ge 119902119875119894+ 119886119875119894minus (1 + 120572
119894) 119871119894 forall119894 isin I (12)
Now to compensate for the income losses of a serviceprovider the SUs will have to pay the price for the sharedspectrum Let 120573 denote the price that each SU will pay foraccessing the shared spectrum The amount that SU
119895pays in
this case is 120573119903119878119895 whereas the revenue of the service provider
is
sum
119895isinJ120573119903119878119895minussum
119894isinI120572119894lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+
(13)
Assuming that a service provider does not incur loss byallowing the secondary users to use the spectrum we have toincorporate the constraint
sum
119895isinJ120573119903119878119895minussum
119894isinI120572119894lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+
ge V (14)
where V is the profit that a service provider would like tomakeby allowing the SUs into the network
Note that in such formulation the SUs get no QoSguarantee and therefore we have to minimize the price that
the SUs pay for their usage Thus the optimization problemis
minimize 120573 (15a)
subject to 119902119875119894+ 119886119875119894minus (1 + 120572
119894) 119871119894le 119903119875119894
le 119902119875119894+ 119886119875119894
forall119894 isin I
(15b)
sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (15c)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(15d)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(15e)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(15f)
sum
119895isinJ120573119903119878119895minussum
119894isinI120572119894lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+
ge V (15g)
for the UL direction For the DL direction constraint (15e) isreplaced by constraint (8g)The value of120573 obtained by solving(15a)ndash(15g) is then broadcasted by a service provider to theSUs that will have to pay a determined price
We note in passing that there are many other ways inwhich the pricing problem could be addressed For instancethe numbers 120572
119894may be negotiated between the PUs and a
service provider One can also think of a scenario wheredifferent SUs may be able to express their willingness to payvia bidding the prices 120573
119895 The options are numerous but they
are beyond the scope of this paper
3 Implementation Issues
31 Rate as a Function of Bandwidth and Power Note thatthe transmission rates in the UL and DL channels of a LTEsystem can be found using the modified Shannon equation[21] expressed as
119903119875119894(b119875 p119875) = 120596120595
119875119894119887119875119894log (1 + 120585
119875119894SNR119875119894)
= 120596120595119875119894119887119875119894log (1 + 120585
119875119894ℎ119875119894119901119875119894)
0 lt 120595119875119894 120585119875119894le 1 forall119894 isin I
(16a)
6 Mobile Information Systems
119903119878119895(b119878 p119878) = 120596120595
119878119895119887119878119895log (1 + 120585
119878119895SNR119878119895)
= 120596120595119878119895119887119878119895log (1 + 120585
119878119895ℎ119878119895119901119878119895)
0 lt 120595119878119895 120585119878119895le 1 forall119895 isin J
(16b)
where SNR119875119894and SNR
119878119895are the SNRs in the channels of PU
119894
and SU119895 respectively 120595
119875119894and 120595
119878119895are the system bandwidth
efficiencies for PU119894and SU
119895 respectively 120585
119875119894and 120585
119878119895are
the SNR efficiencies for PU119894and SU
119895 respectively 120596 is the
bandwidth of one RB (120596 = 180 kHz) [21]In real LTE networks the system bandwidth efficiency
is strictly less than 1 due to the overheads on the link andsystem levels The bandwidth efficiency is fully determinedby the design and internal settings of the system and doesnot depend on the physical characteristics of the wirelesschannels between the user and the eNB [21 22] Hence it isreasonable to assume that
120595119875119894= 120595119878119895= 120595 forall119894 isin I forall119895 isin J (17)
The SNR efficiency is mainly limited by the maximumefficiency of the supported modulation and coding scheme(MCS) [16] In LTE MCS is chosen using AMC to maximizethe data rate by adjusting the transmission parameters to thecurrent channel conditions AMC is one of the realizations ofa dynamic link adaptation In AMC algorithm the appropri-ate MCSs for packet transmissions are assigned periodically(within short fixed time interval usually equal to one slot)by the eNB based on the instantaneous channel conditionsreported by the usersThe higherMCS values are allocated tothe high-quality channels to achieve higher transmission rateThe lower MCS values are assigned to the channels of poorquality to decrease the transmission rate and consequentlyensure the transmission quality [16 17]
The method for choosing MCS can be expressed asfollows Based on the instantaneous radio channel conditionsthe SNR is calculated for the DL wireless channels betweenthe eNB and the users A supported MCS index is chosenusing expression [16 17]
MCS =
MCS1 SNR lt 120574
1
MCS2 1205741le SNR lt 120574
2
MCS119897 120574119897minus1
le SNR lt 120574119897
(18)
where 1205741
lt 1205742
lt sdot sdot sdot lt 120574119897are the SNR thresholds
corresponding to minus10 dB bit error ratio (BER) given by theAdditive White Gaussian Noise (AWGN) curves for eachMCS (the standard AWGN curves can be found in [17]) TheLTE standard allows 119897 = 15 MCS levels (description of MCSlevels their code rate and efficiency is shown in Table 1) [17]
Table 1 Allowed MCS values in LTE standard [17]
MCS index Modulation Code rate Efficiency0 No transmission1 QPSK 78 015232 QPSK 120 023443 QPSK 193 037704 QPSK 308 060165 QPSK 449 087706 QPSK 602 117587 16 QAM 378 147668 16 QAM 490 191419 16 QAM 616 2406310 64 QAM 466 2730511 64 QAM 567 3322312 64 QAM 666 3902313 64 QAM 772 4523414 64 QAM 873 5115215 64 QAM 948 55547
Based on the above the SNR efficiency depends onthe SNR of the DL wireless channel and therefore can berepresented by a function
119892 (SNR) =
1205851 SNR lt 120574
1
1205852 1205741le SNR lt 120574
2
120585119897 120574119897minus1
le SNR lt 120574119897
(19)
where 0 lt 1205851lt 1205852lt sdot sdot sdot lt 120585
119897are the values of the SNR
efficiency corresponding to the supported MCSUsing (17) and (19) the transmission rates of the users can
be expressed as
119903119875119894(b119875 p119875) = 120596120595119887
119875119894log (1 + 119892 (SNR
119875119894) sdot SNR
119875119894)
= 120596120595119887119875119894log (1 + 119892 (119901
119875119894) sdot ℎ119875119894119901119875119894)
forall119894 isin I
(20a)
119903119878119895(b119878 p119878) = 120596120595119887
119878119895log (1 + 119892 (SNR
119878119895) sdot SNR
119878119895)
= 120596120595119887119878119895log (1 + 119892 (119901
119878119895) ℎ119878119895119901119878119895)
forall119895 isin J
(20b)
32 Solution Methodology In this subsection we describe asolution methodology for the resource allocation problemin Scenario 1 in the UL direction (with the objective givenby (11) and the constraints defined in (8b)ndash(8f)) A resourceallocation problem for the DL direction as well as problem(15a)ndash(15g) for Scenario 2 can be solved analogously
Mobile Information Systems 7
Note that in Scenario 1 a resource allocation problem inthe UL direction is equivalent to
minimize Ω + Φ (21a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (21b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(21c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(21d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(21e)
Ω ge 0
Φ ge 0
(21f)
1198911
119894(b119875 p119875) = 119903119875119894(b119875 p119875) minus (119902
119875119894+ 119886119875119894)
le 0
forall119894 isin I
(21g)
1198912
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894minus 119871119894) minus 119903119875119894(b119875 p119875)
le 0
forall119894 isin I
(21h)
1198913
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894) minus 119903119875119894(b119875 p119875) minus Ω
le 0
forall119894 isin I
(21i)
1198914
119895(b119878 p119878)
= (119902119878119895+ 119886119878119895) minus 119903119878119895(b119878 p119878) minus Φ
le 0
forall119895 isin J
(21j)
In above problem some of the optimization variables(particularly the components of b
119875and b
119878) can take only
integer values whereas the other variables (the componentsof p119875and p
119878) are real-valued ones In addition constraints
(21g)ndash(21j) are represented by the nonsmooth nonlinear
functions of (b119875 p119875) and (b
119875 p119875) Hence (21a)ndash(21j) is a
nonlinear mixed integer programming (MINLP) problemwhich is Nondeterministic Polynomial-time (NP) hard Forimmediate proof of NP-hardness note that MINLP includesmixed integer linear programming (MILP) problem which isNP-hard [23]
Before applying any MINLP method for solving (21a)ndash(21j) the nonsmooth function 119892(sdot) in (19) included in theexpressions of 119903
119875119894(b119875 p119875) and 119903
119878119895(b119875 p119875) should be replaced
by its smooth approximation To construct a smooth approx-imation of 119892(119909) note that this function is equivalent to thesum of the shifted and scaled versions of a Heaviside stepfunction119867(119909) [24] That is
119892 (119909) =
15
sum
119897=1
(120577119897minus 120577119897minus1)119867 (119909 minus 120574
119897)
119867 (119909) =
1 if 119909 ge 0
0 otherwise
(22)
where 1205770= 0
Recall that a smooth approximation for a step function119867(119909) is given by a logistic sigmoid function [25]
119902(119909) =
1
1 + 119890minus2119902119909
(23)
where 119902 gt 0 119909 is in range of real numbers from minusinfin to +infinIf we take 119867(0) = 12 then larger 119902 corresponds to a closertransition to119867(119909) that is
lim119902rarrinfin
119902(119909) = 119867 (119909) (24)
The above holds because for 119909 lt 0 we have
119890minus2119902119909
997888rarr +infin
119902(119909) asymp 119867 (119909) = 1
(25)
for 119909 gt 0
119890minus2119902119909
997888rarr 0
119902(119909) asymp 119867 (119909) = 1
(26)
for 119909 = 0
119890minus2119902119909
= 1
119902(119909) = 119867 (119909) =
1
2
(27)
Consequently an approximation for a shifted Heavisidefunction is represented by a shifted logistic function
119902(119909 minus 120574
119897) =
1
1 + 119890minus2119902(119909minus120574119897)
(28)
defined for 119902 gt 0 with real 119909 in range from minusinfin to +infin
8 Mobile Information Systems
Based on (28) we can construct a smooth approximationfor 119892(119909) as
119902(119909) =
15
sum
119897=1
(120577119897minus 120577119897minus1) 119902(119909 minus 120574
119897) =
15
sum
119897=1
120577119897minus 120577119897minus1
1 + 1198902119902(119909minus120574119897)
(29)
Then it is rather straightforward to verify that
lim119902rarrinfin
119902(119909) = 119892 (119909) (30)
and the approximations for 119903119875119894(b119875 p119875) and 119903
119878119895(b119875 p119875) will
take the form
119875119894(b119875 p119875) = 120596120595119887
119875119894log (1 + (119901
119875119894) sdot ℎ119875119894119901119875119894)
forall119894 isin I(31a)
119878119895(b119878 p119878) = 120596120595119887
119878119895log (1 + (119901
119878119895) ℎ119878119895119901119878119895)
forall119895 isin J(31b)
With the approximations given by (31a) and (31b) prob-lem (21a)ndash(21j) can be solved using a sequential optimizationapproach as
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (32a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (32b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(32c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(32d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(32e)
Ω ge 0
Φ ge 0
(32f)
119891
1
119894(b119875 p119875)
= 119875119894(b119875 p119875)
minus (119902119875119894+ 119886119875119894) le 0
forall119894 isin I
(32g)
119891
2
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894minus 119871119894)
minus 119875119894(b119875 p119875) le 0
forall119894 isin I
(32h)
119891
3
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894)
minus 119875119894(b119875 p119875) minus Ω
le 0
forall119894 isin I
(32i)
119891
4
119895(b119878 p119878)
= (119902119878119895+ 119886119878119895)
minus 119878119895(b119878 p119878) minus Φ
le 0
forall119895 isin J
(32j)
The above problem is smooth MINLP which can besolved using some fast and effective MINLP method Notethat most of the MINLP techniques involve constructionof the following relaxations to the considered problem thenonlinear programming (NLP) relaxation (original problemwithout integer restrictions) and the MILP relaxation (origi-nal problem where nonlinearities are replaced by supportinghyperplanes) In our case a smooth MILP relaxation to(32a)ndash(32j) in a given point (b0
119875 p0119875 b0119878 p0119878) is given by
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (33a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (33b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(33c)
Mobile Information Systems 9
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(33d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(33e)
Ω ge 0
Φ ge 0
(33f)
119891
1
119894(b0119875 p0119875) + nabla
119891
1
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33g)
119891
2
119894(b0119875 p0119875) + nabla
119891
2
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33h)
119891
3
119894(b0119875 p0119875) + nabla
119891
3
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33i)
119891
4
119895(b0119878 p0119878) + nabla
119891
4
119895(b0119878 p0119878)
119879
[
b119878minus b0119878
p119878minus p0119878
]
le 0
forall119895 isin J
(33j)
The NLP relaxation to (32a)ndash(32j) is
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (34a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (34b)
119887119875119894ge 0
119887119878119895ge 0
forall119894 isin I forall119895 isin J
(34c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(34d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(34e)
Ω ge 0
Φ ge 0
(34f)
119891
1
119894(b119875 p119875) le 0
forall119894 isin I(34g)
119891
2
119894(b119875 p119875) le 0
forall119894 isin I(34h)
119891
3
119894(b119875 p119875) le 0
forall119894 isin I(34i)
119891
4
119895(b119878 p119878) le 0
forall119895 isin J(34j)
Note that theMINLP problems can be solved using eitherdeterministic technique or an approximation A typical exact
10 Mobile Information Systems
method for solving MINLPs is a well-known branch-and-bound algorithmand its variousmodifications [26] examplesof heuristic approaches include local branching [27] largeneighborhood search [28] and feasibility pump [29] to namea few Since we are interested in a reasonably simple and fastalgorithm it is more convenient to use heuristics for solvingthe problem In this paper a Feasibility Pump (FP) heuristic[29 30] is applied to solve (32a)ndash(32j) FP is perhaps the mostsimple and most effective method for producing more andbetter solutions in a shorter average running time For theproblems with nonbinary integer variables the complexity ofFP is exponential in size of a problem [31]
A fundamental idea of FP algorithm is to decomposethe problem into two parts integer feasibility and constraint
feasibility The former is achieved by rounding (solvinga NLP relaxation to the original problem) and the latterby projection (solving a MILP relaxation) Consequentlytwo sequences of points are generated The first sequence(b119875 p119875 b119878 p119878)119896119870
119896=1 119870 = 1 2 contains the integral
points that may violate the nonlinear constraintsThe secondsequence (b
119875 p119875 b119878 p119878)119896119870
119896=1contains the points which are
feasible for a continuous relaxation to the original problembut might not be integral
More specifically with input (b119875 p119875 b119878 p119878)1being a
solution to the NLP relaxation given by (34a)ndash(34j) thealgorithm generates two sequences by solving the followingproblems for 119896 = 1 119870
(b119875 p119875 b119878 p119878)119896= argmin
100381710038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b
119875 p119875 b119878 p119878)119896
1003817100381710038171003817100381710038171
(35a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (35b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(35c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(35d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(35e)
Ω ge 0
Φ ge 0
(35f)
119891
1
119894(b0119875 p0119875) + nabla
119891
1
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35g)
119891
2
119894(b0119875 p0119875) + nabla
119891
2
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35h)
119891
3
119894(b0119875 p0119875) + nabla
119891
3
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35i)
Mobile Information Systems 11
119891
4
119895(b0119878 p0119878) + nabla
119891
4
119895(b0119878 p0119878)
119879
[
b119878minus b0119878
p119878minus p0119878
] le 0
forall119895 isin J
(35j)
(b119875 p119875 b119878 p119878)119896+1
= argmin 10038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b
119875 p119875 b119878 p119878)119896
100381710038171003817100381710038172
(36a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (36b)
119887119875119894ge 0
119887119878119895ge 0
forall119894 isin I forall119895 isin J
(36c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(36d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(36e)
Ω ge 0
Φ ge 0
(36f)
119891
1
119894(b119875 p119875) le 0
forall119894 isin I(36g)
119891
2
119894(b119875 p119875) le 0
forall119894 isin I(36h)
119891
3
119894(b119875 p119875) le 0
forall119894 isin I(36i)
119891
4
119895(b119878 p119878) le 0
forall119895 isin J(36j)
where sdot1and sdot
2are 1198971norm and 119897
2norm respectivelyThe
rounding step is carried out by solving (35a)ndash(35j) whereasthe projection is the solution to (36a)ndash(36j) A suggested FPalgorithm alternates between the rounding and projectionsteps until (b
119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896(which implies
feasibility) or the number of iterations 119896 has reached thepredefined limit 119870 The workflow of a corresponding FPalgorithm is illustrated in the following part
FP Algorithm for Non-Convex MINLP(0) INITIALIZATION input119870 set 119896 = 1
solve (34a)ndash(34j) to obtain (b119875 p119875 b119878 p119878)119896
(1) WHILE (119896 lt 119870) do
(2) ROUNDING solve (35a)ndash(35j) to obtain(b119875 p119875 b119878 p119878)119896
(3) IF ((b119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896) THEN goto
step (6)(4) PROJECTION solve (36a)ndash(36j) to obtain
(b119875 p119875 b119878 p119878)119896+1
(5) Set 119896 = 119896 + 1
12 Mobile Information Systems
(6) OUTPUT solution (b119875 p119875 b119878 p119878)lowast
=
(b119875 p119875 b119878 p119878)119896
Note that in order to retain the convergence of thealgorithm both problems (35a)ndash(35j) and (36a)ndash(36j) needto be solved exactly Problem (36a)ndash(36j) (and consequentlyproblem (34a)ndash(34j)) can be solved using any standard NLPmethod In this paper an interior point algorithm (describedeg in [32]) with polynomial complexity is applied to solve(36a)ndash(36j) and (34a)ndash(34j) MILP problem (35a)ndash(35j) isrelatively simple and therefore can be solved efficiently foroptimality by any technique from the family of the branch-and-bound methods (eg [26])
33 Target Buffer Size for PUs and Feasibility Issues Recallthat 119871
119894represents the target buffer size for PU
119894 which
indicates that the QoS requirements of PU119894are satisfied By
limiting the buffer size of PUs we restrict the QoS of PUs(measured in terms of their buffer size) to be higher (or atleast not smaller) than the required minimum From thispoint of view constraints (5) and (12) guarantee the QoSprotection of PUs in Scenario 1 and Scenario 2 respectivelyApparently one can always restrict the target buffer size ofPUs to be equal to zero so that after each subsequent dataarrival the buffer of each PU is fully cleared This approachrepresents a ldquogreedyrdquo policy which ensures that the PUs arealways served with the best possible QoS but does not guar-antee that some spare capacity will be left to serve the SUs
A ldquoless greedyrdquo strategy would be to establish somelower bound on QoS for the PUs which will provide anldquoopportunityrdquo for SUs to be served To establish this lowerbound recall that the growing delay and loss indicate thata buffer of a corresponding node is congested whereas inan uncongested node the packet delay and loss are alwaysminimal [33] On the other hand it has been reported in[33 34] that in an uncongested node the buffer size 119902(119905) isincreasing very slowly that is 119902(119905 + 1)119902(119905) asymp 1 whereas ina congested node the buffer size is growing very fast so that119902(119905+1)119902(119905) ≫ 1 Hence to serve the PUs withminimal delayand loss it is enough to prevent the growth of their buffersthat is for each PU set
119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)
where 120576 ge 0 is some small value such that
120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)
More sophisticated approach to find the lowerQoS boundcan be deployed if information about the past buffer size isavailable at any time slot 119905 In this case one can set the targetbuffer size based on past T observations 119902(119905) 119902(119905 minus 119879 + 1)as
119871119894= min120591isinT
119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38a)
or
119871119894=
1
119879
sum
120591isinT119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38b)
where T = 1 119879
UBADPC MBC
60
70
80
90
100
110
120
130
140
Alg
orith
m it
erat
ions
10020 8040 50 60 7030 90100Number of SUs m
120572i = 1 v = m lowast 1Mbps
Figure 1 Average number of iterations before convergence as afunction of number of SUs in simulations with 119899 = 100 PUs andaverage SNR = 0 dB
MBC
070
075
080
085
090
095
100
120572i=0
v=0
120572i=1
v=0
120572i=0
v=m
lowast1
Mbp
s
120572i=1
v=m
lowast1
Mbp
s
Fairness among SUs FSU
Fairness among PUs FPU
Fairness among all users F
Figure 2 Jainrsquos index of fairness119865SU119865PU and119865 for the PUs SUs andall users in simulations with 119899 = 100 PUs119898 = 100 SUs and averageSNR = 0 dB
In some (very rare) cases (when the service capacity of theeNB is not enough to guarantee that the buffer sizes in all PUsdo not exceed the target buffer size) constraints (5) and (12)in Scenarios 1 and 2 may be not feasible In the following weshow how to identify such situation and what should be theoptimal resource allocation strategy in this case
Note that the service capacity of LTE system greatlydepends on physical characteristics (eg SINR and MCS) of
Mobile Information Systems 13
UBADPCGBC
NBCMBCABC
780
800
820
840
860
880
900
920
940
960Th
roug
hput
for P
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r PU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for P
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
Figure 3 Mean throughput packet delay and loss for PUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
the wireless channels between the eNB and the users Henceat the moment preceding the bandwidthpower allocation itis rather difficult to estimate the service capacity of a systemNevertheless it is possible to find the average service capacityand to determine the upper and lower bounds on servicecapacity of the eNB in the UL and DL directions such that
119877min le sum119894isinI119903119875119894(119905) asymp 119877ave le 119877max (39)
where119877min119877ave and119877max are the lower bound upper boundand average service capacity of the eNB respectively
In our case the upper bound on service capacity of theeNB is given by
119877max = 120596120595119861 log (1 + 119892 (SNRmax) sdot SNRmax) (40a)
where SNRmax is the maximal possible SNR value
The lower bound on service capacity of eNB is
119877min = 120596120595119861 log (1 + 119892 (SNRmin) sdot SNRmin) (40b)
where SNRmin is the minimal possible SNR valueThe average service capacity of the eNB equals
119877ave = 120596120595119861 log (1 + 119892 (SNRave) sdot SNRave) (40c)
where SNRave is the average SNR valueIf SNR information is available then the values SNRmax
SNRmin and SNRave can be set as
SNRmax = max119894isinI
SNR119894 (41a)
14 Mobile Information Systems
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r SU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for S
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
Figure 4 Mean throughput packet delay and loss for SUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
SNRmin = min119894isinI
SNR119894 (41b)
SNRave =1
119899
sum
119894isinISNR119894 (41c)
Otherwise (ie if SNR information is not available) thevalues are set arbitrarily
Now we can identify the situation when constraints (5)and (12) cannot be satisfied For this we should perform thefollowing test For Scenario 1 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus 119871
119894) (42)
then constraint (5) is feasible Otherwise condition (5)cannot be satisfiedHence all the SUs receive zero allocations
andwe assign the bandwidthpower resources only to the PUsby solving the following optimization problem
minimize max119894isinI
lceil119902119875119894+ 119886119875119894minus 119903119875119894(b119875 p119875)rceil+
(43a)
subject to 119903119875119894(b119875 p119875) le 119902119875119894+ 119886119875119894 forall119894 isin I (43b)
sum
119894isinI119887119875119894le 119861 (43c)
119887119875119894isin Z+ forall119894 isin I (43d)
119901119875119894le 119875119875119894 forall119894 isin I (43e)
119901119875119894ge 0 forall119894 isin I (43f)
Mobile Information Systems 15
725
750
775
800
825
850
875
900
925
950Th
roug
hput
for P
Us (
kbits
s)
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
10
20
30
40
50
60
70
Dela
y fo
r PU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Loss
for P
Us (
)
0
005
01
015
02
025
03
035
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Figure 5 Mean throughput packet delay and loss for PUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
for the UL direction For the DL directions constraint (43e)should be replaced by
sum
119894isinI119901119875119894le 119875eNB (43g)
For Scenario 2 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus (1 + 120572
119894) 119871119894) (44)
then constraint (12) is feasible Otherwise inequality (12)cannot be satisfied and the bandwidthpower resources areassigned only to the PUs (according to (43a)ndash(43g)) whereasthe SUs receive zero allocations
4 Performance Evaluation
41 Simulation Model A simulation model of the networkconsisting of one eNB 119899 PUs and 119898 SUs randomly locatedin a service area with 3 km radius has been developed upona standard LTE platform using the OPNET package [35]Thebandwidth of the eNB equals 119861 = 50RBs (which is equivalentto 10MHz) The slot duration in the algorithm equals 119879
119904=
1msThemaximal number of iterations in FP algorithm is set119870 = 200Themaximal transmission power of the eNB equals119875eNB = 46 dBm and the maximal transmission power of eachPUSU equals 119875
1198751= sdot sdot sdot = 119875
119875119899= 1198751198781= sdot sdot sdot = 119875
119878119898= 23 dBm
Other simulation settings of the model are listed in Table 2(all the parameters are based on LTE specifications [36])
16 Mobile Information Systems
Table 2 Simulation parameters of the model
Parameter ValueRadio network model
Pass loss 119871 = 40log10119877 + 30log
10119891 + 49 119877 distance (km) 119891
carrier frequency (Hz)
Shadow fading Log-normal shadow fading with a standard deviation of1012 dB for outdoorindoor users
Penetration loss The average building penetration loss is 12 dB with astandard deviation of 8 dB
Multipath fading Spatial Channel Model (SCM) Suburban macroUE velocity 0 kmsTransmitterreceiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver noise figure 5 dBThermal noise density minus174 dBmHzCableconnectorcombiner losses 2 dB
Physical profileOperation mode FDDCyclic prefix type Normal (7 symbols per slot)Evolved packet core (EPC) bearer definitions 348 kbits (nonguaranteed bit rate)Subcarrier spacing 15 kHz
Admission control parametersPhysical downlink control channel (PDCCH) symbols per subframe 3UL loading factor 1DL loading factor 1Inactive bearer timeout 20 sec
Buffer status report parametersPeriodic timer 5 subframesRetransmission timer 2560 subframes
L1L2 control parametersReserved size 2 RBsCyclic shifts 6Starting RB preserver for Format 1 messages 0Allocation periodicity 5 subframes
Random access (RA) parametersNumber of preambles 64Preamble format Format 0 (1-subframe long)Number of RA resources per frame 4Preamble retransmission limit 5 subframesRA response timer 5 subframesContention resolution timer 40 subframes
HARQ parametersMaximal number of retransmissions 3 (UL and DL)HARQ retransmission timer 8 subframes (UL and DL)Maximal number of HARQ processes 8 per UE (UL and DL)
A radio model of the network corresponds to the require-ments of ITU-T Recommendation M1225
The algorithms proposed in the paper are denoted asfollows
(i) GBC (greedy buffer Control) where the target buffersize equals 0 for all the PUs
(ii) NBC (nongreedy buffer control) with the target buffersize calculated according to (37a) and (37b)
(iii) MBC (Minimal Buffer Control) with 119879 = 10 slots andthe target buffer size given by (38a)
(iv) ABC (Average Buffer Control) with 119879 = 10 slots andthe target buffer size equaling (38b)
Two previously proposed schemes used to benchmark theperformance of the algorithms proposed in this paper are
(i) UBA (Utility Based Allocation) presented in [11]where the network resources (bandwidth and trans-mission power) are allocated to the UL channels tomaximize the total transmission rate of the userssubject to the capacity and transmission power con-straints
Mobile Information Systems 17
0 10 20 30 40 50 60 70 80Average SNR (dB)
UBADPCGBC
NBCMBCABC
30
35
40
45
50
55
60
65
70
Dela
y fo
r SU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
012
015
018
021
024
027
03
033
Loss
for S
Us (
)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
250
300
350
400
450
500Th
roug
hput
for S
Us (
kbits
s)
Figure 6 Mean throughput packet delay and loss for SUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
(ii) DPC (Delay Power Control) derived in [5] whichis used to balance the transmission delay againsttransmission power in wireless channels between theeNB and the users
We also gather simulation results for a proposed resourceallocation approach in Scenario 2 with different settings ofthe parameters120572
119894and V and benchmark its performancewith
the performance of the algorithm in Scenario 1All algorithms are simulated using identical settings
The data traffic in simulations is represented by voice overInternet Protocol (VoIP) video and Hypertext TransferProtocol (HTTP) applications mixed in proportion 2 3 5using the models defined in [37]
42 Complexity and Fairness Issues Let us first evaluatethe complexity and the fairness of resource allocation indifferent algorithms Figure 1 shows the average numberof iterations before convergence for UBA DPC and theproposed algorithms in Scenario 1 (denoted as MBC) andScenario 2 gathered in simulations with 119899 = 100 PUs andaverage SNR = 0 dB Note that the target buffer size for thePUs is calculated according to (38a) with T = 10 slots (inScenarios 1 and 2) and 120572
119894= 1 V = 119898 lowast 1Mbps (for
Scenario 2) Results demonstrate that the complexity of FPmethod deployed for resource allocation in Scenarios 1 and2 is exponential in size of the problem (which correspondsto the findings reported in [31]) and is comparable to thecomplexities of other techniques (UBA and DPC)
18 Mobile Information Systems
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
080020 090070050 060 100000 030010 040120572i
10
20
30
40
50
60
70
80
90
100
110
Dela
y fo
r PU
s (m
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
040030 090000 080060010 020 050 100070120572i
005
010
015
020
025
030
035
040
045
050
Loss
for P
Us (
)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
030020 040 090010 060 070 080 100000 050120572i
Figure 7 Mean throughput packet delay and loss for the PUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
Figure 2 shows the fairness of different methods calcu-lated according to Jainrsquos equation [38] as
119865PU =
(sum119894isinI 119903119875119894)
2
119899 sdot sum119894isinI 1199032
119875119894
119865SU =
(sum119895isinJ 119903119878119895)
2
119898 sdot sum119895isinJ 1199032
119878119895
119865 =
(sum119894isinI 119903119875119894 + sum119895isinJ 119903119878119895)
2
(119899 + 119898) sdot (sum119894isinI 1199032
119875119894+ sum119895isinJ 1199032
119878119895)
(45)
where 119865PU 119865SU and 119865 stand for Jainrsquos index of fairness forthe PUs SUs and all of the users respectively 119903
119875119894 119903119878119895
arethe mean throughputs for PU
119894and SU
119895 respectively Results
have been gathered for 119899 = 100 PUs 119898 = 100 SUs average
Mobile Information Systems 19
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
410
420
430
440
450
460
470
480
490
500
510Th
roug
hput
for S
Us (
kbits
s)
010 020 080 090050 060 070030 100000 040120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
15
20
25
30
35
40
45
50
Dela
y fo
r SU
s (m
s)
070 090030 040 050 080000 020010 100060120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
007
009
011
013
015
017
019
021
023
Loss
for S
Us (
)
080070 090020 050 060030 100040010000120572i
Figure 8 Mean throughput packet delay and loss for the SUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
SNR = 0 dB and target buffer size for the PUs calculatedaccording to (38a) (Scenarios 1 and 2) with different settingsof 120572119894and V in Scenario 2
It follows from these graphs that the fairness index amongall of the users (denoted as 119865) is higher in Scenario 2 with120572119894= 1 and lower in Scenario 1 and Scenario 2 with 120572
119894= 0
Such results are rather expectable in Scenario 1 and Scenario2 with 120572
119894= 0 the SUs are served for free on a best-effort
basis whereas the PUs enjoy full QoS guarantees Hence thenetwork resources are shared nonequally between the PUs
and the SUs with most of the RBs allocated to the PUs andthe rest of the bandwidth distributed among the SUs Onthe other hand the fairness index for the PUs and SUs (ie119865PU and 119865SU) is rather high in both scenarios with differentsettings of 120572
119894and V which indicates that the users of the same
type are treated equally during resource allocation
43 Simulation Results in Scenario 1 Let us evaluate theperformance of a resource allocation algorithm in Scenario1 in terms of mean throughput packet end-to-end delay and
20 Mobile Information Systems
MBC
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
20
30
40
50
60
70
80
90
Dela
y fo
r PU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
005
010
015
020
025
030
035
040
045
Loss
for P
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 9 Mean throughput packet delay and loss for the PUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
loss for different user types Figures 3ndash6 show results obtainedin simulations with 119899 = 100 PUs and average SNR = 0 dBResults demonstrate that aUBA scheme has the largest packetdelay and loss and the lowest throughput for both the PUs andthe SUs A poor performance of this scheme is explained asfollows
(i) QoS protection of PUs is not considered in UBAHence the throughput delay and loss are the samefor PUs and SUs
(ii) Buffer sizes of individual users are not consideredin resource allocation and therefore the QoS for
Mobile Information Systems 21
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
30
50
70
90
110
130
Dela
y fo
r SU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
000
010
020
030
040
050
060
Loss
for S
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
different users varies significantly (since differentusers have different traffic demands)
(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer
size and therefore there is no need to maximize theirtransmission rate and spend the network resources
Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
2 Mobile Information Systems
wireless networks The majority of the works on resourceallocation in LTE-based CRNs focus on various lower layertechniques for spectrum sensing and spectrummobility (seeeg [8ndash10])These techniques are very effective in identifyingand reducing the interference in the physical channels butdo not improve the overall user-perceived QoS which ismainly expressed in terms of the packet end-to-end delay andloss for the network users Consequently the results of theseworks are applicable only in combination with the techniquesdesigned for MAC and higher layers [11]
The QoS protection for the PUs and the admissibility ofthe SUs have been studied using the theoretical analysis ofuser behaviour For instance in [12] the authors propose astatistical traffic control for the LTE-based CRNs To satisfythe timing constraints of all packets belonging to differentstreams (with diverse QoS characteristics and requirements)and achieve the statistical QoS guarantees the authorsdeploy admission control and coordinated transmissions ofthe constant-bit-rate (CBR) and the variable-bit-rate (VBR)streams Dynamic channel selection for autonomous wirelessusers transmitting delay-sensitive multimedia applicationsover a CRN has been studied in [13] Unlike prior workswhere the application-layer requirements of the users havenot been considered here the rate and delay requirements ofheterogeneous multimedia users are taken into account Theauthors propose a novel priority based virtual queue interfaceto efficiently manage the available spectrum resources Thisinterface is used to (i) determine the required informationexchanges (ii) evaluate the expected delays experiencedby various priority traffics (iii) design a dynamic strategylearning (DSL) algorithm deployed at each user that exploitsthe expected delay and (iv) adapt to the channel selectionstrategies to maximize the userrsquos utility function
The authors of [5] present a delay-power control (DPC)exploiting the trade-off between the transmission delayand transmission power in wireless networks In a pro-posed resource allocation procedure each wireless linkautonomously updates its power based on the interferenceobserved at its receiver (without any crosslink communi-cation) The DPC scheme has been proved to convergeto a unique equilibrium point and contrasted to the well-known Foschini-Miljanic (FM) formulation Some theoreti-cal underpinnings of DPC and their practical implications forefficient protocol design have also been established In [14]the problem of allocating the network resources (channelsand transmission power) in a multihop CRN is modeledas a multicommodity flow problem with the dynamic linkcapacity resulting from dynamic resource allocation Basedon such queue-balancing the authors propose a distributedscheme for optimal resource allocation without exchangingthe spectrum dynamics between remote nodes Consideringthe power masks each node makes resource allocationdecisions based on current or past local information fromneighboring nodes to satisfy the throughput requirement ofeach flow and maintain the network stability
In this paper we suggest an alternative strategy forresource allocation in a LTE-based CRN and propose toassign the network resources (bandwidth and transmissionpower) to the UL and DL of LTE system based on buffer
size of user equipment (UE) pieces Note that in manypreviously proposed algorithms (eg [8ndash13]) the bandwidthand transmission power are assigned without considering thebuffer occupancy of UE pieces which may lead to a ratherunfair resource allocation (when users with lower demandsare allocated larger bandwidth than the users with higherdemands)
To ensure that the QoS requirements of the PUs aresatisfied we put the constraints on the sizes of their buffersTwo network usage scenarios are considered In the firstscenario the PUs pay full price for accessing the spectrumand get the full QoS protection whereas the SUs access thenetwork for free and are served on a best-effort basis In thesecond scenario the PUs pay less in exchange for sharingthe bandwidth and get the reduced QoS guarantees SUs paysome price for their usage without any QoS guarantees Theproposed resource allocation algorithm is derived based on adiscrete spectrum assumption with the spectrum resourcescounted in terms of LTE resource blocks (RBs) Note thata continuous spectrum assumption (used in all past works)is not applicable for a practical LTE realization since thenumber of RBs comprising the bandwidth is relatively small(6 10 20 50 and 100 RBs corresponding to 14 3 5 10and 100MHzwidebands resp [15]) Unlike existing researchcontributions the transmission rates of SUs and DUs arecalculated using the modified Shannon expression whichaccounts for the adaptive modulation and coding (AMC)used in LTE
The rest of the paper is organized as follows In Section 2we describe the network model and formulate the resourceallocation problems in two network usage scenarios InSection 3 we provide the solution methodology and dis-cuss the implementation of a presented resource allocationapproach in a real LTE system In Section 4 we outline asimulation model and evaluate performance of the proposedresource allocation algorithms in two network usage scenar-ios The paper is finalized in Conclusion
2 Problem Statement
21 NetworkModel Assumptions and Notation In this workthe problem of joint power and bandwidth allocation forthe LTE-based CRN is investigated for both the UL and theDL directions Similarly the discussion through the rest ofthe paper is applicable (if not stated otherwise) to eitherdirection
Consider a basic LTE-based CRN architecture whichconsists of one eNB providing wireless access to 119899 PUs num-bered PU
1 PU
119899 and 119898 SUs numbered SU
1 SU
119898
Two spectrum usage scenarios are considered in this paperIn the first scenario PUs are the licensed network users whopay some price for accessing the spectrum and thereforemustbe provided with the certain guaranteed QoS levels SUs arethe unlicensed network users who can access the spectrumfor free and therefore they are served on a best-effort basis Inthe second scenario the PUs pay less in exchange for sharingthe spectrum the SUs have to pay some price for the sharedspectrum to compensate for the income losses of a serviceprovider
Mobile Information Systems 3
The considered network operates on a slotted-time basiswith the time axis partitioned into mutually disjoint timeintervals (slots) 119879
119904 (119905+1)119879
119904 119905 = 0 1 2 with 119879
119904denoting
the slot length and 119905 being the slot indexThenumber of activePUs and SUs can be tracked using an LTE random accesschannel (RACH) procedure [15] which is used for initialaccess to the network (ie for originating terminating orregistration calls)
In the UL direction the user-generated traffic (in bits perslot or bps) is enqueued in the buffers of UE pieces and thentransmitted to the eNB using a standard packet schedulingprocedure [15] In this procedure the information about theamount of data (in bps) enqueued in the buffers of UE piecesis constantly transmitted to the eNB so that the eNB ldquoknowsrdquothe exact amount of data generated by the users at any slot 119905This information is then used by the eNB to allocate the ULtransmission resources to UE pieces In the DL direction thetransmission resources are allocated based on the amount ofdata transmitted by eNB to the users
In LTE system the transmission resources are allocatedto the users in terms of RBs Each user can be allocatedonly the integer number of RBs and these RBs should notbe adjacent to each other [7 15] Another important featureof both the SC-FDMA (applied in the UL direction) andOFDMA (applied in the DL direction) is the orthogonal-ity of resource allocation which allows achieving minimallevel of cochannel interference between different transmitter-receiver pairs located within one cell (ie when no frequencyreuse is considered)
It is assumed that the bandwidth of the eNB is fixed andequal to 119861 RBs For any 119894 in I = 1 119899 and any 119895 in J =1 119898 consider the following
(i) The channel between the eNB and PU119894is character-
ized by the noise and interference coefficient 0 lt
ℎ119875119894
le 1 which is known to the eNB and PU119894 The
channel between the eNB and SU119895is characterized by
the noise and interference coefficient 0 lt ℎ119878119895le 1
which is known to the eNB and SU119895 The values of ℎ
119875119894
and ℎ119878119895in the UL and DL directions can be obtained
from the channel state information (CSI) through theuse of the LTE reference signals (RSs) [16 17]
(ii) The size of the buffers and the arrival rates (in bits) ofPU119894and SU
119895can be observed at any slot 119905 in the UL
and DL directions
The following notations are used throughout the paper
(i) 119887119875119894(119905) and 119887
119878119895(119905) denote the number of RBs allocated
at slot 119905 to PU119894and SU
119895 respectively
(ii) 119901119875119894(119905) and 119901
119878119895(119905) denote the transmission power
allocated at slot 119905 to PU119894and SU
119895 respectively
(iii) 119886119875119894(119905) and 119886
119878119895(119905) denote the arrival rate (in bps) at slot
119905 in PU119894and SU
119895 respectively
(iv) 119902119875119894(119905) and 119902
119878119895(119905) denote the buffer size (in bits) at slot
119905 of PU119894and SU
119895 respectively
(v) 119903119875119894(119905) and 119903
119878119895(119905) denote the transmission rate (in bps)
at slot t in the channels of PU119894and SU
119895 respectively
(vi) 119875eNB 119875119875119894 and 119875119878119895denote the maximal transmission
power of the eNB PU119894 and SU
119895 respectively
22 Scenario 1 The objective of this paper is to devise asustainable algorithm for joint bandwidth and transmissionpower allocation based on two goals
(1) QoS Protection for the PUs PUs should maintain theirtarget QoS irrespective of how many SUs enter thenetwork and how much load they are generating
(2) Admissibility of the SUs SUs should be able to utilizethe spare capacity of the eNB (if left) to maximizetheir QoS
These goals however cannot be achieved without pro-viding the quantified measures for the user-perceived QoSNote that because of the orthogonality of the RB allocationthe need for interference mitigation in a considered CRNis eliminated In this case the use of such physical layercharacteristics as signal-to-noise ratio (SNR) is not well-reasoned More practical QoS measures can be obtainedfrom the higher layers network information For instancesuch metrics as round-trip latency and loss are traditionallyused for performance evaluation in wireless networks [5]Unfortunately in LTE system the direct estimation of delayand loss is rather complex For instance the end-to-endlatency consists of various delay components includingtransmission and queuing delays propagation andprocessingdelays the UL delay due to scheduling and delay due tohybrid automatic repeat request (HARQ) [18] The accurateanalysis of these delay components requires knowledge ofmany system parameters which may be not available duringresource allocation
Consequently in this paper we argue in favour of usingthe buffer size of UE pieces as a QoS measure The buffersize of PUs and SUs can be easily estimated from the knownparameters 119902
119875119894(119905) 119886119875119894(119905) and 119902
119878119895(119905) 119886119878119895(119905) using well-known
Lindleyrsquos equation [19]
119902119875119894(119905 + 1) = lceil119902
119875119894(119905) + 119886
119875119894(119905) minus 119903
119875119894(119905)rceil+
forall119894 isin I (1a)
119902119878119895(119905 + 1) = lceil119902
119878119895(119905) + 119886
119878119895(119905) minus 119903
119878119895(119905)rceil
+
forall119895 isin J (1b)
where lceil119909rceil+ = max0 119909 whereas the transmission rates119903119875119894(119905) 119903119878119895(119905) depend on the unknown bandwidth and trans-
mission power allocation vectors given by (relationshipbetween the transmission rate transmission power and thebandwidth will be established in the next section)
p119875= [1199011198751(119905) 119901
119875119899(119905)]119879
b119875= [1198871198751(119905) 119887
119875119899(119905)]119879
(2a)
p119878= [1199011198781(119905) 119901
119878119898(119905)]119879
b119878= [1198871198781(119905) 119887
119878119898(119905)]119879
(2b)
Note that the average round-trip latency of any primaryUE can be retained below some upper bound level by
4 Mobile Information Systems
restricting its buffer size to be less than a certain target buffersize The only information which is necessary in this case isthe desired upper bound on delay and the average arrival ratein PUs during some interval 119879 gt 0 Then we can find thetarget buffer size by deploying Littlersquos formula [20]
119863119894sdot 119886119875119894(119905) = 119871
119894 forall119894 isin I (3a)
where119863119894is the upper bound on delay for PU
119894 119871119894is the target
buffer size for PU119894 119886119875119894(119905) is the average arrival in PU
119894during
time interval [119905 minus 119879 + 1 119905] given by
119886119875119894(119905) =
119905
sum
120591=119905minus119879+1
119886119875119894(119905) forall119894 isin I (3b)
To maintain the desired upper bound on the end-to-enddelay the buffer size of PUs should be constrained as follows
119902119875119894(119905 + 1) le 119871
119894 forall119894 isin I (4)
or equivalently using (1a)
119902119875119894(119905) + 119886
119875119894(119905) minus 119871
119894le 119903119875119894(119905) le 119902
119875119894(119905) + 119886
119875119894(119905)
forall119894 isin I(5)
If added to an optimization problem constraint (5) canguarantee the QoS protection for PUs Except some (veryrare) cases when constraint (5) is not feasible the buffersize will always stay below the target level irrespective ofhow many SUs are in the network and how much load theyare generating The setting of the parameters 119871
119894 as well as
the cases when constraint (5) is unfeasible is discussed inSection 3
Note that at any slot 119905 the number of RBs allocatedfor data transmissions of PUs and SUs in the UL and DLdirections should not exceed 119861 RBs That is
sum
119894isinI119887119875119894(119905) + sum
119895isinJ119887119878119895(119905) le 119861 (6a)
where
119887119875119894(119905) isin Z+
119887119878119895(119905) isin Z+
forall119894 isin I forall119895 isin J
(6b)
where Z+ represents the set of all nonnegative integersAdditionally the transmission power allocated to the
users at any slot 119905 should be nonnegative and cannot exceedthe maximal transmission power levels Hence
119901119875119894(119905) le 119875
119875119894
119901119878119895(119905) le 119875
119878119895
forall119894 isin I forall119895 isin J
(7a)
for the UL direction and
sum
119894isinI119901119875119894(119905) + sum
119895isinJ119901119878119895(119905) le 119875eNB (7b)
for the DL direction where119901119875119894(119905) ge 0
119901119878119895(119905) ge 0
forall119894 isin I forall119895 isin J
(7c)
We are now ready to show how to attain the second goalof resource allocation As in case with QoS protection of PUswe use the buffer sizes of SUs as ameasure of the SUsrsquoQoSWesay that the admissibility of SUs in the network is preserved ifthey are allocated the bandwidth that is not used by the PUsThis can be done for instance byminimizing the sum (or thelogarithmic sum) of the buffer sizes of SUs or minimizing themaximal buffer size of SUs subject to the constraints listedabove
For the UL direction this gives us the following problem(to simplify notation we skip the index t below)
minimize max119895isinJ
lceil119902119878119895+ 119886119878119895minus 119903119878119895rceil
+
(8a)
subject to 119902119875119894+ 119886119875119894minus 119871119894le 119903119875119894le 119902119875119894+ 119886119875119894 forall119894 isin I (8b)
sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (8c)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(8d)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(8e)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(8f)
For the DL direction constraint (8e) should be replaced by
sum
119894isinI119901119875119894+sum
119895isinJ119901119878119895le 119875eNB (8g)
In above formulation each PU is guaranteed a certaintarget QoS level and the optimal allocations for PUs are suchthat
119902119875119894+ 119886119875119894minus 119903119875119894= 119871119894 forall119894 isin I (9)
The spare bandwidth (if left) is distributed among the SUsto minimize the size of their buffer which means that thetwo goals of resource allocation are achieved However thisformulation works well only if the aggregated traffic demandof the SUs is greater than that of the PUs Otherwise theremight be a situationwhen the optimal solution for SUs is suchthat
max119895isinJ
lceil119902119878119895+ 119886119878119895minus 119903119878119895rceil
+
le 119871119894 forall119894 isin I (10)
Mobile Information Systems 5
which is apparently not fair since the PUs have larger buffersizes than the SUs and therefore they will experience longerdelays than the SUs
To avoid such situation we propose to modify problem(8a)ndash(8g) by replacing its objective (8a) with
minimize max119894isinI
lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+
+max119895isinJ
lceil119902119878119895+ 119886119878119895minus 119903119878119895rceil
+
(11)
Objective (11) guarantees that PUs are served with max-imal QoS even if the aggregated traffic demand of SUs isgreater than that of the PUs
23 Scenario 2 We now consider a different scenario inwhich the PUs will benefit (by paying less in exchange) fromsharing their bandwidth with the SUs Let us assume that inthe network without price benefits (ie in Scenario 1) theprice for accessing the licensed spectrum of the PUs equals1 In this case all the PUs get the full QoS protection (ieguaranteed target buffer size 119871
119894and the average end-to-end
latency 119863119894) Suppose that each PU can define the portion of
allocated spectrum that it is willing to share with the SUsThedelay in turn is related to lceil119902
119875119894+ 119886119875119894minus 119903119875119894rceil+
Let us denote by 120572119894 0 le 120572
119894lt 1 the price for the portion
of spectrum that PU119894is willing to share with the SUs So
120572119894represents the willingness of PU
119894to trade off its QoS for
money Subsequently the guaranteed QoS level of PU119894will
reduce and instead of the QoS protection constraint (8b) wewill have
119903119875119894ge 119902119875119894+ 119886119875119894minus (1 + 120572
119894) 119871119894 forall119894 isin I (12)
Now to compensate for the income losses of a serviceprovider the SUs will have to pay the price for the sharedspectrum Let 120573 denote the price that each SU will pay foraccessing the shared spectrum The amount that SU
119895pays in
this case is 120573119903119878119895 whereas the revenue of the service provider
is
sum
119895isinJ120573119903119878119895minussum
119894isinI120572119894lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+
(13)
Assuming that a service provider does not incur loss byallowing the secondary users to use the spectrum we have toincorporate the constraint
sum
119895isinJ120573119903119878119895minussum
119894isinI120572119894lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+
ge V (14)
where V is the profit that a service provider would like tomakeby allowing the SUs into the network
Note that in such formulation the SUs get no QoSguarantee and therefore we have to minimize the price that
the SUs pay for their usage Thus the optimization problemis
minimize 120573 (15a)
subject to 119902119875119894+ 119886119875119894minus (1 + 120572
119894) 119871119894le 119903119875119894
le 119902119875119894+ 119886119875119894
forall119894 isin I
(15b)
sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (15c)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(15d)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(15e)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(15f)
sum
119895isinJ120573119903119878119895minussum
119894isinI120572119894lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+
ge V (15g)
for the UL direction For the DL direction constraint (15e) isreplaced by constraint (8g)The value of120573 obtained by solving(15a)ndash(15g) is then broadcasted by a service provider to theSUs that will have to pay a determined price
We note in passing that there are many other ways inwhich the pricing problem could be addressed For instancethe numbers 120572
119894may be negotiated between the PUs and a
service provider One can also think of a scenario wheredifferent SUs may be able to express their willingness to payvia bidding the prices 120573
119895 The options are numerous but they
are beyond the scope of this paper
3 Implementation Issues
31 Rate as a Function of Bandwidth and Power Note thatthe transmission rates in the UL and DL channels of a LTEsystem can be found using the modified Shannon equation[21] expressed as
119903119875119894(b119875 p119875) = 120596120595
119875119894119887119875119894log (1 + 120585
119875119894SNR119875119894)
= 120596120595119875119894119887119875119894log (1 + 120585
119875119894ℎ119875119894119901119875119894)
0 lt 120595119875119894 120585119875119894le 1 forall119894 isin I
(16a)
6 Mobile Information Systems
119903119878119895(b119878 p119878) = 120596120595
119878119895119887119878119895log (1 + 120585
119878119895SNR119878119895)
= 120596120595119878119895119887119878119895log (1 + 120585
119878119895ℎ119878119895119901119878119895)
0 lt 120595119878119895 120585119878119895le 1 forall119895 isin J
(16b)
where SNR119875119894and SNR
119878119895are the SNRs in the channels of PU
119894
and SU119895 respectively 120595
119875119894and 120595
119878119895are the system bandwidth
efficiencies for PU119894and SU
119895 respectively 120585
119875119894and 120585
119878119895are
the SNR efficiencies for PU119894and SU
119895 respectively 120596 is the
bandwidth of one RB (120596 = 180 kHz) [21]In real LTE networks the system bandwidth efficiency
is strictly less than 1 due to the overheads on the link andsystem levels The bandwidth efficiency is fully determinedby the design and internal settings of the system and doesnot depend on the physical characteristics of the wirelesschannels between the user and the eNB [21 22] Hence it isreasonable to assume that
120595119875119894= 120595119878119895= 120595 forall119894 isin I forall119895 isin J (17)
The SNR efficiency is mainly limited by the maximumefficiency of the supported modulation and coding scheme(MCS) [16] In LTE MCS is chosen using AMC to maximizethe data rate by adjusting the transmission parameters to thecurrent channel conditions AMC is one of the realizations ofa dynamic link adaptation In AMC algorithm the appropri-ate MCSs for packet transmissions are assigned periodically(within short fixed time interval usually equal to one slot)by the eNB based on the instantaneous channel conditionsreported by the usersThe higherMCS values are allocated tothe high-quality channels to achieve higher transmission rateThe lower MCS values are assigned to the channels of poorquality to decrease the transmission rate and consequentlyensure the transmission quality [16 17]
The method for choosing MCS can be expressed asfollows Based on the instantaneous radio channel conditionsthe SNR is calculated for the DL wireless channels betweenthe eNB and the users A supported MCS index is chosenusing expression [16 17]
MCS =
MCS1 SNR lt 120574
1
MCS2 1205741le SNR lt 120574
2
MCS119897 120574119897minus1
le SNR lt 120574119897
(18)
where 1205741
lt 1205742
lt sdot sdot sdot lt 120574119897are the SNR thresholds
corresponding to minus10 dB bit error ratio (BER) given by theAdditive White Gaussian Noise (AWGN) curves for eachMCS (the standard AWGN curves can be found in [17]) TheLTE standard allows 119897 = 15 MCS levels (description of MCSlevels their code rate and efficiency is shown in Table 1) [17]
Table 1 Allowed MCS values in LTE standard [17]
MCS index Modulation Code rate Efficiency0 No transmission1 QPSK 78 015232 QPSK 120 023443 QPSK 193 037704 QPSK 308 060165 QPSK 449 087706 QPSK 602 117587 16 QAM 378 147668 16 QAM 490 191419 16 QAM 616 2406310 64 QAM 466 2730511 64 QAM 567 3322312 64 QAM 666 3902313 64 QAM 772 4523414 64 QAM 873 5115215 64 QAM 948 55547
Based on the above the SNR efficiency depends onthe SNR of the DL wireless channel and therefore can berepresented by a function
119892 (SNR) =
1205851 SNR lt 120574
1
1205852 1205741le SNR lt 120574
2
120585119897 120574119897minus1
le SNR lt 120574119897
(19)
where 0 lt 1205851lt 1205852lt sdot sdot sdot lt 120585
119897are the values of the SNR
efficiency corresponding to the supported MCSUsing (17) and (19) the transmission rates of the users can
be expressed as
119903119875119894(b119875 p119875) = 120596120595119887
119875119894log (1 + 119892 (SNR
119875119894) sdot SNR
119875119894)
= 120596120595119887119875119894log (1 + 119892 (119901
119875119894) sdot ℎ119875119894119901119875119894)
forall119894 isin I
(20a)
119903119878119895(b119878 p119878) = 120596120595119887
119878119895log (1 + 119892 (SNR
119878119895) sdot SNR
119878119895)
= 120596120595119887119878119895log (1 + 119892 (119901
119878119895) ℎ119878119895119901119878119895)
forall119895 isin J
(20b)
32 Solution Methodology In this subsection we describe asolution methodology for the resource allocation problemin Scenario 1 in the UL direction (with the objective givenby (11) and the constraints defined in (8b)ndash(8f)) A resourceallocation problem for the DL direction as well as problem(15a)ndash(15g) for Scenario 2 can be solved analogously
Mobile Information Systems 7
Note that in Scenario 1 a resource allocation problem inthe UL direction is equivalent to
minimize Ω + Φ (21a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (21b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(21c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(21d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(21e)
Ω ge 0
Φ ge 0
(21f)
1198911
119894(b119875 p119875) = 119903119875119894(b119875 p119875) minus (119902
119875119894+ 119886119875119894)
le 0
forall119894 isin I
(21g)
1198912
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894minus 119871119894) minus 119903119875119894(b119875 p119875)
le 0
forall119894 isin I
(21h)
1198913
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894) minus 119903119875119894(b119875 p119875) minus Ω
le 0
forall119894 isin I
(21i)
1198914
119895(b119878 p119878)
= (119902119878119895+ 119886119878119895) minus 119903119878119895(b119878 p119878) minus Φ
le 0
forall119895 isin J
(21j)
In above problem some of the optimization variables(particularly the components of b
119875and b
119878) can take only
integer values whereas the other variables (the componentsof p119875and p
119878) are real-valued ones In addition constraints
(21g)ndash(21j) are represented by the nonsmooth nonlinear
functions of (b119875 p119875) and (b
119875 p119875) Hence (21a)ndash(21j) is a
nonlinear mixed integer programming (MINLP) problemwhich is Nondeterministic Polynomial-time (NP) hard Forimmediate proof of NP-hardness note that MINLP includesmixed integer linear programming (MILP) problem which isNP-hard [23]
Before applying any MINLP method for solving (21a)ndash(21j) the nonsmooth function 119892(sdot) in (19) included in theexpressions of 119903
119875119894(b119875 p119875) and 119903
119878119895(b119875 p119875) should be replaced
by its smooth approximation To construct a smooth approx-imation of 119892(119909) note that this function is equivalent to thesum of the shifted and scaled versions of a Heaviside stepfunction119867(119909) [24] That is
119892 (119909) =
15
sum
119897=1
(120577119897minus 120577119897minus1)119867 (119909 minus 120574
119897)
119867 (119909) =
1 if 119909 ge 0
0 otherwise
(22)
where 1205770= 0
Recall that a smooth approximation for a step function119867(119909) is given by a logistic sigmoid function [25]
119902(119909) =
1
1 + 119890minus2119902119909
(23)
where 119902 gt 0 119909 is in range of real numbers from minusinfin to +infinIf we take 119867(0) = 12 then larger 119902 corresponds to a closertransition to119867(119909) that is
lim119902rarrinfin
119902(119909) = 119867 (119909) (24)
The above holds because for 119909 lt 0 we have
119890minus2119902119909
997888rarr +infin
119902(119909) asymp 119867 (119909) = 1
(25)
for 119909 gt 0
119890minus2119902119909
997888rarr 0
119902(119909) asymp 119867 (119909) = 1
(26)
for 119909 = 0
119890minus2119902119909
= 1
119902(119909) = 119867 (119909) =
1
2
(27)
Consequently an approximation for a shifted Heavisidefunction is represented by a shifted logistic function
119902(119909 minus 120574
119897) =
1
1 + 119890minus2119902(119909minus120574119897)
(28)
defined for 119902 gt 0 with real 119909 in range from minusinfin to +infin
8 Mobile Information Systems
Based on (28) we can construct a smooth approximationfor 119892(119909) as
119902(119909) =
15
sum
119897=1
(120577119897minus 120577119897minus1) 119902(119909 minus 120574
119897) =
15
sum
119897=1
120577119897minus 120577119897minus1
1 + 1198902119902(119909minus120574119897)
(29)
Then it is rather straightforward to verify that
lim119902rarrinfin
119902(119909) = 119892 (119909) (30)
and the approximations for 119903119875119894(b119875 p119875) and 119903
119878119895(b119875 p119875) will
take the form
119875119894(b119875 p119875) = 120596120595119887
119875119894log (1 + (119901
119875119894) sdot ℎ119875119894119901119875119894)
forall119894 isin I(31a)
119878119895(b119878 p119878) = 120596120595119887
119878119895log (1 + (119901
119878119895) ℎ119878119895119901119878119895)
forall119895 isin J(31b)
With the approximations given by (31a) and (31b) prob-lem (21a)ndash(21j) can be solved using a sequential optimizationapproach as
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (32a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (32b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(32c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(32d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(32e)
Ω ge 0
Φ ge 0
(32f)
119891
1
119894(b119875 p119875)
= 119875119894(b119875 p119875)
minus (119902119875119894+ 119886119875119894) le 0
forall119894 isin I
(32g)
119891
2
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894minus 119871119894)
minus 119875119894(b119875 p119875) le 0
forall119894 isin I
(32h)
119891
3
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894)
minus 119875119894(b119875 p119875) minus Ω
le 0
forall119894 isin I
(32i)
119891
4
119895(b119878 p119878)
= (119902119878119895+ 119886119878119895)
minus 119878119895(b119878 p119878) minus Φ
le 0
forall119895 isin J
(32j)
The above problem is smooth MINLP which can besolved using some fast and effective MINLP method Notethat most of the MINLP techniques involve constructionof the following relaxations to the considered problem thenonlinear programming (NLP) relaxation (original problemwithout integer restrictions) and the MILP relaxation (origi-nal problem where nonlinearities are replaced by supportinghyperplanes) In our case a smooth MILP relaxation to(32a)ndash(32j) in a given point (b0
119875 p0119875 b0119878 p0119878) is given by
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (33a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (33b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(33c)
Mobile Information Systems 9
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(33d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(33e)
Ω ge 0
Φ ge 0
(33f)
119891
1
119894(b0119875 p0119875) + nabla
119891
1
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33g)
119891
2
119894(b0119875 p0119875) + nabla
119891
2
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33h)
119891
3
119894(b0119875 p0119875) + nabla
119891
3
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33i)
119891
4
119895(b0119878 p0119878) + nabla
119891
4
119895(b0119878 p0119878)
119879
[
b119878minus b0119878
p119878minus p0119878
]
le 0
forall119895 isin J
(33j)
The NLP relaxation to (32a)ndash(32j) is
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (34a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (34b)
119887119875119894ge 0
119887119878119895ge 0
forall119894 isin I forall119895 isin J
(34c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(34d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(34e)
Ω ge 0
Φ ge 0
(34f)
119891
1
119894(b119875 p119875) le 0
forall119894 isin I(34g)
119891
2
119894(b119875 p119875) le 0
forall119894 isin I(34h)
119891
3
119894(b119875 p119875) le 0
forall119894 isin I(34i)
119891
4
119895(b119878 p119878) le 0
forall119895 isin J(34j)
Note that theMINLP problems can be solved using eitherdeterministic technique or an approximation A typical exact
10 Mobile Information Systems
method for solving MINLPs is a well-known branch-and-bound algorithmand its variousmodifications [26] examplesof heuristic approaches include local branching [27] largeneighborhood search [28] and feasibility pump [29] to namea few Since we are interested in a reasonably simple and fastalgorithm it is more convenient to use heuristics for solvingthe problem In this paper a Feasibility Pump (FP) heuristic[29 30] is applied to solve (32a)ndash(32j) FP is perhaps the mostsimple and most effective method for producing more andbetter solutions in a shorter average running time For theproblems with nonbinary integer variables the complexity ofFP is exponential in size of a problem [31]
A fundamental idea of FP algorithm is to decomposethe problem into two parts integer feasibility and constraint
feasibility The former is achieved by rounding (solvinga NLP relaxation to the original problem) and the latterby projection (solving a MILP relaxation) Consequentlytwo sequences of points are generated The first sequence(b119875 p119875 b119878 p119878)119896119870
119896=1 119870 = 1 2 contains the integral
points that may violate the nonlinear constraintsThe secondsequence (b
119875 p119875 b119878 p119878)119896119870
119896=1contains the points which are
feasible for a continuous relaxation to the original problembut might not be integral
More specifically with input (b119875 p119875 b119878 p119878)1being a
solution to the NLP relaxation given by (34a)ndash(34j) thealgorithm generates two sequences by solving the followingproblems for 119896 = 1 119870
(b119875 p119875 b119878 p119878)119896= argmin
100381710038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b
119875 p119875 b119878 p119878)119896
1003817100381710038171003817100381710038171
(35a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (35b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(35c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(35d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(35e)
Ω ge 0
Φ ge 0
(35f)
119891
1
119894(b0119875 p0119875) + nabla
119891
1
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35g)
119891
2
119894(b0119875 p0119875) + nabla
119891
2
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35h)
119891
3
119894(b0119875 p0119875) + nabla
119891
3
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35i)
Mobile Information Systems 11
119891
4
119895(b0119878 p0119878) + nabla
119891
4
119895(b0119878 p0119878)
119879
[
b119878minus b0119878
p119878minus p0119878
] le 0
forall119895 isin J
(35j)
(b119875 p119875 b119878 p119878)119896+1
= argmin 10038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b
119875 p119875 b119878 p119878)119896
100381710038171003817100381710038172
(36a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (36b)
119887119875119894ge 0
119887119878119895ge 0
forall119894 isin I forall119895 isin J
(36c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(36d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(36e)
Ω ge 0
Φ ge 0
(36f)
119891
1
119894(b119875 p119875) le 0
forall119894 isin I(36g)
119891
2
119894(b119875 p119875) le 0
forall119894 isin I(36h)
119891
3
119894(b119875 p119875) le 0
forall119894 isin I(36i)
119891
4
119895(b119878 p119878) le 0
forall119895 isin J(36j)
where sdot1and sdot
2are 1198971norm and 119897
2norm respectivelyThe
rounding step is carried out by solving (35a)ndash(35j) whereasthe projection is the solution to (36a)ndash(36j) A suggested FPalgorithm alternates between the rounding and projectionsteps until (b
119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896(which implies
feasibility) or the number of iterations 119896 has reached thepredefined limit 119870 The workflow of a corresponding FPalgorithm is illustrated in the following part
FP Algorithm for Non-Convex MINLP(0) INITIALIZATION input119870 set 119896 = 1
solve (34a)ndash(34j) to obtain (b119875 p119875 b119878 p119878)119896
(1) WHILE (119896 lt 119870) do
(2) ROUNDING solve (35a)ndash(35j) to obtain(b119875 p119875 b119878 p119878)119896
(3) IF ((b119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896) THEN goto
step (6)(4) PROJECTION solve (36a)ndash(36j) to obtain
(b119875 p119875 b119878 p119878)119896+1
(5) Set 119896 = 119896 + 1
12 Mobile Information Systems
(6) OUTPUT solution (b119875 p119875 b119878 p119878)lowast
=
(b119875 p119875 b119878 p119878)119896
Note that in order to retain the convergence of thealgorithm both problems (35a)ndash(35j) and (36a)ndash(36j) needto be solved exactly Problem (36a)ndash(36j) (and consequentlyproblem (34a)ndash(34j)) can be solved using any standard NLPmethod In this paper an interior point algorithm (describedeg in [32]) with polynomial complexity is applied to solve(36a)ndash(36j) and (34a)ndash(34j) MILP problem (35a)ndash(35j) isrelatively simple and therefore can be solved efficiently foroptimality by any technique from the family of the branch-and-bound methods (eg [26])
33 Target Buffer Size for PUs and Feasibility Issues Recallthat 119871
119894represents the target buffer size for PU
119894 which
indicates that the QoS requirements of PU119894are satisfied By
limiting the buffer size of PUs we restrict the QoS of PUs(measured in terms of their buffer size) to be higher (or atleast not smaller) than the required minimum From thispoint of view constraints (5) and (12) guarantee the QoSprotection of PUs in Scenario 1 and Scenario 2 respectivelyApparently one can always restrict the target buffer size ofPUs to be equal to zero so that after each subsequent dataarrival the buffer of each PU is fully cleared This approachrepresents a ldquogreedyrdquo policy which ensures that the PUs arealways served with the best possible QoS but does not guar-antee that some spare capacity will be left to serve the SUs
A ldquoless greedyrdquo strategy would be to establish somelower bound on QoS for the PUs which will provide anldquoopportunityrdquo for SUs to be served To establish this lowerbound recall that the growing delay and loss indicate thata buffer of a corresponding node is congested whereas inan uncongested node the packet delay and loss are alwaysminimal [33] On the other hand it has been reported in[33 34] that in an uncongested node the buffer size 119902(119905) isincreasing very slowly that is 119902(119905 + 1)119902(119905) asymp 1 whereas ina congested node the buffer size is growing very fast so that119902(119905+1)119902(119905) ≫ 1 Hence to serve the PUs withminimal delayand loss it is enough to prevent the growth of their buffersthat is for each PU set
119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)
where 120576 ge 0 is some small value such that
120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)
More sophisticated approach to find the lowerQoS boundcan be deployed if information about the past buffer size isavailable at any time slot 119905 In this case one can set the targetbuffer size based on past T observations 119902(119905) 119902(119905 minus 119879 + 1)as
119871119894= min120591isinT
119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38a)
or
119871119894=
1
119879
sum
120591isinT119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38b)
where T = 1 119879
UBADPC MBC
60
70
80
90
100
110
120
130
140
Alg
orith
m it
erat
ions
10020 8040 50 60 7030 90100Number of SUs m
120572i = 1 v = m lowast 1Mbps
Figure 1 Average number of iterations before convergence as afunction of number of SUs in simulations with 119899 = 100 PUs andaverage SNR = 0 dB
MBC
070
075
080
085
090
095
100
120572i=0
v=0
120572i=1
v=0
120572i=0
v=m
lowast1
Mbp
s
120572i=1
v=m
lowast1
Mbp
s
Fairness among SUs FSU
Fairness among PUs FPU
Fairness among all users F
Figure 2 Jainrsquos index of fairness119865SU119865PU and119865 for the PUs SUs andall users in simulations with 119899 = 100 PUs119898 = 100 SUs and averageSNR = 0 dB
In some (very rare) cases (when the service capacity of theeNB is not enough to guarantee that the buffer sizes in all PUsdo not exceed the target buffer size) constraints (5) and (12)in Scenarios 1 and 2 may be not feasible In the following weshow how to identify such situation and what should be theoptimal resource allocation strategy in this case
Note that the service capacity of LTE system greatlydepends on physical characteristics (eg SINR and MCS) of
Mobile Information Systems 13
UBADPCGBC
NBCMBCABC
780
800
820
840
860
880
900
920
940
960Th
roug
hput
for P
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r PU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for P
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
Figure 3 Mean throughput packet delay and loss for PUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
the wireless channels between the eNB and the users Henceat the moment preceding the bandwidthpower allocation itis rather difficult to estimate the service capacity of a systemNevertheless it is possible to find the average service capacityand to determine the upper and lower bounds on servicecapacity of the eNB in the UL and DL directions such that
119877min le sum119894isinI119903119875119894(119905) asymp 119877ave le 119877max (39)
where119877min119877ave and119877max are the lower bound upper boundand average service capacity of the eNB respectively
In our case the upper bound on service capacity of theeNB is given by
119877max = 120596120595119861 log (1 + 119892 (SNRmax) sdot SNRmax) (40a)
where SNRmax is the maximal possible SNR value
The lower bound on service capacity of eNB is
119877min = 120596120595119861 log (1 + 119892 (SNRmin) sdot SNRmin) (40b)
where SNRmin is the minimal possible SNR valueThe average service capacity of the eNB equals
119877ave = 120596120595119861 log (1 + 119892 (SNRave) sdot SNRave) (40c)
where SNRave is the average SNR valueIf SNR information is available then the values SNRmax
SNRmin and SNRave can be set as
SNRmax = max119894isinI
SNR119894 (41a)
14 Mobile Information Systems
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r SU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for S
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
Figure 4 Mean throughput packet delay and loss for SUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
SNRmin = min119894isinI
SNR119894 (41b)
SNRave =1
119899
sum
119894isinISNR119894 (41c)
Otherwise (ie if SNR information is not available) thevalues are set arbitrarily
Now we can identify the situation when constraints (5)and (12) cannot be satisfied For this we should perform thefollowing test For Scenario 1 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus 119871
119894) (42)
then constraint (5) is feasible Otherwise condition (5)cannot be satisfiedHence all the SUs receive zero allocations
andwe assign the bandwidthpower resources only to the PUsby solving the following optimization problem
minimize max119894isinI
lceil119902119875119894+ 119886119875119894minus 119903119875119894(b119875 p119875)rceil+
(43a)
subject to 119903119875119894(b119875 p119875) le 119902119875119894+ 119886119875119894 forall119894 isin I (43b)
sum
119894isinI119887119875119894le 119861 (43c)
119887119875119894isin Z+ forall119894 isin I (43d)
119901119875119894le 119875119875119894 forall119894 isin I (43e)
119901119875119894ge 0 forall119894 isin I (43f)
Mobile Information Systems 15
725
750
775
800
825
850
875
900
925
950Th
roug
hput
for P
Us (
kbits
s)
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
10
20
30
40
50
60
70
Dela
y fo
r PU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Loss
for P
Us (
)
0
005
01
015
02
025
03
035
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Figure 5 Mean throughput packet delay and loss for PUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
for the UL direction For the DL directions constraint (43e)should be replaced by
sum
119894isinI119901119875119894le 119875eNB (43g)
For Scenario 2 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus (1 + 120572
119894) 119871119894) (44)
then constraint (12) is feasible Otherwise inequality (12)cannot be satisfied and the bandwidthpower resources areassigned only to the PUs (according to (43a)ndash(43g)) whereasthe SUs receive zero allocations
4 Performance Evaluation
41 Simulation Model A simulation model of the networkconsisting of one eNB 119899 PUs and 119898 SUs randomly locatedin a service area with 3 km radius has been developed upona standard LTE platform using the OPNET package [35]Thebandwidth of the eNB equals 119861 = 50RBs (which is equivalentto 10MHz) The slot duration in the algorithm equals 119879
119904=
1msThemaximal number of iterations in FP algorithm is set119870 = 200Themaximal transmission power of the eNB equals119875eNB = 46 dBm and the maximal transmission power of eachPUSU equals 119875
1198751= sdot sdot sdot = 119875
119875119899= 1198751198781= sdot sdot sdot = 119875
119878119898= 23 dBm
Other simulation settings of the model are listed in Table 2(all the parameters are based on LTE specifications [36])
16 Mobile Information Systems
Table 2 Simulation parameters of the model
Parameter ValueRadio network model
Pass loss 119871 = 40log10119877 + 30log
10119891 + 49 119877 distance (km) 119891
carrier frequency (Hz)
Shadow fading Log-normal shadow fading with a standard deviation of1012 dB for outdoorindoor users
Penetration loss The average building penetration loss is 12 dB with astandard deviation of 8 dB
Multipath fading Spatial Channel Model (SCM) Suburban macroUE velocity 0 kmsTransmitterreceiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver noise figure 5 dBThermal noise density minus174 dBmHzCableconnectorcombiner losses 2 dB
Physical profileOperation mode FDDCyclic prefix type Normal (7 symbols per slot)Evolved packet core (EPC) bearer definitions 348 kbits (nonguaranteed bit rate)Subcarrier spacing 15 kHz
Admission control parametersPhysical downlink control channel (PDCCH) symbols per subframe 3UL loading factor 1DL loading factor 1Inactive bearer timeout 20 sec
Buffer status report parametersPeriodic timer 5 subframesRetransmission timer 2560 subframes
L1L2 control parametersReserved size 2 RBsCyclic shifts 6Starting RB preserver for Format 1 messages 0Allocation periodicity 5 subframes
Random access (RA) parametersNumber of preambles 64Preamble format Format 0 (1-subframe long)Number of RA resources per frame 4Preamble retransmission limit 5 subframesRA response timer 5 subframesContention resolution timer 40 subframes
HARQ parametersMaximal number of retransmissions 3 (UL and DL)HARQ retransmission timer 8 subframes (UL and DL)Maximal number of HARQ processes 8 per UE (UL and DL)
A radio model of the network corresponds to the require-ments of ITU-T Recommendation M1225
The algorithms proposed in the paper are denoted asfollows
(i) GBC (greedy buffer Control) where the target buffersize equals 0 for all the PUs
(ii) NBC (nongreedy buffer control) with the target buffersize calculated according to (37a) and (37b)
(iii) MBC (Minimal Buffer Control) with 119879 = 10 slots andthe target buffer size given by (38a)
(iv) ABC (Average Buffer Control) with 119879 = 10 slots andthe target buffer size equaling (38b)
Two previously proposed schemes used to benchmark theperformance of the algorithms proposed in this paper are
(i) UBA (Utility Based Allocation) presented in [11]where the network resources (bandwidth and trans-mission power) are allocated to the UL channels tomaximize the total transmission rate of the userssubject to the capacity and transmission power con-straints
Mobile Information Systems 17
0 10 20 30 40 50 60 70 80Average SNR (dB)
UBADPCGBC
NBCMBCABC
30
35
40
45
50
55
60
65
70
Dela
y fo
r SU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
012
015
018
021
024
027
03
033
Loss
for S
Us (
)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
250
300
350
400
450
500Th
roug
hput
for S
Us (
kbits
s)
Figure 6 Mean throughput packet delay and loss for SUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
(ii) DPC (Delay Power Control) derived in [5] whichis used to balance the transmission delay againsttransmission power in wireless channels between theeNB and the users
We also gather simulation results for a proposed resourceallocation approach in Scenario 2 with different settings ofthe parameters120572
119894and V and benchmark its performancewith
the performance of the algorithm in Scenario 1All algorithms are simulated using identical settings
The data traffic in simulations is represented by voice overInternet Protocol (VoIP) video and Hypertext TransferProtocol (HTTP) applications mixed in proportion 2 3 5using the models defined in [37]
42 Complexity and Fairness Issues Let us first evaluatethe complexity and the fairness of resource allocation indifferent algorithms Figure 1 shows the average numberof iterations before convergence for UBA DPC and theproposed algorithms in Scenario 1 (denoted as MBC) andScenario 2 gathered in simulations with 119899 = 100 PUs andaverage SNR = 0 dB Note that the target buffer size for thePUs is calculated according to (38a) with T = 10 slots (inScenarios 1 and 2) and 120572
119894= 1 V = 119898 lowast 1Mbps (for
Scenario 2) Results demonstrate that the complexity of FPmethod deployed for resource allocation in Scenarios 1 and2 is exponential in size of the problem (which correspondsto the findings reported in [31]) and is comparable to thecomplexities of other techniques (UBA and DPC)
18 Mobile Information Systems
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
080020 090070050 060 100000 030010 040120572i
10
20
30
40
50
60
70
80
90
100
110
Dela
y fo
r PU
s (m
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
040030 090000 080060010 020 050 100070120572i
005
010
015
020
025
030
035
040
045
050
Loss
for P
Us (
)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
030020 040 090010 060 070 080 100000 050120572i
Figure 7 Mean throughput packet delay and loss for the PUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
Figure 2 shows the fairness of different methods calcu-lated according to Jainrsquos equation [38] as
119865PU =
(sum119894isinI 119903119875119894)
2
119899 sdot sum119894isinI 1199032
119875119894
119865SU =
(sum119895isinJ 119903119878119895)
2
119898 sdot sum119895isinJ 1199032
119878119895
119865 =
(sum119894isinI 119903119875119894 + sum119895isinJ 119903119878119895)
2
(119899 + 119898) sdot (sum119894isinI 1199032
119875119894+ sum119895isinJ 1199032
119878119895)
(45)
where 119865PU 119865SU and 119865 stand for Jainrsquos index of fairness forthe PUs SUs and all of the users respectively 119903
119875119894 119903119878119895
arethe mean throughputs for PU
119894and SU
119895 respectively Results
have been gathered for 119899 = 100 PUs 119898 = 100 SUs average
Mobile Information Systems 19
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
410
420
430
440
450
460
470
480
490
500
510Th
roug
hput
for S
Us (
kbits
s)
010 020 080 090050 060 070030 100000 040120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
15
20
25
30
35
40
45
50
Dela
y fo
r SU
s (m
s)
070 090030 040 050 080000 020010 100060120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
007
009
011
013
015
017
019
021
023
Loss
for S
Us (
)
080070 090020 050 060030 100040010000120572i
Figure 8 Mean throughput packet delay and loss for the SUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
SNR = 0 dB and target buffer size for the PUs calculatedaccording to (38a) (Scenarios 1 and 2) with different settingsof 120572119894and V in Scenario 2
It follows from these graphs that the fairness index amongall of the users (denoted as 119865) is higher in Scenario 2 with120572119894= 1 and lower in Scenario 1 and Scenario 2 with 120572
119894= 0
Such results are rather expectable in Scenario 1 and Scenario2 with 120572
119894= 0 the SUs are served for free on a best-effort
basis whereas the PUs enjoy full QoS guarantees Hence thenetwork resources are shared nonequally between the PUs
and the SUs with most of the RBs allocated to the PUs andthe rest of the bandwidth distributed among the SUs Onthe other hand the fairness index for the PUs and SUs (ie119865PU and 119865SU) is rather high in both scenarios with differentsettings of 120572
119894and V which indicates that the users of the same
type are treated equally during resource allocation
43 Simulation Results in Scenario 1 Let us evaluate theperformance of a resource allocation algorithm in Scenario1 in terms of mean throughput packet end-to-end delay and
20 Mobile Information Systems
MBC
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
20
30
40
50
60
70
80
90
Dela
y fo
r PU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
005
010
015
020
025
030
035
040
045
Loss
for P
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 9 Mean throughput packet delay and loss for the PUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
loss for different user types Figures 3ndash6 show results obtainedin simulations with 119899 = 100 PUs and average SNR = 0 dBResults demonstrate that aUBA scheme has the largest packetdelay and loss and the lowest throughput for both the PUs andthe SUs A poor performance of this scheme is explained asfollows
(i) QoS protection of PUs is not considered in UBAHence the throughput delay and loss are the samefor PUs and SUs
(ii) Buffer sizes of individual users are not consideredin resource allocation and therefore the QoS for
Mobile Information Systems 21
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
30
50
70
90
110
130
Dela
y fo
r SU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
000
010
020
030
040
050
060
Loss
for S
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
different users varies significantly (since differentusers have different traffic demands)
(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer
size and therefore there is no need to maximize theirtransmission rate and spend the network resources
Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mobile Information Systems 3
The considered network operates on a slotted-time basiswith the time axis partitioned into mutually disjoint timeintervals (slots) 119879
119904 (119905+1)119879
119904 119905 = 0 1 2 with 119879
119904denoting
the slot length and 119905 being the slot indexThenumber of activePUs and SUs can be tracked using an LTE random accesschannel (RACH) procedure [15] which is used for initialaccess to the network (ie for originating terminating orregistration calls)
In the UL direction the user-generated traffic (in bits perslot or bps) is enqueued in the buffers of UE pieces and thentransmitted to the eNB using a standard packet schedulingprocedure [15] In this procedure the information about theamount of data (in bps) enqueued in the buffers of UE piecesis constantly transmitted to the eNB so that the eNB ldquoknowsrdquothe exact amount of data generated by the users at any slot 119905This information is then used by the eNB to allocate the ULtransmission resources to UE pieces In the DL direction thetransmission resources are allocated based on the amount ofdata transmitted by eNB to the users
In LTE system the transmission resources are allocatedto the users in terms of RBs Each user can be allocatedonly the integer number of RBs and these RBs should notbe adjacent to each other [7 15] Another important featureof both the SC-FDMA (applied in the UL direction) andOFDMA (applied in the DL direction) is the orthogonal-ity of resource allocation which allows achieving minimallevel of cochannel interference between different transmitter-receiver pairs located within one cell (ie when no frequencyreuse is considered)
It is assumed that the bandwidth of the eNB is fixed andequal to 119861 RBs For any 119894 in I = 1 119899 and any 119895 in J =1 119898 consider the following
(i) The channel between the eNB and PU119894is character-
ized by the noise and interference coefficient 0 lt
ℎ119875119894
le 1 which is known to the eNB and PU119894 The
channel between the eNB and SU119895is characterized by
the noise and interference coefficient 0 lt ℎ119878119895le 1
which is known to the eNB and SU119895 The values of ℎ
119875119894
and ℎ119878119895in the UL and DL directions can be obtained
from the channel state information (CSI) through theuse of the LTE reference signals (RSs) [16 17]
(ii) The size of the buffers and the arrival rates (in bits) ofPU119894and SU
119895can be observed at any slot 119905 in the UL
and DL directions
The following notations are used throughout the paper
(i) 119887119875119894(119905) and 119887
119878119895(119905) denote the number of RBs allocated
at slot 119905 to PU119894and SU
119895 respectively
(ii) 119901119875119894(119905) and 119901
119878119895(119905) denote the transmission power
allocated at slot 119905 to PU119894and SU
119895 respectively
(iii) 119886119875119894(119905) and 119886
119878119895(119905) denote the arrival rate (in bps) at slot
119905 in PU119894and SU
119895 respectively
(iv) 119902119875119894(119905) and 119902
119878119895(119905) denote the buffer size (in bits) at slot
119905 of PU119894and SU
119895 respectively
(v) 119903119875119894(119905) and 119903
119878119895(119905) denote the transmission rate (in bps)
at slot t in the channels of PU119894and SU
119895 respectively
(vi) 119875eNB 119875119875119894 and 119875119878119895denote the maximal transmission
power of the eNB PU119894 and SU
119895 respectively
22 Scenario 1 The objective of this paper is to devise asustainable algorithm for joint bandwidth and transmissionpower allocation based on two goals
(1) QoS Protection for the PUs PUs should maintain theirtarget QoS irrespective of how many SUs enter thenetwork and how much load they are generating
(2) Admissibility of the SUs SUs should be able to utilizethe spare capacity of the eNB (if left) to maximizetheir QoS
These goals however cannot be achieved without pro-viding the quantified measures for the user-perceived QoSNote that because of the orthogonality of the RB allocationthe need for interference mitigation in a considered CRNis eliminated In this case the use of such physical layercharacteristics as signal-to-noise ratio (SNR) is not well-reasoned More practical QoS measures can be obtainedfrom the higher layers network information For instancesuch metrics as round-trip latency and loss are traditionallyused for performance evaluation in wireless networks [5]Unfortunately in LTE system the direct estimation of delayand loss is rather complex For instance the end-to-endlatency consists of various delay components includingtransmission and queuing delays propagation andprocessingdelays the UL delay due to scheduling and delay due tohybrid automatic repeat request (HARQ) [18] The accurateanalysis of these delay components requires knowledge ofmany system parameters which may be not available duringresource allocation
Consequently in this paper we argue in favour of usingthe buffer size of UE pieces as a QoS measure The buffersize of PUs and SUs can be easily estimated from the knownparameters 119902
119875119894(119905) 119886119875119894(119905) and 119902
119878119895(119905) 119886119878119895(119905) using well-known
Lindleyrsquos equation [19]
119902119875119894(119905 + 1) = lceil119902
119875119894(119905) + 119886
119875119894(119905) minus 119903
119875119894(119905)rceil+
forall119894 isin I (1a)
119902119878119895(119905 + 1) = lceil119902
119878119895(119905) + 119886
119878119895(119905) minus 119903
119878119895(119905)rceil
+
forall119895 isin J (1b)
where lceil119909rceil+ = max0 119909 whereas the transmission rates119903119875119894(119905) 119903119878119895(119905) depend on the unknown bandwidth and trans-
mission power allocation vectors given by (relationshipbetween the transmission rate transmission power and thebandwidth will be established in the next section)
p119875= [1199011198751(119905) 119901
119875119899(119905)]119879
b119875= [1198871198751(119905) 119887
119875119899(119905)]119879
(2a)
p119878= [1199011198781(119905) 119901
119878119898(119905)]119879
b119878= [1198871198781(119905) 119887
119878119898(119905)]119879
(2b)
Note that the average round-trip latency of any primaryUE can be retained below some upper bound level by
4 Mobile Information Systems
restricting its buffer size to be less than a certain target buffersize The only information which is necessary in this case isthe desired upper bound on delay and the average arrival ratein PUs during some interval 119879 gt 0 Then we can find thetarget buffer size by deploying Littlersquos formula [20]
119863119894sdot 119886119875119894(119905) = 119871
119894 forall119894 isin I (3a)
where119863119894is the upper bound on delay for PU
119894 119871119894is the target
buffer size for PU119894 119886119875119894(119905) is the average arrival in PU
119894during
time interval [119905 minus 119879 + 1 119905] given by
119886119875119894(119905) =
119905
sum
120591=119905minus119879+1
119886119875119894(119905) forall119894 isin I (3b)
To maintain the desired upper bound on the end-to-enddelay the buffer size of PUs should be constrained as follows
119902119875119894(119905 + 1) le 119871
119894 forall119894 isin I (4)
or equivalently using (1a)
119902119875119894(119905) + 119886
119875119894(119905) minus 119871
119894le 119903119875119894(119905) le 119902
119875119894(119905) + 119886
119875119894(119905)
forall119894 isin I(5)
If added to an optimization problem constraint (5) canguarantee the QoS protection for PUs Except some (veryrare) cases when constraint (5) is not feasible the buffersize will always stay below the target level irrespective ofhow many SUs are in the network and how much load theyare generating The setting of the parameters 119871
119894 as well as
the cases when constraint (5) is unfeasible is discussed inSection 3
Note that at any slot 119905 the number of RBs allocatedfor data transmissions of PUs and SUs in the UL and DLdirections should not exceed 119861 RBs That is
sum
119894isinI119887119875119894(119905) + sum
119895isinJ119887119878119895(119905) le 119861 (6a)
where
119887119875119894(119905) isin Z+
119887119878119895(119905) isin Z+
forall119894 isin I forall119895 isin J
(6b)
where Z+ represents the set of all nonnegative integersAdditionally the transmission power allocated to the
users at any slot 119905 should be nonnegative and cannot exceedthe maximal transmission power levels Hence
119901119875119894(119905) le 119875
119875119894
119901119878119895(119905) le 119875
119878119895
forall119894 isin I forall119895 isin J
(7a)
for the UL direction and
sum
119894isinI119901119875119894(119905) + sum
119895isinJ119901119878119895(119905) le 119875eNB (7b)
for the DL direction where119901119875119894(119905) ge 0
119901119878119895(119905) ge 0
forall119894 isin I forall119895 isin J
(7c)
We are now ready to show how to attain the second goalof resource allocation As in case with QoS protection of PUswe use the buffer sizes of SUs as ameasure of the SUsrsquoQoSWesay that the admissibility of SUs in the network is preserved ifthey are allocated the bandwidth that is not used by the PUsThis can be done for instance byminimizing the sum (or thelogarithmic sum) of the buffer sizes of SUs or minimizing themaximal buffer size of SUs subject to the constraints listedabove
For the UL direction this gives us the following problem(to simplify notation we skip the index t below)
minimize max119895isinJ
lceil119902119878119895+ 119886119878119895minus 119903119878119895rceil
+
(8a)
subject to 119902119875119894+ 119886119875119894minus 119871119894le 119903119875119894le 119902119875119894+ 119886119875119894 forall119894 isin I (8b)
sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (8c)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(8d)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(8e)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(8f)
For the DL direction constraint (8e) should be replaced by
sum
119894isinI119901119875119894+sum
119895isinJ119901119878119895le 119875eNB (8g)
In above formulation each PU is guaranteed a certaintarget QoS level and the optimal allocations for PUs are suchthat
119902119875119894+ 119886119875119894minus 119903119875119894= 119871119894 forall119894 isin I (9)
The spare bandwidth (if left) is distributed among the SUsto minimize the size of their buffer which means that thetwo goals of resource allocation are achieved However thisformulation works well only if the aggregated traffic demandof the SUs is greater than that of the PUs Otherwise theremight be a situationwhen the optimal solution for SUs is suchthat
max119895isinJ
lceil119902119878119895+ 119886119878119895minus 119903119878119895rceil
+
le 119871119894 forall119894 isin I (10)
Mobile Information Systems 5
which is apparently not fair since the PUs have larger buffersizes than the SUs and therefore they will experience longerdelays than the SUs
To avoid such situation we propose to modify problem(8a)ndash(8g) by replacing its objective (8a) with
minimize max119894isinI
lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+
+max119895isinJ
lceil119902119878119895+ 119886119878119895minus 119903119878119895rceil
+
(11)
Objective (11) guarantees that PUs are served with max-imal QoS even if the aggregated traffic demand of SUs isgreater than that of the PUs
23 Scenario 2 We now consider a different scenario inwhich the PUs will benefit (by paying less in exchange) fromsharing their bandwidth with the SUs Let us assume that inthe network without price benefits (ie in Scenario 1) theprice for accessing the licensed spectrum of the PUs equals1 In this case all the PUs get the full QoS protection (ieguaranteed target buffer size 119871
119894and the average end-to-end
latency 119863119894) Suppose that each PU can define the portion of
allocated spectrum that it is willing to share with the SUsThedelay in turn is related to lceil119902
119875119894+ 119886119875119894minus 119903119875119894rceil+
Let us denote by 120572119894 0 le 120572
119894lt 1 the price for the portion
of spectrum that PU119894is willing to share with the SUs So
120572119894represents the willingness of PU
119894to trade off its QoS for
money Subsequently the guaranteed QoS level of PU119894will
reduce and instead of the QoS protection constraint (8b) wewill have
119903119875119894ge 119902119875119894+ 119886119875119894minus (1 + 120572
119894) 119871119894 forall119894 isin I (12)
Now to compensate for the income losses of a serviceprovider the SUs will have to pay the price for the sharedspectrum Let 120573 denote the price that each SU will pay foraccessing the shared spectrum The amount that SU
119895pays in
this case is 120573119903119878119895 whereas the revenue of the service provider
is
sum
119895isinJ120573119903119878119895minussum
119894isinI120572119894lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+
(13)
Assuming that a service provider does not incur loss byallowing the secondary users to use the spectrum we have toincorporate the constraint
sum
119895isinJ120573119903119878119895minussum
119894isinI120572119894lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+
ge V (14)
where V is the profit that a service provider would like tomakeby allowing the SUs into the network
Note that in such formulation the SUs get no QoSguarantee and therefore we have to minimize the price that
the SUs pay for their usage Thus the optimization problemis
minimize 120573 (15a)
subject to 119902119875119894+ 119886119875119894minus (1 + 120572
119894) 119871119894le 119903119875119894
le 119902119875119894+ 119886119875119894
forall119894 isin I
(15b)
sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (15c)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(15d)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(15e)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(15f)
sum
119895isinJ120573119903119878119895minussum
119894isinI120572119894lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+
ge V (15g)
for the UL direction For the DL direction constraint (15e) isreplaced by constraint (8g)The value of120573 obtained by solving(15a)ndash(15g) is then broadcasted by a service provider to theSUs that will have to pay a determined price
We note in passing that there are many other ways inwhich the pricing problem could be addressed For instancethe numbers 120572
119894may be negotiated between the PUs and a
service provider One can also think of a scenario wheredifferent SUs may be able to express their willingness to payvia bidding the prices 120573
119895 The options are numerous but they
are beyond the scope of this paper
3 Implementation Issues
31 Rate as a Function of Bandwidth and Power Note thatthe transmission rates in the UL and DL channels of a LTEsystem can be found using the modified Shannon equation[21] expressed as
119903119875119894(b119875 p119875) = 120596120595
119875119894119887119875119894log (1 + 120585
119875119894SNR119875119894)
= 120596120595119875119894119887119875119894log (1 + 120585
119875119894ℎ119875119894119901119875119894)
0 lt 120595119875119894 120585119875119894le 1 forall119894 isin I
(16a)
6 Mobile Information Systems
119903119878119895(b119878 p119878) = 120596120595
119878119895119887119878119895log (1 + 120585
119878119895SNR119878119895)
= 120596120595119878119895119887119878119895log (1 + 120585
119878119895ℎ119878119895119901119878119895)
0 lt 120595119878119895 120585119878119895le 1 forall119895 isin J
(16b)
where SNR119875119894and SNR
119878119895are the SNRs in the channels of PU
119894
and SU119895 respectively 120595
119875119894and 120595
119878119895are the system bandwidth
efficiencies for PU119894and SU
119895 respectively 120585
119875119894and 120585
119878119895are
the SNR efficiencies for PU119894and SU
119895 respectively 120596 is the
bandwidth of one RB (120596 = 180 kHz) [21]In real LTE networks the system bandwidth efficiency
is strictly less than 1 due to the overheads on the link andsystem levels The bandwidth efficiency is fully determinedby the design and internal settings of the system and doesnot depend on the physical characteristics of the wirelesschannels between the user and the eNB [21 22] Hence it isreasonable to assume that
120595119875119894= 120595119878119895= 120595 forall119894 isin I forall119895 isin J (17)
The SNR efficiency is mainly limited by the maximumefficiency of the supported modulation and coding scheme(MCS) [16] In LTE MCS is chosen using AMC to maximizethe data rate by adjusting the transmission parameters to thecurrent channel conditions AMC is one of the realizations ofa dynamic link adaptation In AMC algorithm the appropri-ate MCSs for packet transmissions are assigned periodically(within short fixed time interval usually equal to one slot)by the eNB based on the instantaneous channel conditionsreported by the usersThe higherMCS values are allocated tothe high-quality channels to achieve higher transmission rateThe lower MCS values are assigned to the channels of poorquality to decrease the transmission rate and consequentlyensure the transmission quality [16 17]
The method for choosing MCS can be expressed asfollows Based on the instantaneous radio channel conditionsthe SNR is calculated for the DL wireless channels betweenthe eNB and the users A supported MCS index is chosenusing expression [16 17]
MCS =
MCS1 SNR lt 120574
1
MCS2 1205741le SNR lt 120574
2
MCS119897 120574119897minus1
le SNR lt 120574119897
(18)
where 1205741
lt 1205742
lt sdot sdot sdot lt 120574119897are the SNR thresholds
corresponding to minus10 dB bit error ratio (BER) given by theAdditive White Gaussian Noise (AWGN) curves for eachMCS (the standard AWGN curves can be found in [17]) TheLTE standard allows 119897 = 15 MCS levels (description of MCSlevels their code rate and efficiency is shown in Table 1) [17]
Table 1 Allowed MCS values in LTE standard [17]
MCS index Modulation Code rate Efficiency0 No transmission1 QPSK 78 015232 QPSK 120 023443 QPSK 193 037704 QPSK 308 060165 QPSK 449 087706 QPSK 602 117587 16 QAM 378 147668 16 QAM 490 191419 16 QAM 616 2406310 64 QAM 466 2730511 64 QAM 567 3322312 64 QAM 666 3902313 64 QAM 772 4523414 64 QAM 873 5115215 64 QAM 948 55547
Based on the above the SNR efficiency depends onthe SNR of the DL wireless channel and therefore can berepresented by a function
119892 (SNR) =
1205851 SNR lt 120574
1
1205852 1205741le SNR lt 120574
2
120585119897 120574119897minus1
le SNR lt 120574119897
(19)
where 0 lt 1205851lt 1205852lt sdot sdot sdot lt 120585
119897are the values of the SNR
efficiency corresponding to the supported MCSUsing (17) and (19) the transmission rates of the users can
be expressed as
119903119875119894(b119875 p119875) = 120596120595119887
119875119894log (1 + 119892 (SNR
119875119894) sdot SNR
119875119894)
= 120596120595119887119875119894log (1 + 119892 (119901
119875119894) sdot ℎ119875119894119901119875119894)
forall119894 isin I
(20a)
119903119878119895(b119878 p119878) = 120596120595119887
119878119895log (1 + 119892 (SNR
119878119895) sdot SNR
119878119895)
= 120596120595119887119878119895log (1 + 119892 (119901
119878119895) ℎ119878119895119901119878119895)
forall119895 isin J
(20b)
32 Solution Methodology In this subsection we describe asolution methodology for the resource allocation problemin Scenario 1 in the UL direction (with the objective givenby (11) and the constraints defined in (8b)ndash(8f)) A resourceallocation problem for the DL direction as well as problem(15a)ndash(15g) for Scenario 2 can be solved analogously
Mobile Information Systems 7
Note that in Scenario 1 a resource allocation problem inthe UL direction is equivalent to
minimize Ω + Φ (21a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (21b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(21c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(21d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(21e)
Ω ge 0
Φ ge 0
(21f)
1198911
119894(b119875 p119875) = 119903119875119894(b119875 p119875) minus (119902
119875119894+ 119886119875119894)
le 0
forall119894 isin I
(21g)
1198912
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894minus 119871119894) minus 119903119875119894(b119875 p119875)
le 0
forall119894 isin I
(21h)
1198913
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894) minus 119903119875119894(b119875 p119875) minus Ω
le 0
forall119894 isin I
(21i)
1198914
119895(b119878 p119878)
= (119902119878119895+ 119886119878119895) minus 119903119878119895(b119878 p119878) minus Φ
le 0
forall119895 isin J
(21j)
In above problem some of the optimization variables(particularly the components of b
119875and b
119878) can take only
integer values whereas the other variables (the componentsof p119875and p
119878) are real-valued ones In addition constraints
(21g)ndash(21j) are represented by the nonsmooth nonlinear
functions of (b119875 p119875) and (b
119875 p119875) Hence (21a)ndash(21j) is a
nonlinear mixed integer programming (MINLP) problemwhich is Nondeterministic Polynomial-time (NP) hard Forimmediate proof of NP-hardness note that MINLP includesmixed integer linear programming (MILP) problem which isNP-hard [23]
Before applying any MINLP method for solving (21a)ndash(21j) the nonsmooth function 119892(sdot) in (19) included in theexpressions of 119903
119875119894(b119875 p119875) and 119903
119878119895(b119875 p119875) should be replaced
by its smooth approximation To construct a smooth approx-imation of 119892(119909) note that this function is equivalent to thesum of the shifted and scaled versions of a Heaviside stepfunction119867(119909) [24] That is
119892 (119909) =
15
sum
119897=1
(120577119897minus 120577119897minus1)119867 (119909 minus 120574
119897)
119867 (119909) =
1 if 119909 ge 0
0 otherwise
(22)
where 1205770= 0
Recall that a smooth approximation for a step function119867(119909) is given by a logistic sigmoid function [25]
119902(119909) =
1
1 + 119890minus2119902119909
(23)
where 119902 gt 0 119909 is in range of real numbers from minusinfin to +infinIf we take 119867(0) = 12 then larger 119902 corresponds to a closertransition to119867(119909) that is
lim119902rarrinfin
119902(119909) = 119867 (119909) (24)
The above holds because for 119909 lt 0 we have
119890minus2119902119909
997888rarr +infin
119902(119909) asymp 119867 (119909) = 1
(25)
for 119909 gt 0
119890minus2119902119909
997888rarr 0
119902(119909) asymp 119867 (119909) = 1
(26)
for 119909 = 0
119890minus2119902119909
= 1
119902(119909) = 119867 (119909) =
1
2
(27)
Consequently an approximation for a shifted Heavisidefunction is represented by a shifted logistic function
119902(119909 minus 120574
119897) =
1
1 + 119890minus2119902(119909minus120574119897)
(28)
defined for 119902 gt 0 with real 119909 in range from minusinfin to +infin
8 Mobile Information Systems
Based on (28) we can construct a smooth approximationfor 119892(119909) as
119902(119909) =
15
sum
119897=1
(120577119897minus 120577119897minus1) 119902(119909 minus 120574
119897) =
15
sum
119897=1
120577119897minus 120577119897minus1
1 + 1198902119902(119909minus120574119897)
(29)
Then it is rather straightforward to verify that
lim119902rarrinfin
119902(119909) = 119892 (119909) (30)
and the approximations for 119903119875119894(b119875 p119875) and 119903
119878119895(b119875 p119875) will
take the form
119875119894(b119875 p119875) = 120596120595119887
119875119894log (1 + (119901
119875119894) sdot ℎ119875119894119901119875119894)
forall119894 isin I(31a)
119878119895(b119878 p119878) = 120596120595119887
119878119895log (1 + (119901
119878119895) ℎ119878119895119901119878119895)
forall119895 isin J(31b)
With the approximations given by (31a) and (31b) prob-lem (21a)ndash(21j) can be solved using a sequential optimizationapproach as
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (32a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (32b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(32c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(32d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(32e)
Ω ge 0
Φ ge 0
(32f)
119891
1
119894(b119875 p119875)
= 119875119894(b119875 p119875)
minus (119902119875119894+ 119886119875119894) le 0
forall119894 isin I
(32g)
119891
2
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894minus 119871119894)
minus 119875119894(b119875 p119875) le 0
forall119894 isin I
(32h)
119891
3
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894)
minus 119875119894(b119875 p119875) minus Ω
le 0
forall119894 isin I
(32i)
119891
4
119895(b119878 p119878)
= (119902119878119895+ 119886119878119895)
minus 119878119895(b119878 p119878) minus Φ
le 0
forall119895 isin J
(32j)
The above problem is smooth MINLP which can besolved using some fast and effective MINLP method Notethat most of the MINLP techniques involve constructionof the following relaxations to the considered problem thenonlinear programming (NLP) relaxation (original problemwithout integer restrictions) and the MILP relaxation (origi-nal problem where nonlinearities are replaced by supportinghyperplanes) In our case a smooth MILP relaxation to(32a)ndash(32j) in a given point (b0
119875 p0119875 b0119878 p0119878) is given by
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (33a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (33b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(33c)
Mobile Information Systems 9
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(33d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(33e)
Ω ge 0
Φ ge 0
(33f)
119891
1
119894(b0119875 p0119875) + nabla
119891
1
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33g)
119891
2
119894(b0119875 p0119875) + nabla
119891
2
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33h)
119891
3
119894(b0119875 p0119875) + nabla
119891
3
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33i)
119891
4
119895(b0119878 p0119878) + nabla
119891
4
119895(b0119878 p0119878)
119879
[
b119878minus b0119878
p119878minus p0119878
]
le 0
forall119895 isin J
(33j)
The NLP relaxation to (32a)ndash(32j) is
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (34a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (34b)
119887119875119894ge 0
119887119878119895ge 0
forall119894 isin I forall119895 isin J
(34c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(34d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(34e)
Ω ge 0
Φ ge 0
(34f)
119891
1
119894(b119875 p119875) le 0
forall119894 isin I(34g)
119891
2
119894(b119875 p119875) le 0
forall119894 isin I(34h)
119891
3
119894(b119875 p119875) le 0
forall119894 isin I(34i)
119891
4
119895(b119878 p119878) le 0
forall119895 isin J(34j)
Note that theMINLP problems can be solved using eitherdeterministic technique or an approximation A typical exact
10 Mobile Information Systems
method for solving MINLPs is a well-known branch-and-bound algorithmand its variousmodifications [26] examplesof heuristic approaches include local branching [27] largeneighborhood search [28] and feasibility pump [29] to namea few Since we are interested in a reasonably simple and fastalgorithm it is more convenient to use heuristics for solvingthe problem In this paper a Feasibility Pump (FP) heuristic[29 30] is applied to solve (32a)ndash(32j) FP is perhaps the mostsimple and most effective method for producing more andbetter solutions in a shorter average running time For theproblems with nonbinary integer variables the complexity ofFP is exponential in size of a problem [31]
A fundamental idea of FP algorithm is to decomposethe problem into two parts integer feasibility and constraint
feasibility The former is achieved by rounding (solvinga NLP relaxation to the original problem) and the latterby projection (solving a MILP relaxation) Consequentlytwo sequences of points are generated The first sequence(b119875 p119875 b119878 p119878)119896119870
119896=1 119870 = 1 2 contains the integral
points that may violate the nonlinear constraintsThe secondsequence (b
119875 p119875 b119878 p119878)119896119870
119896=1contains the points which are
feasible for a continuous relaxation to the original problembut might not be integral
More specifically with input (b119875 p119875 b119878 p119878)1being a
solution to the NLP relaxation given by (34a)ndash(34j) thealgorithm generates two sequences by solving the followingproblems for 119896 = 1 119870
(b119875 p119875 b119878 p119878)119896= argmin
100381710038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b
119875 p119875 b119878 p119878)119896
1003817100381710038171003817100381710038171
(35a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (35b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(35c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(35d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(35e)
Ω ge 0
Φ ge 0
(35f)
119891
1
119894(b0119875 p0119875) + nabla
119891
1
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35g)
119891
2
119894(b0119875 p0119875) + nabla
119891
2
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35h)
119891
3
119894(b0119875 p0119875) + nabla
119891
3
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35i)
Mobile Information Systems 11
119891
4
119895(b0119878 p0119878) + nabla
119891
4
119895(b0119878 p0119878)
119879
[
b119878minus b0119878
p119878minus p0119878
] le 0
forall119895 isin J
(35j)
(b119875 p119875 b119878 p119878)119896+1
= argmin 10038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b
119875 p119875 b119878 p119878)119896
100381710038171003817100381710038172
(36a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (36b)
119887119875119894ge 0
119887119878119895ge 0
forall119894 isin I forall119895 isin J
(36c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(36d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(36e)
Ω ge 0
Φ ge 0
(36f)
119891
1
119894(b119875 p119875) le 0
forall119894 isin I(36g)
119891
2
119894(b119875 p119875) le 0
forall119894 isin I(36h)
119891
3
119894(b119875 p119875) le 0
forall119894 isin I(36i)
119891
4
119895(b119878 p119878) le 0
forall119895 isin J(36j)
where sdot1and sdot
2are 1198971norm and 119897
2norm respectivelyThe
rounding step is carried out by solving (35a)ndash(35j) whereasthe projection is the solution to (36a)ndash(36j) A suggested FPalgorithm alternates between the rounding and projectionsteps until (b
119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896(which implies
feasibility) or the number of iterations 119896 has reached thepredefined limit 119870 The workflow of a corresponding FPalgorithm is illustrated in the following part
FP Algorithm for Non-Convex MINLP(0) INITIALIZATION input119870 set 119896 = 1
solve (34a)ndash(34j) to obtain (b119875 p119875 b119878 p119878)119896
(1) WHILE (119896 lt 119870) do
(2) ROUNDING solve (35a)ndash(35j) to obtain(b119875 p119875 b119878 p119878)119896
(3) IF ((b119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896) THEN goto
step (6)(4) PROJECTION solve (36a)ndash(36j) to obtain
(b119875 p119875 b119878 p119878)119896+1
(5) Set 119896 = 119896 + 1
12 Mobile Information Systems
(6) OUTPUT solution (b119875 p119875 b119878 p119878)lowast
=
(b119875 p119875 b119878 p119878)119896
Note that in order to retain the convergence of thealgorithm both problems (35a)ndash(35j) and (36a)ndash(36j) needto be solved exactly Problem (36a)ndash(36j) (and consequentlyproblem (34a)ndash(34j)) can be solved using any standard NLPmethod In this paper an interior point algorithm (describedeg in [32]) with polynomial complexity is applied to solve(36a)ndash(36j) and (34a)ndash(34j) MILP problem (35a)ndash(35j) isrelatively simple and therefore can be solved efficiently foroptimality by any technique from the family of the branch-and-bound methods (eg [26])
33 Target Buffer Size for PUs and Feasibility Issues Recallthat 119871
119894represents the target buffer size for PU
119894 which
indicates that the QoS requirements of PU119894are satisfied By
limiting the buffer size of PUs we restrict the QoS of PUs(measured in terms of their buffer size) to be higher (or atleast not smaller) than the required minimum From thispoint of view constraints (5) and (12) guarantee the QoSprotection of PUs in Scenario 1 and Scenario 2 respectivelyApparently one can always restrict the target buffer size ofPUs to be equal to zero so that after each subsequent dataarrival the buffer of each PU is fully cleared This approachrepresents a ldquogreedyrdquo policy which ensures that the PUs arealways served with the best possible QoS but does not guar-antee that some spare capacity will be left to serve the SUs
A ldquoless greedyrdquo strategy would be to establish somelower bound on QoS for the PUs which will provide anldquoopportunityrdquo for SUs to be served To establish this lowerbound recall that the growing delay and loss indicate thata buffer of a corresponding node is congested whereas inan uncongested node the packet delay and loss are alwaysminimal [33] On the other hand it has been reported in[33 34] that in an uncongested node the buffer size 119902(119905) isincreasing very slowly that is 119902(119905 + 1)119902(119905) asymp 1 whereas ina congested node the buffer size is growing very fast so that119902(119905+1)119902(119905) ≫ 1 Hence to serve the PUs withminimal delayand loss it is enough to prevent the growth of their buffersthat is for each PU set
119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)
where 120576 ge 0 is some small value such that
120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)
More sophisticated approach to find the lowerQoS boundcan be deployed if information about the past buffer size isavailable at any time slot 119905 In this case one can set the targetbuffer size based on past T observations 119902(119905) 119902(119905 minus 119879 + 1)as
119871119894= min120591isinT
119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38a)
or
119871119894=
1
119879
sum
120591isinT119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38b)
where T = 1 119879
UBADPC MBC
60
70
80
90
100
110
120
130
140
Alg
orith
m it
erat
ions
10020 8040 50 60 7030 90100Number of SUs m
120572i = 1 v = m lowast 1Mbps
Figure 1 Average number of iterations before convergence as afunction of number of SUs in simulations with 119899 = 100 PUs andaverage SNR = 0 dB
MBC
070
075
080
085
090
095
100
120572i=0
v=0
120572i=1
v=0
120572i=0
v=m
lowast1
Mbp
s
120572i=1
v=m
lowast1
Mbp
s
Fairness among SUs FSU
Fairness among PUs FPU
Fairness among all users F
Figure 2 Jainrsquos index of fairness119865SU119865PU and119865 for the PUs SUs andall users in simulations with 119899 = 100 PUs119898 = 100 SUs and averageSNR = 0 dB
In some (very rare) cases (when the service capacity of theeNB is not enough to guarantee that the buffer sizes in all PUsdo not exceed the target buffer size) constraints (5) and (12)in Scenarios 1 and 2 may be not feasible In the following weshow how to identify such situation and what should be theoptimal resource allocation strategy in this case
Note that the service capacity of LTE system greatlydepends on physical characteristics (eg SINR and MCS) of
Mobile Information Systems 13
UBADPCGBC
NBCMBCABC
780
800
820
840
860
880
900
920
940
960Th
roug
hput
for P
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r PU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for P
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
Figure 3 Mean throughput packet delay and loss for PUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
the wireless channels between the eNB and the users Henceat the moment preceding the bandwidthpower allocation itis rather difficult to estimate the service capacity of a systemNevertheless it is possible to find the average service capacityand to determine the upper and lower bounds on servicecapacity of the eNB in the UL and DL directions such that
119877min le sum119894isinI119903119875119894(119905) asymp 119877ave le 119877max (39)
where119877min119877ave and119877max are the lower bound upper boundand average service capacity of the eNB respectively
In our case the upper bound on service capacity of theeNB is given by
119877max = 120596120595119861 log (1 + 119892 (SNRmax) sdot SNRmax) (40a)
where SNRmax is the maximal possible SNR value
The lower bound on service capacity of eNB is
119877min = 120596120595119861 log (1 + 119892 (SNRmin) sdot SNRmin) (40b)
where SNRmin is the minimal possible SNR valueThe average service capacity of the eNB equals
119877ave = 120596120595119861 log (1 + 119892 (SNRave) sdot SNRave) (40c)
where SNRave is the average SNR valueIf SNR information is available then the values SNRmax
SNRmin and SNRave can be set as
SNRmax = max119894isinI
SNR119894 (41a)
14 Mobile Information Systems
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r SU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for S
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
Figure 4 Mean throughput packet delay and loss for SUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
SNRmin = min119894isinI
SNR119894 (41b)
SNRave =1
119899
sum
119894isinISNR119894 (41c)
Otherwise (ie if SNR information is not available) thevalues are set arbitrarily
Now we can identify the situation when constraints (5)and (12) cannot be satisfied For this we should perform thefollowing test For Scenario 1 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus 119871
119894) (42)
then constraint (5) is feasible Otherwise condition (5)cannot be satisfiedHence all the SUs receive zero allocations
andwe assign the bandwidthpower resources only to the PUsby solving the following optimization problem
minimize max119894isinI
lceil119902119875119894+ 119886119875119894minus 119903119875119894(b119875 p119875)rceil+
(43a)
subject to 119903119875119894(b119875 p119875) le 119902119875119894+ 119886119875119894 forall119894 isin I (43b)
sum
119894isinI119887119875119894le 119861 (43c)
119887119875119894isin Z+ forall119894 isin I (43d)
119901119875119894le 119875119875119894 forall119894 isin I (43e)
119901119875119894ge 0 forall119894 isin I (43f)
Mobile Information Systems 15
725
750
775
800
825
850
875
900
925
950Th
roug
hput
for P
Us (
kbits
s)
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
10
20
30
40
50
60
70
Dela
y fo
r PU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Loss
for P
Us (
)
0
005
01
015
02
025
03
035
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Figure 5 Mean throughput packet delay and loss for PUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
for the UL direction For the DL directions constraint (43e)should be replaced by
sum
119894isinI119901119875119894le 119875eNB (43g)
For Scenario 2 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus (1 + 120572
119894) 119871119894) (44)
then constraint (12) is feasible Otherwise inequality (12)cannot be satisfied and the bandwidthpower resources areassigned only to the PUs (according to (43a)ndash(43g)) whereasthe SUs receive zero allocations
4 Performance Evaluation
41 Simulation Model A simulation model of the networkconsisting of one eNB 119899 PUs and 119898 SUs randomly locatedin a service area with 3 km radius has been developed upona standard LTE platform using the OPNET package [35]Thebandwidth of the eNB equals 119861 = 50RBs (which is equivalentto 10MHz) The slot duration in the algorithm equals 119879
119904=
1msThemaximal number of iterations in FP algorithm is set119870 = 200Themaximal transmission power of the eNB equals119875eNB = 46 dBm and the maximal transmission power of eachPUSU equals 119875
1198751= sdot sdot sdot = 119875
119875119899= 1198751198781= sdot sdot sdot = 119875
119878119898= 23 dBm
Other simulation settings of the model are listed in Table 2(all the parameters are based on LTE specifications [36])
16 Mobile Information Systems
Table 2 Simulation parameters of the model
Parameter ValueRadio network model
Pass loss 119871 = 40log10119877 + 30log
10119891 + 49 119877 distance (km) 119891
carrier frequency (Hz)
Shadow fading Log-normal shadow fading with a standard deviation of1012 dB for outdoorindoor users
Penetration loss The average building penetration loss is 12 dB with astandard deviation of 8 dB
Multipath fading Spatial Channel Model (SCM) Suburban macroUE velocity 0 kmsTransmitterreceiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver noise figure 5 dBThermal noise density minus174 dBmHzCableconnectorcombiner losses 2 dB
Physical profileOperation mode FDDCyclic prefix type Normal (7 symbols per slot)Evolved packet core (EPC) bearer definitions 348 kbits (nonguaranteed bit rate)Subcarrier spacing 15 kHz
Admission control parametersPhysical downlink control channel (PDCCH) symbols per subframe 3UL loading factor 1DL loading factor 1Inactive bearer timeout 20 sec
Buffer status report parametersPeriodic timer 5 subframesRetransmission timer 2560 subframes
L1L2 control parametersReserved size 2 RBsCyclic shifts 6Starting RB preserver for Format 1 messages 0Allocation periodicity 5 subframes
Random access (RA) parametersNumber of preambles 64Preamble format Format 0 (1-subframe long)Number of RA resources per frame 4Preamble retransmission limit 5 subframesRA response timer 5 subframesContention resolution timer 40 subframes
HARQ parametersMaximal number of retransmissions 3 (UL and DL)HARQ retransmission timer 8 subframes (UL and DL)Maximal number of HARQ processes 8 per UE (UL and DL)
A radio model of the network corresponds to the require-ments of ITU-T Recommendation M1225
The algorithms proposed in the paper are denoted asfollows
(i) GBC (greedy buffer Control) where the target buffersize equals 0 for all the PUs
(ii) NBC (nongreedy buffer control) with the target buffersize calculated according to (37a) and (37b)
(iii) MBC (Minimal Buffer Control) with 119879 = 10 slots andthe target buffer size given by (38a)
(iv) ABC (Average Buffer Control) with 119879 = 10 slots andthe target buffer size equaling (38b)
Two previously proposed schemes used to benchmark theperformance of the algorithms proposed in this paper are
(i) UBA (Utility Based Allocation) presented in [11]where the network resources (bandwidth and trans-mission power) are allocated to the UL channels tomaximize the total transmission rate of the userssubject to the capacity and transmission power con-straints
Mobile Information Systems 17
0 10 20 30 40 50 60 70 80Average SNR (dB)
UBADPCGBC
NBCMBCABC
30
35
40
45
50
55
60
65
70
Dela
y fo
r SU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
012
015
018
021
024
027
03
033
Loss
for S
Us (
)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
250
300
350
400
450
500Th
roug
hput
for S
Us (
kbits
s)
Figure 6 Mean throughput packet delay and loss for SUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
(ii) DPC (Delay Power Control) derived in [5] whichis used to balance the transmission delay againsttransmission power in wireless channels between theeNB and the users
We also gather simulation results for a proposed resourceallocation approach in Scenario 2 with different settings ofthe parameters120572
119894and V and benchmark its performancewith
the performance of the algorithm in Scenario 1All algorithms are simulated using identical settings
The data traffic in simulations is represented by voice overInternet Protocol (VoIP) video and Hypertext TransferProtocol (HTTP) applications mixed in proportion 2 3 5using the models defined in [37]
42 Complexity and Fairness Issues Let us first evaluatethe complexity and the fairness of resource allocation indifferent algorithms Figure 1 shows the average numberof iterations before convergence for UBA DPC and theproposed algorithms in Scenario 1 (denoted as MBC) andScenario 2 gathered in simulations with 119899 = 100 PUs andaverage SNR = 0 dB Note that the target buffer size for thePUs is calculated according to (38a) with T = 10 slots (inScenarios 1 and 2) and 120572
119894= 1 V = 119898 lowast 1Mbps (for
Scenario 2) Results demonstrate that the complexity of FPmethod deployed for resource allocation in Scenarios 1 and2 is exponential in size of the problem (which correspondsto the findings reported in [31]) and is comparable to thecomplexities of other techniques (UBA and DPC)
18 Mobile Information Systems
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
080020 090070050 060 100000 030010 040120572i
10
20
30
40
50
60
70
80
90
100
110
Dela
y fo
r PU
s (m
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
040030 090000 080060010 020 050 100070120572i
005
010
015
020
025
030
035
040
045
050
Loss
for P
Us (
)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
030020 040 090010 060 070 080 100000 050120572i
Figure 7 Mean throughput packet delay and loss for the PUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
Figure 2 shows the fairness of different methods calcu-lated according to Jainrsquos equation [38] as
119865PU =
(sum119894isinI 119903119875119894)
2
119899 sdot sum119894isinI 1199032
119875119894
119865SU =
(sum119895isinJ 119903119878119895)
2
119898 sdot sum119895isinJ 1199032
119878119895
119865 =
(sum119894isinI 119903119875119894 + sum119895isinJ 119903119878119895)
2
(119899 + 119898) sdot (sum119894isinI 1199032
119875119894+ sum119895isinJ 1199032
119878119895)
(45)
where 119865PU 119865SU and 119865 stand for Jainrsquos index of fairness forthe PUs SUs and all of the users respectively 119903
119875119894 119903119878119895
arethe mean throughputs for PU
119894and SU
119895 respectively Results
have been gathered for 119899 = 100 PUs 119898 = 100 SUs average
Mobile Information Systems 19
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
410
420
430
440
450
460
470
480
490
500
510Th
roug
hput
for S
Us (
kbits
s)
010 020 080 090050 060 070030 100000 040120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
15
20
25
30
35
40
45
50
Dela
y fo
r SU
s (m
s)
070 090030 040 050 080000 020010 100060120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
007
009
011
013
015
017
019
021
023
Loss
for S
Us (
)
080070 090020 050 060030 100040010000120572i
Figure 8 Mean throughput packet delay and loss for the SUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
SNR = 0 dB and target buffer size for the PUs calculatedaccording to (38a) (Scenarios 1 and 2) with different settingsof 120572119894and V in Scenario 2
It follows from these graphs that the fairness index amongall of the users (denoted as 119865) is higher in Scenario 2 with120572119894= 1 and lower in Scenario 1 and Scenario 2 with 120572
119894= 0
Such results are rather expectable in Scenario 1 and Scenario2 with 120572
119894= 0 the SUs are served for free on a best-effort
basis whereas the PUs enjoy full QoS guarantees Hence thenetwork resources are shared nonequally between the PUs
and the SUs with most of the RBs allocated to the PUs andthe rest of the bandwidth distributed among the SUs Onthe other hand the fairness index for the PUs and SUs (ie119865PU and 119865SU) is rather high in both scenarios with differentsettings of 120572
119894and V which indicates that the users of the same
type are treated equally during resource allocation
43 Simulation Results in Scenario 1 Let us evaluate theperformance of a resource allocation algorithm in Scenario1 in terms of mean throughput packet end-to-end delay and
20 Mobile Information Systems
MBC
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
20
30
40
50
60
70
80
90
Dela
y fo
r PU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
005
010
015
020
025
030
035
040
045
Loss
for P
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 9 Mean throughput packet delay and loss for the PUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
loss for different user types Figures 3ndash6 show results obtainedin simulations with 119899 = 100 PUs and average SNR = 0 dBResults demonstrate that aUBA scheme has the largest packetdelay and loss and the lowest throughput for both the PUs andthe SUs A poor performance of this scheme is explained asfollows
(i) QoS protection of PUs is not considered in UBAHence the throughput delay and loss are the samefor PUs and SUs
(ii) Buffer sizes of individual users are not consideredin resource allocation and therefore the QoS for
Mobile Information Systems 21
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
30
50
70
90
110
130
Dela
y fo
r SU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
000
010
020
030
040
050
060
Loss
for S
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
different users varies significantly (since differentusers have different traffic demands)
(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer
size and therefore there is no need to maximize theirtransmission rate and spend the network resources
Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
4 Mobile Information Systems
restricting its buffer size to be less than a certain target buffersize The only information which is necessary in this case isthe desired upper bound on delay and the average arrival ratein PUs during some interval 119879 gt 0 Then we can find thetarget buffer size by deploying Littlersquos formula [20]
119863119894sdot 119886119875119894(119905) = 119871
119894 forall119894 isin I (3a)
where119863119894is the upper bound on delay for PU
119894 119871119894is the target
buffer size for PU119894 119886119875119894(119905) is the average arrival in PU
119894during
time interval [119905 minus 119879 + 1 119905] given by
119886119875119894(119905) =
119905
sum
120591=119905minus119879+1
119886119875119894(119905) forall119894 isin I (3b)
To maintain the desired upper bound on the end-to-enddelay the buffer size of PUs should be constrained as follows
119902119875119894(119905 + 1) le 119871
119894 forall119894 isin I (4)
or equivalently using (1a)
119902119875119894(119905) + 119886
119875119894(119905) minus 119871
119894le 119903119875119894(119905) le 119902
119875119894(119905) + 119886
119875119894(119905)
forall119894 isin I(5)
If added to an optimization problem constraint (5) canguarantee the QoS protection for PUs Except some (veryrare) cases when constraint (5) is not feasible the buffersize will always stay below the target level irrespective ofhow many SUs are in the network and how much load theyare generating The setting of the parameters 119871
119894 as well as
the cases when constraint (5) is unfeasible is discussed inSection 3
Note that at any slot 119905 the number of RBs allocatedfor data transmissions of PUs and SUs in the UL and DLdirections should not exceed 119861 RBs That is
sum
119894isinI119887119875119894(119905) + sum
119895isinJ119887119878119895(119905) le 119861 (6a)
where
119887119875119894(119905) isin Z+
119887119878119895(119905) isin Z+
forall119894 isin I forall119895 isin J
(6b)
where Z+ represents the set of all nonnegative integersAdditionally the transmission power allocated to the
users at any slot 119905 should be nonnegative and cannot exceedthe maximal transmission power levels Hence
119901119875119894(119905) le 119875
119875119894
119901119878119895(119905) le 119875
119878119895
forall119894 isin I forall119895 isin J
(7a)
for the UL direction and
sum
119894isinI119901119875119894(119905) + sum
119895isinJ119901119878119895(119905) le 119875eNB (7b)
for the DL direction where119901119875119894(119905) ge 0
119901119878119895(119905) ge 0
forall119894 isin I forall119895 isin J
(7c)
We are now ready to show how to attain the second goalof resource allocation As in case with QoS protection of PUswe use the buffer sizes of SUs as ameasure of the SUsrsquoQoSWesay that the admissibility of SUs in the network is preserved ifthey are allocated the bandwidth that is not used by the PUsThis can be done for instance byminimizing the sum (or thelogarithmic sum) of the buffer sizes of SUs or minimizing themaximal buffer size of SUs subject to the constraints listedabove
For the UL direction this gives us the following problem(to simplify notation we skip the index t below)
minimize max119895isinJ
lceil119902119878119895+ 119886119878119895minus 119903119878119895rceil
+
(8a)
subject to 119902119875119894+ 119886119875119894minus 119871119894le 119903119875119894le 119902119875119894+ 119886119875119894 forall119894 isin I (8b)
sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (8c)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(8d)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(8e)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(8f)
For the DL direction constraint (8e) should be replaced by
sum
119894isinI119901119875119894+sum
119895isinJ119901119878119895le 119875eNB (8g)
In above formulation each PU is guaranteed a certaintarget QoS level and the optimal allocations for PUs are suchthat
119902119875119894+ 119886119875119894minus 119903119875119894= 119871119894 forall119894 isin I (9)
The spare bandwidth (if left) is distributed among the SUsto minimize the size of their buffer which means that thetwo goals of resource allocation are achieved However thisformulation works well only if the aggregated traffic demandof the SUs is greater than that of the PUs Otherwise theremight be a situationwhen the optimal solution for SUs is suchthat
max119895isinJ
lceil119902119878119895+ 119886119878119895minus 119903119878119895rceil
+
le 119871119894 forall119894 isin I (10)
Mobile Information Systems 5
which is apparently not fair since the PUs have larger buffersizes than the SUs and therefore they will experience longerdelays than the SUs
To avoid such situation we propose to modify problem(8a)ndash(8g) by replacing its objective (8a) with
minimize max119894isinI
lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+
+max119895isinJ
lceil119902119878119895+ 119886119878119895minus 119903119878119895rceil
+
(11)
Objective (11) guarantees that PUs are served with max-imal QoS even if the aggregated traffic demand of SUs isgreater than that of the PUs
23 Scenario 2 We now consider a different scenario inwhich the PUs will benefit (by paying less in exchange) fromsharing their bandwidth with the SUs Let us assume that inthe network without price benefits (ie in Scenario 1) theprice for accessing the licensed spectrum of the PUs equals1 In this case all the PUs get the full QoS protection (ieguaranteed target buffer size 119871
119894and the average end-to-end
latency 119863119894) Suppose that each PU can define the portion of
allocated spectrum that it is willing to share with the SUsThedelay in turn is related to lceil119902
119875119894+ 119886119875119894minus 119903119875119894rceil+
Let us denote by 120572119894 0 le 120572
119894lt 1 the price for the portion
of spectrum that PU119894is willing to share with the SUs So
120572119894represents the willingness of PU
119894to trade off its QoS for
money Subsequently the guaranteed QoS level of PU119894will
reduce and instead of the QoS protection constraint (8b) wewill have
119903119875119894ge 119902119875119894+ 119886119875119894minus (1 + 120572
119894) 119871119894 forall119894 isin I (12)
Now to compensate for the income losses of a serviceprovider the SUs will have to pay the price for the sharedspectrum Let 120573 denote the price that each SU will pay foraccessing the shared spectrum The amount that SU
119895pays in
this case is 120573119903119878119895 whereas the revenue of the service provider
is
sum
119895isinJ120573119903119878119895minussum
119894isinI120572119894lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+
(13)
Assuming that a service provider does not incur loss byallowing the secondary users to use the spectrum we have toincorporate the constraint
sum
119895isinJ120573119903119878119895minussum
119894isinI120572119894lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+
ge V (14)
where V is the profit that a service provider would like tomakeby allowing the SUs into the network
Note that in such formulation the SUs get no QoSguarantee and therefore we have to minimize the price that
the SUs pay for their usage Thus the optimization problemis
minimize 120573 (15a)
subject to 119902119875119894+ 119886119875119894minus (1 + 120572
119894) 119871119894le 119903119875119894
le 119902119875119894+ 119886119875119894
forall119894 isin I
(15b)
sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (15c)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(15d)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(15e)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(15f)
sum
119895isinJ120573119903119878119895minussum
119894isinI120572119894lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+
ge V (15g)
for the UL direction For the DL direction constraint (15e) isreplaced by constraint (8g)The value of120573 obtained by solving(15a)ndash(15g) is then broadcasted by a service provider to theSUs that will have to pay a determined price
We note in passing that there are many other ways inwhich the pricing problem could be addressed For instancethe numbers 120572
119894may be negotiated between the PUs and a
service provider One can also think of a scenario wheredifferent SUs may be able to express their willingness to payvia bidding the prices 120573
119895 The options are numerous but they
are beyond the scope of this paper
3 Implementation Issues
31 Rate as a Function of Bandwidth and Power Note thatthe transmission rates in the UL and DL channels of a LTEsystem can be found using the modified Shannon equation[21] expressed as
119903119875119894(b119875 p119875) = 120596120595
119875119894119887119875119894log (1 + 120585
119875119894SNR119875119894)
= 120596120595119875119894119887119875119894log (1 + 120585
119875119894ℎ119875119894119901119875119894)
0 lt 120595119875119894 120585119875119894le 1 forall119894 isin I
(16a)
6 Mobile Information Systems
119903119878119895(b119878 p119878) = 120596120595
119878119895119887119878119895log (1 + 120585
119878119895SNR119878119895)
= 120596120595119878119895119887119878119895log (1 + 120585
119878119895ℎ119878119895119901119878119895)
0 lt 120595119878119895 120585119878119895le 1 forall119895 isin J
(16b)
where SNR119875119894and SNR
119878119895are the SNRs in the channels of PU
119894
and SU119895 respectively 120595
119875119894and 120595
119878119895are the system bandwidth
efficiencies for PU119894and SU
119895 respectively 120585
119875119894and 120585
119878119895are
the SNR efficiencies for PU119894and SU
119895 respectively 120596 is the
bandwidth of one RB (120596 = 180 kHz) [21]In real LTE networks the system bandwidth efficiency
is strictly less than 1 due to the overheads on the link andsystem levels The bandwidth efficiency is fully determinedby the design and internal settings of the system and doesnot depend on the physical characteristics of the wirelesschannels between the user and the eNB [21 22] Hence it isreasonable to assume that
120595119875119894= 120595119878119895= 120595 forall119894 isin I forall119895 isin J (17)
The SNR efficiency is mainly limited by the maximumefficiency of the supported modulation and coding scheme(MCS) [16] In LTE MCS is chosen using AMC to maximizethe data rate by adjusting the transmission parameters to thecurrent channel conditions AMC is one of the realizations ofa dynamic link adaptation In AMC algorithm the appropri-ate MCSs for packet transmissions are assigned periodically(within short fixed time interval usually equal to one slot)by the eNB based on the instantaneous channel conditionsreported by the usersThe higherMCS values are allocated tothe high-quality channels to achieve higher transmission rateThe lower MCS values are assigned to the channels of poorquality to decrease the transmission rate and consequentlyensure the transmission quality [16 17]
The method for choosing MCS can be expressed asfollows Based on the instantaneous radio channel conditionsthe SNR is calculated for the DL wireless channels betweenthe eNB and the users A supported MCS index is chosenusing expression [16 17]
MCS =
MCS1 SNR lt 120574
1
MCS2 1205741le SNR lt 120574
2
MCS119897 120574119897minus1
le SNR lt 120574119897
(18)
where 1205741
lt 1205742
lt sdot sdot sdot lt 120574119897are the SNR thresholds
corresponding to minus10 dB bit error ratio (BER) given by theAdditive White Gaussian Noise (AWGN) curves for eachMCS (the standard AWGN curves can be found in [17]) TheLTE standard allows 119897 = 15 MCS levels (description of MCSlevels their code rate and efficiency is shown in Table 1) [17]
Table 1 Allowed MCS values in LTE standard [17]
MCS index Modulation Code rate Efficiency0 No transmission1 QPSK 78 015232 QPSK 120 023443 QPSK 193 037704 QPSK 308 060165 QPSK 449 087706 QPSK 602 117587 16 QAM 378 147668 16 QAM 490 191419 16 QAM 616 2406310 64 QAM 466 2730511 64 QAM 567 3322312 64 QAM 666 3902313 64 QAM 772 4523414 64 QAM 873 5115215 64 QAM 948 55547
Based on the above the SNR efficiency depends onthe SNR of the DL wireless channel and therefore can berepresented by a function
119892 (SNR) =
1205851 SNR lt 120574
1
1205852 1205741le SNR lt 120574
2
120585119897 120574119897minus1
le SNR lt 120574119897
(19)
where 0 lt 1205851lt 1205852lt sdot sdot sdot lt 120585
119897are the values of the SNR
efficiency corresponding to the supported MCSUsing (17) and (19) the transmission rates of the users can
be expressed as
119903119875119894(b119875 p119875) = 120596120595119887
119875119894log (1 + 119892 (SNR
119875119894) sdot SNR
119875119894)
= 120596120595119887119875119894log (1 + 119892 (119901
119875119894) sdot ℎ119875119894119901119875119894)
forall119894 isin I
(20a)
119903119878119895(b119878 p119878) = 120596120595119887
119878119895log (1 + 119892 (SNR
119878119895) sdot SNR
119878119895)
= 120596120595119887119878119895log (1 + 119892 (119901
119878119895) ℎ119878119895119901119878119895)
forall119895 isin J
(20b)
32 Solution Methodology In this subsection we describe asolution methodology for the resource allocation problemin Scenario 1 in the UL direction (with the objective givenby (11) and the constraints defined in (8b)ndash(8f)) A resourceallocation problem for the DL direction as well as problem(15a)ndash(15g) for Scenario 2 can be solved analogously
Mobile Information Systems 7
Note that in Scenario 1 a resource allocation problem inthe UL direction is equivalent to
minimize Ω + Φ (21a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (21b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(21c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(21d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(21e)
Ω ge 0
Φ ge 0
(21f)
1198911
119894(b119875 p119875) = 119903119875119894(b119875 p119875) minus (119902
119875119894+ 119886119875119894)
le 0
forall119894 isin I
(21g)
1198912
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894minus 119871119894) minus 119903119875119894(b119875 p119875)
le 0
forall119894 isin I
(21h)
1198913
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894) minus 119903119875119894(b119875 p119875) minus Ω
le 0
forall119894 isin I
(21i)
1198914
119895(b119878 p119878)
= (119902119878119895+ 119886119878119895) minus 119903119878119895(b119878 p119878) minus Φ
le 0
forall119895 isin J
(21j)
In above problem some of the optimization variables(particularly the components of b
119875and b
119878) can take only
integer values whereas the other variables (the componentsof p119875and p
119878) are real-valued ones In addition constraints
(21g)ndash(21j) are represented by the nonsmooth nonlinear
functions of (b119875 p119875) and (b
119875 p119875) Hence (21a)ndash(21j) is a
nonlinear mixed integer programming (MINLP) problemwhich is Nondeterministic Polynomial-time (NP) hard Forimmediate proof of NP-hardness note that MINLP includesmixed integer linear programming (MILP) problem which isNP-hard [23]
Before applying any MINLP method for solving (21a)ndash(21j) the nonsmooth function 119892(sdot) in (19) included in theexpressions of 119903
119875119894(b119875 p119875) and 119903
119878119895(b119875 p119875) should be replaced
by its smooth approximation To construct a smooth approx-imation of 119892(119909) note that this function is equivalent to thesum of the shifted and scaled versions of a Heaviside stepfunction119867(119909) [24] That is
119892 (119909) =
15
sum
119897=1
(120577119897minus 120577119897minus1)119867 (119909 minus 120574
119897)
119867 (119909) =
1 if 119909 ge 0
0 otherwise
(22)
where 1205770= 0
Recall that a smooth approximation for a step function119867(119909) is given by a logistic sigmoid function [25]
119902(119909) =
1
1 + 119890minus2119902119909
(23)
where 119902 gt 0 119909 is in range of real numbers from minusinfin to +infinIf we take 119867(0) = 12 then larger 119902 corresponds to a closertransition to119867(119909) that is
lim119902rarrinfin
119902(119909) = 119867 (119909) (24)
The above holds because for 119909 lt 0 we have
119890minus2119902119909
997888rarr +infin
119902(119909) asymp 119867 (119909) = 1
(25)
for 119909 gt 0
119890minus2119902119909
997888rarr 0
119902(119909) asymp 119867 (119909) = 1
(26)
for 119909 = 0
119890minus2119902119909
= 1
119902(119909) = 119867 (119909) =
1
2
(27)
Consequently an approximation for a shifted Heavisidefunction is represented by a shifted logistic function
119902(119909 minus 120574
119897) =
1
1 + 119890minus2119902(119909minus120574119897)
(28)
defined for 119902 gt 0 with real 119909 in range from minusinfin to +infin
8 Mobile Information Systems
Based on (28) we can construct a smooth approximationfor 119892(119909) as
119902(119909) =
15
sum
119897=1
(120577119897minus 120577119897minus1) 119902(119909 minus 120574
119897) =
15
sum
119897=1
120577119897minus 120577119897minus1
1 + 1198902119902(119909minus120574119897)
(29)
Then it is rather straightforward to verify that
lim119902rarrinfin
119902(119909) = 119892 (119909) (30)
and the approximations for 119903119875119894(b119875 p119875) and 119903
119878119895(b119875 p119875) will
take the form
119875119894(b119875 p119875) = 120596120595119887
119875119894log (1 + (119901
119875119894) sdot ℎ119875119894119901119875119894)
forall119894 isin I(31a)
119878119895(b119878 p119878) = 120596120595119887
119878119895log (1 + (119901
119878119895) ℎ119878119895119901119878119895)
forall119895 isin J(31b)
With the approximations given by (31a) and (31b) prob-lem (21a)ndash(21j) can be solved using a sequential optimizationapproach as
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (32a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (32b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(32c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(32d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(32e)
Ω ge 0
Φ ge 0
(32f)
119891
1
119894(b119875 p119875)
= 119875119894(b119875 p119875)
minus (119902119875119894+ 119886119875119894) le 0
forall119894 isin I
(32g)
119891
2
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894minus 119871119894)
minus 119875119894(b119875 p119875) le 0
forall119894 isin I
(32h)
119891
3
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894)
minus 119875119894(b119875 p119875) minus Ω
le 0
forall119894 isin I
(32i)
119891
4
119895(b119878 p119878)
= (119902119878119895+ 119886119878119895)
minus 119878119895(b119878 p119878) minus Φ
le 0
forall119895 isin J
(32j)
The above problem is smooth MINLP which can besolved using some fast and effective MINLP method Notethat most of the MINLP techniques involve constructionof the following relaxations to the considered problem thenonlinear programming (NLP) relaxation (original problemwithout integer restrictions) and the MILP relaxation (origi-nal problem where nonlinearities are replaced by supportinghyperplanes) In our case a smooth MILP relaxation to(32a)ndash(32j) in a given point (b0
119875 p0119875 b0119878 p0119878) is given by
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (33a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (33b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(33c)
Mobile Information Systems 9
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(33d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(33e)
Ω ge 0
Φ ge 0
(33f)
119891
1
119894(b0119875 p0119875) + nabla
119891
1
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33g)
119891
2
119894(b0119875 p0119875) + nabla
119891
2
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33h)
119891
3
119894(b0119875 p0119875) + nabla
119891
3
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33i)
119891
4
119895(b0119878 p0119878) + nabla
119891
4
119895(b0119878 p0119878)
119879
[
b119878minus b0119878
p119878minus p0119878
]
le 0
forall119895 isin J
(33j)
The NLP relaxation to (32a)ndash(32j) is
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (34a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (34b)
119887119875119894ge 0
119887119878119895ge 0
forall119894 isin I forall119895 isin J
(34c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(34d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(34e)
Ω ge 0
Φ ge 0
(34f)
119891
1
119894(b119875 p119875) le 0
forall119894 isin I(34g)
119891
2
119894(b119875 p119875) le 0
forall119894 isin I(34h)
119891
3
119894(b119875 p119875) le 0
forall119894 isin I(34i)
119891
4
119895(b119878 p119878) le 0
forall119895 isin J(34j)
Note that theMINLP problems can be solved using eitherdeterministic technique or an approximation A typical exact
10 Mobile Information Systems
method for solving MINLPs is a well-known branch-and-bound algorithmand its variousmodifications [26] examplesof heuristic approaches include local branching [27] largeneighborhood search [28] and feasibility pump [29] to namea few Since we are interested in a reasonably simple and fastalgorithm it is more convenient to use heuristics for solvingthe problem In this paper a Feasibility Pump (FP) heuristic[29 30] is applied to solve (32a)ndash(32j) FP is perhaps the mostsimple and most effective method for producing more andbetter solutions in a shorter average running time For theproblems with nonbinary integer variables the complexity ofFP is exponential in size of a problem [31]
A fundamental idea of FP algorithm is to decomposethe problem into two parts integer feasibility and constraint
feasibility The former is achieved by rounding (solvinga NLP relaxation to the original problem) and the latterby projection (solving a MILP relaxation) Consequentlytwo sequences of points are generated The first sequence(b119875 p119875 b119878 p119878)119896119870
119896=1 119870 = 1 2 contains the integral
points that may violate the nonlinear constraintsThe secondsequence (b
119875 p119875 b119878 p119878)119896119870
119896=1contains the points which are
feasible for a continuous relaxation to the original problembut might not be integral
More specifically with input (b119875 p119875 b119878 p119878)1being a
solution to the NLP relaxation given by (34a)ndash(34j) thealgorithm generates two sequences by solving the followingproblems for 119896 = 1 119870
(b119875 p119875 b119878 p119878)119896= argmin
100381710038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b
119875 p119875 b119878 p119878)119896
1003817100381710038171003817100381710038171
(35a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (35b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(35c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(35d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(35e)
Ω ge 0
Φ ge 0
(35f)
119891
1
119894(b0119875 p0119875) + nabla
119891
1
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35g)
119891
2
119894(b0119875 p0119875) + nabla
119891
2
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35h)
119891
3
119894(b0119875 p0119875) + nabla
119891
3
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35i)
Mobile Information Systems 11
119891
4
119895(b0119878 p0119878) + nabla
119891
4
119895(b0119878 p0119878)
119879
[
b119878minus b0119878
p119878minus p0119878
] le 0
forall119895 isin J
(35j)
(b119875 p119875 b119878 p119878)119896+1
= argmin 10038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b
119875 p119875 b119878 p119878)119896
100381710038171003817100381710038172
(36a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (36b)
119887119875119894ge 0
119887119878119895ge 0
forall119894 isin I forall119895 isin J
(36c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(36d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(36e)
Ω ge 0
Φ ge 0
(36f)
119891
1
119894(b119875 p119875) le 0
forall119894 isin I(36g)
119891
2
119894(b119875 p119875) le 0
forall119894 isin I(36h)
119891
3
119894(b119875 p119875) le 0
forall119894 isin I(36i)
119891
4
119895(b119878 p119878) le 0
forall119895 isin J(36j)
where sdot1and sdot
2are 1198971norm and 119897
2norm respectivelyThe
rounding step is carried out by solving (35a)ndash(35j) whereasthe projection is the solution to (36a)ndash(36j) A suggested FPalgorithm alternates between the rounding and projectionsteps until (b
119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896(which implies
feasibility) or the number of iterations 119896 has reached thepredefined limit 119870 The workflow of a corresponding FPalgorithm is illustrated in the following part
FP Algorithm for Non-Convex MINLP(0) INITIALIZATION input119870 set 119896 = 1
solve (34a)ndash(34j) to obtain (b119875 p119875 b119878 p119878)119896
(1) WHILE (119896 lt 119870) do
(2) ROUNDING solve (35a)ndash(35j) to obtain(b119875 p119875 b119878 p119878)119896
(3) IF ((b119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896) THEN goto
step (6)(4) PROJECTION solve (36a)ndash(36j) to obtain
(b119875 p119875 b119878 p119878)119896+1
(5) Set 119896 = 119896 + 1
12 Mobile Information Systems
(6) OUTPUT solution (b119875 p119875 b119878 p119878)lowast
=
(b119875 p119875 b119878 p119878)119896
Note that in order to retain the convergence of thealgorithm both problems (35a)ndash(35j) and (36a)ndash(36j) needto be solved exactly Problem (36a)ndash(36j) (and consequentlyproblem (34a)ndash(34j)) can be solved using any standard NLPmethod In this paper an interior point algorithm (describedeg in [32]) with polynomial complexity is applied to solve(36a)ndash(36j) and (34a)ndash(34j) MILP problem (35a)ndash(35j) isrelatively simple and therefore can be solved efficiently foroptimality by any technique from the family of the branch-and-bound methods (eg [26])
33 Target Buffer Size for PUs and Feasibility Issues Recallthat 119871
119894represents the target buffer size for PU
119894 which
indicates that the QoS requirements of PU119894are satisfied By
limiting the buffer size of PUs we restrict the QoS of PUs(measured in terms of their buffer size) to be higher (or atleast not smaller) than the required minimum From thispoint of view constraints (5) and (12) guarantee the QoSprotection of PUs in Scenario 1 and Scenario 2 respectivelyApparently one can always restrict the target buffer size ofPUs to be equal to zero so that after each subsequent dataarrival the buffer of each PU is fully cleared This approachrepresents a ldquogreedyrdquo policy which ensures that the PUs arealways served with the best possible QoS but does not guar-antee that some spare capacity will be left to serve the SUs
A ldquoless greedyrdquo strategy would be to establish somelower bound on QoS for the PUs which will provide anldquoopportunityrdquo for SUs to be served To establish this lowerbound recall that the growing delay and loss indicate thata buffer of a corresponding node is congested whereas inan uncongested node the packet delay and loss are alwaysminimal [33] On the other hand it has been reported in[33 34] that in an uncongested node the buffer size 119902(119905) isincreasing very slowly that is 119902(119905 + 1)119902(119905) asymp 1 whereas ina congested node the buffer size is growing very fast so that119902(119905+1)119902(119905) ≫ 1 Hence to serve the PUs withminimal delayand loss it is enough to prevent the growth of their buffersthat is for each PU set
119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)
where 120576 ge 0 is some small value such that
120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)
More sophisticated approach to find the lowerQoS boundcan be deployed if information about the past buffer size isavailable at any time slot 119905 In this case one can set the targetbuffer size based on past T observations 119902(119905) 119902(119905 minus 119879 + 1)as
119871119894= min120591isinT
119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38a)
or
119871119894=
1
119879
sum
120591isinT119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38b)
where T = 1 119879
UBADPC MBC
60
70
80
90
100
110
120
130
140
Alg
orith
m it
erat
ions
10020 8040 50 60 7030 90100Number of SUs m
120572i = 1 v = m lowast 1Mbps
Figure 1 Average number of iterations before convergence as afunction of number of SUs in simulations with 119899 = 100 PUs andaverage SNR = 0 dB
MBC
070
075
080
085
090
095
100
120572i=0
v=0
120572i=1
v=0
120572i=0
v=m
lowast1
Mbp
s
120572i=1
v=m
lowast1
Mbp
s
Fairness among SUs FSU
Fairness among PUs FPU
Fairness among all users F
Figure 2 Jainrsquos index of fairness119865SU119865PU and119865 for the PUs SUs andall users in simulations with 119899 = 100 PUs119898 = 100 SUs and averageSNR = 0 dB
In some (very rare) cases (when the service capacity of theeNB is not enough to guarantee that the buffer sizes in all PUsdo not exceed the target buffer size) constraints (5) and (12)in Scenarios 1 and 2 may be not feasible In the following weshow how to identify such situation and what should be theoptimal resource allocation strategy in this case
Note that the service capacity of LTE system greatlydepends on physical characteristics (eg SINR and MCS) of
Mobile Information Systems 13
UBADPCGBC
NBCMBCABC
780
800
820
840
860
880
900
920
940
960Th
roug
hput
for P
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r PU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for P
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
Figure 3 Mean throughput packet delay and loss for PUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
the wireless channels between the eNB and the users Henceat the moment preceding the bandwidthpower allocation itis rather difficult to estimate the service capacity of a systemNevertheless it is possible to find the average service capacityand to determine the upper and lower bounds on servicecapacity of the eNB in the UL and DL directions such that
119877min le sum119894isinI119903119875119894(119905) asymp 119877ave le 119877max (39)
where119877min119877ave and119877max are the lower bound upper boundand average service capacity of the eNB respectively
In our case the upper bound on service capacity of theeNB is given by
119877max = 120596120595119861 log (1 + 119892 (SNRmax) sdot SNRmax) (40a)
where SNRmax is the maximal possible SNR value
The lower bound on service capacity of eNB is
119877min = 120596120595119861 log (1 + 119892 (SNRmin) sdot SNRmin) (40b)
where SNRmin is the minimal possible SNR valueThe average service capacity of the eNB equals
119877ave = 120596120595119861 log (1 + 119892 (SNRave) sdot SNRave) (40c)
where SNRave is the average SNR valueIf SNR information is available then the values SNRmax
SNRmin and SNRave can be set as
SNRmax = max119894isinI
SNR119894 (41a)
14 Mobile Information Systems
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r SU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for S
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
Figure 4 Mean throughput packet delay and loss for SUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
SNRmin = min119894isinI
SNR119894 (41b)
SNRave =1
119899
sum
119894isinISNR119894 (41c)
Otherwise (ie if SNR information is not available) thevalues are set arbitrarily
Now we can identify the situation when constraints (5)and (12) cannot be satisfied For this we should perform thefollowing test For Scenario 1 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus 119871
119894) (42)
then constraint (5) is feasible Otherwise condition (5)cannot be satisfiedHence all the SUs receive zero allocations
andwe assign the bandwidthpower resources only to the PUsby solving the following optimization problem
minimize max119894isinI
lceil119902119875119894+ 119886119875119894minus 119903119875119894(b119875 p119875)rceil+
(43a)
subject to 119903119875119894(b119875 p119875) le 119902119875119894+ 119886119875119894 forall119894 isin I (43b)
sum
119894isinI119887119875119894le 119861 (43c)
119887119875119894isin Z+ forall119894 isin I (43d)
119901119875119894le 119875119875119894 forall119894 isin I (43e)
119901119875119894ge 0 forall119894 isin I (43f)
Mobile Information Systems 15
725
750
775
800
825
850
875
900
925
950Th
roug
hput
for P
Us (
kbits
s)
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
10
20
30
40
50
60
70
Dela
y fo
r PU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Loss
for P
Us (
)
0
005
01
015
02
025
03
035
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Figure 5 Mean throughput packet delay and loss for PUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
for the UL direction For the DL directions constraint (43e)should be replaced by
sum
119894isinI119901119875119894le 119875eNB (43g)
For Scenario 2 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus (1 + 120572
119894) 119871119894) (44)
then constraint (12) is feasible Otherwise inequality (12)cannot be satisfied and the bandwidthpower resources areassigned only to the PUs (according to (43a)ndash(43g)) whereasthe SUs receive zero allocations
4 Performance Evaluation
41 Simulation Model A simulation model of the networkconsisting of one eNB 119899 PUs and 119898 SUs randomly locatedin a service area with 3 km radius has been developed upona standard LTE platform using the OPNET package [35]Thebandwidth of the eNB equals 119861 = 50RBs (which is equivalentto 10MHz) The slot duration in the algorithm equals 119879
119904=
1msThemaximal number of iterations in FP algorithm is set119870 = 200Themaximal transmission power of the eNB equals119875eNB = 46 dBm and the maximal transmission power of eachPUSU equals 119875
1198751= sdot sdot sdot = 119875
119875119899= 1198751198781= sdot sdot sdot = 119875
119878119898= 23 dBm
Other simulation settings of the model are listed in Table 2(all the parameters are based on LTE specifications [36])
16 Mobile Information Systems
Table 2 Simulation parameters of the model
Parameter ValueRadio network model
Pass loss 119871 = 40log10119877 + 30log
10119891 + 49 119877 distance (km) 119891
carrier frequency (Hz)
Shadow fading Log-normal shadow fading with a standard deviation of1012 dB for outdoorindoor users
Penetration loss The average building penetration loss is 12 dB with astandard deviation of 8 dB
Multipath fading Spatial Channel Model (SCM) Suburban macroUE velocity 0 kmsTransmitterreceiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver noise figure 5 dBThermal noise density minus174 dBmHzCableconnectorcombiner losses 2 dB
Physical profileOperation mode FDDCyclic prefix type Normal (7 symbols per slot)Evolved packet core (EPC) bearer definitions 348 kbits (nonguaranteed bit rate)Subcarrier spacing 15 kHz
Admission control parametersPhysical downlink control channel (PDCCH) symbols per subframe 3UL loading factor 1DL loading factor 1Inactive bearer timeout 20 sec
Buffer status report parametersPeriodic timer 5 subframesRetransmission timer 2560 subframes
L1L2 control parametersReserved size 2 RBsCyclic shifts 6Starting RB preserver for Format 1 messages 0Allocation periodicity 5 subframes
Random access (RA) parametersNumber of preambles 64Preamble format Format 0 (1-subframe long)Number of RA resources per frame 4Preamble retransmission limit 5 subframesRA response timer 5 subframesContention resolution timer 40 subframes
HARQ parametersMaximal number of retransmissions 3 (UL and DL)HARQ retransmission timer 8 subframes (UL and DL)Maximal number of HARQ processes 8 per UE (UL and DL)
A radio model of the network corresponds to the require-ments of ITU-T Recommendation M1225
The algorithms proposed in the paper are denoted asfollows
(i) GBC (greedy buffer Control) where the target buffersize equals 0 for all the PUs
(ii) NBC (nongreedy buffer control) with the target buffersize calculated according to (37a) and (37b)
(iii) MBC (Minimal Buffer Control) with 119879 = 10 slots andthe target buffer size given by (38a)
(iv) ABC (Average Buffer Control) with 119879 = 10 slots andthe target buffer size equaling (38b)
Two previously proposed schemes used to benchmark theperformance of the algorithms proposed in this paper are
(i) UBA (Utility Based Allocation) presented in [11]where the network resources (bandwidth and trans-mission power) are allocated to the UL channels tomaximize the total transmission rate of the userssubject to the capacity and transmission power con-straints
Mobile Information Systems 17
0 10 20 30 40 50 60 70 80Average SNR (dB)
UBADPCGBC
NBCMBCABC
30
35
40
45
50
55
60
65
70
Dela
y fo
r SU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
012
015
018
021
024
027
03
033
Loss
for S
Us (
)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
250
300
350
400
450
500Th
roug
hput
for S
Us (
kbits
s)
Figure 6 Mean throughput packet delay and loss for SUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
(ii) DPC (Delay Power Control) derived in [5] whichis used to balance the transmission delay againsttransmission power in wireless channels between theeNB and the users
We also gather simulation results for a proposed resourceallocation approach in Scenario 2 with different settings ofthe parameters120572
119894and V and benchmark its performancewith
the performance of the algorithm in Scenario 1All algorithms are simulated using identical settings
The data traffic in simulations is represented by voice overInternet Protocol (VoIP) video and Hypertext TransferProtocol (HTTP) applications mixed in proportion 2 3 5using the models defined in [37]
42 Complexity and Fairness Issues Let us first evaluatethe complexity and the fairness of resource allocation indifferent algorithms Figure 1 shows the average numberof iterations before convergence for UBA DPC and theproposed algorithms in Scenario 1 (denoted as MBC) andScenario 2 gathered in simulations with 119899 = 100 PUs andaverage SNR = 0 dB Note that the target buffer size for thePUs is calculated according to (38a) with T = 10 slots (inScenarios 1 and 2) and 120572
119894= 1 V = 119898 lowast 1Mbps (for
Scenario 2) Results demonstrate that the complexity of FPmethod deployed for resource allocation in Scenarios 1 and2 is exponential in size of the problem (which correspondsto the findings reported in [31]) and is comparable to thecomplexities of other techniques (UBA and DPC)
18 Mobile Information Systems
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
080020 090070050 060 100000 030010 040120572i
10
20
30
40
50
60
70
80
90
100
110
Dela
y fo
r PU
s (m
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
040030 090000 080060010 020 050 100070120572i
005
010
015
020
025
030
035
040
045
050
Loss
for P
Us (
)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
030020 040 090010 060 070 080 100000 050120572i
Figure 7 Mean throughput packet delay and loss for the PUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
Figure 2 shows the fairness of different methods calcu-lated according to Jainrsquos equation [38] as
119865PU =
(sum119894isinI 119903119875119894)
2
119899 sdot sum119894isinI 1199032
119875119894
119865SU =
(sum119895isinJ 119903119878119895)
2
119898 sdot sum119895isinJ 1199032
119878119895
119865 =
(sum119894isinI 119903119875119894 + sum119895isinJ 119903119878119895)
2
(119899 + 119898) sdot (sum119894isinI 1199032
119875119894+ sum119895isinJ 1199032
119878119895)
(45)
where 119865PU 119865SU and 119865 stand for Jainrsquos index of fairness forthe PUs SUs and all of the users respectively 119903
119875119894 119903119878119895
arethe mean throughputs for PU
119894and SU
119895 respectively Results
have been gathered for 119899 = 100 PUs 119898 = 100 SUs average
Mobile Information Systems 19
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
410
420
430
440
450
460
470
480
490
500
510Th
roug
hput
for S
Us (
kbits
s)
010 020 080 090050 060 070030 100000 040120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
15
20
25
30
35
40
45
50
Dela
y fo
r SU
s (m
s)
070 090030 040 050 080000 020010 100060120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
007
009
011
013
015
017
019
021
023
Loss
for S
Us (
)
080070 090020 050 060030 100040010000120572i
Figure 8 Mean throughput packet delay and loss for the SUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
SNR = 0 dB and target buffer size for the PUs calculatedaccording to (38a) (Scenarios 1 and 2) with different settingsof 120572119894and V in Scenario 2
It follows from these graphs that the fairness index amongall of the users (denoted as 119865) is higher in Scenario 2 with120572119894= 1 and lower in Scenario 1 and Scenario 2 with 120572
119894= 0
Such results are rather expectable in Scenario 1 and Scenario2 with 120572
119894= 0 the SUs are served for free on a best-effort
basis whereas the PUs enjoy full QoS guarantees Hence thenetwork resources are shared nonequally between the PUs
and the SUs with most of the RBs allocated to the PUs andthe rest of the bandwidth distributed among the SUs Onthe other hand the fairness index for the PUs and SUs (ie119865PU and 119865SU) is rather high in both scenarios with differentsettings of 120572
119894and V which indicates that the users of the same
type are treated equally during resource allocation
43 Simulation Results in Scenario 1 Let us evaluate theperformance of a resource allocation algorithm in Scenario1 in terms of mean throughput packet end-to-end delay and
20 Mobile Information Systems
MBC
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
20
30
40
50
60
70
80
90
Dela
y fo
r PU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
005
010
015
020
025
030
035
040
045
Loss
for P
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 9 Mean throughput packet delay and loss for the PUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
loss for different user types Figures 3ndash6 show results obtainedin simulations with 119899 = 100 PUs and average SNR = 0 dBResults demonstrate that aUBA scheme has the largest packetdelay and loss and the lowest throughput for both the PUs andthe SUs A poor performance of this scheme is explained asfollows
(i) QoS protection of PUs is not considered in UBAHence the throughput delay and loss are the samefor PUs and SUs
(ii) Buffer sizes of individual users are not consideredin resource allocation and therefore the QoS for
Mobile Information Systems 21
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
30
50
70
90
110
130
Dela
y fo
r SU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
000
010
020
030
040
050
060
Loss
for S
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
different users varies significantly (since differentusers have different traffic demands)
(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer
size and therefore there is no need to maximize theirtransmission rate and spend the network resources
Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mobile Information Systems 5
which is apparently not fair since the PUs have larger buffersizes than the SUs and therefore they will experience longerdelays than the SUs
To avoid such situation we propose to modify problem(8a)ndash(8g) by replacing its objective (8a) with
minimize max119894isinI
lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+
+max119895isinJ
lceil119902119878119895+ 119886119878119895minus 119903119878119895rceil
+
(11)
Objective (11) guarantees that PUs are served with max-imal QoS even if the aggregated traffic demand of SUs isgreater than that of the PUs
23 Scenario 2 We now consider a different scenario inwhich the PUs will benefit (by paying less in exchange) fromsharing their bandwidth with the SUs Let us assume that inthe network without price benefits (ie in Scenario 1) theprice for accessing the licensed spectrum of the PUs equals1 In this case all the PUs get the full QoS protection (ieguaranteed target buffer size 119871
119894and the average end-to-end
latency 119863119894) Suppose that each PU can define the portion of
allocated spectrum that it is willing to share with the SUsThedelay in turn is related to lceil119902
119875119894+ 119886119875119894minus 119903119875119894rceil+
Let us denote by 120572119894 0 le 120572
119894lt 1 the price for the portion
of spectrum that PU119894is willing to share with the SUs So
120572119894represents the willingness of PU
119894to trade off its QoS for
money Subsequently the guaranteed QoS level of PU119894will
reduce and instead of the QoS protection constraint (8b) wewill have
119903119875119894ge 119902119875119894+ 119886119875119894minus (1 + 120572
119894) 119871119894 forall119894 isin I (12)
Now to compensate for the income losses of a serviceprovider the SUs will have to pay the price for the sharedspectrum Let 120573 denote the price that each SU will pay foraccessing the shared spectrum The amount that SU
119895pays in
this case is 120573119903119878119895 whereas the revenue of the service provider
is
sum
119895isinJ120573119903119878119895minussum
119894isinI120572119894lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+
(13)
Assuming that a service provider does not incur loss byallowing the secondary users to use the spectrum we have toincorporate the constraint
sum
119895isinJ120573119903119878119895minussum
119894isinI120572119894lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+
ge V (14)
where V is the profit that a service provider would like tomakeby allowing the SUs into the network
Note that in such formulation the SUs get no QoSguarantee and therefore we have to minimize the price that
the SUs pay for their usage Thus the optimization problemis
minimize 120573 (15a)
subject to 119902119875119894+ 119886119875119894minus (1 + 120572
119894) 119871119894le 119903119875119894
le 119902119875119894+ 119886119875119894
forall119894 isin I
(15b)
sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (15c)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(15d)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(15e)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(15f)
sum
119895isinJ120573119903119878119895minussum
119894isinI120572119894lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+
ge V (15g)
for the UL direction For the DL direction constraint (15e) isreplaced by constraint (8g)The value of120573 obtained by solving(15a)ndash(15g) is then broadcasted by a service provider to theSUs that will have to pay a determined price
We note in passing that there are many other ways inwhich the pricing problem could be addressed For instancethe numbers 120572
119894may be negotiated between the PUs and a
service provider One can also think of a scenario wheredifferent SUs may be able to express their willingness to payvia bidding the prices 120573
119895 The options are numerous but they
are beyond the scope of this paper
3 Implementation Issues
31 Rate as a Function of Bandwidth and Power Note thatthe transmission rates in the UL and DL channels of a LTEsystem can be found using the modified Shannon equation[21] expressed as
119903119875119894(b119875 p119875) = 120596120595
119875119894119887119875119894log (1 + 120585
119875119894SNR119875119894)
= 120596120595119875119894119887119875119894log (1 + 120585
119875119894ℎ119875119894119901119875119894)
0 lt 120595119875119894 120585119875119894le 1 forall119894 isin I
(16a)
6 Mobile Information Systems
119903119878119895(b119878 p119878) = 120596120595
119878119895119887119878119895log (1 + 120585
119878119895SNR119878119895)
= 120596120595119878119895119887119878119895log (1 + 120585
119878119895ℎ119878119895119901119878119895)
0 lt 120595119878119895 120585119878119895le 1 forall119895 isin J
(16b)
where SNR119875119894and SNR
119878119895are the SNRs in the channels of PU
119894
and SU119895 respectively 120595
119875119894and 120595
119878119895are the system bandwidth
efficiencies for PU119894and SU
119895 respectively 120585
119875119894and 120585
119878119895are
the SNR efficiencies for PU119894and SU
119895 respectively 120596 is the
bandwidth of one RB (120596 = 180 kHz) [21]In real LTE networks the system bandwidth efficiency
is strictly less than 1 due to the overheads on the link andsystem levels The bandwidth efficiency is fully determinedby the design and internal settings of the system and doesnot depend on the physical characteristics of the wirelesschannels between the user and the eNB [21 22] Hence it isreasonable to assume that
120595119875119894= 120595119878119895= 120595 forall119894 isin I forall119895 isin J (17)
The SNR efficiency is mainly limited by the maximumefficiency of the supported modulation and coding scheme(MCS) [16] In LTE MCS is chosen using AMC to maximizethe data rate by adjusting the transmission parameters to thecurrent channel conditions AMC is one of the realizations ofa dynamic link adaptation In AMC algorithm the appropri-ate MCSs for packet transmissions are assigned periodically(within short fixed time interval usually equal to one slot)by the eNB based on the instantaneous channel conditionsreported by the usersThe higherMCS values are allocated tothe high-quality channels to achieve higher transmission rateThe lower MCS values are assigned to the channels of poorquality to decrease the transmission rate and consequentlyensure the transmission quality [16 17]
The method for choosing MCS can be expressed asfollows Based on the instantaneous radio channel conditionsthe SNR is calculated for the DL wireless channels betweenthe eNB and the users A supported MCS index is chosenusing expression [16 17]
MCS =
MCS1 SNR lt 120574
1
MCS2 1205741le SNR lt 120574
2
MCS119897 120574119897minus1
le SNR lt 120574119897
(18)
where 1205741
lt 1205742
lt sdot sdot sdot lt 120574119897are the SNR thresholds
corresponding to minus10 dB bit error ratio (BER) given by theAdditive White Gaussian Noise (AWGN) curves for eachMCS (the standard AWGN curves can be found in [17]) TheLTE standard allows 119897 = 15 MCS levels (description of MCSlevels their code rate and efficiency is shown in Table 1) [17]
Table 1 Allowed MCS values in LTE standard [17]
MCS index Modulation Code rate Efficiency0 No transmission1 QPSK 78 015232 QPSK 120 023443 QPSK 193 037704 QPSK 308 060165 QPSK 449 087706 QPSK 602 117587 16 QAM 378 147668 16 QAM 490 191419 16 QAM 616 2406310 64 QAM 466 2730511 64 QAM 567 3322312 64 QAM 666 3902313 64 QAM 772 4523414 64 QAM 873 5115215 64 QAM 948 55547
Based on the above the SNR efficiency depends onthe SNR of the DL wireless channel and therefore can berepresented by a function
119892 (SNR) =
1205851 SNR lt 120574
1
1205852 1205741le SNR lt 120574
2
120585119897 120574119897minus1
le SNR lt 120574119897
(19)
where 0 lt 1205851lt 1205852lt sdot sdot sdot lt 120585
119897are the values of the SNR
efficiency corresponding to the supported MCSUsing (17) and (19) the transmission rates of the users can
be expressed as
119903119875119894(b119875 p119875) = 120596120595119887
119875119894log (1 + 119892 (SNR
119875119894) sdot SNR
119875119894)
= 120596120595119887119875119894log (1 + 119892 (119901
119875119894) sdot ℎ119875119894119901119875119894)
forall119894 isin I
(20a)
119903119878119895(b119878 p119878) = 120596120595119887
119878119895log (1 + 119892 (SNR
119878119895) sdot SNR
119878119895)
= 120596120595119887119878119895log (1 + 119892 (119901
119878119895) ℎ119878119895119901119878119895)
forall119895 isin J
(20b)
32 Solution Methodology In this subsection we describe asolution methodology for the resource allocation problemin Scenario 1 in the UL direction (with the objective givenby (11) and the constraints defined in (8b)ndash(8f)) A resourceallocation problem for the DL direction as well as problem(15a)ndash(15g) for Scenario 2 can be solved analogously
Mobile Information Systems 7
Note that in Scenario 1 a resource allocation problem inthe UL direction is equivalent to
minimize Ω + Φ (21a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (21b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(21c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(21d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(21e)
Ω ge 0
Φ ge 0
(21f)
1198911
119894(b119875 p119875) = 119903119875119894(b119875 p119875) minus (119902
119875119894+ 119886119875119894)
le 0
forall119894 isin I
(21g)
1198912
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894minus 119871119894) minus 119903119875119894(b119875 p119875)
le 0
forall119894 isin I
(21h)
1198913
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894) minus 119903119875119894(b119875 p119875) minus Ω
le 0
forall119894 isin I
(21i)
1198914
119895(b119878 p119878)
= (119902119878119895+ 119886119878119895) minus 119903119878119895(b119878 p119878) minus Φ
le 0
forall119895 isin J
(21j)
In above problem some of the optimization variables(particularly the components of b
119875and b
119878) can take only
integer values whereas the other variables (the componentsof p119875and p
119878) are real-valued ones In addition constraints
(21g)ndash(21j) are represented by the nonsmooth nonlinear
functions of (b119875 p119875) and (b
119875 p119875) Hence (21a)ndash(21j) is a
nonlinear mixed integer programming (MINLP) problemwhich is Nondeterministic Polynomial-time (NP) hard Forimmediate proof of NP-hardness note that MINLP includesmixed integer linear programming (MILP) problem which isNP-hard [23]
Before applying any MINLP method for solving (21a)ndash(21j) the nonsmooth function 119892(sdot) in (19) included in theexpressions of 119903
119875119894(b119875 p119875) and 119903
119878119895(b119875 p119875) should be replaced
by its smooth approximation To construct a smooth approx-imation of 119892(119909) note that this function is equivalent to thesum of the shifted and scaled versions of a Heaviside stepfunction119867(119909) [24] That is
119892 (119909) =
15
sum
119897=1
(120577119897minus 120577119897minus1)119867 (119909 minus 120574
119897)
119867 (119909) =
1 if 119909 ge 0
0 otherwise
(22)
where 1205770= 0
Recall that a smooth approximation for a step function119867(119909) is given by a logistic sigmoid function [25]
119902(119909) =
1
1 + 119890minus2119902119909
(23)
where 119902 gt 0 119909 is in range of real numbers from minusinfin to +infinIf we take 119867(0) = 12 then larger 119902 corresponds to a closertransition to119867(119909) that is
lim119902rarrinfin
119902(119909) = 119867 (119909) (24)
The above holds because for 119909 lt 0 we have
119890minus2119902119909
997888rarr +infin
119902(119909) asymp 119867 (119909) = 1
(25)
for 119909 gt 0
119890minus2119902119909
997888rarr 0
119902(119909) asymp 119867 (119909) = 1
(26)
for 119909 = 0
119890minus2119902119909
= 1
119902(119909) = 119867 (119909) =
1
2
(27)
Consequently an approximation for a shifted Heavisidefunction is represented by a shifted logistic function
119902(119909 minus 120574
119897) =
1
1 + 119890minus2119902(119909minus120574119897)
(28)
defined for 119902 gt 0 with real 119909 in range from minusinfin to +infin
8 Mobile Information Systems
Based on (28) we can construct a smooth approximationfor 119892(119909) as
119902(119909) =
15
sum
119897=1
(120577119897minus 120577119897minus1) 119902(119909 minus 120574
119897) =
15
sum
119897=1
120577119897minus 120577119897minus1
1 + 1198902119902(119909minus120574119897)
(29)
Then it is rather straightforward to verify that
lim119902rarrinfin
119902(119909) = 119892 (119909) (30)
and the approximations for 119903119875119894(b119875 p119875) and 119903
119878119895(b119875 p119875) will
take the form
119875119894(b119875 p119875) = 120596120595119887
119875119894log (1 + (119901
119875119894) sdot ℎ119875119894119901119875119894)
forall119894 isin I(31a)
119878119895(b119878 p119878) = 120596120595119887
119878119895log (1 + (119901
119878119895) ℎ119878119895119901119878119895)
forall119895 isin J(31b)
With the approximations given by (31a) and (31b) prob-lem (21a)ndash(21j) can be solved using a sequential optimizationapproach as
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (32a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (32b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(32c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(32d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(32e)
Ω ge 0
Φ ge 0
(32f)
119891
1
119894(b119875 p119875)
= 119875119894(b119875 p119875)
minus (119902119875119894+ 119886119875119894) le 0
forall119894 isin I
(32g)
119891
2
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894minus 119871119894)
minus 119875119894(b119875 p119875) le 0
forall119894 isin I
(32h)
119891
3
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894)
minus 119875119894(b119875 p119875) minus Ω
le 0
forall119894 isin I
(32i)
119891
4
119895(b119878 p119878)
= (119902119878119895+ 119886119878119895)
minus 119878119895(b119878 p119878) minus Φ
le 0
forall119895 isin J
(32j)
The above problem is smooth MINLP which can besolved using some fast and effective MINLP method Notethat most of the MINLP techniques involve constructionof the following relaxations to the considered problem thenonlinear programming (NLP) relaxation (original problemwithout integer restrictions) and the MILP relaxation (origi-nal problem where nonlinearities are replaced by supportinghyperplanes) In our case a smooth MILP relaxation to(32a)ndash(32j) in a given point (b0
119875 p0119875 b0119878 p0119878) is given by
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (33a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (33b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(33c)
Mobile Information Systems 9
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(33d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(33e)
Ω ge 0
Φ ge 0
(33f)
119891
1
119894(b0119875 p0119875) + nabla
119891
1
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33g)
119891
2
119894(b0119875 p0119875) + nabla
119891
2
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33h)
119891
3
119894(b0119875 p0119875) + nabla
119891
3
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33i)
119891
4
119895(b0119878 p0119878) + nabla
119891
4
119895(b0119878 p0119878)
119879
[
b119878minus b0119878
p119878minus p0119878
]
le 0
forall119895 isin J
(33j)
The NLP relaxation to (32a)ndash(32j) is
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (34a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (34b)
119887119875119894ge 0
119887119878119895ge 0
forall119894 isin I forall119895 isin J
(34c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(34d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(34e)
Ω ge 0
Φ ge 0
(34f)
119891
1
119894(b119875 p119875) le 0
forall119894 isin I(34g)
119891
2
119894(b119875 p119875) le 0
forall119894 isin I(34h)
119891
3
119894(b119875 p119875) le 0
forall119894 isin I(34i)
119891
4
119895(b119878 p119878) le 0
forall119895 isin J(34j)
Note that theMINLP problems can be solved using eitherdeterministic technique or an approximation A typical exact
10 Mobile Information Systems
method for solving MINLPs is a well-known branch-and-bound algorithmand its variousmodifications [26] examplesof heuristic approaches include local branching [27] largeneighborhood search [28] and feasibility pump [29] to namea few Since we are interested in a reasonably simple and fastalgorithm it is more convenient to use heuristics for solvingthe problem In this paper a Feasibility Pump (FP) heuristic[29 30] is applied to solve (32a)ndash(32j) FP is perhaps the mostsimple and most effective method for producing more andbetter solutions in a shorter average running time For theproblems with nonbinary integer variables the complexity ofFP is exponential in size of a problem [31]
A fundamental idea of FP algorithm is to decomposethe problem into two parts integer feasibility and constraint
feasibility The former is achieved by rounding (solvinga NLP relaxation to the original problem) and the latterby projection (solving a MILP relaxation) Consequentlytwo sequences of points are generated The first sequence(b119875 p119875 b119878 p119878)119896119870
119896=1 119870 = 1 2 contains the integral
points that may violate the nonlinear constraintsThe secondsequence (b
119875 p119875 b119878 p119878)119896119870
119896=1contains the points which are
feasible for a continuous relaxation to the original problembut might not be integral
More specifically with input (b119875 p119875 b119878 p119878)1being a
solution to the NLP relaxation given by (34a)ndash(34j) thealgorithm generates two sequences by solving the followingproblems for 119896 = 1 119870
(b119875 p119875 b119878 p119878)119896= argmin
100381710038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b
119875 p119875 b119878 p119878)119896
1003817100381710038171003817100381710038171
(35a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (35b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(35c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(35d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(35e)
Ω ge 0
Φ ge 0
(35f)
119891
1
119894(b0119875 p0119875) + nabla
119891
1
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35g)
119891
2
119894(b0119875 p0119875) + nabla
119891
2
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35h)
119891
3
119894(b0119875 p0119875) + nabla
119891
3
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35i)
Mobile Information Systems 11
119891
4
119895(b0119878 p0119878) + nabla
119891
4
119895(b0119878 p0119878)
119879
[
b119878minus b0119878
p119878minus p0119878
] le 0
forall119895 isin J
(35j)
(b119875 p119875 b119878 p119878)119896+1
= argmin 10038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b
119875 p119875 b119878 p119878)119896
100381710038171003817100381710038172
(36a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (36b)
119887119875119894ge 0
119887119878119895ge 0
forall119894 isin I forall119895 isin J
(36c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(36d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(36e)
Ω ge 0
Φ ge 0
(36f)
119891
1
119894(b119875 p119875) le 0
forall119894 isin I(36g)
119891
2
119894(b119875 p119875) le 0
forall119894 isin I(36h)
119891
3
119894(b119875 p119875) le 0
forall119894 isin I(36i)
119891
4
119895(b119878 p119878) le 0
forall119895 isin J(36j)
where sdot1and sdot
2are 1198971norm and 119897
2norm respectivelyThe
rounding step is carried out by solving (35a)ndash(35j) whereasthe projection is the solution to (36a)ndash(36j) A suggested FPalgorithm alternates between the rounding and projectionsteps until (b
119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896(which implies
feasibility) or the number of iterations 119896 has reached thepredefined limit 119870 The workflow of a corresponding FPalgorithm is illustrated in the following part
FP Algorithm for Non-Convex MINLP(0) INITIALIZATION input119870 set 119896 = 1
solve (34a)ndash(34j) to obtain (b119875 p119875 b119878 p119878)119896
(1) WHILE (119896 lt 119870) do
(2) ROUNDING solve (35a)ndash(35j) to obtain(b119875 p119875 b119878 p119878)119896
(3) IF ((b119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896) THEN goto
step (6)(4) PROJECTION solve (36a)ndash(36j) to obtain
(b119875 p119875 b119878 p119878)119896+1
(5) Set 119896 = 119896 + 1
12 Mobile Information Systems
(6) OUTPUT solution (b119875 p119875 b119878 p119878)lowast
=
(b119875 p119875 b119878 p119878)119896
Note that in order to retain the convergence of thealgorithm both problems (35a)ndash(35j) and (36a)ndash(36j) needto be solved exactly Problem (36a)ndash(36j) (and consequentlyproblem (34a)ndash(34j)) can be solved using any standard NLPmethod In this paper an interior point algorithm (describedeg in [32]) with polynomial complexity is applied to solve(36a)ndash(36j) and (34a)ndash(34j) MILP problem (35a)ndash(35j) isrelatively simple and therefore can be solved efficiently foroptimality by any technique from the family of the branch-and-bound methods (eg [26])
33 Target Buffer Size for PUs and Feasibility Issues Recallthat 119871
119894represents the target buffer size for PU
119894 which
indicates that the QoS requirements of PU119894are satisfied By
limiting the buffer size of PUs we restrict the QoS of PUs(measured in terms of their buffer size) to be higher (or atleast not smaller) than the required minimum From thispoint of view constraints (5) and (12) guarantee the QoSprotection of PUs in Scenario 1 and Scenario 2 respectivelyApparently one can always restrict the target buffer size ofPUs to be equal to zero so that after each subsequent dataarrival the buffer of each PU is fully cleared This approachrepresents a ldquogreedyrdquo policy which ensures that the PUs arealways served with the best possible QoS but does not guar-antee that some spare capacity will be left to serve the SUs
A ldquoless greedyrdquo strategy would be to establish somelower bound on QoS for the PUs which will provide anldquoopportunityrdquo for SUs to be served To establish this lowerbound recall that the growing delay and loss indicate thata buffer of a corresponding node is congested whereas inan uncongested node the packet delay and loss are alwaysminimal [33] On the other hand it has been reported in[33 34] that in an uncongested node the buffer size 119902(119905) isincreasing very slowly that is 119902(119905 + 1)119902(119905) asymp 1 whereas ina congested node the buffer size is growing very fast so that119902(119905+1)119902(119905) ≫ 1 Hence to serve the PUs withminimal delayand loss it is enough to prevent the growth of their buffersthat is for each PU set
119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)
where 120576 ge 0 is some small value such that
120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)
More sophisticated approach to find the lowerQoS boundcan be deployed if information about the past buffer size isavailable at any time slot 119905 In this case one can set the targetbuffer size based on past T observations 119902(119905) 119902(119905 minus 119879 + 1)as
119871119894= min120591isinT
119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38a)
or
119871119894=
1
119879
sum
120591isinT119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38b)
where T = 1 119879
UBADPC MBC
60
70
80
90
100
110
120
130
140
Alg
orith
m it
erat
ions
10020 8040 50 60 7030 90100Number of SUs m
120572i = 1 v = m lowast 1Mbps
Figure 1 Average number of iterations before convergence as afunction of number of SUs in simulations with 119899 = 100 PUs andaverage SNR = 0 dB
MBC
070
075
080
085
090
095
100
120572i=0
v=0
120572i=1
v=0
120572i=0
v=m
lowast1
Mbp
s
120572i=1
v=m
lowast1
Mbp
s
Fairness among SUs FSU
Fairness among PUs FPU
Fairness among all users F
Figure 2 Jainrsquos index of fairness119865SU119865PU and119865 for the PUs SUs andall users in simulations with 119899 = 100 PUs119898 = 100 SUs and averageSNR = 0 dB
In some (very rare) cases (when the service capacity of theeNB is not enough to guarantee that the buffer sizes in all PUsdo not exceed the target buffer size) constraints (5) and (12)in Scenarios 1 and 2 may be not feasible In the following weshow how to identify such situation and what should be theoptimal resource allocation strategy in this case
Note that the service capacity of LTE system greatlydepends on physical characteristics (eg SINR and MCS) of
Mobile Information Systems 13
UBADPCGBC
NBCMBCABC
780
800
820
840
860
880
900
920
940
960Th
roug
hput
for P
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r PU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for P
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
Figure 3 Mean throughput packet delay and loss for PUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
the wireless channels between the eNB and the users Henceat the moment preceding the bandwidthpower allocation itis rather difficult to estimate the service capacity of a systemNevertheless it is possible to find the average service capacityand to determine the upper and lower bounds on servicecapacity of the eNB in the UL and DL directions such that
119877min le sum119894isinI119903119875119894(119905) asymp 119877ave le 119877max (39)
where119877min119877ave and119877max are the lower bound upper boundand average service capacity of the eNB respectively
In our case the upper bound on service capacity of theeNB is given by
119877max = 120596120595119861 log (1 + 119892 (SNRmax) sdot SNRmax) (40a)
where SNRmax is the maximal possible SNR value
The lower bound on service capacity of eNB is
119877min = 120596120595119861 log (1 + 119892 (SNRmin) sdot SNRmin) (40b)
where SNRmin is the minimal possible SNR valueThe average service capacity of the eNB equals
119877ave = 120596120595119861 log (1 + 119892 (SNRave) sdot SNRave) (40c)
where SNRave is the average SNR valueIf SNR information is available then the values SNRmax
SNRmin and SNRave can be set as
SNRmax = max119894isinI
SNR119894 (41a)
14 Mobile Information Systems
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r SU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for S
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
Figure 4 Mean throughput packet delay and loss for SUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
SNRmin = min119894isinI
SNR119894 (41b)
SNRave =1
119899
sum
119894isinISNR119894 (41c)
Otherwise (ie if SNR information is not available) thevalues are set arbitrarily
Now we can identify the situation when constraints (5)and (12) cannot be satisfied For this we should perform thefollowing test For Scenario 1 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus 119871
119894) (42)
then constraint (5) is feasible Otherwise condition (5)cannot be satisfiedHence all the SUs receive zero allocations
andwe assign the bandwidthpower resources only to the PUsby solving the following optimization problem
minimize max119894isinI
lceil119902119875119894+ 119886119875119894minus 119903119875119894(b119875 p119875)rceil+
(43a)
subject to 119903119875119894(b119875 p119875) le 119902119875119894+ 119886119875119894 forall119894 isin I (43b)
sum
119894isinI119887119875119894le 119861 (43c)
119887119875119894isin Z+ forall119894 isin I (43d)
119901119875119894le 119875119875119894 forall119894 isin I (43e)
119901119875119894ge 0 forall119894 isin I (43f)
Mobile Information Systems 15
725
750
775
800
825
850
875
900
925
950Th
roug
hput
for P
Us (
kbits
s)
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
10
20
30
40
50
60
70
Dela
y fo
r PU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Loss
for P
Us (
)
0
005
01
015
02
025
03
035
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Figure 5 Mean throughput packet delay and loss for PUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
for the UL direction For the DL directions constraint (43e)should be replaced by
sum
119894isinI119901119875119894le 119875eNB (43g)
For Scenario 2 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus (1 + 120572
119894) 119871119894) (44)
then constraint (12) is feasible Otherwise inequality (12)cannot be satisfied and the bandwidthpower resources areassigned only to the PUs (according to (43a)ndash(43g)) whereasthe SUs receive zero allocations
4 Performance Evaluation
41 Simulation Model A simulation model of the networkconsisting of one eNB 119899 PUs and 119898 SUs randomly locatedin a service area with 3 km radius has been developed upona standard LTE platform using the OPNET package [35]Thebandwidth of the eNB equals 119861 = 50RBs (which is equivalentto 10MHz) The slot duration in the algorithm equals 119879
119904=
1msThemaximal number of iterations in FP algorithm is set119870 = 200Themaximal transmission power of the eNB equals119875eNB = 46 dBm and the maximal transmission power of eachPUSU equals 119875
1198751= sdot sdot sdot = 119875
119875119899= 1198751198781= sdot sdot sdot = 119875
119878119898= 23 dBm
Other simulation settings of the model are listed in Table 2(all the parameters are based on LTE specifications [36])
16 Mobile Information Systems
Table 2 Simulation parameters of the model
Parameter ValueRadio network model
Pass loss 119871 = 40log10119877 + 30log
10119891 + 49 119877 distance (km) 119891
carrier frequency (Hz)
Shadow fading Log-normal shadow fading with a standard deviation of1012 dB for outdoorindoor users
Penetration loss The average building penetration loss is 12 dB with astandard deviation of 8 dB
Multipath fading Spatial Channel Model (SCM) Suburban macroUE velocity 0 kmsTransmitterreceiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver noise figure 5 dBThermal noise density minus174 dBmHzCableconnectorcombiner losses 2 dB
Physical profileOperation mode FDDCyclic prefix type Normal (7 symbols per slot)Evolved packet core (EPC) bearer definitions 348 kbits (nonguaranteed bit rate)Subcarrier spacing 15 kHz
Admission control parametersPhysical downlink control channel (PDCCH) symbols per subframe 3UL loading factor 1DL loading factor 1Inactive bearer timeout 20 sec
Buffer status report parametersPeriodic timer 5 subframesRetransmission timer 2560 subframes
L1L2 control parametersReserved size 2 RBsCyclic shifts 6Starting RB preserver for Format 1 messages 0Allocation periodicity 5 subframes
Random access (RA) parametersNumber of preambles 64Preamble format Format 0 (1-subframe long)Number of RA resources per frame 4Preamble retransmission limit 5 subframesRA response timer 5 subframesContention resolution timer 40 subframes
HARQ parametersMaximal number of retransmissions 3 (UL and DL)HARQ retransmission timer 8 subframes (UL and DL)Maximal number of HARQ processes 8 per UE (UL and DL)
A radio model of the network corresponds to the require-ments of ITU-T Recommendation M1225
The algorithms proposed in the paper are denoted asfollows
(i) GBC (greedy buffer Control) where the target buffersize equals 0 for all the PUs
(ii) NBC (nongreedy buffer control) with the target buffersize calculated according to (37a) and (37b)
(iii) MBC (Minimal Buffer Control) with 119879 = 10 slots andthe target buffer size given by (38a)
(iv) ABC (Average Buffer Control) with 119879 = 10 slots andthe target buffer size equaling (38b)
Two previously proposed schemes used to benchmark theperformance of the algorithms proposed in this paper are
(i) UBA (Utility Based Allocation) presented in [11]where the network resources (bandwidth and trans-mission power) are allocated to the UL channels tomaximize the total transmission rate of the userssubject to the capacity and transmission power con-straints
Mobile Information Systems 17
0 10 20 30 40 50 60 70 80Average SNR (dB)
UBADPCGBC
NBCMBCABC
30
35
40
45
50
55
60
65
70
Dela
y fo
r SU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
012
015
018
021
024
027
03
033
Loss
for S
Us (
)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
250
300
350
400
450
500Th
roug
hput
for S
Us (
kbits
s)
Figure 6 Mean throughput packet delay and loss for SUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
(ii) DPC (Delay Power Control) derived in [5] whichis used to balance the transmission delay againsttransmission power in wireless channels between theeNB and the users
We also gather simulation results for a proposed resourceallocation approach in Scenario 2 with different settings ofthe parameters120572
119894and V and benchmark its performancewith
the performance of the algorithm in Scenario 1All algorithms are simulated using identical settings
The data traffic in simulations is represented by voice overInternet Protocol (VoIP) video and Hypertext TransferProtocol (HTTP) applications mixed in proportion 2 3 5using the models defined in [37]
42 Complexity and Fairness Issues Let us first evaluatethe complexity and the fairness of resource allocation indifferent algorithms Figure 1 shows the average numberof iterations before convergence for UBA DPC and theproposed algorithms in Scenario 1 (denoted as MBC) andScenario 2 gathered in simulations with 119899 = 100 PUs andaverage SNR = 0 dB Note that the target buffer size for thePUs is calculated according to (38a) with T = 10 slots (inScenarios 1 and 2) and 120572
119894= 1 V = 119898 lowast 1Mbps (for
Scenario 2) Results demonstrate that the complexity of FPmethod deployed for resource allocation in Scenarios 1 and2 is exponential in size of the problem (which correspondsto the findings reported in [31]) and is comparable to thecomplexities of other techniques (UBA and DPC)
18 Mobile Information Systems
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
080020 090070050 060 100000 030010 040120572i
10
20
30
40
50
60
70
80
90
100
110
Dela
y fo
r PU
s (m
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
040030 090000 080060010 020 050 100070120572i
005
010
015
020
025
030
035
040
045
050
Loss
for P
Us (
)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
030020 040 090010 060 070 080 100000 050120572i
Figure 7 Mean throughput packet delay and loss for the PUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
Figure 2 shows the fairness of different methods calcu-lated according to Jainrsquos equation [38] as
119865PU =
(sum119894isinI 119903119875119894)
2
119899 sdot sum119894isinI 1199032
119875119894
119865SU =
(sum119895isinJ 119903119878119895)
2
119898 sdot sum119895isinJ 1199032
119878119895
119865 =
(sum119894isinI 119903119875119894 + sum119895isinJ 119903119878119895)
2
(119899 + 119898) sdot (sum119894isinI 1199032
119875119894+ sum119895isinJ 1199032
119878119895)
(45)
where 119865PU 119865SU and 119865 stand for Jainrsquos index of fairness forthe PUs SUs and all of the users respectively 119903
119875119894 119903119878119895
arethe mean throughputs for PU
119894and SU
119895 respectively Results
have been gathered for 119899 = 100 PUs 119898 = 100 SUs average
Mobile Information Systems 19
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
410
420
430
440
450
460
470
480
490
500
510Th
roug
hput
for S
Us (
kbits
s)
010 020 080 090050 060 070030 100000 040120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
15
20
25
30
35
40
45
50
Dela
y fo
r SU
s (m
s)
070 090030 040 050 080000 020010 100060120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
007
009
011
013
015
017
019
021
023
Loss
for S
Us (
)
080070 090020 050 060030 100040010000120572i
Figure 8 Mean throughput packet delay and loss for the SUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
SNR = 0 dB and target buffer size for the PUs calculatedaccording to (38a) (Scenarios 1 and 2) with different settingsof 120572119894and V in Scenario 2
It follows from these graphs that the fairness index amongall of the users (denoted as 119865) is higher in Scenario 2 with120572119894= 1 and lower in Scenario 1 and Scenario 2 with 120572
119894= 0
Such results are rather expectable in Scenario 1 and Scenario2 with 120572
119894= 0 the SUs are served for free on a best-effort
basis whereas the PUs enjoy full QoS guarantees Hence thenetwork resources are shared nonequally between the PUs
and the SUs with most of the RBs allocated to the PUs andthe rest of the bandwidth distributed among the SUs Onthe other hand the fairness index for the PUs and SUs (ie119865PU and 119865SU) is rather high in both scenarios with differentsettings of 120572
119894and V which indicates that the users of the same
type are treated equally during resource allocation
43 Simulation Results in Scenario 1 Let us evaluate theperformance of a resource allocation algorithm in Scenario1 in terms of mean throughput packet end-to-end delay and
20 Mobile Information Systems
MBC
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
20
30
40
50
60
70
80
90
Dela
y fo
r PU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
005
010
015
020
025
030
035
040
045
Loss
for P
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 9 Mean throughput packet delay and loss for the PUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
loss for different user types Figures 3ndash6 show results obtainedin simulations with 119899 = 100 PUs and average SNR = 0 dBResults demonstrate that aUBA scheme has the largest packetdelay and loss and the lowest throughput for both the PUs andthe SUs A poor performance of this scheme is explained asfollows
(i) QoS protection of PUs is not considered in UBAHence the throughput delay and loss are the samefor PUs and SUs
(ii) Buffer sizes of individual users are not consideredin resource allocation and therefore the QoS for
Mobile Information Systems 21
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
30
50
70
90
110
130
Dela
y fo
r SU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
000
010
020
030
040
050
060
Loss
for S
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
different users varies significantly (since differentusers have different traffic demands)
(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer
size and therefore there is no need to maximize theirtransmission rate and spend the network resources
Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
6 Mobile Information Systems
119903119878119895(b119878 p119878) = 120596120595
119878119895119887119878119895log (1 + 120585
119878119895SNR119878119895)
= 120596120595119878119895119887119878119895log (1 + 120585
119878119895ℎ119878119895119901119878119895)
0 lt 120595119878119895 120585119878119895le 1 forall119895 isin J
(16b)
where SNR119875119894and SNR
119878119895are the SNRs in the channels of PU
119894
and SU119895 respectively 120595
119875119894and 120595
119878119895are the system bandwidth
efficiencies for PU119894and SU
119895 respectively 120585
119875119894and 120585
119878119895are
the SNR efficiencies for PU119894and SU
119895 respectively 120596 is the
bandwidth of one RB (120596 = 180 kHz) [21]In real LTE networks the system bandwidth efficiency
is strictly less than 1 due to the overheads on the link andsystem levels The bandwidth efficiency is fully determinedby the design and internal settings of the system and doesnot depend on the physical characteristics of the wirelesschannels between the user and the eNB [21 22] Hence it isreasonable to assume that
120595119875119894= 120595119878119895= 120595 forall119894 isin I forall119895 isin J (17)
The SNR efficiency is mainly limited by the maximumefficiency of the supported modulation and coding scheme(MCS) [16] In LTE MCS is chosen using AMC to maximizethe data rate by adjusting the transmission parameters to thecurrent channel conditions AMC is one of the realizations ofa dynamic link adaptation In AMC algorithm the appropri-ate MCSs for packet transmissions are assigned periodically(within short fixed time interval usually equal to one slot)by the eNB based on the instantaneous channel conditionsreported by the usersThe higherMCS values are allocated tothe high-quality channels to achieve higher transmission rateThe lower MCS values are assigned to the channels of poorquality to decrease the transmission rate and consequentlyensure the transmission quality [16 17]
The method for choosing MCS can be expressed asfollows Based on the instantaneous radio channel conditionsthe SNR is calculated for the DL wireless channels betweenthe eNB and the users A supported MCS index is chosenusing expression [16 17]
MCS =
MCS1 SNR lt 120574
1
MCS2 1205741le SNR lt 120574
2
MCS119897 120574119897minus1
le SNR lt 120574119897
(18)
where 1205741
lt 1205742
lt sdot sdot sdot lt 120574119897are the SNR thresholds
corresponding to minus10 dB bit error ratio (BER) given by theAdditive White Gaussian Noise (AWGN) curves for eachMCS (the standard AWGN curves can be found in [17]) TheLTE standard allows 119897 = 15 MCS levels (description of MCSlevels their code rate and efficiency is shown in Table 1) [17]
Table 1 Allowed MCS values in LTE standard [17]
MCS index Modulation Code rate Efficiency0 No transmission1 QPSK 78 015232 QPSK 120 023443 QPSK 193 037704 QPSK 308 060165 QPSK 449 087706 QPSK 602 117587 16 QAM 378 147668 16 QAM 490 191419 16 QAM 616 2406310 64 QAM 466 2730511 64 QAM 567 3322312 64 QAM 666 3902313 64 QAM 772 4523414 64 QAM 873 5115215 64 QAM 948 55547
Based on the above the SNR efficiency depends onthe SNR of the DL wireless channel and therefore can berepresented by a function
119892 (SNR) =
1205851 SNR lt 120574
1
1205852 1205741le SNR lt 120574
2
120585119897 120574119897minus1
le SNR lt 120574119897
(19)
where 0 lt 1205851lt 1205852lt sdot sdot sdot lt 120585
119897are the values of the SNR
efficiency corresponding to the supported MCSUsing (17) and (19) the transmission rates of the users can
be expressed as
119903119875119894(b119875 p119875) = 120596120595119887
119875119894log (1 + 119892 (SNR
119875119894) sdot SNR
119875119894)
= 120596120595119887119875119894log (1 + 119892 (119901
119875119894) sdot ℎ119875119894119901119875119894)
forall119894 isin I
(20a)
119903119878119895(b119878 p119878) = 120596120595119887
119878119895log (1 + 119892 (SNR
119878119895) sdot SNR
119878119895)
= 120596120595119887119878119895log (1 + 119892 (119901
119878119895) ℎ119878119895119901119878119895)
forall119895 isin J
(20b)
32 Solution Methodology In this subsection we describe asolution methodology for the resource allocation problemin Scenario 1 in the UL direction (with the objective givenby (11) and the constraints defined in (8b)ndash(8f)) A resourceallocation problem for the DL direction as well as problem(15a)ndash(15g) for Scenario 2 can be solved analogously
Mobile Information Systems 7
Note that in Scenario 1 a resource allocation problem inthe UL direction is equivalent to
minimize Ω + Φ (21a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (21b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(21c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(21d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(21e)
Ω ge 0
Φ ge 0
(21f)
1198911
119894(b119875 p119875) = 119903119875119894(b119875 p119875) minus (119902
119875119894+ 119886119875119894)
le 0
forall119894 isin I
(21g)
1198912
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894minus 119871119894) minus 119903119875119894(b119875 p119875)
le 0
forall119894 isin I
(21h)
1198913
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894) minus 119903119875119894(b119875 p119875) minus Ω
le 0
forall119894 isin I
(21i)
1198914
119895(b119878 p119878)
= (119902119878119895+ 119886119878119895) minus 119903119878119895(b119878 p119878) minus Φ
le 0
forall119895 isin J
(21j)
In above problem some of the optimization variables(particularly the components of b
119875and b
119878) can take only
integer values whereas the other variables (the componentsof p119875and p
119878) are real-valued ones In addition constraints
(21g)ndash(21j) are represented by the nonsmooth nonlinear
functions of (b119875 p119875) and (b
119875 p119875) Hence (21a)ndash(21j) is a
nonlinear mixed integer programming (MINLP) problemwhich is Nondeterministic Polynomial-time (NP) hard Forimmediate proof of NP-hardness note that MINLP includesmixed integer linear programming (MILP) problem which isNP-hard [23]
Before applying any MINLP method for solving (21a)ndash(21j) the nonsmooth function 119892(sdot) in (19) included in theexpressions of 119903
119875119894(b119875 p119875) and 119903
119878119895(b119875 p119875) should be replaced
by its smooth approximation To construct a smooth approx-imation of 119892(119909) note that this function is equivalent to thesum of the shifted and scaled versions of a Heaviside stepfunction119867(119909) [24] That is
119892 (119909) =
15
sum
119897=1
(120577119897minus 120577119897minus1)119867 (119909 minus 120574
119897)
119867 (119909) =
1 if 119909 ge 0
0 otherwise
(22)
where 1205770= 0
Recall that a smooth approximation for a step function119867(119909) is given by a logistic sigmoid function [25]
119902(119909) =
1
1 + 119890minus2119902119909
(23)
where 119902 gt 0 119909 is in range of real numbers from minusinfin to +infinIf we take 119867(0) = 12 then larger 119902 corresponds to a closertransition to119867(119909) that is
lim119902rarrinfin
119902(119909) = 119867 (119909) (24)
The above holds because for 119909 lt 0 we have
119890minus2119902119909
997888rarr +infin
119902(119909) asymp 119867 (119909) = 1
(25)
for 119909 gt 0
119890minus2119902119909
997888rarr 0
119902(119909) asymp 119867 (119909) = 1
(26)
for 119909 = 0
119890minus2119902119909
= 1
119902(119909) = 119867 (119909) =
1
2
(27)
Consequently an approximation for a shifted Heavisidefunction is represented by a shifted logistic function
119902(119909 minus 120574
119897) =
1
1 + 119890minus2119902(119909minus120574119897)
(28)
defined for 119902 gt 0 with real 119909 in range from minusinfin to +infin
8 Mobile Information Systems
Based on (28) we can construct a smooth approximationfor 119892(119909) as
119902(119909) =
15
sum
119897=1
(120577119897minus 120577119897minus1) 119902(119909 minus 120574
119897) =
15
sum
119897=1
120577119897minus 120577119897minus1
1 + 1198902119902(119909minus120574119897)
(29)
Then it is rather straightforward to verify that
lim119902rarrinfin
119902(119909) = 119892 (119909) (30)
and the approximations for 119903119875119894(b119875 p119875) and 119903
119878119895(b119875 p119875) will
take the form
119875119894(b119875 p119875) = 120596120595119887
119875119894log (1 + (119901
119875119894) sdot ℎ119875119894119901119875119894)
forall119894 isin I(31a)
119878119895(b119878 p119878) = 120596120595119887
119878119895log (1 + (119901
119878119895) ℎ119878119895119901119878119895)
forall119895 isin J(31b)
With the approximations given by (31a) and (31b) prob-lem (21a)ndash(21j) can be solved using a sequential optimizationapproach as
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (32a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (32b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(32c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(32d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(32e)
Ω ge 0
Φ ge 0
(32f)
119891
1
119894(b119875 p119875)
= 119875119894(b119875 p119875)
minus (119902119875119894+ 119886119875119894) le 0
forall119894 isin I
(32g)
119891
2
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894minus 119871119894)
minus 119875119894(b119875 p119875) le 0
forall119894 isin I
(32h)
119891
3
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894)
minus 119875119894(b119875 p119875) minus Ω
le 0
forall119894 isin I
(32i)
119891
4
119895(b119878 p119878)
= (119902119878119895+ 119886119878119895)
minus 119878119895(b119878 p119878) minus Φ
le 0
forall119895 isin J
(32j)
The above problem is smooth MINLP which can besolved using some fast and effective MINLP method Notethat most of the MINLP techniques involve constructionof the following relaxations to the considered problem thenonlinear programming (NLP) relaxation (original problemwithout integer restrictions) and the MILP relaxation (origi-nal problem where nonlinearities are replaced by supportinghyperplanes) In our case a smooth MILP relaxation to(32a)ndash(32j) in a given point (b0
119875 p0119875 b0119878 p0119878) is given by
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (33a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (33b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(33c)
Mobile Information Systems 9
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(33d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(33e)
Ω ge 0
Φ ge 0
(33f)
119891
1
119894(b0119875 p0119875) + nabla
119891
1
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33g)
119891
2
119894(b0119875 p0119875) + nabla
119891
2
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33h)
119891
3
119894(b0119875 p0119875) + nabla
119891
3
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33i)
119891
4
119895(b0119878 p0119878) + nabla
119891
4
119895(b0119878 p0119878)
119879
[
b119878minus b0119878
p119878minus p0119878
]
le 0
forall119895 isin J
(33j)
The NLP relaxation to (32a)ndash(32j) is
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (34a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (34b)
119887119875119894ge 0
119887119878119895ge 0
forall119894 isin I forall119895 isin J
(34c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(34d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(34e)
Ω ge 0
Φ ge 0
(34f)
119891
1
119894(b119875 p119875) le 0
forall119894 isin I(34g)
119891
2
119894(b119875 p119875) le 0
forall119894 isin I(34h)
119891
3
119894(b119875 p119875) le 0
forall119894 isin I(34i)
119891
4
119895(b119878 p119878) le 0
forall119895 isin J(34j)
Note that theMINLP problems can be solved using eitherdeterministic technique or an approximation A typical exact
10 Mobile Information Systems
method for solving MINLPs is a well-known branch-and-bound algorithmand its variousmodifications [26] examplesof heuristic approaches include local branching [27] largeneighborhood search [28] and feasibility pump [29] to namea few Since we are interested in a reasonably simple and fastalgorithm it is more convenient to use heuristics for solvingthe problem In this paper a Feasibility Pump (FP) heuristic[29 30] is applied to solve (32a)ndash(32j) FP is perhaps the mostsimple and most effective method for producing more andbetter solutions in a shorter average running time For theproblems with nonbinary integer variables the complexity ofFP is exponential in size of a problem [31]
A fundamental idea of FP algorithm is to decomposethe problem into two parts integer feasibility and constraint
feasibility The former is achieved by rounding (solvinga NLP relaxation to the original problem) and the latterby projection (solving a MILP relaxation) Consequentlytwo sequences of points are generated The first sequence(b119875 p119875 b119878 p119878)119896119870
119896=1 119870 = 1 2 contains the integral
points that may violate the nonlinear constraintsThe secondsequence (b
119875 p119875 b119878 p119878)119896119870
119896=1contains the points which are
feasible for a continuous relaxation to the original problembut might not be integral
More specifically with input (b119875 p119875 b119878 p119878)1being a
solution to the NLP relaxation given by (34a)ndash(34j) thealgorithm generates two sequences by solving the followingproblems for 119896 = 1 119870
(b119875 p119875 b119878 p119878)119896= argmin
100381710038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b
119875 p119875 b119878 p119878)119896
1003817100381710038171003817100381710038171
(35a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (35b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(35c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(35d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(35e)
Ω ge 0
Φ ge 0
(35f)
119891
1
119894(b0119875 p0119875) + nabla
119891
1
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35g)
119891
2
119894(b0119875 p0119875) + nabla
119891
2
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35h)
119891
3
119894(b0119875 p0119875) + nabla
119891
3
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35i)
Mobile Information Systems 11
119891
4
119895(b0119878 p0119878) + nabla
119891
4
119895(b0119878 p0119878)
119879
[
b119878minus b0119878
p119878minus p0119878
] le 0
forall119895 isin J
(35j)
(b119875 p119875 b119878 p119878)119896+1
= argmin 10038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b
119875 p119875 b119878 p119878)119896
100381710038171003817100381710038172
(36a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (36b)
119887119875119894ge 0
119887119878119895ge 0
forall119894 isin I forall119895 isin J
(36c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(36d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(36e)
Ω ge 0
Φ ge 0
(36f)
119891
1
119894(b119875 p119875) le 0
forall119894 isin I(36g)
119891
2
119894(b119875 p119875) le 0
forall119894 isin I(36h)
119891
3
119894(b119875 p119875) le 0
forall119894 isin I(36i)
119891
4
119895(b119878 p119878) le 0
forall119895 isin J(36j)
where sdot1and sdot
2are 1198971norm and 119897
2norm respectivelyThe
rounding step is carried out by solving (35a)ndash(35j) whereasthe projection is the solution to (36a)ndash(36j) A suggested FPalgorithm alternates between the rounding and projectionsteps until (b
119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896(which implies
feasibility) or the number of iterations 119896 has reached thepredefined limit 119870 The workflow of a corresponding FPalgorithm is illustrated in the following part
FP Algorithm for Non-Convex MINLP(0) INITIALIZATION input119870 set 119896 = 1
solve (34a)ndash(34j) to obtain (b119875 p119875 b119878 p119878)119896
(1) WHILE (119896 lt 119870) do
(2) ROUNDING solve (35a)ndash(35j) to obtain(b119875 p119875 b119878 p119878)119896
(3) IF ((b119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896) THEN goto
step (6)(4) PROJECTION solve (36a)ndash(36j) to obtain
(b119875 p119875 b119878 p119878)119896+1
(5) Set 119896 = 119896 + 1
12 Mobile Information Systems
(6) OUTPUT solution (b119875 p119875 b119878 p119878)lowast
=
(b119875 p119875 b119878 p119878)119896
Note that in order to retain the convergence of thealgorithm both problems (35a)ndash(35j) and (36a)ndash(36j) needto be solved exactly Problem (36a)ndash(36j) (and consequentlyproblem (34a)ndash(34j)) can be solved using any standard NLPmethod In this paper an interior point algorithm (describedeg in [32]) with polynomial complexity is applied to solve(36a)ndash(36j) and (34a)ndash(34j) MILP problem (35a)ndash(35j) isrelatively simple and therefore can be solved efficiently foroptimality by any technique from the family of the branch-and-bound methods (eg [26])
33 Target Buffer Size for PUs and Feasibility Issues Recallthat 119871
119894represents the target buffer size for PU
119894 which
indicates that the QoS requirements of PU119894are satisfied By
limiting the buffer size of PUs we restrict the QoS of PUs(measured in terms of their buffer size) to be higher (or atleast not smaller) than the required minimum From thispoint of view constraints (5) and (12) guarantee the QoSprotection of PUs in Scenario 1 and Scenario 2 respectivelyApparently one can always restrict the target buffer size ofPUs to be equal to zero so that after each subsequent dataarrival the buffer of each PU is fully cleared This approachrepresents a ldquogreedyrdquo policy which ensures that the PUs arealways served with the best possible QoS but does not guar-antee that some spare capacity will be left to serve the SUs
A ldquoless greedyrdquo strategy would be to establish somelower bound on QoS for the PUs which will provide anldquoopportunityrdquo for SUs to be served To establish this lowerbound recall that the growing delay and loss indicate thata buffer of a corresponding node is congested whereas inan uncongested node the packet delay and loss are alwaysminimal [33] On the other hand it has been reported in[33 34] that in an uncongested node the buffer size 119902(119905) isincreasing very slowly that is 119902(119905 + 1)119902(119905) asymp 1 whereas ina congested node the buffer size is growing very fast so that119902(119905+1)119902(119905) ≫ 1 Hence to serve the PUs withminimal delayand loss it is enough to prevent the growth of their buffersthat is for each PU set
119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)
where 120576 ge 0 is some small value such that
120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)
More sophisticated approach to find the lowerQoS boundcan be deployed if information about the past buffer size isavailable at any time slot 119905 In this case one can set the targetbuffer size based on past T observations 119902(119905) 119902(119905 minus 119879 + 1)as
119871119894= min120591isinT
119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38a)
or
119871119894=
1
119879
sum
120591isinT119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38b)
where T = 1 119879
UBADPC MBC
60
70
80
90
100
110
120
130
140
Alg
orith
m it
erat
ions
10020 8040 50 60 7030 90100Number of SUs m
120572i = 1 v = m lowast 1Mbps
Figure 1 Average number of iterations before convergence as afunction of number of SUs in simulations with 119899 = 100 PUs andaverage SNR = 0 dB
MBC
070
075
080
085
090
095
100
120572i=0
v=0
120572i=1
v=0
120572i=0
v=m
lowast1
Mbp
s
120572i=1
v=m
lowast1
Mbp
s
Fairness among SUs FSU
Fairness among PUs FPU
Fairness among all users F
Figure 2 Jainrsquos index of fairness119865SU119865PU and119865 for the PUs SUs andall users in simulations with 119899 = 100 PUs119898 = 100 SUs and averageSNR = 0 dB
In some (very rare) cases (when the service capacity of theeNB is not enough to guarantee that the buffer sizes in all PUsdo not exceed the target buffer size) constraints (5) and (12)in Scenarios 1 and 2 may be not feasible In the following weshow how to identify such situation and what should be theoptimal resource allocation strategy in this case
Note that the service capacity of LTE system greatlydepends on physical characteristics (eg SINR and MCS) of
Mobile Information Systems 13
UBADPCGBC
NBCMBCABC
780
800
820
840
860
880
900
920
940
960Th
roug
hput
for P
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r PU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for P
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
Figure 3 Mean throughput packet delay and loss for PUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
the wireless channels between the eNB and the users Henceat the moment preceding the bandwidthpower allocation itis rather difficult to estimate the service capacity of a systemNevertheless it is possible to find the average service capacityand to determine the upper and lower bounds on servicecapacity of the eNB in the UL and DL directions such that
119877min le sum119894isinI119903119875119894(119905) asymp 119877ave le 119877max (39)
where119877min119877ave and119877max are the lower bound upper boundand average service capacity of the eNB respectively
In our case the upper bound on service capacity of theeNB is given by
119877max = 120596120595119861 log (1 + 119892 (SNRmax) sdot SNRmax) (40a)
where SNRmax is the maximal possible SNR value
The lower bound on service capacity of eNB is
119877min = 120596120595119861 log (1 + 119892 (SNRmin) sdot SNRmin) (40b)
where SNRmin is the minimal possible SNR valueThe average service capacity of the eNB equals
119877ave = 120596120595119861 log (1 + 119892 (SNRave) sdot SNRave) (40c)
where SNRave is the average SNR valueIf SNR information is available then the values SNRmax
SNRmin and SNRave can be set as
SNRmax = max119894isinI
SNR119894 (41a)
14 Mobile Information Systems
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r SU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for S
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
Figure 4 Mean throughput packet delay and loss for SUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
SNRmin = min119894isinI
SNR119894 (41b)
SNRave =1
119899
sum
119894isinISNR119894 (41c)
Otherwise (ie if SNR information is not available) thevalues are set arbitrarily
Now we can identify the situation when constraints (5)and (12) cannot be satisfied For this we should perform thefollowing test For Scenario 1 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus 119871
119894) (42)
then constraint (5) is feasible Otherwise condition (5)cannot be satisfiedHence all the SUs receive zero allocations
andwe assign the bandwidthpower resources only to the PUsby solving the following optimization problem
minimize max119894isinI
lceil119902119875119894+ 119886119875119894minus 119903119875119894(b119875 p119875)rceil+
(43a)
subject to 119903119875119894(b119875 p119875) le 119902119875119894+ 119886119875119894 forall119894 isin I (43b)
sum
119894isinI119887119875119894le 119861 (43c)
119887119875119894isin Z+ forall119894 isin I (43d)
119901119875119894le 119875119875119894 forall119894 isin I (43e)
119901119875119894ge 0 forall119894 isin I (43f)
Mobile Information Systems 15
725
750
775
800
825
850
875
900
925
950Th
roug
hput
for P
Us (
kbits
s)
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
10
20
30
40
50
60
70
Dela
y fo
r PU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Loss
for P
Us (
)
0
005
01
015
02
025
03
035
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Figure 5 Mean throughput packet delay and loss for PUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
for the UL direction For the DL directions constraint (43e)should be replaced by
sum
119894isinI119901119875119894le 119875eNB (43g)
For Scenario 2 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus (1 + 120572
119894) 119871119894) (44)
then constraint (12) is feasible Otherwise inequality (12)cannot be satisfied and the bandwidthpower resources areassigned only to the PUs (according to (43a)ndash(43g)) whereasthe SUs receive zero allocations
4 Performance Evaluation
41 Simulation Model A simulation model of the networkconsisting of one eNB 119899 PUs and 119898 SUs randomly locatedin a service area with 3 km radius has been developed upona standard LTE platform using the OPNET package [35]Thebandwidth of the eNB equals 119861 = 50RBs (which is equivalentto 10MHz) The slot duration in the algorithm equals 119879
119904=
1msThemaximal number of iterations in FP algorithm is set119870 = 200Themaximal transmission power of the eNB equals119875eNB = 46 dBm and the maximal transmission power of eachPUSU equals 119875
1198751= sdot sdot sdot = 119875
119875119899= 1198751198781= sdot sdot sdot = 119875
119878119898= 23 dBm
Other simulation settings of the model are listed in Table 2(all the parameters are based on LTE specifications [36])
16 Mobile Information Systems
Table 2 Simulation parameters of the model
Parameter ValueRadio network model
Pass loss 119871 = 40log10119877 + 30log
10119891 + 49 119877 distance (km) 119891
carrier frequency (Hz)
Shadow fading Log-normal shadow fading with a standard deviation of1012 dB for outdoorindoor users
Penetration loss The average building penetration loss is 12 dB with astandard deviation of 8 dB
Multipath fading Spatial Channel Model (SCM) Suburban macroUE velocity 0 kmsTransmitterreceiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver noise figure 5 dBThermal noise density minus174 dBmHzCableconnectorcombiner losses 2 dB
Physical profileOperation mode FDDCyclic prefix type Normal (7 symbols per slot)Evolved packet core (EPC) bearer definitions 348 kbits (nonguaranteed bit rate)Subcarrier spacing 15 kHz
Admission control parametersPhysical downlink control channel (PDCCH) symbols per subframe 3UL loading factor 1DL loading factor 1Inactive bearer timeout 20 sec
Buffer status report parametersPeriodic timer 5 subframesRetransmission timer 2560 subframes
L1L2 control parametersReserved size 2 RBsCyclic shifts 6Starting RB preserver for Format 1 messages 0Allocation periodicity 5 subframes
Random access (RA) parametersNumber of preambles 64Preamble format Format 0 (1-subframe long)Number of RA resources per frame 4Preamble retransmission limit 5 subframesRA response timer 5 subframesContention resolution timer 40 subframes
HARQ parametersMaximal number of retransmissions 3 (UL and DL)HARQ retransmission timer 8 subframes (UL and DL)Maximal number of HARQ processes 8 per UE (UL and DL)
A radio model of the network corresponds to the require-ments of ITU-T Recommendation M1225
The algorithms proposed in the paper are denoted asfollows
(i) GBC (greedy buffer Control) where the target buffersize equals 0 for all the PUs
(ii) NBC (nongreedy buffer control) with the target buffersize calculated according to (37a) and (37b)
(iii) MBC (Minimal Buffer Control) with 119879 = 10 slots andthe target buffer size given by (38a)
(iv) ABC (Average Buffer Control) with 119879 = 10 slots andthe target buffer size equaling (38b)
Two previously proposed schemes used to benchmark theperformance of the algorithms proposed in this paper are
(i) UBA (Utility Based Allocation) presented in [11]where the network resources (bandwidth and trans-mission power) are allocated to the UL channels tomaximize the total transmission rate of the userssubject to the capacity and transmission power con-straints
Mobile Information Systems 17
0 10 20 30 40 50 60 70 80Average SNR (dB)
UBADPCGBC
NBCMBCABC
30
35
40
45
50
55
60
65
70
Dela
y fo
r SU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
012
015
018
021
024
027
03
033
Loss
for S
Us (
)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
250
300
350
400
450
500Th
roug
hput
for S
Us (
kbits
s)
Figure 6 Mean throughput packet delay and loss for SUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
(ii) DPC (Delay Power Control) derived in [5] whichis used to balance the transmission delay againsttransmission power in wireless channels between theeNB and the users
We also gather simulation results for a proposed resourceallocation approach in Scenario 2 with different settings ofthe parameters120572
119894and V and benchmark its performancewith
the performance of the algorithm in Scenario 1All algorithms are simulated using identical settings
The data traffic in simulations is represented by voice overInternet Protocol (VoIP) video and Hypertext TransferProtocol (HTTP) applications mixed in proportion 2 3 5using the models defined in [37]
42 Complexity and Fairness Issues Let us first evaluatethe complexity and the fairness of resource allocation indifferent algorithms Figure 1 shows the average numberof iterations before convergence for UBA DPC and theproposed algorithms in Scenario 1 (denoted as MBC) andScenario 2 gathered in simulations with 119899 = 100 PUs andaverage SNR = 0 dB Note that the target buffer size for thePUs is calculated according to (38a) with T = 10 slots (inScenarios 1 and 2) and 120572
119894= 1 V = 119898 lowast 1Mbps (for
Scenario 2) Results demonstrate that the complexity of FPmethod deployed for resource allocation in Scenarios 1 and2 is exponential in size of the problem (which correspondsto the findings reported in [31]) and is comparable to thecomplexities of other techniques (UBA and DPC)
18 Mobile Information Systems
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
080020 090070050 060 100000 030010 040120572i
10
20
30
40
50
60
70
80
90
100
110
Dela
y fo
r PU
s (m
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
040030 090000 080060010 020 050 100070120572i
005
010
015
020
025
030
035
040
045
050
Loss
for P
Us (
)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
030020 040 090010 060 070 080 100000 050120572i
Figure 7 Mean throughput packet delay and loss for the PUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
Figure 2 shows the fairness of different methods calcu-lated according to Jainrsquos equation [38] as
119865PU =
(sum119894isinI 119903119875119894)
2
119899 sdot sum119894isinI 1199032
119875119894
119865SU =
(sum119895isinJ 119903119878119895)
2
119898 sdot sum119895isinJ 1199032
119878119895
119865 =
(sum119894isinI 119903119875119894 + sum119895isinJ 119903119878119895)
2
(119899 + 119898) sdot (sum119894isinI 1199032
119875119894+ sum119895isinJ 1199032
119878119895)
(45)
where 119865PU 119865SU and 119865 stand for Jainrsquos index of fairness forthe PUs SUs and all of the users respectively 119903
119875119894 119903119878119895
arethe mean throughputs for PU
119894and SU
119895 respectively Results
have been gathered for 119899 = 100 PUs 119898 = 100 SUs average
Mobile Information Systems 19
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
410
420
430
440
450
460
470
480
490
500
510Th
roug
hput
for S
Us (
kbits
s)
010 020 080 090050 060 070030 100000 040120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
15
20
25
30
35
40
45
50
Dela
y fo
r SU
s (m
s)
070 090030 040 050 080000 020010 100060120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
007
009
011
013
015
017
019
021
023
Loss
for S
Us (
)
080070 090020 050 060030 100040010000120572i
Figure 8 Mean throughput packet delay and loss for the SUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
SNR = 0 dB and target buffer size for the PUs calculatedaccording to (38a) (Scenarios 1 and 2) with different settingsof 120572119894and V in Scenario 2
It follows from these graphs that the fairness index amongall of the users (denoted as 119865) is higher in Scenario 2 with120572119894= 1 and lower in Scenario 1 and Scenario 2 with 120572
119894= 0
Such results are rather expectable in Scenario 1 and Scenario2 with 120572
119894= 0 the SUs are served for free on a best-effort
basis whereas the PUs enjoy full QoS guarantees Hence thenetwork resources are shared nonequally between the PUs
and the SUs with most of the RBs allocated to the PUs andthe rest of the bandwidth distributed among the SUs Onthe other hand the fairness index for the PUs and SUs (ie119865PU and 119865SU) is rather high in both scenarios with differentsettings of 120572
119894and V which indicates that the users of the same
type are treated equally during resource allocation
43 Simulation Results in Scenario 1 Let us evaluate theperformance of a resource allocation algorithm in Scenario1 in terms of mean throughput packet end-to-end delay and
20 Mobile Information Systems
MBC
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
20
30
40
50
60
70
80
90
Dela
y fo
r PU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
005
010
015
020
025
030
035
040
045
Loss
for P
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 9 Mean throughput packet delay and loss for the PUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
loss for different user types Figures 3ndash6 show results obtainedin simulations with 119899 = 100 PUs and average SNR = 0 dBResults demonstrate that aUBA scheme has the largest packetdelay and loss and the lowest throughput for both the PUs andthe SUs A poor performance of this scheme is explained asfollows
(i) QoS protection of PUs is not considered in UBAHence the throughput delay and loss are the samefor PUs and SUs
(ii) Buffer sizes of individual users are not consideredin resource allocation and therefore the QoS for
Mobile Information Systems 21
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
30
50
70
90
110
130
Dela
y fo
r SU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
000
010
020
030
040
050
060
Loss
for S
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
different users varies significantly (since differentusers have different traffic demands)
(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer
size and therefore there is no need to maximize theirtransmission rate and spend the network resources
Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mobile Information Systems 7
Note that in Scenario 1 a resource allocation problem inthe UL direction is equivalent to
minimize Ω + Φ (21a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (21b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(21c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(21d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(21e)
Ω ge 0
Φ ge 0
(21f)
1198911
119894(b119875 p119875) = 119903119875119894(b119875 p119875) minus (119902
119875119894+ 119886119875119894)
le 0
forall119894 isin I
(21g)
1198912
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894minus 119871119894) minus 119903119875119894(b119875 p119875)
le 0
forall119894 isin I
(21h)
1198913
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894) minus 119903119875119894(b119875 p119875) minus Ω
le 0
forall119894 isin I
(21i)
1198914
119895(b119878 p119878)
= (119902119878119895+ 119886119878119895) minus 119903119878119895(b119878 p119878) minus Φ
le 0
forall119895 isin J
(21j)
In above problem some of the optimization variables(particularly the components of b
119875and b
119878) can take only
integer values whereas the other variables (the componentsof p119875and p
119878) are real-valued ones In addition constraints
(21g)ndash(21j) are represented by the nonsmooth nonlinear
functions of (b119875 p119875) and (b
119875 p119875) Hence (21a)ndash(21j) is a
nonlinear mixed integer programming (MINLP) problemwhich is Nondeterministic Polynomial-time (NP) hard Forimmediate proof of NP-hardness note that MINLP includesmixed integer linear programming (MILP) problem which isNP-hard [23]
Before applying any MINLP method for solving (21a)ndash(21j) the nonsmooth function 119892(sdot) in (19) included in theexpressions of 119903
119875119894(b119875 p119875) and 119903
119878119895(b119875 p119875) should be replaced
by its smooth approximation To construct a smooth approx-imation of 119892(119909) note that this function is equivalent to thesum of the shifted and scaled versions of a Heaviside stepfunction119867(119909) [24] That is
119892 (119909) =
15
sum
119897=1
(120577119897minus 120577119897minus1)119867 (119909 minus 120574
119897)
119867 (119909) =
1 if 119909 ge 0
0 otherwise
(22)
where 1205770= 0
Recall that a smooth approximation for a step function119867(119909) is given by a logistic sigmoid function [25]
119902(119909) =
1
1 + 119890minus2119902119909
(23)
where 119902 gt 0 119909 is in range of real numbers from minusinfin to +infinIf we take 119867(0) = 12 then larger 119902 corresponds to a closertransition to119867(119909) that is
lim119902rarrinfin
119902(119909) = 119867 (119909) (24)
The above holds because for 119909 lt 0 we have
119890minus2119902119909
997888rarr +infin
119902(119909) asymp 119867 (119909) = 1
(25)
for 119909 gt 0
119890minus2119902119909
997888rarr 0
119902(119909) asymp 119867 (119909) = 1
(26)
for 119909 = 0
119890minus2119902119909
= 1
119902(119909) = 119867 (119909) =
1
2
(27)
Consequently an approximation for a shifted Heavisidefunction is represented by a shifted logistic function
119902(119909 minus 120574
119897) =
1
1 + 119890minus2119902(119909minus120574119897)
(28)
defined for 119902 gt 0 with real 119909 in range from minusinfin to +infin
8 Mobile Information Systems
Based on (28) we can construct a smooth approximationfor 119892(119909) as
119902(119909) =
15
sum
119897=1
(120577119897minus 120577119897minus1) 119902(119909 minus 120574
119897) =
15
sum
119897=1
120577119897minus 120577119897minus1
1 + 1198902119902(119909minus120574119897)
(29)
Then it is rather straightforward to verify that
lim119902rarrinfin
119902(119909) = 119892 (119909) (30)
and the approximations for 119903119875119894(b119875 p119875) and 119903
119878119895(b119875 p119875) will
take the form
119875119894(b119875 p119875) = 120596120595119887
119875119894log (1 + (119901
119875119894) sdot ℎ119875119894119901119875119894)
forall119894 isin I(31a)
119878119895(b119878 p119878) = 120596120595119887
119878119895log (1 + (119901
119878119895) ℎ119878119895119901119878119895)
forall119895 isin J(31b)
With the approximations given by (31a) and (31b) prob-lem (21a)ndash(21j) can be solved using a sequential optimizationapproach as
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (32a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (32b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(32c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(32d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(32e)
Ω ge 0
Φ ge 0
(32f)
119891
1
119894(b119875 p119875)
= 119875119894(b119875 p119875)
minus (119902119875119894+ 119886119875119894) le 0
forall119894 isin I
(32g)
119891
2
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894minus 119871119894)
minus 119875119894(b119875 p119875) le 0
forall119894 isin I
(32h)
119891
3
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894)
minus 119875119894(b119875 p119875) minus Ω
le 0
forall119894 isin I
(32i)
119891
4
119895(b119878 p119878)
= (119902119878119895+ 119886119878119895)
minus 119878119895(b119878 p119878) minus Φ
le 0
forall119895 isin J
(32j)
The above problem is smooth MINLP which can besolved using some fast and effective MINLP method Notethat most of the MINLP techniques involve constructionof the following relaxations to the considered problem thenonlinear programming (NLP) relaxation (original problemwithout integer restrictions) and the MILP relaxation (origi-nal problem where nonlinearities are replaced by supportinghyperplanes) In our case a smooth MILP relaxation to(32a)ndash(32j) in a given point (b0
119875 p0119875 b0119878 p0119878) is given by
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (33a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (33b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(33c)
Mobile Information Systems 9
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(33d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(33e)
Ω ge 0
Φ ge 0
(33f)
119891
1
119894(b0119875 p0119875) + nabla
119891
1
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33g)
119891
2
119894(b0119875 p0119875) + nabla
119891
2
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33h)
119891
3
119894(b0119875 p0119875) + nabla
119891
3
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33i)
119891
4
119895(b0119878 p0119878) + nabla
119891
4
119895(b0119878 p0119878)
119879
[
b119878minus b0119878
p119878minus p0119878
]
le 0
forall119895 isin J
(33j)
The NLP relaxation to (32a)ndash(32j) is
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (34a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (34b)
119887119875119894ge 0
119887119878119895ge 0
forall119894 isin I forall119895 isin J
(34c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(34d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(34e)
Ω ge 0
Φ ge 0
(34f)
119891
1
119894(b119875 p119875) le 0
forall119894 isin I(34g)
119891
2
119894(b119875 p119875) le 0
forall119894 isin I(34h)
119891
3
119894(b119875 p119875) le 0
forall119894 isin I(34i)
119891
4
119895(b119878 p119878) le 0
forall119895 isin J(34j)
Note that theMINLP problems can be solved using eitherdeterministic technique or an approximation A typical exact
10 Mobile Information Systems
method for solving MINLPs is a well-known branch-and-bound algorithmand its variousmodifications [26] examplesof heuristic approaches include local branching [27] largeneighborhood search [28] and feasibility pump [29] to namea few Since we are interested in a reasonably simple and fastalgorithm it is more convenient to use heuristics for solvingthe problem In this paper a Feasibility Pump (FP) heuristic[29 30] is applied to solve (32a)ndash(32j) FP is perhaps the mostsimple and most effective method for producing more andbetter solutions in a shorter average running time For theproblems with nonbinary integer variables the complexity ofFP is exponential in size of a problem [31]
A fundamental idea of FP algorithm is to decomposethe problem into two parts integer feasibility and constraint
feasibility The former is achieved by rounding (solvinga NLP relaxation to the original problem) and the latterby projection (solving a MILP relaxation) Consequentlytwo sequences of points are generated The first sequence(b119875 p119875 b119878 p119878)119896119870
119896=1 119870 = 1 2 contains the integral
points that may violate the nonlinear constraintsThe secondsequence (b
119875 p119875 b119878 p119878)119896119870
119896=1contains the points which are
feasible for a continuous relaxation to the original problembut might not be integral
More specifically with input (b119875 p119875 b119878 p119878)1being a
solution to the NLP relaxation given by (34a)ndash(34j) thealgorithm generates two sequences by solving the followingproblems for 119896 = 1 119870
(b119875 p119875 b119878 p119878)119896= argmin
100381710038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b
119875 p119875 b119878 p119878)119896
1003817100381710038171003817100381710038171
(35a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (35b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(35c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(35d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(35e)
Ω ge 0
Φ ge 0
(35f)
119891
1
119894(b0119875 p0119875) + nabla
119891
1
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35g)
119891
2
119894(b0119875 p0119875) + nabla
119891
2
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35h)
119891
3
119894(b0119875 p0119875) + nabla
119891
3
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35i)
Mobile Information Systems 11
119891
4
119895(b0119878 p0119878) + nabla
119891
4
119895(b0119878 p0119878)
119879
[
b119878minus b0119878
p119878minus p0119878
] le 0
forall119895 isin J
(35j)
(b119875 p119875 b119878 p119878)119896+1
= argmin 10038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b
119875 p119875 b119878 p119878)119896
100381710038171003817100381710038172
(36a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (36b)
119887119875119894ge 0
119887119878119895ge 0
forall119894 isin I forall119895 isin J
(36c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(36d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(36e)
Ω ge 0
Φ ge 0
(36f)
119891
1
119894(b119875 p119875) le 0
forall119894 isin I(36g)
119891
2
119894(b119875 p119875) le 0
forall119894 isin I(36h)
119891
3
119894(b119875 p119875) le 0
forall119894 isin I(36i)
119891
4
119895(b119878 p119878) le 0
forall119895 isin J(36j)
where sdot1and sdot
2are 1198971norm and 119897
2norm respectivelyThe
rounding step is carried out by solving (35a)ndash(35j) whereasthe projection is the solution to (36a)ndash(36j) A suggested FPalgorithm alternates between the rounding and projectionsteps until (b
119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896(which implies
feasibility) or the number of iterations 119896 has reached thepredefined limit 119870 The workflow of a corresponding FPalgorithm is illustrated in the following part
FP Algorithm for Non-Convex MINLP(0) INITIALIZATION input119870 set 119896 = 1
solve (34a)ndash(34j) to obtain (b119875 p119875 b119878 p119878)119896
(1) WHILE (119896 lt 119870) do
(2) ROUNDING solve (35a)ndash(35j) to obtain(b119875 p119875 b119878 p119878)119896
(3) IF ((b119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896) THEN goto
step (6)(4) PROJECTION solve (36a)ndash(36j) to obtain
(b119875 p119875 b119878 p119878)119896+1
(5) Set 119896 = 119896 + 1
12 Mobile Information Systems
(6) OUTPUT solution (b119875 p119875 b119878 p119878)lowast
=
(b119875 p119875 b119878 p119878)119896
Note that in order to retain the convergence of thealgorithm both problems (35a)ndash(35j) and (36a)ndash(36j) needto be solved exactly Problem (36a)ndash(36j) (and consequentlyproblem (34a)ndash(34j)) can be solved using any standard NLPmethod In this paper an interior point algorithm (describedeg in [32]) with polynomial complexity is applied to solve(36a)ndash(36j) and (34a)ndash(34j) MILP problem (35a)ndash(35j) isrelatively simple and therefore can be solved efficiently foroptimality by any technique from the family of the branch-and-bound methods (eg [26])
33 Target Buffer Size for PUs and Feasibility Issues Recallthat 119871
119894represents the target buffer size for PU
119894 which
indicates that the QoS requirements of PU119894are satisfied By
limiting the buffer size of PUs we restrict the QoS of PUs(measured in terms of their buffer size) to be higher (or atleast not smaller) than the required minimum From thispoint of view constraints (5) and (12) guarantee the QoSprotection of PUs in Scenario 1 and Scenario 2 respectivelyApparently one can always restrict the target buffer size ofPUs to be equal to zero so that after each subsequent dataarrival the buffer of each PU is fully cleared This approachrepresents a ldquogreedyrdquo policy which ensures that the PUs arealways served with the best possible QoS but does not guar-antee that some spare capacity will be left to serve the SUs
A ldquoless greedyrdquo strategy would be to establish somelower bound on QoS for the PUs which will provide anldquoopportunityrdquo for SUs to be served To establish this lowerbound recall that the growing delay and loss indicate thata buffer of a corresponding node is congested whereas inan uncongested node the packet delay and loss are alwaysminimal [33] On the other hand it has been reported in[33 34] that in an uncongested node the buffer size 119902(119905) isincreasing very slowly that is 119902(119905 + 1)119902(119905) asymp 1 whereas ina congested node the buffer size is growing very fast so that119902(119905+1)119902(119905) ≫ 1 Hence to serve the PUs withminimal delayand loss it is enough to prevent the growth of their buffersthat is for each PU set
119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)
where 120576 ge 0 is some small value such that
120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)
More sophisticated approach to find the lowerQoS boundcan be deployed if information about the past buffer size isavailable at any time slot 119905 In this case one can set the targetbuffer size based on past T observations 119902(119905) 119902(119905 minus 119879 + 1)as
119871119894= min120591isinT
119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38a)
or
119871119894=
1
119879
sum
120591isinT119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38b)
where T = 1 119879
UBADPC MBC
60
70
80
90
100
110
120
130
140
Alg
orith
m it
erat
ions
10020 8040 50 60 7030 90100Number of SUs m
120572i = 1 v = m lowast 1Mbps
Figure 1 Average number of iterations before convergence as afunction of number of SUs in simulations with 119899 = 100 PUs andaverage SNR = 0 dB
MBC
070
075
080
085
090
095
100
120572i=0
v=0
120572i=1
v=0
120572i=0
v=m
lowast1
Mbp
s
120572i=1
v=m
lowast1
Mbp
s
Fairness among SUs FSU
Fairness among PUs FPU
Fairness among all users F
Figure 2 Jainrsquos index of fairness119865SU119865PU and119865 for the PUs SUs andall users in simulations with 119899 = 100 PUs119898 = 100 SUs and averageSNR = 0 dB
In some (very rare) cases (when the service capacity of theeNB is not enough to guarantee that the buffer sizes in all PUsdo not exceed the target buffer size) constraints (5) and (12)in Scenarios 1 and 2 may be not feasible In the following weshow how to identify such situation and what should be theoptimal resource allocation strategy in this case
Note that the service capacity of LTE system greatlydepends on physical characteristics (eg SINR and MCS) of
Mobile Information Systems 13
UBADPCGBC
NBCMBCABC
780
800
820
840
860
880
900
920
940
960Th
roug
hput
for P
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r PU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for P
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
Figure 3 Mean throughput packet delay and loss for PUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
the wireless channels between the eNB and the users Henceat the moment preceding the bandwidthpower allocation itis rather difficult to estimate the service capacity of a systemNevertheless it is possible to find the average service capacityand to determine the upper and lower bounds on servicecapacity of the eNB in the UL and DL directions such that
119877min le sum119894isinI119903119875119894(119905) asymp 119877ave le 119877max (39)
where119877min119877ave and119877max are the lower bound upper boundand average service capacity of the eNB respectively
In our case the upper bound on service capacity of theeNB is given by
119877max = 120596120595119861 log (1 + 119892 (SNRmax) sdot SNRmax) (40a)
where SNRmax is the maximal possible SNR value
The lower bound on service capacity of eNB is
119877min = 120596120595119861 log (1 + 119892 (SNRmin) sdot SNRmin) (40b)
where SNRmin is the minimal possible SNR valueThe average service capacity of the eNB equals
119877ave = 120596120595119861 log (1 + 119892 (SNRave) sdot SNRave) (40c)
where SNRave is the average SNR valueIf SNR information is available then the values SNRmax
SNRmin and SNRave can be set as
SNRmax = max119894isinI
SNR119894 (41a)
14 Mobile Information Systems
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r SU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for S
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
Figure 4 Mean throughput packet delay and loss for SUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
SNRmin = min119894isinI
SNR119894 (41b)
SNRave =1
119899
sum
119894isinISNR119894 (41c)
Otherwise (ie if SNR information is not available) thevalues are set arbitrarily
Now we can identify the situation when constraints (5)and (12) cannot be satisfied For this we should perform thefollowing test For Scenario 1 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus 119871
119894) (42)
then constraint (5) is feasible Otherwise condition (5)cannot be satisfiedHence all the SUs receive zero allocations
andwe assign the bandwidthpower resources only to the PUsby solving the following optimization problem
minimize max119894isinI
lceil119902119875119894+ 119886119875119894minus 119903119875119894(b119875 p119875)rceil+
(43a)
subject to 119903119875119894(b119875 p119875) le 119902119875119894+ 119886119875119894 forall119894 isin I (43b)
sum
119894isinI119887119875119894le 119861 (43c)
119887119875119894isin Z+ forall119894 isin I (43d)
119901119875119894le 119875119875119894 forall119894 isin I (43e)
119901119875119894ge 0 forall119894 isin I (43f)
Mobile Information Systems 15
725
750
775
800
825
850
875
900
925
950Th
roug
hput
for P
Us (
kbits
s)
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
10
20
30
40
50
60
70
Dela
y fo
r PU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Loss
for P
Us (
)
0
005
01
015
02
025
03
035
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Figure 5 Mean throughput packet delay and loss for PUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
for the UL direction For the DL directions constraint (43e)should be replaced by
sum
119894isinI119901119875119894le 119875eNB (43g)
For Scenario 2 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus (1 + 120572
119894) 119871119894) (44)
then constraint (12) is feasible Otherwise inequality (12)cannot be satisfied and the bandwidthpower resources areassigned only to the PUs (according to (43a)ndash(43g)) whereasthe SUs receive zero allocations
4 Performance Evaluation
41 Simulation Model A simulation model of the networkconsisting of one eNB 119899 PUs and 119898 SUs randomly locatedin a service area with 3 km radius has been developed upona standard LTE platform using the OPNET package [35]Thebandwidth of the eNB equals 119861 = 50RBs (which is equivalentto 10MHz) The slot duration in the algorithm equals 119879
119904=
1msThemaximal number of iterations in FP algorithm is set119870 = 200Themaximal transmission power of the eNB equals119875eNB = 46 dBm and the maximal transmission power of eachPUSU equals 119875
1198751= sdot sdot sdot = 119875
119875119899= 1198751198781= sdot sdot sdot = 119875
119878119898= 23 dBm
Other simulation settings of the model are listed in Table 2(all the parameters are based on LTE specifications [36])
16 Mobile Information Systems
Table 2 Simulation parameters of the model
Parameter ValueRadio network model
Pass loss 119871 = 40log10119877 + 30log
10119891 + 49 119877 distance (km) 119891
carrier frequency (Hz)
Shadow fading Log-normal shadow fading with a standard deviation of1012 dB for outdoorindoor users
Penetration loss The average building penetration loss is 12 dB with astandard deviation of 8 dB
Multipath fading Spatial Channel Model (SCM) Suburban macroUE velocity 0 kmsTransmitterreceiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver noise figure 5 dBThermal noise density minus174 dBmHzCableconnectorcombiner losses 2 dB
Physical profileOperation mode FDDCyclic prefix type Normal (7 symbols per slot)Evolved packet core (EPC) bearer definitions 348 kbits (nonguaranteed bit rate)Subcarrier spacing 15 kHz
Admission control parametersPhysical downlink control channel (PDCCH) symbols per subframe 3UL loading factor 1DL loading factor 1Inactive bearer timeout 20 sec
Buffer status report parametersPeriodic timer 5 subframesRetransmission timer 2560 subframes
L1L2 control parametersReserved size 2 RBsCyclic shifts 6Starting RB preserver for Format 1 messages 0Allocation periodicity 5 subframes
Random access (RA) parametersNumber of preambles 64Preamble format Format 0 (1-subframe long)Number of RA resources per frame 4Preamble retransmission limit 5 subframesRA response timer 5 subframesContention resolution timer 40 subframes
HARQ parametersMaximal number of retransmissions 3 (UL and DL)HARQ retransmission timer 8 subframes (UL and DL)Maximal number of HARQ processes 8 per UE (UL and DL)
A radio model of the network corresponds to the require-ments of ITU-T Recommendation M1225
The algorithms proposed in the paper are denoted asfollows
(i) GBC (greedy buffer Control) where the target buffersize equals 0 for all the PUs
(ii) NBC (nongreedy buffer control) with the target buffersize calculated according to (37a) and (37b)
(iii) MBC (Minimal Buffer Control) with 119879 = 10 slots andthe target buffer size given by (38a)
(iv) ABC (Average Buffer Control) with 119879 = 10 slots andthe target buffer size equaling (38b)
Two previously proposed schemes used to benchmark theperformance of the algorithms proposed in this paper are
(i) UBA (Utility Based Allocation) presented in [11]where the network resources (bandwidth and trans-mission power) are allocated to the UL channels tomaximize the total transmission rate of the userssubject to the capacity and transmission power con-straints
Mobile Information Systems 17
0 10 20 30 40 50 60 70 80Average SNR (dB)
UBADPCGBC
NBCMBCABC
30
35
40
45
50
55
60
65
70
Dela
y fo
r SU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
012
015
018
021
024
027
03
033
Loss
for S
Us (
)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
250
300
350
400
450
500Th
roug
hput
for S
Us (
kbits
s)
Figure 6 Mean throughput packet delay and loss for SUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
(ii) DPC (Delay Power Control) derived in [5] whichis used to balance the transmission delay againsttransmission power in wireless channels between theeNB and the users
We also gather simulation results for a proposed resourceallocation approach in Scenario 2 with different settings ofthe parameters120572
119894and V and benchmark its performancewith
the performance of the algorithm in Scenario 1All algorithms are simulated using identical settings
The data traffic in simulations is represented by voice overInternet Protocol (VoIP) video and Hypertext TransferProtocol (HTTP) applications mixed in proportion 2 3 5using the models defined in [37]
42 Complexity and Fairness Issues Let us first evaluatethe complexity and the fairness of resource allocation indifferent algorithms Figure 1 shows the average numberof iterations before convergence for UBA DPC and theproposed algorithms in Scenario 1 (denoted as MBC) andScenario 2 gathered in simulations with 119899 = 100 PUs andaverage SNR = 0 dB Note that the target buffer size for thePUs is calculated according to (38a) with T = 10 slots (inScenarios 1 and 2) and 120572
119894= 1 V = 119898 lowast 1Mbps (for
Scenario 2) Results demonstrate that the complexity of FPmethod deployed for resource allocation in Scenarios 1 and2 is exponential in size of the problem (which correspondsto the findings reported in [31]) and is comparable to thecomplexities of other techniques (UBA and DPC)
18 Mobile Information Systems
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
080020 090070050 060 100000 030010 040120572i
10
20
30
40
50
60
70
80
90
100
110
Dela
y fo
r PU
s (m
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
040030 090000 080060010 020 050 100070120572i
005
010
015
020
025
030
035
040
045
050
Loss
for P
Us (
)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
030020 040 090010 060 070 080 100000 050120572i
Figure 7 Mean throughput packet delay and loss for the PUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
Figure 2 shows the fairness of different methods calcu-lated according to Jainrsquos equation [38] as
119865PU =
(sum119894isinI 119903119875119894)
2
119899 sdot sum119894isinI 1199032
119875119894
119865SU =
(sum119895isinJ 119903119878119895)
2
119898 sdot sum119895isinJ 1199032
119878119895
119865 =
(sum119894isinI 119903119875119894 + sum119895isinJ 119903119878119895)
2
(119899 + 119898) sdot (sum119894isinI 1199032
119875119894+ sum119895isinJ 1199032
119878119895)
(45)
where 119865PU 119865SU and 119865 stand for Jainrsquos index of fairness forthe PUs SUs and all of the users respectively 119903
119875119894 119903119878119895
arethe mean throughputs for PU
119894and SU
119895 respectively Results
have been gathered for 119899 = 100 PUs 119898 = 100 SUs average
Mobile Information Systems 19
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
410
420
430
440
450
460
470
480
490
500
510Th
roug
hput
for S
Us (
kbits
s)
010 020 080 090050 060 070030 100000 040120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
15
20
25
30
35
40
45
50
Dela
y fo
r SU
s (m
s)
070 090030 040 050 080000 020010 100060120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
007
009
011
013
015
017
019
021
023
Loss
for S
Us (
)
080070 090020 050 060030 100040010000120572i
Figure 8 Mean throughput packet delay and loss for the SUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
SNR = 0 dB and target buffer size for the PUs calculatedaccording to (38a) (Scenarios 1 and 2) with different settingsof 120572119894and V in Scenario 2
It follows from these graphs that the fairness index amongall of the users (denoted as 119865) is higher in Scenario 2 with120572119894= 1 and lower in Scenario 1 and Scenario 2 with 120572
119894= 0
Such results are rather expectable in Scenario 1 and Scenario2 with 120572
119894= 0 the SUs are served for free on a best-effort
basis whereas the PUs enjoy full QoS guarantees Hence thenetwork resources are shared nonequally between the PUs
and the SUs with most of the RBs allocated to the PUs andthe rest of the bandwidth distributed among the SUs Onthe other hand the fairness index for the PUs and SUs (ie119865PU and 119865SU) is rather high in both scenarios with differentsettings of 120572
119894and V which indicates that the users of the same
type are treated equally during resource allocation
43 Simulation Results in Scenario 1 Let us evaluate theperformance of a resource allocation algorithm in Scenario1 in terms of mean throughput packet end-to-end delay and
20 Mobile Information Systems
MBC
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
20
30
40
50
60
70
80
90
Dela
y fo
r PU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
005
010
015
020
025
030
035
040
045
Loss
for P
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 9 Mean throughput packet delay and loss for the PUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
loss for different user types Figures 3ndash6 show results obtainedin simulations with 119899 = 100 PUs and average SNR = 0 dBResults demonstrate that aUBA scheme has the largest packetdelay and loss and the lowest throughput for both the PUs andthe SUs A poor performance of this scheme is explained asfollows
(i) QoS protection of PUs is not considered in UBAHence the throughput delay and loss are the samefor PUs and SUs
(ii) Buffer sizes of individual users are not consideredin resource allocation and therefore the QoS for
Mobile Information Systems 21
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
30
50
70
90
110
130
Dela
y fo
r SU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
000
010
020
030
040
050
060
Loss
for S
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
different users varies significantly (since differentusers have different traffic demands)
(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer
size and therefore there is no need to maximize theirtransmission rate and spend the network resources
Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
8 Mobile Information Systems
Based on (28) we can construct a smooth approximationfor 119892(119909) as
119902(119909) =
15
sum
119897=1
(120577119897minus 120577119897minus1) 119902(119909 minus 120574
119897) =
15
sum
119897=1
120577119897minus 120577119897minus1
1 + 1198902119902(119909minus120574119897)
(29)
Then it is rather straightforward to verify that
lim119902rarrinfin
119902(119909) = 119892 (119909) (30)
and the approximations for 119903119875119894(b119875 p119875) and 119903
119878119895(b119875 p119875) will
take the form
119875119894(b119875 p119875) = 120596120595119887
119875119894log (1 + (119901
119875119894) sdot ℎ119875119894119901119875119894)
forall119894 isin I(31a)
119878119895(b119878 p119878) = 120596120595119887
119878119895log (1 + (119901
119878119895) ℎ119878119895119901119878119895)
forall119895 isin J(31b)
With the approximations given by (31a) and (31b) prob-lem (21a)ndash(21j) can be solved using a sequential optimizationapproach as
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (32a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (32b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(32c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(32d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(32e)
Ω ge 0
Φ ge 0
(32f)
119891
1
119894(b119875 p119875)
= 119875119894(b119875 p119875)
minus (119902119875119894+ 119886119875119894) le 0
forall119894 isin I
(32g)
119891
2
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894minus 119871119894)
minus 119875119894(b119875 p119875) le 0
forall119894 isin I
(32h)
119891
3
119894(b119875 p119875)
= (119902119875119894+ 119886119875119894)
minus 119875119894(b119875 p119875) minus Ω
le 0
forall119894 isin I
(32i)
119891
4
119895(b119878 p119878)
= (119902119878119895+ 119886119878119895)
minus 119878119895(b119878 p119878) minus Φ
le 0
forall119895 isin J
(32j)
The above problem is smooth MINLP which can besolved using some fast and effective MINLP method Notethat most of the MINLP techniques involve constructionof the following relaxations to the considered problem thenonlinear programming (NLP) relaxation (original problemwithout integer restrictions) and the MILP relaxation (origi-nal problem where nonlinearities are replaced by supportinghyperplanes) In our case a smooth MILP relaxation to(32a)ndash(32j) in a given point (b0
119875 p0119875 b0119878 p0119878) is given by
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (33a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (33b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(33c)
Mobile Information Systems 9
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(33d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(33e)
Ω ge 0
Φ ge 0
(33f)
119891
1
119894(b0119875 p0119875) + nabla
119891
1
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33g)
119891
2
119894(b0119875 p0119875) + nabla
119891
2
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33h)
119891
3
119894(b0119875 p0119875) + nabla
119891
3
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33i)
119891
4
119895(b0119878 p0119878) + nabla
119891
4
119895(b0119878 p0119878)
119879
[
b119878minus b0119878
p119878minus p0119878
]
le 0
forall119895 isin J
(33j)
The NLP relaxation to (32a)ndash(32j) is
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (34a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (34b)
119887119875119894ge 0
119887119878119895ge 0
forall119894 isin I forall119895 isin J
(34c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(34d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(34e)
Ω ge 0
Φ ge 0
(34f)
119891
1
119894(b119875 p119875) le 0
forall119894 isin I(34g)
119891
2
119894(b119875 p119875) le 0
forall119894 isin I(34h)
119891
3
119894(b119875 p119875) le 0
forall119894 isin I(34i)
119891
4
119895(b119878 p119878) le 0
forall119895 isin J(34j)
Note that theMINLP problems can be solved using eitherdeterministic technique or an approximation A typical exact
10 Mobile Information Systems
method for solving MINLPs is a well-known branch-and-bound algorithmand its variousmodifications [26] examplesof heuristic approaches include local branching [27] largeneighborhood search [28] and feasibility pump [29] to namea few Since we are interested in a reasonably simple and fastalgorithm it is more convenient to use heuristics for solvingthe problem In this paper a Feasibility Pump (FP) heuristic[29 30] is applied to solve (32a)ndash(32j) FP is perhaps the mostsimple and most effective method for producing more andbetter solutions in a shorter average running time For theproblems with nonbinary integer variables the complexity ofFP is exponential in size of a problem [31]
A fundamental idea of FP algorithm is to decomposethe problem into two parts integer feasibility and constraint
feasibility The former is achieved by rounding (solvinga NLP relaxation to the original problem) and the latterby projection (solving a MILP relaxation) Consequentlytwo sequences of points are generated The first sequence(b119875 p119875 b119878 p119878)119896119870
119896=1 119870 = 1 2 contains the integral
points that may violate the nonlinear constraintsThe secondsequence (b
119875 p119875 b119878 p119878)119896119870
119896=1contains the points which are
feasible for a continuous relaxation to the original problembut might not be integral
More specifically with input (b119875 p119875 b119878 p119878)1being a
solution to the NLP relaxation given by (34a)ndash(34j) thealgorithm generates two sequences by solving the followingproblems for 119896 = 1 119870
(b119875 p119875 b119878 p119878)119896= argmin
100381710038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b
119875 p119875 b119878 p119878)119896
1003817100381710038171003817100381710038171
(35a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (35b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(35c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(35d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(35e)
Ω ge 0
Φ ge 0
(35f)
119891
1
119894(b0119875 p0119875) + nabla
119891
1
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35g)
119891
2
119894(b0119875 p0119875) + nabla
119891
2
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35h)
119891
3
119894(b0119875 p0119875) + nabla
119891
3
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35i)
Mobile Information Systems 11
119891
4
119895(b0119878 p0119878) + nabla
119891
4
119895(b0119878 p0119878)
119879
[
b119878minus b0119878
p119878minus p0119878
] le 0
forall119895 isin J
(35j)
(b119875 p119875 b119878 p119878)119896+1
= argmin 10038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b
119875 p119875 b119878 p119878)119896
100381710038171003817100381710038172
(36a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (36b)
119887119875119894ge 0
119887119878119895ge 0
forall119894 isin I forall119895 isin J
(36c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(36d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(36e)
Ω ge 0
Φ ge 0
(36f)
119891
1
119894(b119875 p119875) le 0
forall119894 isin I(36g)
119891
2
119894(b119875 p119875) le 0
forall119894 isin I(36h)
119891
3
119894(b119875 p119875) le 0
forall119894 isin I(36i)
119891
4
119895(b119878 p119878) le 0
forall119895 isin J(36j)
where sdot1and sdot
2are 1198971norm and 119897
2norm respectivelyThe
rounding step is carried out by solving (35a)ndash(35j) whereasthe projection is the solution to (36a)ndash(36j) A suggested FPalgorithm alternates between the rounding and projectionsteps until (b
119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896(which implies
feasibility) or the number of iterations 119896 has reached thepredefined limit 119870 The workflow of a corresponding FPalgorithm is illustrated in the following part
FP Algorithm for Non-Convex MINLP(0) INITIALIZATION input119870 set 119896 = 1
solve (34a)ndash(34j) to obtain (b119875 p119875 b119878 p119878)119896
(1) WHILE (119896 lt 119870) do
(2) ROUNDING solve (35a)ndash(35j) to obtain(b119875 p119875 b119878 p119878)119896
(3) IF ((b119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896) THEN goto
step (6)(4) PROJECTION solve (36a)ndash(36j) to obtain
(b119875 p119875 b119878 p119878)119896+1
(5) Set 119896 = 119896 + 1
12 Mobile Information Systems
(6) OUTPUT solution (b119875 p119875 b119878 p119878)lowast
=
(b119875 p119875 b119878 p119878)119896
Note that in order to retain the convergence of thealgorithm both problems (35a)ndash(35j) and (36a)ndash(36j) needto be solved exactly Problem (36a)ndash(36j) (and consequentlyproblem (34a)ndash(34j)) can be solved using any standard NLPmethod In this paper an interior point algorithm (describedeg in [32]) with polynomial complexity is applied to solve(36a)ndash(36j) and (34a)ndash(34j) MILP problem (35a)ndash(35j) isrelatively simple and therefore can be solved efficiently foroptimality by any technique from the family of the branch-and-bound methods (eg [26])
33 Target Buffer Size for PUs and Feasibility Issues Recallthat 119871
119894represents the target buffer size for PU
119894 which
indicates that the QoS requirements of PU119894are satisfied By
limiting the buffer size of PUs we restrict the QoS of PUs(measured in terms of their buffer size) to be higher (or atleast not smaller) than the required minimum From thispoint of view constraints (5) and (12) guarantee the QoSprotection of PUs in Scenario 1 and Scenario 2 respectivelyApparently one can always restrict the target buffer size ofPUs to be equal to zero so that after each subsequent dataarrival the buffer of each PU is fully cleared This approachrepresents a ldquogreedyrdquo policy which ensures that the PUs arealways served with the best possible QoS but does not guar-antee that some spare capacity will be left to serve the SUs
A ldquoless greedyrdquo strategy would be to establish somelower bound on QoS for the PUs which will provide anldquoopportunityrdquo for SUs to be served To establish this lowerbound recall that the growing delay and loss indicate thata buffer of a corresponding node is congested whereas inan uncongested node the packet delay and loss are alwaysminimal [33] On the other hand it has been reported in[33 34] that in an uncongested node the buffer size 119902(119905) isincreasing very slowly that is 119902(119905 + 1)119902(119905) asymp 1 whereas ina congested node the buffer size is growing very fast so that119902(119905+1)119902(119905) ≫ 1 Hence to serve the PUs withminimal delayand loss it is enough to prevent the growth of their buffersthat is for each PU set
119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)
where 120576 ge 0 is some small value such that
120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)
More sophisticated approach to find the lowerQoS boundcan be deployed if information about the past buffer size isavailable at any time slot 119905 In this case one can set the targetbuffer size based on past T observations 119902(119905) 119902(119905 minus 119879 + 1)as
119871119894= min120591isinT
119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38a)
or
119871119894=
1
119879
sum
120591isinT119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38b)
where T = 1 119879
UBADPC MBC
60
70
80
90
100
110
120
130
140
Alg
orith
m it
erat
ions
10020 8040 50 60 7030 90100Number of SUs m
120572i = 1 v = m lowast 1Mbps
Figure 1 Average number of iterations before convergence as afunction of number of SUs in simulations with 119899 = 100 PUs andaverage SNR = 0 dB
MBC
070
075
080
085
090
095
100
120572i=0
v=0
120572i=1
v=0
120572i=0
v=m
lowast1
Mbp
s
120572i=1
v=m
lowast1
Mbp
s
Fairness among SUs FSU
Fairness among PUs FPU
Fairness among all users F
Figure 2 Jainrsquos index of fairness119865SU119865PU and119865 for the PUs SUs andall users in simulations with 119899 = 100 PUs119898 = 100 SUs and averageSNR = 0 dB
In some (very rare) cases (when the service capacity of theeNB is not enough to guarantee that the buffer sizes in all PUsdo not exceed the target buffer size) constraints (5) and (12)in Scenarios 1 and 2 may be not feasible In the following weshow how to identify such situation and what should be theoptimal resource allocation strategy in this case
Note that the service capacity of LTE system greatlydepends on physical characteristics (eg SINR and MCS) of
Mobile Information Systems 13
UBADPCGBC
NBCMBCABC
780
800
820
840
860
880
900
920
940
960Th
roug
hput
for P
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r PU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for P
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
Figure 3 Mean throughput packet delay and loss for PUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
the wireless channels between the eNB and the users Henceat the moment preceding the bandwidthpower allocation itis rather difficult to estimate the service capacity of a systemNevertheless it is possible to find the average service capacityand to determine the upper and lower bounds on servicecapacity of the eNB in the UL and DL directions such that
119877min le sum119894isinI119903119875119894(119905) asymp 119877ave le 119877max (39)
where119877min119877ave and119877max are the lower bound upper boundand average service capacity of the eNB respectively
In our case the upper bound on service capacity of theeNB is given by
119877max = 120596120595119861 log (1 + 119892 (SNRmax) sdot SNRmax) (40a)
where SNRmax is the maximal possible SNR value
The lower bound on service capacity of eNB is
119877min = 120596120595119861 log (1 + 119892 (SNRmin) sdot SNRmin) (40b)
where SNRmin is the minimal possible SNR valueThe average service capacity of the eNB equals
119877ave = 120596120595119861 log (1 + 119892 (SNRave) sdot SNRave) (40c)
where SNRave is the average SNR valueIf SNR information is available then the values SNRmax
SNRmin and SNRave can be set as
SNRmax = max119894isinI
SNR119894 (41a)
14 Mobile Information Systems
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r SU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for S
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
Figure 4 Mean throughput packet delay and loss for SUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
SNRmin = min119894isinI
SNR119894 (41b)
SNRave =1
119899
sum
119894isinISNR119894 (41c)
Otherwise (ie if SNR information is not available) thevalues are set arbitrarily
Now we can identify the situation when constraints (5)and (12) cannot be satisfied For this we should perform thefollowing test For Scenario 1 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus 119871
119894) (42)
then constraint (5) is feasible Otherwise condition (5)cannot be satisfiedHence all the SUs receive zero allocations
andwe assign the bandwidthpower resources only to the PUsby solving the following optimization problem
minimize max119894isinI
lceil119902119875119894+ 119886119875119894minus 119903119875119894(b119875 p119875)rceil+
(43a)
subject to 119903119875119894(b119875 p119875) le 119902119875119894+ 119886119875119894 forall119894 isin I (43b)
sum
119894isinI119887119875119894le 119861 (43c)
119887119875119894isin Z+ forall119894 isin I (43d)
119901119875119894le 119875119875119894 forall119894 isin I (43e)
119901119875119894ge 0 forall119894 isin I (43f)
Mobile Information Systems 15
725
750
775
800
825
850
875
900
925
950Th
roug
hput
for P
Us (
kbits
s)
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
10
20
30
40
50
60
70
Dela
y fo
r PU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Loss
for P
Us (
)
0
005
01
015
02
025
03
035
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Figure 5 Mean throughput packet delay and loss for PUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
for the UL direction For the DL directions constraint (43e)should be replaced by
sum
119894isinI119901119875119894le 119875eNB (43g)
For Scenario 2 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus (1 + 120572
119894) 119871119894) (44)
then constraint (12) is feasible Otherwise inequality (12)cannot be satisfied and the bandwidthpower resources areassigned only to the PUs (according to (43a)ndash(43g)) whereasthe SUs receive zero allocations
4 Performance Evaluation
41 Simulation Model A simulation model of the networkconsisting of one eNB 119899 PUs and 119898 SUs randomly locatedin a service area with 3 km radius has been developed upona standard LTE platform using the OPNET package [35]Thebandwidth of the eNB equals 119861 = 50RBs (which is equivalentto 10MHz) The slot duration in the algorithm equals 119879
119904=
1msThemaximal number of iterations in FP algorithm is set119870 = 200Themaximal transmission power of the eNB equals119875eNB = 46 dBm and the maximal transmission power of eachPUSU equals 119875
1198751= sdot sdot sdot = 119875
119875119899= 1198751198781= sdot sdot sdot = 119875
119878119898= 23 dBm
Other simulation settings of the model are listed in Table 2(all the parameters are based on LTE specifications [36])
16 Mobile Information Systems
Table 2 Simulation parameters of the model
Parameter ValueRadio network model
Pass loss 119871 = 40log10119877 + 30log
10119891 + 49 119877 distance (km) 119891
carrier frequency (Hz)
Shadow fading Log-normal shadow fading with a standard deviation of1012 dB for outdoorindoor users
Penetration loss The average building penetration loss is 12 dB with astandard deviation of 8 dB
Multipath fading Spatial Channel Model (SCM) Suburban macroUE velocity 0 kmsTransmitterreceiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver noise figure 5 dBThermal noise density minus174 dBmHzCableconnectorcombiner losses 2 dB
Physical profileOperation mode FDDCyclic prefix type Normal (7 symbols per slot)Evolved packet core (EPC) bearer definitions 348 kbits (nonguaranteed bit rate)Subcarrier spacing 15 kHz
Admission control parametersPhysical downlink control channel (PDCCH) symbols per subframe 3UL loading factor 1DL loading factor 1Inactive bearer timeout 20 sec
Buffer status report parametersPeriodic timer 5 subframesRetransmission timer 2560 subframes
L1L2 control parametersReserved size 2 RBsCyclic shifts 6Starting RB preserver for Format 1 messages 0Allocation periodicity 5 subframes
Random access (RA) parametersNumber of preambles 64Preamble format Format 0 (1-subframe long)Number of RA resources per frame 4Preamble retransmission limit 5 subframesRA response timer 5 subframesContention resolution timer 40 subframes
HARQ parametersMaximal number of retransmissions 3 (UL and DL)HARQ retransmission timer 8 subframes (UL and DL)Maximal number of HARQ processes 8 per UE (UL and DL)
A radio model of the network corresponds to the require-ments of ITU-T Recommendation M1225
The algorithms proposed in the paper are denoted asfollows
(i) GBC (greedy buffer Control) where the target buffersize equals 0 for all the PUs
(ii) NBC (nongreedy buffer control) with the target buffersize calculated according to (37a) and (37b)
(iii) MBC (Minimal Buffer Control) with 119879 = 10 slots andthe target buffer size given by (38a)
(iv) ABC (Average Buffer Control) with 119879 = 10 slots andthe target buffer size equaling (38b)
Two previously proposed schemes used to benchmark theperformance of the algorithms proposed in this paper are
(i) UBA (Utility Based Allocation) presented in [11]where the network resources (bandwidth and trans-mission power) are allocated to the UL channels tomaximize the total transmission rate of the userssubject to the capacity and transmission power con-straints
Mobile Information Systems 17
0 10 20 30 40 50 60 70 80Average SNR (dB)
UBADPCGBC
NBCMBCABC
30
35
40
45
50
55
60
65
70
Dela
y fo
r SU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
012
015
018
021
024
027
03
033
Loss
for S
Us (
)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
250
300
350
400
450
500Th
roug
hput
for S
Us (
kbits
s)
Figure 6 Mean throughput packet delay and loss for SUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
(ii) DPC (Delay Power Control) derived in [5] whichis used to balance the transmission delay againsttransmission power in wireless channels between theeNB and the users
We also gather simulation results for a proposed resourceallocation approach in Scenario 2 with different settings ofthe parameters120572
119894and V and benchmark its performancewith
the performance of the algorithm in Scenario 1All algorithms are simulated using identical settings
The data traffic in simulations is represented by voice overInternet Protocol (VoIP) video and Hypertext TransferProtocol (HTTP) applications mixed in proportion 2 3 5using the models defined in [37]
42 Complexity and Fairness Issues Let us first evaluatethe complexity and the fairness of resource allocation indifferent algorithms Figure 1 shows the average numberof iterations before convergence for UBA DPC and theproposed algorithms in Scenario 1 (denoted as MBC) andScenario 2 gathered in simulations with 119899 = 100 PUs andaverage SNR = 0 dB Note that the target buffer size for thePUs is calculated according to (38a) with T = 10 slots (inScenarios 1 and 2) and 120572
119894= 1 V = 119898 lowast 1Mbps (for
Scenario 2) Results demonstrate that the complexity of FPmethod deployed for resource allocation in Scenarios 1 and2 is exponential in size of the problem (which correspondsto the findings reported in [31]) and is comparable to thecomplexities of other techniques (UBA and DPC)
18 Mobile Information Systems
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
080020 090070050 060 100000 030010 040120572i
10
20
30
40
50
60
70
80
90
100
110
Dela
y fo
r PU
s (m
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
040030 090000 080060010 020 050 100070120572i
005
010
015
020
025
030
035
040
045
050
Loss
for P
Us (
)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
030020 040 090010 060 070 080 100000 050120572i
Figure 7 Mean throughput packet delay and loss for the PUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
Figure 2 shows the fairness of different methods calcu-lated according to Jainrsquos equation [38] as
119865PU =
(sum119894isinI 119903119875119894)
2
119899 sdot sum119894isinI 1199032
119875119894
119865SU =
(sum119895isinJ 119903119878119895)
2
119898 sdot sum119895isinJ 1199032
119878119895
119865 =
(sum119894isinI 119903119875119894 + sum119895isinJ 119903119878119895)
2
(119899 + 119898) sdot (sum119894isinI 1199032
119875119894+ sum119895isinJ 1199032
119878119895)
(45)
where 119865PU 119865SU and 119865 stand for Jainrsquos index of fairness forthe PUs SUs and all of the users respectively 119903
119875119894 119903119878119895
arethe mean throughputs for PU
119894and SU
119895 respectively Results
have been gathered for 119899 = 100 PUs 119898 = 100 SUs average
Mobile Information Systems 19
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
410
420
430
440
450
460
470
480
490
500
510Th
roug
hput
for S
Us (
kbits
s)
010 020 080 090050 060 070030 100000 040120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
15
20
25
30
35
40
45
50
Dela
y fo
r SU
s (m
s)
070 090030 040 050 080000 020010 100060120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
007
009
011
013
015
017
019
021
023
Loss
for S
Us (
)
080070 090020 050 060030 100040010000120572i
Figure 8 Mean throughput packet delay and loss for the SUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
SNR = 0 dB and target buffer size for the PUs calculatedaccording to (38a) (Scenarios 1 and 2) with different settingsof 120572119894and V in Scenario 2
It follows from these graphs that the fairness index amongall of the users (denoted as 119865) is higher in Scenario 2 with120572119894= 1 and lower in Scenario 1 and Scenario 2 with 120572
119894= 0
Such results are rather expectable in Scenario 1 and Scenario2 with 120572
119894= 0 the SUs are served for free on a best-effort
basis whereas the PUs enjoy full QoS guarantees Hence thenetwork resources are shared nonequally between the PUs
and the SUs with most of the RBs allocated to the PUs andthe rest of the bandwidth distributed among the SUs Onthe other hand the fairness index for the PUs and SUs (ie119865PU and 119865SU) is rather high in both scenarios with differentsettings of 120572
119894and V which indicates that the users of the same
type are treated equally during resource allocation
43 Simulation Results in Scenario 1 Let us evaluate theperformance of a resource allocation algorithm in Scenario1 in terms of mean throughput packet end-to-end delay and
20 Mobile Information Systems
MBC
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
20
30
40
50
60
70
80
90
Dela
y fo
r PU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
005
010
015
020
025
030
035
040
045
Loss
for P
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 9 Mean throughput packet delay and loss for the PUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
loss for different user types Figures 3ndash6 show results obtainedin simulations with 119899 = 100 PUs and average SNR = 0 dBResults demonstrate that aUBA scheme has the largest packetdelay and loss and the lowest throughput for both the PUs andthe SUs A poor performance of this scheme is explained asfollows
(i) QoS protection of PUs is not considered in UBAHence the throughput delay and loss are the samefor PUs and SUs
(ii) Buffer sizes of individual users are not consideredin resource allocation and therefore the QoS for
Mobile Information Systems 21
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
30
50
70
90
110
130
Dela
y fo
r SU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
000
010
020
030
040
050
060
Loss
for S
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
different users varies significantly (since differentusers have different traffic demands)
(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer
size and therefore there is no need to maximize theirtransmission rate and spend the network resources
Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mobile Information Systems 9
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(33d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(33e)
Ω ge 0
Φ ge 0
(33f)
119891
1
119894(b0119875 p0119875) + nabla
119891
1
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33g)
119891
2
119894(b0119875 p0119875) + nabla
119891
2
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33h)
119891
3
119894(b0119875 p0119875) + nabla
119891
3
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(33i)
119891
4
119895(b0119878 p0119878) + nabla
119891
4
119895(b0119878 p0119878)
119879
[
b119878minus b0119878
p119878minus p0119878
]
le 0
forall119895 isin J
(33j)
The NLP relaxation to (32a)ndash(32j) is
(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (34a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (34b)
119887119875119894ge 0
119887119878119895ge 0
forall119894 isin I forall119895 isin J
(34c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(34d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(34e)
Ω ge 0
Φ ge 0
(34f)
119891
1
119894(b119875 p119875) le 0
forall119894 isin I(34g)
119891
2
119894(b119875 p119875) le 0
forall119894 isin I(34h)
119891
3
119894(b119875 p119875) le 0
forall119894 isin I(34i)
119891
4
119895(b119878 p119878) le 0
forall119895 isin J(34j)
Note that theMINLP problems can be solved using eitherdeterministic technique or an approximation A typical exact
10 Mobile Information Systems
method for solving MINLPs is a well-known branch-and-bound algorithmand its variousmodifications [26] examplesof heuristic approaches include local branching [27] largeneighborhood search [28] and feasibility pump [29] to namea few Since we are interested in a reasonably simple and fastalgorithm it is more convenient to use heuristics for solvingthe problem In this paper a Feasibility Pump (FP) heuristic[29 30] is applied to solve (32a)ndash(32j) FP is perhaps the mostsimple and most effective method for producing more andbetter solutions in a shorter average running time For theproblems with nonbinary integer variables the complexity ofFP is exponential in size of a problem [31]
A fundamental idea of FP algorithm is to decomposethe problem into two parts integer feasibility and constraint
feasibility The former is achieved by rounding (solvinga NLP relaxation to the original problem) and the latterby projection (solving a MILP relaxation) Consequentlytwo sequences of points are generated The first sequence(b119875 p119875 b119878 p119878)119896119870
119896=1 119870 = 1 2 contains the integral
points that may violate the nonlinear constraintsThe secondsequence (b
119875 p119875 b119878 p119878)119896119870
119896=1contains the points which are
feasible for a continuous relaxation to the original problembut might not be integral
More specifically with input (b119875 p119875 b119878 p119878)1being a
solution to the NLP relaxation given by (34a)ndash(34j) thealgorithm generates two sequences by solving the followingproblems for 119896 = 1 119870
(b119875 p119875 b119878 p119878)119896= argmin
100381710038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b
119875 p119875 b119878 p119878)119896
1003817100381710038171003817100381710038171
(35a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (35b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(35c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(35d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(35e)
Ω ge 0
Φ ge 0
(35f)
119891
1
119894(b0119875 p0119875) + nabla
119891
1
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35g)
119891
2
119894(b0119875 p0119875) + nabla
119891
2
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35h)
119891
3
119894(b0119875 p0119875) + nabla
119891
3
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35i)
Mobile Information Systems 11
119891
4
119895(b0119878 p0119878) + nabla
119891
4
119895(b0119878 p0119878)
119879
[
b119878minus b0119878
p119878minus p0119878
] le 0
forall119895 isin J
(35j)
(b119875 p119875 b119878 p119878)119896+1
= argmin 10038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b
119875 p119875 b119878 p119878)119896
100381710038171003817100381710038172
(36a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (36b)
119887119875119894ge 0
119887119878119895ge 0
forall119894 isin I forall119895 isin J
(36c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(36d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(36e)
Ω ge 0
Φ ge 0
(36f)
119891
1
119894(b119875 p119875) le 0
forall119894 isin I(36g)
119891
2
119894(b119875 p119875) le 0
forall119894 isin I(36h)
119891
3
119894(b119875 p119875) le 0
forall119894 isin I(36i)
119891
4
119895(b119878 p119878) le 0
forall119895 isin J(36j)
where sdot1and sdot
2are 1198971norm and 119897
2norm respectivelyThe
rounding step is carried out by solving (35a)ndash(35j) whereasthe projection is the solution to (36a)ndash(36j) A suggested FPalgorithm alternates between the rounding and projectionsteps until (b
119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896(which implies
feasibility) or the number of iterations 119896 has reached thepredefined limit 119870 The workflow of a corresponding FPalgorithm is illustrated in the following part
FP Algorithm for Non-Convex MINLP(0) INITIALIZATION input119870 set 119896 = 1
solve (34a)ndash(34j) to obtain (b119875 p119875 b119878 p119878)119896
(1) WHILE (119896 lt 119870) do
(2) ROUNDING solve (35a)ndash(35j) to obtain(b119875 p119875 b119878 p119878)119896
(3) IF ((b119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896) THEN goto
step (6)(4) PROJECTION solve (36a)ndash(36j) to obtain
(b119875 p119875 b119878 p119878)119896+1
(5) Set 119896 = 119896 + 1
12 Mobile Information Systems
(6) OUTPUT solution (b119875 p119875 b119878 p119878)lowast
=
(b119875 p119875 b119878 p119878)119896
Note that in order to retain the convergence of thealgorithm both problems (35a)ndash(35j) and (36a)ndash(36j) needto be solved exactly Problem (36a)ndash(36j) (and consequentlyproblem (34a)ndash(34j)) can be solved using any standard NLPmethod In this paper an interior point algorithm (describedeg in [32]) with polynomial complexity is applied to solve(36a)ndash(36j) and (34a)ndash(34j) MILP problem (35a)ndash(35j) isrelatively simple and therefore can be solved efficiently foroptimality by any technique from the family of the branch-and-bound methods (eg [26])
33 Target Buffer Size for PUs and Feasibility Issues Recallthat 119871
119894represents the target buffer size for PU
119894 which
indicates that the QoS requirements of PU119894are satisfied By
limiting the buffer size of PUs we restrict the QoS of PUs(measured in terms of their buffer size) to be higher (or atleast not smaller) than the required minimum From thispoint of view constraints (5) and (12) guarantee the QoSprotection of PUs in Scenario 1 and Scenario 2 respectivelyApparently one can always restrict the target buffer size ofPUs to be equal to zero so that after each subsequent dataarrival the buffer of each PU is fully cleared This approachrepresents a ldquogreedyrdquo policy which ensures that the PUs arealways served with the best possible QoS but does not guar-antee that some spare capacity will be left to serve the SUs
A ldquoless greedyrdquo strategy would be to establish somelower bound on QoS for the PUs which will provide anldquoopportunityrdquo for SUs to be served To establish this lowerbound recall that the growing delay and loss indicate thata buffer of a corresponding node is congested whereas inan uncongested node the packet delay and loss are alwaysminimal [33] On the other hand it has been reported in[33 34] that in an uncongested node the buffer size 119902(119905) isincreasing very slowly that is 119902(119905 + 1)119902(119905) asymp 1 whereas ina congested node the buffer size is growing very fast so that119902(119905+1)119902(119905) ≫ 1 Hence to serve the PUs withminimal delayand loss it is enough to prevent the growth of their buffersthat is for each PU set
119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)
where 120576 ge 0 is some small value such that
120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)
More sophisticated approach to find the lowerQoS boundcan be deployed if information about the past buffer size isavailable at any time slot 119905 In this case one can set the targetbuffer size based on past T observations 119902(119905) 119902(119905 minus 119879 + 1)as
119871119894= min120591isinT
119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38a)
or
119871119894=
1
119879
sum
120591isinT119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38b)
where T = 1 119879
UBADPC MBC
60
70
80
90
100
110
120
130
140
Alg
orith
m it
erat
ions
10020 8040 50 60 7030 90100Number of SUs m
120572i = 1 v = m lowast 1Mbps
Figure 1 Average number of iterations before convergence as afunction of number of SUs in simulations with 119899 = 100 PUs andaverage SNR = 0 dB
MBC
070
075
080
085
090
095
100
120572i=0
v=0
120572i=1
v=0
120572i=0
v=m
lowast1
Mbp
s
120572i=1
v=m
lowast1
Mbp
s
Fairness among SUs FSU
Fairness among PUs FPU
Fairness among all users F
Figure 2 Jainrsquos index of fairness119865SU119865PU and119865 for the PUs SUs andall users in simulations with 119899 = 100 PUs119898 = 100 SUs and averageSNR = 0 dB
In some (very rare) cases (when the service capacity of theeNB is not enough to guarantee that the buffer sizes in all PUsdo not exceed the target buffer size) constraints (5) and (12)in Scenarios 1 and 2 may be not feasible In the following weshow how to identify such situation and what should be theoptimal resource allocation strategy in this case
Note that the service capacity of LTE system greatlydepends on physical characteristics (eg SINR and MCS) of
Mobile Information Systems 13
UBADPCGBC
NBCMBCABC
780
800
820
840
860
880
900
920
940
960Th
roug
hput
for P
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r PU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for P
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
Figure 3 Mean throughput packet delay and loss for PUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
the wireless channels between the eNB and the users Henceat the moment preceding the bandwidthpower allocation itis rather difficult to estimate the service capacity of a systemNevertheless it is possible to find the average service capacityand to determine the upper and lower bounds on servicecapacity of the eNB in the UL and DL directions such that
119877min le sum119894isinI119903119875119894(119905) asymp 119877ave le 119877max (39)
where119877min119877ave and119877max are the lower bound upper boundand average service capacity of the eNB respectively
In our case the upper bound on service capacity of theeNB is given by
119877max = 120596120595119861 log (1 + 119892 (SNRmax) sdot SNRmax) (40a)
where SNRmax is the maximal possible SNR value
The lower bound on service capacity of eNB is
119877min = 120596120595119861 log (1 + 119892 (SNRmin) sdot SNRmin) (40b)
where SNRmin is the minimal possible SNR valueThe average service capacity of the eNB equals
119877ave = 120596120595119861 log (1 + 119892 (SNRave) sdot SNRave) (40c)
where SNRave is the average SNR valueIf SNR information is available then the values SNRmax
SNRmin and SNRave can be set as
SNRmax = max119894isinI
SNR119894 (41a)
14 Mobile Information Systems
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r SU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for S
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
Figure 4 Mean throughput packet delay and loss for SUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
SNRmin = min119894isinI
SNR119894 (41b)
SNRave =1
119899
sum
119894isinISNR119894 (41c)
Otherwise (ie if SNR information is not available) thevalues are set arbitrarily
Now we can identify the situation when constraints (5)and (12) cannot be satisfied For this we should perform thefollowing test For Scenario 1 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus 119871
119894) (42)
then constraint (5) is feasible Otherwise condition (5)cannot be satisfiedHence all the SUs receive zero allocations
andwe assign the bandwidthpower resources only to the PUsby solving the following optimization problem
minimize max119894isinI
lceil119902119875119894+ 119886119875119894minus 119903119875119894(b119875 p119875)rceil+
(43a)
subject to 119903119875119894(b119875 p119875) le 119902119875119894+ 119886119875119894 forall119894 isin I (43b)
sum
119894isinI119887119875119894le 119861 (43c)
119887119875119894isin Z+ forall119894 isin I (43d)
119901119875119894le 119875119875119894 forall119894 isin I (43e)
119901119875119894ge 0 forall119894 isin I (43f)
Mobile Information Systems 15
725
750
775
800
825
850
875
900
925
950Th
roug
hput
for P
Us (
kbits
s)
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
10
20
30
40
50
60
70
Dela
y fo
r PU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Loss
for P
Us (
)
0
005
01
015
02
025
03
035
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Figure 5 Mean throughput packet delay and loss for PUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
for the UL direction For the DL directions constraint (43e)should be replaced by
sum
119894isinI119901119875119894le 119875eNB (43g)
For Scenario 2 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus (1 + 120572
119894) 119871119894) (44)
then constraint (12) is feasible Otherwise inequality (12)cannot be satisfied and the bandwidthpower resources areassigned only to the PUs (according to (43a)ndash(43g)) whereasthe SUs receive zero allocations
4 Performance Evaluation
41 Simulation Model A simulation model of the networkconsisting of one eNB 119899 PUs and 119898 SUs randomly locatedin a service area with 3 km radius has been developed upona standard LTE platform using the OPNET package [35]Thebandwidth of the eNB equals 119861 = 50RBs (which is equivalentto 10MHz) The slot duration in the algorithm equals 119879
119904=
1msThemaximal number of iterations in FP algorithm is set119870 = 200Themaximal transmission power of the eNB equals119875eNB = 46 dBm and the maximal transmission power of eachPUSU equals 119875
1198751= sdot sdot sdot = 119875
119875119899= 1198751198781= sdot sdot sdot = 119875
119878119898= 23 dBm
Other simulation settings of the model are listed in Table 2(all the parameters are based on LTE specifications [36])
16 Mobile Information Systems
Table 2 Simulation parameters of the model
Parameter ValueRadio network model
Pass loss 119871 = 40log10119877 + 30log
10119891 + 49 119877 distance (km) 119891
carrier frequency (Hz)
Shadow fading Log-normal shadow fading with a standard deviation of1012 dB for outdoorindoor users
Penetration loss The average building penetration loss is 12 dB with astandard deviation of 8 dB
Multipath fading Spatial Channel Model (SCM) Suburban macroUE velocity 0 kmsTransmitterreceiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver noise figure 5 dBThermal noise density minus174 dBmHzCableconnectorcombiner losses 2 dB
Physical profileOperation mode FDDCyclic prefix type Normal (7 symbols per slot)Evolved packet core (EPC) bearer definitions 348 kbits (nonguaranteed bit rate)Subcarrier spacing 15 kHz
Admission control parametersPhysical downlink control channel (PDCCH) symbols per subframe 3UL loading factor 1DL loading factor 1Inactive bearer timeout 20 sec
Buffer status report parametersPeriodic timer 5 subframesRetransmission timer 2560 subframes
L1L2 control parametersReserved size 2 RBsCyclic shifts 6Starting RB preserver for Format 1 messages 0Allocation periodicity 5 subframes
Random access (RA) parametersNumber of preambles 64Preamble format Format 0 (1-subframe long)Number of RA resources per frame 4Preamble retransmission limit 5 subframesRA response timer 5 subframesContention resolution timer 40 subframes
HARQ parametersMaximal number of retransmissions 3 (UL and DL)HARQ retransmission timer 8 subframes (UL and DL)Maximal number of HARQ processes 8 per UE (UL and DL)
A radio model of the network corresponds to the require-ments of ITU-T Recommendation M1225
The algorithms proposed in the paper are denoted asfollows
(i) GBC (greedy buffer Control) where the target buffersize equals 0 for all the PUs
(ii) NBC (nongreedy buffer control) with the target buffersize calculated according to (37a) and (37b)
(iii) MBC (Minimal Buffer Control) with 119879 = 10 slots andthe target buffer size given by (38a)
(iv) ABC (Average Buffer Control) with 119879 = 10 slots andthe target buffer size equaling (38b)
Two previously proposed schemes used to benchmark theperformance of the algorithms proposed in this paper are
(i) UBA (Utility Based Allocation) presented in [11]where the network resources (bandwidth and trans-mission power) are allocated to the UL channels tomaximize the total transmission rate of the userssubject to the capacity and transmission power con-straints
Mobile Information Systems 17
0 10 20 30 40 50 60 70 80Average SNR (dB)
UBADPCGBC
NBCMBCABC
30
35
40
45
50
55
60
65
70
Dela
y fo
r SU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
012
015
018
021
024
027
03
033
Loss
for S
Us (
)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
250
300
350
400
450
500Th
roug
hput
for S
Us (
kbits
s)
Figure 6 Mean throughput packet delay and loss for SUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
(ii) DPC (Delay Power Control) derived in [5] whichis used to balance the transmission delay againsttransmission power in wireless channels between theeNB and the users
We also gather simulation results for a proposed resourceallocation approach in Scenario 2 with different settings ofthe parameters120572
119894and V and benchmark its performancewith
the performance of the algorithm in Scenario 1All algorithms are simulated using identical settings
The data traffic in simulations is represented by voice overInternet Protocol (VoIP) video and Hypertext TransferProtocol (HTTP) applications mixed in proportion 2 3 5using the models defined in [37]
42 Complexity and Fairness Issues Let us first evaluatethe complexity and the fairness of resource allocation indifferent algorithms Figure 1 shows the average numberof iterations before convergence for UBA DPC and theproposed algorithms in Scenario 1 (denoted as MBC) andScenario 2 gathered in simulations with 119899 = 100 PUs andaverage SNR = 0 dB Note that the target buffer size for thePUs is calculated according to (38a) with T = 10 slots (inScenarios 1 and 2) and 120572
119894= 1 V = 119898 lowast 1Mbps (for
Scenario 2) Results demonstrate that the complexity of FPmethod deployed for resource allocation in Scenarios 1 and2 is exponential in size of the problem (which correspondsto the findings reported in [31]) and is comparable to thecomplexities of other techniques (UBA and DPC)
18 Mobile Information Systems
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
080020 090070050 060 100000 030010 040120572i
10
20
30
40
50
60
70
80
90
100
110
Dela
y fo
r PU
s (m
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
040030 090000 080060010 020 050 100070120572i
005
010
015
020
025
030
035
040
045
050
Loss
for P
Us (
)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
030020 040 090010 060 070 080 100000 050120572i
Figure 7 Mean throughput packet delay and loss for the PUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
Figure 2 shows the fairness of different methods calcu-lated according to Jainrsquos equation [38] as
119865PU =
(sum119894isinI 119903119875119894)
2
119899 sdot sum119894isinI 1199032
119875119894
119865SU =
(sum119895isinJ 119903119878119895)
2
119898 sdot sum119895isinJ 1199032
119878119895
119865 =
(sum119894isinI 119903119875119894 + sum119895isinJ 119903119878119895)
2
(119899 + 119898) sdot (sum119894isinI 1199032
119875119894+ sum119895isinJ 1199032
119878119895)
(45)
where 119865PU 119865SU and 119865 stand for Jainrsquos index of fairness forthe PUs SUs and all of the users respectively 119903
119875119894 119903119878119895
arethe mean throughputs for PU
119894and SU
119895 respectively Results
have been gathered for 119899 = 100 PUs 119898 = 100 SUs average
Mobile Information Systems 19
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
410
420
430
440
450
460
470
480
490
500
510Th
roug
hput
for S
Us (
kbits
s)
010 020 080 090050 060 070030 100000 040120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
15
20
25
30
35
40
45
50
Dela
y fo
r SU
s (m
s)
070 090030 040 050 080000 020010 100060120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
007
009
011
013
015
017
019
021
023
Loss
for S
Us (
)
080070 090020 050 060030 100040010000120572i
Figure 8 Mean throughput packet delay and loss for the SUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
SNR = 0 dB and target buffer size for the PUs calculatedaccording to (38a) (Scenarios 1 and 2) with different settingsof 120572119894and V in Scenario 2
It follows from these graphs that the fairness index amongall of the users (denoted as 119865) is higher in Scenario 2 with120572119894= 1 and lower in Scenario 1 and Scenario 2 with 120572
119894= 0
Such results are rather expectable in Scenario 1 and Scenario2 with 120572
119894= 0 the SUs are served for free on a best-effort
basis whereas the PUs enjoy full QoS guarantees Hence thenetwork resources are shared nonequally between the PUs
and the SUs with most of the RBs allocated to the PUs andthe rest of the bandwidth distributed among the SUs Onthe other hand the fairness index for the PUs and SUs (ie119865PU and 119865SU) is rather high in both scenarios with differentsettings of 120572
119894and V which indicates that the users of the same
type are treated equally during resource allocation
43 Simulation Results in Scenario 1 Let us evaluate theperformance of a resource allocation algorithm in Scenario1 in terms of mean throughput packet end-to-end delay and
20 Mobile Information Systems
MBC
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
20
30
40
50
60
70
80
90
Dela
y fo
r PU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
005
010
015
020
025
030
035
040
045
Loss
for P
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 9 Mean throughput packet delay and loss for the PUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
loss for different user types Figures 3ndash6 show results obtainedin simulations with 119899 = 100 PUs and average SNR = 0 dBResults demonstrate that aUBA scheme has the largest packetdelay and loss and the lowest throughput for both the PUs andthe SUs A poor performance of this scheme is explained asfollows
(i) QoS protection of PUs is not considered in UBAHence the throughput delay and loss are the samefor PUs and SUs
(ii) Buffer sizes of individual users are not consideredin resource allocation and therefore the QoS for
Mobile Information Systems 21
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
30
50
70
90
110
130
Dela
y fo
r SU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
000
010
020
030
040
050
060
Loss
for S
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
different users varies significantly (since differentusers have different traffic demands)
(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer
size and therefore there is no need to maximize theirtransmission rate and spend the network resources
Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
10 Mobile Information Systems
method for solving MINLPs is a well-known branch-and-bound algorithmand its variousmodifications [26] examplesof heuristic approaches include local branching [27] largeneighborhood search [28] and feasibility pump [29] to namea few Since we are interested in a reasonably simple and fastalgorithm it is more convenient to use heuristics for solvingthe problem In this paper a Feasibility Pump (FP) heuristic[29 30] is applied to solve (32a)ndash(32j) FP is perhaps the mostsimple and most effective method for producing more andbetter solutions in a shorter average running time For theproblems with nonbinary integer variables the complexity ofFP is exponential in size of a problem [31]
A fundamental idea of FP algorithm is to decomposethe problem into two parts integer feasibility and constraint
feasibility The former is achieved by rounding (solvinga NLP relaxation to the original problem) and the latterby projection (solving a MILP relaxation) Consequentlytwo sequences of points are generated The first sequence(b119875 p119875 b119878 p119878)119896119870
119896=1 119870 = 1 2 contains the integral
points that may violate the nonlinear constraintsThe secondsequence (b
119875 p119875 b119878 p119878)119896119870
119896=1contains the points which are
feasible for a continuous relaxation to the original problembut might not be integral
More specifically with input (b119875 p119875 b119878 p119878)1being a
solution to the NLP relaxation given by (34a)ndash(34j) thealgorithm generates two sequences by solving the followingproblems for 119896 = 1 119870
(b119875 p119875 b119878 p119878)119896= argmin
100381710038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b
119875 p119875 b119878 p119878)119896
1003817100381710038171003817100381710038171
(35a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (35b)
119887119875119894isin Z+
119887119878119895isin Z+
forall119894 isin I forall119895 isin J
(35c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(35d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(35e)
Ω ge 0
Φ ge 0
(35f)
119891
1
119894(b0119875 p0119875) + nabla
119891
1
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35g)
119891
2
119894(b0119875 p0119875) + nabla
119891
2
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35h)
119891
3
119894(b0119875 p0119875) + nabla
119891
3
119894(b0119875 p0119875)
119879
[
b119875minus b0119875
p119875minus p0119875
] le 0
forall119894 isin I
(35i)
Mobile Information Systems 11
119891
4
119895(b0119878 p0119878) + nabla
119891
4
119895(b0119878 p0119878)
119879
[
b119878minus b0119878
p119878minus p0119878
] le 0
forall119895 isin J
(35j)
(b119875 p119875 b119878 p119878)119896+1
= argmin 10038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b
119875 p119875 b119878 p119878)119896
100381710038171003817100381710038172
(36a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (36b)
119887119875119894ge 0
119887119878119895ge 0
forall119894 isin I forall119895 isin J
(36c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(36d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(36e)
Ω ge 0
Φ ge 0
(36f)
119891
1
119894(b119875 p119875) le 0
forall119894 isin I(36g)
119891
2
119894(b119875 p119875) le 0
forall119894 isin I(36h)
119891
3
119894(b119875 p119875) le 0
forall119894 isin I(36i)
119891
4
119895(b119878 p119878) le 0
forall119895 isin J(36j)
where sdot1and sdot
2are 1198971norm and 119897
2norm respectivelyThe
rounding step is carried out by solving (35a)ndash(35j) whereasthe projection is the solution to (36a)ndash(36j) A suggested FPalgorithm alternates between the rounding and projectionsteps until (b
119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896(which implies
feasibility) or the number of iterations 119896 has reached thepredefined limit 119870 The workflow of a corresponding FPalgorithm is illustrated in the following part
FP Algorithm for Non-Convex MINLP(0) INITIALIZATION input119870 set 119896 = 1
solve (34a)ndash(34j) to obtain (b119875 p119875 b119878 p119878)119896
(1) WHILE (119896 lt 119870) do
(2) ROUNDING solve (35a)ndash(35j) to obtain(b119875 p119875 b119878 p119878)119896
(3) IF ((b119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896) THEN goto
step (6)(4) PROJECTION solve (36a)ndash(36j) to obtain
(b119875 p119875 b119878 p119878)119896+1
(5) Set 119896 = 119896 + 1
12 Mobile Information Systems
(6) OUTPUT solution (b119875 p119875 b119878 p119878)lowast
=
(b119875 p119875 b119878 p119878)119896
Note that in order to retain the convergence of thealgorithm both problems (35a)ndash(35j) and (36a)ndash(36j) needto be solved exactly Problem (36a)ndash(36j) (and consequentlyproblem (34a)ndash(34j)) can be solved using any standard NLPmethod In this paper an interior point algorithm (describedeg in [32]) with polynomial complexity is applied to solve(36a)ndash(36j) and (34a)ndash(34j) MILP problem (35a)ndash(35j) isrelatively simple and therefore can be solved efficiently foroptimality by any technique from the family of the branch-and-bound methods (eg [26])
33 Target Buffer Size for PUs and Feasibility Issues Recallthat 119871
119894represents the target buffer size for PU
119894 which
indicates that the QoS requirements of PU119894are satisfied By
limiting the buffer size of PUs we restrict the QoS of PUs(measured in terms of their buffer size) to be higher (or atleast not smaller) than the required minimum From thispoint of view constraints (5) and (12) guarantee the QoSprotection of PUs in Scenario 1 and Scenario 2 respectivelyApparently one can always restrict the target buffer size ofPUs to be equal to zero so that after each subsequent dataarrival the buffer of each PU is fully cleared This approachrepresents a ldquogreedyrdquo policy which ensures that the PUs arealways served with the best possible QoS but does not guar-antee that some spare capacity will be left to serve the SUs
A ldquoless greedyrdquo strategy would be to establish somelower bound on QoS for the PUs which will provide anldquoopportunityrdquo for SUs to be served To establish this lowerbound recall that the growing delay and loss indicate thata buffer of a corresponding node is congested whereas inan uncongested node the packet delay and loss are alwaysminimal [33] On the other hand it has been reported in[33 34] that in an uncongested node the buffer size 119902(119905) isincreasing very slowly that is 119902(119905 + 1)119902(119905) asymp 1 whereas ina congested node the buffer size is growing very fast so that119902(119905+1)119902(119905) ≫ 1 Hence to serve the PUs withminimal delayand loss it is enough to prevent the growth of their buffersthat is for each PU set
119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)
where 120576 ge 0 is some small value such that
120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)
More sophisticated approach to find the lowerQoS boundcan be deployed if information about the past buffer size isavailable at any time slot 119905 In this case one can set the targetbuffer size based on past T observations 119902(119905) 119902(119905 minus 119879 + 1)as
119871119894= min120591isinT
119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38a)
or
119871119894=
1
119879
sum
120591isinT119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38b)
where T = 1 119879
UBADPC MBC
60
70
80
90
100
110
120
130
140
Alg
orith
m it
erat
ions
10020 8040 50 60 7030 90100Number of SUs m
120572i = 1 v = m lowast 1Mbps
Figure 1 Average number of iterations before convergence as afunction of number of SUs in simulations with 119899 = 100 PUs andaverage SNR = 0 dB
MBC
070
075
080
085
090
095
100
120572i=0
v=0
120572i=1
v=0
120572i=0
v=m
lowast1
Mbp
s
120572i=1
v=m
lowast1
Mbp
s
Fairness among SUs FSU
Fairness among PUs FPU
Fairness among all users F
Figure 2 Jainrsquos index of fairness119865SU119865PU and119865 for the PUs SUs andall users in simulations with 119899 = 100 PUs119898 = 100 SUs and averageSNR = 0 dB
In some (very rare) cases (when the service capacity of theeNB is not enough to guarantee that the buffer sizes in all PUsdo not exceed the target buffer size) constraints (5) and (12)in Scenarios 1 and 2 may be not feasible In the following weshow how to identify such situation and what should be theoptimal resource allocation strategy in this case
Note that the service capacity of LTE system greatlydepends on physical characteristics (eg SINR and MCS) of
Mobile Information Systems 13
UBADPCGBC
NBCMBCABC
780
800
820
840
860
880
900
920
940
960Th
roug
hput
for P
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r PU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for P
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
Figure 3 Mean throughput packet delay and loss for PUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
the wireless channels between the eNB and the users Henceat the moment preceding the bandwidthpower allocation itis rather difficult to estimate the service capacity of a systemNevertheless it is possible to find the average service capacityand to determine the upper and lower bounds on servicecapacity of the eNB in the UL and DL directions such that
119877min le sum119894isinI119903119875119894(119905) asymp 119877ave le 119877max (39)
where119877min119877ave and119877max are the lower bound upper boundand average service capacity of the eNB respectively
In our case the upper bound on service capacity of theeNB is given by
119877max = 120596120595119861 log (1 + 119892 (SNRmax) sdot SNRmax) (40a)
where SNRmax is the maximal possible SNR value
The lower bound on service capacity of eNB is
119877min = 120596120595119861 log (1 + 119892 (SNRmin) sdot SNRmin) (40b)
where SNRmin is the minimal possible SNR valueThe average service capacity of the eNB equals
119877ave = 120596120595119861 log (1 + 119892 (SNRave) sdot SNRave) (40c)
where SNRave is the average SNR valueIf SNR information is available then the values SNRmax
SNRmin and SNRave can be set as
SNRmax = max119894isinI
SNR119894 (41a)
14 Mobile Information Systems
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r SU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for S
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
Figure 4 Mean throughput packet delay and loss for SUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
SNRmin = min119894isinI
SNR119894 (41b)
SNRave =1
119899
sum
119894isinISNR119894 (41c)
Otherwise (ie if SNR information is not available) thevalues are set arbitrarily
Now we can identify the situation when constraints (5)and (12) cannot be satisfied For this we should perform thefollowing test For Scenario 1 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus 119871
119894) (42)
then constraint (5) is feasible Otherwise condition (5)cannot be satisfiedHence all the SUs receive zero allocations
andwe assign the bandwidthpower resources only to the PUsby solving the following optimization problem
minimize max119894isinI
lceil119902119875119894+ 119886119875119894minus 119903119875119894(b119875 p119875)rceil+
(43a)
subject to 119903119875119894(b119875 p119875) le 119902119875119894+ 119886119875119894 forall119894 isin I (43b)
sum
119894isinI119887119875119894le 119861 (43c)
119887119875119894isin Z+ forall119894 isin I (43d)
119901119875119894le 119875119875119894 forall119894 isin I (43e)
119901119875119894ge 0 forall119894 isin I (43f)
Mobile Information Systems 15
725
750
775
800
825
850
875
900
925
950Th
roug
hput
for P
Us (
kbits
s)
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
10
20
30
40
50
60
70
Dela
y fo
r PU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Loss
for P
Us (
)
0
005
01
015
02
025
03
035
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Figure 5 Mean throughput packet delay and loss for PUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
for the UL direction For the DL directions constraint (43e)should be replaced by
sum
119894isinI119901119875119894le 119875eNB (43g)
For Scenario 2 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus (1 + 120572
119894) 119871119894) (44)
then constraint (12) is feasible Otherwise inequality (12)cannot be satisfied and the bandwidthpower resources areassigned only to the PUs (according to (43a)ndash(43g)) whereasthe SUs receive zero allocations
4 Performance Evaluation
41 Simulation Model A simulation model of the networkconsisting of one eNB 119899 PUs and 119898 SUs randomly locatedin a service area with 3 km radius has been developed upona standard LTE platform using the OPNET package [35]Thebandwidth of the eNB equals 119861 = 50RBs (which is equivalentto 10MHz) The slot duration in the algorithm equals 119879
119904=
1msThemaximal number of iterations in FP algorithm is set119870 = 200Themaximal transmission power of the eNB equals119875eNB = 46 dBm and the maximal transmission power of eachPUSU equals 119875
1198751= sdot sdot sdot = 119875
119875119899= 1198751198781= sdot sdot sdot = 119875
119878119898= 23 dBm
Other simulation settings of the model are listed in Table 2(all the parameters are based on LTE specifications [36])
16 Mobile Information Systems
Table 2 Simulation parameters of the model
Parameter ValueRadio network model
Pass loss 119871 = 40log10119877 + 30log
10119891 + 49 119877 distance (km) 119891
carrier frequency (Hz)
Shadow fading Log-normal shadow fading with a standard deviation of1012 dB for outdoorindoor users
Penetration loss The average building penetration loss is 12 dB with astandard deviation of 8 dB
Multipath fading Spatial Channel Model (SCM) Suburban macroUE velocity 0 kmsTransmitterreceiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver noise figure 5 dBThermal noise density minus174 dBmHzCableconnectorcombiner losses 2 dB
Physical profileOperation mode FDDCyclic prefix type Normal (7 symbols per slot)Evolved packet core (EPC) bearer definitions 348 kbits (nonguaranteed bit rate)Subcarrier spacing 15 kHz
Admission control parametersPhysical downlink control channel (PDCCH) symbols per subframe 3UL loading factor 1DL loading factor 1Inactive bearer timeout 20 sec
Buffer status report parametersPeriodic timer 5 subframesRetransmission timer 2560 subframes
L1L2 control parametersReserved size 2 RBsCyclic shifts 6Starting RB preserver for Format 1 messages 0Allocation periodicity 5 subframes
Random access (RA) parametersNumber of preambles 64Preamble format Format 0 (1-subframe long)Number of RA resources per frame 4Preamble retransmission limit 5 subframesRA response timer 5 subframesContention resolution timer 40 subframes
HARQ parametersMaximal number of retransmissions 3 (UL and DL)HARQ retransmission timer 8 subframes (UL and DL)Maximal number of HARQ processes 8 per UE (UL and DL)
A radio model of the network corresponds to the require-ments of ITU-T Recommendation M1225
The algorithms proposed in the paper are denoted asfollows
(i) GBC (greedy buffer Control) where the target buffersize equals 0 for all the PUs
(ii) NBC (nongreedy buffer control) with the target buffersize calculated according to (37a) and (37b)
(iii) MBC (Minimal Buffer Control) with 119879 = 10 slots andthe target buffer size given by (38a)
(iv) ABC (Average Buffer Control) with 119879 = 10 slots andthe target buffer size equaling (38b)
Two previously proposed schemes used to benchmark theperformance of the algorithms proposed in this paper are
(i) UBA (Utility Based Allocation) presented in [11]where the network resources (bandwidth and trans-mission power) are allocated to the UL channels tomaximize the total transmission rate of the userssubject to the capacity and transmission power con-straints
Mobile Information Systems 17
0 10 20 30 40 50 60 70 80Average SNR (dB)
UBADPCGBC
NBCMBCABC
30
35
40
45
50
55
60
65
70
Dela
y fo
r SU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
012
015
018
021
024
027
03
033
Loss
for S
Us (
)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
250
300
350
400
450
500Th
roug
hput
for S
Us (
kbits
s)
Figure 6 Mean throughput packet delay and loss for SUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
(ii) DPC (Delay Power Control) derived in [5] whichis used to balance the transmission delay againsttransmission power in wireless channels between theeNB and the users
We also gather simulation results for a proposed resourceallocation approach in Scenario 2 with different settings ofthe parameters120572
119894and V and benchmark its performancewith
the performance of the algorithm in Scenario 1All algorithms are simulated using identical settings
The data traffic in simulations is represented by voice overInternet Protocol (VoIP) video and Hypertext TransferProtocol (HTTP) applications mixed in proportion 2 3 5using the models defined in [37]
42 Complexity and Fairness Issues Let us first evaluatethe complexity and the fairness of resource allocation indifferent algorithms Figure 1 shows the average numberof iterations before convergence for UBA DPC and theproposed algorithms in Scenario 1 (denoted as MBC) andScenario 2 gathered in simulations with 119899 = 100 PUs andaverage SNR = 0 dB Note that the target buffer size for thePUs is calculated according to (38a) with T = 10 slots (inScenarios 1 and 2) and 120572
119894= 1 V = 119898 lowast 1Mbps (for
Scenario 2) Results demonstrate that the complexity of FPmethod deployed for resource allocation in Scenarios 1 and2 is exponential in size of the problem (which correspondsto the findings reported in [31]) and is comparable to thecomplexities of other techniques (UBA and DPC)
18 Mobile Information Systems
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
080020 090070050 060 100000 030010 040120572i
10
20
30
40
50
60
70
80
90
100
110
Dela
y fo
r PU
s (m
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
040030 090000 080060010 020 050 100070120572i
005
010
015
020
025
030
035
040
045
050
Loss
for P
Us (
)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
030020 040 090010 060 070 080 100000 050120572i
Figure 7 Mean throughput packet delay and loss for the PUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
Figure 2 shows the fairness of different methods calcu-lated according to Jainrsquos equation [38] as
119865PU =
(sum119894isinI 119903119875119894)
2
119899 sdot sum119894isinI 1199032
119875119894
119865SU =
(sum119895isinJ 119903119878119895)
2
119898 sdot sum119895isinJ 1199032
119878119895
119865 =
(sum119894isinI 119903119875119894 + sum119895isinJ 119903119878119895)
2
(119899 + 119898) sdot (sum119894isinI 1199032
119875119894+ sum119895isinJ 1199032
119878119895)
(45)
where 119865PU 119865SU and 119865 stand for Jainrsquos index of fairness forthe PUs SUs and all of the users respectively 119903
119875119894 119903119878119895
arethe mean throughputs for PU
119894and SU
119895 respectively Results
have been gathered for 119899 = 100 PUs 119898 = 100 SUs average
Mobile Information Systems 19
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
410
420
430
440
450
460
470
480
490
500
510Th
roug
hput
for S
Us (
kbits
s)
010 020 080 090050 060 070030 100000 040120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
15
20
25
30
35
40
45
50
Dela
y fo
r SU
s (m
s)
070 090030 040 050 080000 020010 100060120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
007
009
011
013
015
017
019
021
023
Loss
for S
Us (
)
080070 090020 050 060030 100040010000120572i
Figure 8 Mean throughput packet delay and loss for the SUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
SNR = 0 dB and target buffer size for the PUs calculatedaccording to (38a) (Scenarios 1 and 2) with different settingsof 120572119894and V in Scenario 2
It follows from these graphs that the fairness index amongall of the users (denoted as 119865) is higher in Scenario 2 with120572119894= 1 and lower in Scenario 1 and Scenario 2 with 120572
119894= 0
Such results are rather expectable in Scenario 1 and Scenario2 with 120572
119894= 0 the SUs are served for free on a best-effort
basis whereas the PUs enjoy full QoS guarantees Hence thenetwork resources are shared nonequally between the PUs
and the SUs with most of the RBs allocated to the PUs andthe rest of the bandwidth distributed among the SUs Onthe other hand the fairness index for the PUs and SUs (ie119865PU and 119865SU) is rather high in both scenarios with differentsettings of 120572
119894and V which indicates that the users of the same
type are treated equally during resource allocation
43 Simulation Results in Scenario 1 Let us evaluate theperformance of a resource allocation algorithm in Scenario1 in terms of mean throughput packet end-to-end delay and
20 Mobile Information Systems
MBC
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
20
30
40
50
60
70
80
90
Dela
y fo
r PU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
005
010
015
020
025
030
035
040
045
Loss
for P
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 9 Mean throughput packet delay and loss for the PUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
loss for different user types Figures 3ndash6 show results obtainedin simulations with 119899 = 100 PUs and average SNR = 0 dBResults demonstrate that aUBA scheme has the largest packetdelay and loss and the lowest throughput for both the PUs andthe SUs A poor performance of this scheme is explained asfollows
(i) QoS protection of PUs is not considered in UBAHence the throughput delay and loss are the samefor PUs and SUs
(ii) Buffer sizes of individual users are not consideredin resource allocation and therefore the QoS for
Mobile Information Systems 21
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
30
50
70
90
110
130
Dela
y fo
r SU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
000
010
020
030
040
050
060
Loss
for S
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
different users varies significantly (since differentusers have different traffic demands)
(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer
size and therefore there is no need to maximize theirtransmission rate and spend the network resources
Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mobile Information Systems 11
119891
4
119895(b0119878 p0119878) + nabla
119891
4
119895(b0119878 p0119878)
119879
[
b119878minus b0119878
p119878minus p0119878
] le 0
forall119895 isin J
(35j)
(b119875 p119875 b119878 p119878)119896+1
= argmin 10038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b
119875 p119875 b119878 p119878)119896
100381710038171003817100381710038172
(36a)
subject to sum
119894isinI119887119875119894+sum
119895isinJ119887119878119895le 119861 (36b)
119887119875119894ge 0
119887119878119895ge 0
forall119894 isin I forall119895 isin J
(36c)
119901119875119894le 119875119875119894
119901119878119895le 119875119878119895
forall119894 isin I forall119895 isin J
(36d)
119901119875119894ge 0
119901119878119895ge 0
forall119894 isin I forall119895 isin J
(36e)
Ω ge 0
Φ ge 0
(36f)
119891
1
119894(b119875 p119875) le 0
forall119894 isin I(36g)
119891
2
119894(b119875 p119875) le 0
forall119894 isin I(36h)
119891
3
119894(b119875 p119875) le 0
forall119894 isin I(36i)
119891
4
119895(b119878 p119878) le 0
forall119895 isin J(36j)
where sdot1and sdot
2are 1198971norm and 119897
2norm respectivelyThe
rounding step is carried out by solving (35a)ndash(35j) whereasthe projection is the solution to (36a)ndash(36j) A suggested FPalgorithm alternates between the rounding and projectionsteps until (b
119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896(which implies
feasibility) or the number of iterations 119896 has reached thepredefined limit 119870 The workflow of a corresponding FPalgorithm is illustrated in the following part
FP Algorithm for Non-Convex MINLP(0) INITIALIZATION input119870 set 119896 = 1
solve (34a)ndash(34j) to obtain (b119875 p119875 b119878 p119878)119896
(1) WHILE (119896 lt 119870) do
(2) ROUNDING solve (35a)ndash(35j) to obtain(b119875 p119875 b119878 p119878)119896
(3) IF ((b119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896) THEN goto
step (6)(4) PROJECTION solve (36a)ndash(36j) to obtain
(b119875 p119875 b119878 p119878)119896+1
(5) Set 119896 = 119896 + 1
12 Mobile Information Systems
(6) OUTPUT solution (b119875 p119875 b119878 p119878)lowast
=
(b119875 p119875 b119878 p119878)119896
Note that in order to retain the convergence of thealgorithm both problems (35a)ndash(35j) and (36a)ndash(36j) needto be solved exactly Problem (36a)ndash(36j) (and consequentlyproblem (34a)ndash(34j)) can be solved using any standard NLPmethod In this paper an interior point algorithm (describedeg in [32]) with polynomial complexity is applied to solve(36a)ndash(36j) and (34a)ndash(34j) MILP problem (35a)ndash(35j) isrelatively simple and therefore can be solved efficiently foroptimality by any technique from the family of the branch-and-bound methods (eg [26])
33 Target Buffer Size for PUs and Feasibility Issues Recallthat 119871
119894represents the target buffer size for PU
119894 which
indicates that the QoS requirements of PU119894are satisfied By
limiting the buffer size of PUs we restrict the QoS of PUs(measured in terms of their buffer size) to be higher (or atleast not smaller) than the required minimum From thispoint of view constraints (5) and (12) guarantee the QoSprotection of PUs in Scenario 1 and Scenario 2 respectivelyApparently one can always restrict the target buffer size ofPUs to be equal to zero so that after each subsequent dataarrival the buffer of each PU is fully cleared This approachrepresents a ldquogreedyrdquo policy which ensures that the PUs arealways served with the best possible QoS but does not guar-antee that some spare capacity will be left to serve the SUs
A ldquoless greedyrdquo strategy would be to establish somelower bound on QoS for the PUs which will provide anldquoopportunityrdquo for SUs to be served To establish this lowerbound recall that the growing delay and loss indicate thata buffer of a corresponding node is congested whereas inan uncongested node the packet delay and loss are alwaysminimal [33] On the other hand it has been reported in[33 34] that in an uncongested node the buffer size 119902(119905) isincreasing very slowly that is 119902(119905 + 1)119902(119905) asymp 1 whereas ina congested node the buffer size is growing very fast so that119902(119905+1)119902(119905) ≫ 1 Hence to serve the PUs withminimal delayand loss it is enough to prevent the growth of their buffersthat is for each PU set
119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)
where 120576 ge 0 is some small value such that
120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)
More sophisticated approach to find the lowerQoS boundcan be deployed if information about the past buffer size isavailable at any time slot 119905 In this case one can set the targetbuffer size based on past T observations 119902(119905) 119902(119905 minus 119879 + 1)as
119871119894= min120591isinT
119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38a)
or
119871119894=
1
119879
sum
120591isinT119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38b)
where T = 1 119879
UBADPC MBC
60
70
80
90
100
110
120
130
140
Alg
orith
m it
erat
ions
10020 8040 50 60 7030 90100Number of SUs m
120572i = 1 v = m lowast 1Mbps
Figure 1 Average number of iterations before convergence as afunction of number of SUs in simulations with 119899 = 100 PUs andaverage SNR = 0 dB
MBC
070
075
080
085
090
095
100
120572i=0
v=0
120572i=1
v=0
120572i=0
v=m
lowast1
Mbp
s
120572i=1
v=m
lowast1
Mbp
s
Fairness among SUs FSU
Fairness among PUs FPU
Fairness among all users F
Figure 2 Jainrsquos index of fairness119865SU119865PU and119865 for the PUs SUs andall users in simulations with 119899 = 100 PUs119898 = 100 SUs and averageSNR = 0 dB
In some (very rare) cases (when the service capacity of theeNB is not enough to guarantee that the buffer sizes in all PUsdo not exceed the target buffer size) constraints (5) and (12)in Scenarios 1 and 2 may be not feasible In the following weshow how to identify such situation and what should be theoptimal resource allocation strategy in this case
Note that the service capacity of LTE system greatlydepends on physical characteristics (eg SINR and MCS) of
Mobile Information Systems 13
UBADPCGBC
NBCMBCABC
780
800
820
840
860
880
900
920
940
960Th
roug
hput
for P
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r PU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for P
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
Figure 3 Mean throughput packet delay and loss for PUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
the wireless channels between the eNB and the users Henceat the moment preceding the bandwidthpower allocation itis rather difficult to estimate the service capacity of a systemNevertheless it is possible to find the average service capacityand to determine the upper and lower bounds on servicecapacity of the eNB in the UL and DL directions such that
119877min le sum119894isinI119903119875119894(119905) asymp 119877ave le 119877max (39)
where119877min119877ave and119877max are the lower bound upper boundand average service capacity of the eNB respectively
In our case the upper bound on service capacity of theeNB is given by
119877max = 120596120595119861 log (1 + 119892 (SNRmax) sdot SNRmax) (40a)
where SNRmax is the maximal possible SNR value
The lower bound on service capacity of eNB is
119877min = 120596120595119861 log (1 + 119892 (SNRmin) sdot SNRmin) (40b)
where SNRmin is the minimal possible SNR valueThe average service capacity of the eNB equals
119877ave = 120596120595119861 log (1 + 119892 (SNRave) sdot SNRave) (40c)
where SNRave is the average SNR valueIf SNR information is available then the values SNRmax
SNRmin and SNRave can be set as
SNRmax = max119894isinI
SNR119894 (41a)
14 Mobile Information Systems
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r SU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for S
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
Figure 4 Mean throughput packet delay and loss for SUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
SNRmin = min119894isinI
SNR119894 (41b)
SNRave =1
119899
sum
119894isinISNR119894 (41c)
Otherwise (ie if SNR information is not available) thevalues are set arbitrarily
Now we can identify the situation when constraints (5)and (12) cannot be satisfied For this we should perform thefollowing test For Scenario 1 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus 119871
119894) (42)
then constraint (5) is feasible Otherwise condition (5)cannot be satisfiedHence all the SUs receive zero allocations
andwe assign the bandwidthpower resources only to the PUsby solving the following optimization problem
minimize max119894isinI
lceil119902119875119894+ 119886119875119894minus 119903119875119894(b119875 p119875)rceil+
(43a)
subject to 119903119875119894(b119875 p119875) le 119902119875119894+ 119886119875119894 forall119894 isin I (43b)
sum
119894isinI119887119875119894le 119861 (43c)
119887119875119894isin Z+ forall119894 isin I (43d)
119901119875119894le 119875119875119894 forall119894 isin I (43e)
119901119875119894ge 0 forall119894 isin I (43f)
Mobile Information Systems 15
725
750
775
800
825
850
875
900
925
950Th
roug
hput
for P
Us (
kbits
s)
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
10
20
30
40
50
60
70
Dela
y fo
r PU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Loss
for P
Us (
)
0
005
01
015
02
025
03
035
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Figure 5 Mean throughput packet delay and loss for PUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
for the UL direction For the DL directions constraint (43e)should be replaced by
sum
119894isinI119901119875119894le 119875eNB (43g)
For Scenario 2 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus (1 + 120572
119894) 119871119894) (44)
then constraint (12) is feasible Otherwise inequality (12)cannot be satisfied and the bandwidthpower resources areassigned only to the PUs (according to (43a)ndash(43g)) whereasthe SUs receive zero allocations
4 Performance Evaluation
41 Simulation Model A simulation model of the networkconsisting of one eNB 119899 PUs and 119898 SUs randomly locatedin a service area with 3 km radius has been developed upona standard LTE platform using the OPNET package [35]Thebandwidth of the eNB equals 119861 = 50RBs (which is equivalentto 10MHz) The slot duration in the algorithm equals 119879
119904=
1msThemaximal number of iterations in FP algorithm is set119870 = 200Themaximal transmission power of the eNB equals119875eNB = 46 dBm and the maximal transmission power of eachPUSU equals 119875
1198751= sdot sdot sdot = 119875
119875119899= 1198751198781= sdot sdot sdot = 119875
119878119898= 23 dBm
Other simulation settings of the model are listed in Table 2(all the parameters are based on LTE specifications [36])
16 Mobile Information Systems
Table 2 Simulation parameters of the model
Parameter ValueRadio network model
Pass loss 119871 = 40log10119877 + 30log
10119891 + 49 119877 distance (km) 119891
carrier frequency (Hz)
Shadow fading Log-normal shadow fading with a standard deviation of1012 dB for outdoorindoor users
Penetration loss The average building penetration loss is 12 dB with astandard deviation of 8 dB
Multipath fading Spatial Channel Model (SCM) Suburban macroUE velocity 0 kmsTransmitterreceiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver noise figure 5 dBThermal noise density minus174 dBmHzCableconnectorcombiner losses 2 dB
Physical profileOperation mode FDDCyclic prefix type Normal (7 symbols per slot)Evolved packet core (EPC) bearer definitions 348 kbits (nonguaranteed bit rate)Subcarrier spacing 15 kHz
Admission control parametersPhysical downlink control channel (PDCCH) symbols per subframe 3UL loading factor 1DL loading factor 1Inactive bearer timeout 20 sec
Buffer status report parametersPeriodic timer 5 subframesRetransmission timer 2560 subframes
L1L2 control parametersReserved size 2 RBsCyclic shifts 6Starting RB preserver for Format 1 messages 0Allocation periodicity 5 subframes
Random access (RA) parametersNumber of preambles 64Preamble format Format 0 (1-subframe long)Number of RA resources per frame 4Preamble retransmission limit 5 subframesRA response timer 5 subframesContention resolution timer 40 subframes
HARQ parametersMaximal number of retransmissions 3 (UL and DL)HARQ retransmission timer 8 subframes (UL and DL)Maximal number of HARQ processes 8 per UE (UL and DL)
A radio model of the network corresponds to the require-ments of ITU-T Recommendation M1225
The algorithms proposed in the paper are denoted asfollows
(i) GBC (greedy buffer Control) where the target buffersize equals 0 for all the PUs
(ii) NBC (nongreedy buffer control) with the target buffersize calculated according to (37a) and (37b)
(iii) MBC (Minimal Buffer Control) with 119879 = 10 slots andthe target buffer size given by (38a)
(iv) ABC (Average Buffer Control) with 119879 = 10 slots andthe target buffer size equaling (38b)
Two previously proposed schemes used to benchmark theperformance of the algorithms proposed in this paper are
(i) UBA (Utility Based Allocation) presented in [11]where the network resources (bandwidth and trans-mission power) are allocated to the UL channels tomaximize the total transmission rate of the userssubject to the capacity and transmission power con-straints
Mobile Information Systems 17
0 10 20 30 40 50 60 70 80Average SNR (dB)
UBADPCGBC
NBCMBCABC
30
35
40
45
50
55
60
65
70
Dela
y fo
r SU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
012
015
018
021
024
027
03
033
Loss
for S
Us (
)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
250
300
350
400
450
500Th
roug
hput
for S
Us (
kbits
s)
Figure 6 Mean throughput packet delay and loss for SUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
(ii) DPC (Delay Power Control) derived in [5] whichis used to balance the transmission delay againsttransmission power in wireless channels between theeNB and the users
We also gather simulation results for a proposed resourceallocation approach in Scenario 2 with different settings ofthe parameters120572
119894and V and benchmark its performancewith
the performance of the algorithm in Scenario 1All algorithms are simulated using identical settings
The data traffic in simulations is represented by voice overInternet Protocol (VoIP) video and Hypertext TransferProtocol (HTTP) applications mixed in proportion 2 3 5using the models defined in [37]
42 Complexity and Fairness Issues Let us first evaluatethe complexity and the fairness of resource allocation indifferent algorithms Figure 1 shows the average numberof iterations before convergence for UBA DPC and theproposed algorithms in Scenario 1 (denoted as MBC) andScenario 2 gathered in simulations with 119899 = 100 PUs andaverage SNR = 0 dB Note that the target buffer size for thePUs is calculated according to (38a) with T = 10 slots (inScenarios 1 and 2) and 120572
119894= 1 V = 119898 lowast 1Mbps (for
Scenario 2) Results demonstrate that the complexity of FPmethod deployed for resource allocation in Scenarios 1 and2 is exponential in size of the problem (which correspondsto the findings reported in [31]) and is comparable to thecomplexities of other techniques (UBA and DPC)
18 Mobile Information Systems
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
080020 090070050 060 100000 030010 040120572i
10
20
30
40
50
60
70
80
90
100
110
Dela
y fo
r PU
s (m
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
040030 090000 080060010 020 050 100070120572i
005
010
015
020
025
030
035
040
045
050
Loss
for P
Us (
)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
030020 040 090010 060 070 080 100000 050120572i
Figure 7 Mean throughput packet delay and loss for the PUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
Figure 2 shows the fairness of different methods calcu-lated according to Jainrsquos equation [38] as
119865PU =
(sum119894isinI 119903119875119894)
2
119899 sdot sum119894isinI 1199032
119875119894
119865SU =
(sum119895isinJ 119903119878119895)
2
119898 sdot sum119895isinJ 1199032
119878119895
119865 =
(sum119894isinI 119903119875119894 + sum119895isinJ 119903119878119895)
2
(119899 + 119898) sdot (sum119894isinI 1199032
119875119894+ sum119895isinJ 1199032
119878119895)
(45)
where 119865PU 119865SU and 119865 stand for Jainrsquos index of fairness forthe PUs SUs and all of the users respectively 119903
119875119894 119903119878119895
arethe mean throughputs for PU
119894and SU
119895 respectively Results
have been gathered for 119899 = 100 PUs 119898 = 100 SUs average
Mobile Information Systems 19
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
410
420
430
440
450
460
470
480
490
500
510Th
roug
hput
for S
Us (
kbits
s)
010 020 080 090050 060 070030 100000 040120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
15
20
25
30
35
40
45
50
Dela
y fo
r SU
s (m
s)
070 090030 040 050 080000 020010 100060120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
007
009
011
013
015
017
019
021
023
Loss
for S
Us (
)
080070 090020 050 060030 100040010000120572i
Figure 8 Mean throughput packet delay and loss for the SUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
SNR = 0 dB and target buffer size for the PUs calculatedaccording to (38a) (Scenarios 1 and 2) with different settingsof 120572119894and V in Scenario 2
It follows from these graphs that the fairness index amongall of the users (denoted as 119865) is higher in Scenario 2 with120572119894= 1 and lower in Scenario 1 and Scenario 2 with 120572
119894= 0
Such results are rather expectable in Scenario 1 and Scenario2 with 120572
119894= 0 the SUs are served for free on a best-effort
basis whereas the PUs enjoy full QoS guarantees Hence thenetwork resources are shared nonequally between the PUs
and the SUs with most of the RBs allocated to the PUs andthe rest of the bandwidth distributed among the SUs Onthe other hand the fairness index for the PUs and SUs (ie119865PU and 119865SU) is rather high in both scenarios with differentsettings of 120572
119894and V which indicates that the users of the same
type are treated equally during resource allocation
43 Simulation Results in Scenario 1 Let us evaluate theperformance of a resource allocation algorithm in Scenario1 in terms of mean throughput packet end-to-end delay and
20 Mobile Information Systems
MBC
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
20
30
40
50
60
70
80
90
Dela
y fo
r PU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
005
010
015
020
025
030
035
040
045
Loss
for P
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 9 Mean throughput packet delay and loss for the PUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
loss for different user types Figures 3ndash6 show results obtainedin simulations with 119899 = 100 PUs and average SNR = 0 dBResults demonstrate that aUBA scheme has the largest packetdelay and loss and the lowest throughput for both the PUs andthe SUs A poor performance of this scheme is explained asfollows
(i) QoS protection of PUs is not considered in UBAHence the throughput delay and loss are the samefor PUs and SUs
(ii) Buffer sizes of individual users are not consideredin resource allocation and therefore the QoS for
Mobile Information Systems 21
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
30
50
70
90
110
130
Dela
y fo
r SU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
000
010
020
030
040
050
060
Loss
for S
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
different users varies significantly (since differentusers have different traffic demands)
(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer
size and therefore there is no need to maximize theirtransmission rate and spend the network resources
Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
12 Mobile Information Systems
(6) OUTPUT solution (b119875 p119875 b119878 p119878)lowast
=
(b119875 p119875 b119878 p119878)119896
Note that in order to retain the convergence of thealgorithm both problems (35a)ndash(35j) and (36a)ndash(36j) needto be solved exactly Problem (36a)ndash(36j) (and consequentlyproblem (34a)ndash(34j)) can be solved using any standard NLPmethod In this paper an interior point algorithm (describedeg in [32]) with polynomial complexity is applied to solve(36a)ndash(36j) and (34a)ndash(34j) MILP problem (35a)ndash(35j) isrelatively simple and therefore can be solved efficiently foroptimality by any technique from the family of the branch-and-bound methods (eg [26])
33 Target Buffer Size for PUs and Feasibility Issues Recallthat 119871
119894represents the target buffer size for PU
119894 which
indicates that the QoS requirements of PU119894are satisfied By
limiting the buffer size of PUs we restrict the QoS of PUs(measured in terms of their buffer size) to be higher (or atleast not smaller) than the required minimum From thispoint of view constraints (5) and (12) guarantee the QoSprotection of PUs in Scenario 1 and Scenario 2 respectivelyApparently one can always restrict the target buffer size ofPUs to be equal to zero so that after each subsequent dataarrival the buffer of each PU is fully cleared This approachrepresents a ldquogreedyrdquo policy which ensures that the PUs arealways served with the best possible QoS but does not guar-antee that some spare capacity will be left to serve the SUs
A ldquoless greedyrdquo strategy would be to establish somelower bound on QoS for the PUs which will provide anldquoopportunityrdquo for SUs to be served To establish this lowerbound recall that the growing delay and loss indicate thata buffer of a corresponding node is congested whereas inan uncongested node the packet delay and loss are alwaysminimal [33] On the other hand it has been reported in[33 34] that in an uncongested node the buffer size 119902(119905) isincreasing very slowly that is 119902(119905 + 1)119902(119905) asymp 1 whereas ina congested node the buffer size is growing very fast so that119902(119905+1)119902(119905) ≫ 1 Hence to serve the PUs withminimal delayand loss it is enough to prevent the growth of their buffersthat is for each PU set
119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)
where 120576 ge 0 is some small value such that
120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)
More sophisticated approach to find the lowerQoS boundcan be deployed if information about the past buffer size isavailable at any time slot 119905 In this case one can set the targetbuffer size based on past T observations 119902(119905) 119902(119905 minus 119879 + 1)as
119871119894= min120591isinT
119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38a)
or
119871119894=
1
119879
sum
120591isinT119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38b)
where T = 1 119879
UBADPC MBC
60
70
80
90
100
110
120
130
140
Alg
orith
m it
erat
ions
10020 8040 50 60 7030 90100Number of SUs m
120572i = 1 v = m lowast 1Mbps
Figure 1 Average number of iterations before convergence as afunction of number of SUs in simulations with 119899 = 100 PUs andaverage SNR = 0 dB
MBC
070
075
080
085
090
095
100
120572i=0
v=0
120572i=1
v=0
120572i=0
v=m
lowast1
Mbp
s
120572i=1
v=m
lowast1
Mbp
s
Fairness among SUs FSU
Fairness among PUs FPU
Fairness among all users F
Figure 2 Jainrsquos index of fairness119865SU119865PU and119865 for the PUs SUs andall users in simulations with 119899 = 100 PUs119898 = 100 SUs and averageSNR = 0 dB
In some (very rare) cases (when the service capacity of theeNB is not enough to guarantee that the buffer sizes in all PUsdo not exceed the target buffer size) constraints (5) and (12)in Scenarios 1 and 2 may be not feasible In the following weshow how to identify such situation and what should be theoptimal resource allocation strategy in this case
Note that the service capacity of LTE system greatlydepends on physical characteristics (eg SINR and MCS) of
Mobile Information Systems 13
UBADPCGBC
NBCMBCABC
780
800
820
840
860
880
900
920
940
960Th
roug
hput
for P
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r PU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for P
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
Figure 3 Mean throughput packet delay and loss for PUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
the wireless channels between the eNB and the users Henceat the moment preceding the bandwidthpower allocation itis rather difficult to estimate the service capacity of a systemNevertheless it is possible to find the average service capacityand to determine the upper and lower bounds on servicecapacity of the eNB in the UL and DL directions such that
119877min le sum119894isinI119903119875119894(119905) asymp 119877ave le 119877max (39)
where119877min119877ave and119877max are the lower bound upper boundand average service capacity of the eNB respectively
In our case the upper bound on service capacity of theeNB is given by
119877max = 120596120595119861 log (1 + 119892 (SNRmax) sdot SNRmax) (40a)
where SNRmax is the maximal possible SNR value
The lower bound on service capacity of eNB is
119877min = 120596120595119861 log (1 + 119892 (SNRmin) sdot SNRmin) (40b)
where SNRmin is the minimal possible SNR valueThe average service capacity of the eNB equals
119877ave = 120596120595119861 log (1 + 119892 (SNRave) sdot SNRave) (40c)
where SNRave is the average SNR valueIf SNR information is available then the values SNRmax
SNRmin and SNRave can be set as
SNRmax = max119894isinI
SNR119894 (41a)
14 Mobile Information Systems
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r SU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for S
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
Figure 4 Mean throughput packet delay and loss for SUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
SNRmin = min119894isinI
SNR119894 (41b)
SNRave =1
119899
sum
119894isinISNR119894 (41c)
Otherwise (ie if SNR information is not available) thevalues are set arbitrarily
Now we can identify the situation when constraints (5)and (12) cannot be satisfied For this we should perform thefollowing test For Scenario 1 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus 119871
119894) (42)
then constraint (5) is feasible Otherwise condition (5)cannot be satisfiedHence all the SUs receive zero allocations
andwe assign the bandwidthpower resources only to the PUsby solving the following optimization problem
minimize max119894isinI
lceil119902119875119894+ 119886119875119894minus 119903119875119894(b119875 p119875)rceil+
(43a)
subject to 119903119875119894(b119875 p119875) le 119902119875119894+ 119886119875119894 forall119894 isin I (43b)
sum
119894isinI119887119875119894le 119861 (43c)
119887119875119894isin Z+ forall119894 isin I (43d)
119901119875119894le 119875119875119894 forall119894 isin I (43e)
119901119875119894ge 0 forall119894 isin I (43f)
Mobile Information Systems 15
725
750
775
800
825
850
875
900
925
950Th
roug
hput
for P
Us (
kbits
s)
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
10
20
30
40
50
60
70
Dela
y fo
r PU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Loss
for P
Us (
)
0
005
01
015
02
025
03
035
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Figure 5 Mean throughput packet delay and loss for PUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
for the UL direction For the DL directions constraint (43e)should be replaced by
sum
119894isinI119901119875119894le 119875eNB (43g)
For Scenario 2 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus (1 + 120572
119894) 119871119894) (44)
then constraint (12) is feasible Otherwise inequality (12)cannot be satisfied and the bandwidthpower resources areassigned only to the PUs (according to (43a)ndash(43g)) whereasthe SUs receive zero allocations
4 Performance Evaluation
41 Simulation Model A simulation model of the networkconsisting of one eNB 119899 PUs and 119898 SUs randomly locatedin a service area with 3 km radius has been developed upona standard LTE platform using the OPNET package [35]Thebandwidth of the eNB equals 119861 = 50RBs (which is equivalentto 10MHz) The slot duration in the algorithm equals 119879
119904=
1msThemaximal number of iterations in FP algorithm is set119870 = 200Themaximal transmission power of the eNB equals119875eNB = 46 dBm and the maximal transmission power of eachPUSU equals 119875
1198751= sdot sdot sdot = 119875
119875119899= 1198751198781= sdot sdot sdot = 119875
119878119898= 23 dBm
Other simulation settings of the model are listed in Table 2(all the parameters are based on LTE specifications [36])
16 Mobile Information Systems
Table 2 Simulation parameters of the model
Parameter ValueRadio network model
Pass loss 119871 = 40log10119877 + 30log
10119891 + 49 119877 distance (km) 119891
carrier frequency (Hz)
Shadow fading Log-normal shadow fading with a standard deviation of1012 dB for outdoorindoor users
Penetration loss The average building penetration loss is 12 dB with astandard deviation of 8 dB
Multipath fading Spatial Channel Model (SCM) Suburban macroUE velocity 0 kmsTransmitterreceiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver noise figure 5 dBThermal noise density minus174 dBmHzCableconnectorcombiner losses 2 dB
Physical profileOperation mode FDDCyclic prefix type Normal (7 symbols per slot)Evolved packet core (EPC) bearer definitions 348 kbits (nonguaranteed bit rate)Subcarrier spacing 15 kHz
Admission control parametersPhysical downlink control channel (PDCCH) symbols per subframe 3UL loading factor 1DL loading factor 1Inactive bearer timeout 20 sec
Buffer status report parametersPeriodic timer 5 subframesRetransmission timer 2560 subframes
L1L2 control parametersReserved size 2 RBsCyclic shifts 6Starting RB preserver for Format 1 messages 0Allocation periodicity 5 subframes
Random access (RA) parametersNumber of preambles 64Preamble format Format 0 (1-subframe long)Number of RA resources per frame 4Preamble retransmission limit 5 subframesRA response timer 5 subframesContention resolution timer 40 subframes
HARQ parametersMaximal number of retransmissions 3 (UL and DL)HARQ retransmission timer 8 subframes (UL and DL)Maximal number of HARQ processes 8 per UE (UL and DL)
A radio model of the network corresponds to the require-ments of ITU-T Recommendation M1225
The algorithms proposed in the paper are denoted asfollows
(i) GBC (greedy buffer Control) where the target buffersize equals 0 for all the PUs
(ii) NBC (nongreedy buffer control) with the target buffersize calculated according to (37a) and (37b)
(iii) MBC (Minimal Buffer Control) with 119879 = 10 slots andthe target buffer size given by (38a)
(iv) ABC (Average Buffer Control) with 119879 = 10 slots andthe target buffer size equaling (38b)
Two previously proposed schemes used to benchmark theperformance of the algorithms proposed in this paper are
(i) UBA (Utility Based Allocation) presented in [11]where the network resources (bandwidth and trans-mission power) are allocated to the UL channels tomaximize the total transmission rate of the userssubject to the capacity and transmission power con-straints
Mobile Information Systems 17
0 10 20 30 40 50 60 70 80Average SNR (dB)
UBADPCGBC
NBCMBCABC
30
35
40
45
50
55
60
65
70
Dela
y fo
r SU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
012
015
018
021
024
027
03
033
Loss
for S
Us (
)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
250
300
350
400
450
500Th
roug
hput
for S
Us (
kbits
s)
Figure 6 Mean throughput packet delay and loss for SUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
(ii) DPC (Delay Power Control) derived in [5] whichis used to balance the transmission delay againsttransmission power in wireless channels between theeNB and the users
We also gather simulation results for a proposed resourceallocation approach in Scenario 2 with different settings ofthe parameters120572
119894and V and benchmark its performancewith
the performance of the algorithm in Scenario 1All algorithms are simulated using identical settings
The data traffic in simulations is represented by voice overInternet Protocol (VoIP) video and Hypertext TransferProtocol (HTTP) applications mixed in proportion 2 3 5using the models defined in [37]
42 Complexity and Fairness Issues Let us first evaluatethe complexity and the fairness of resource allocation indifferent algorithms Figure 1 shows the average numberof iterations before convergence for UBA DPC and theproposed algorithms in Scenario 1 (denoted as MBC) andScenario 2 gathered in simulations with 119899 = 100 PUs andaverage SNR = 0 dB Note that the target buffer size for thePUs is calculated according to (38a) with T = 10 slots (inScenarios 1 and 2) and 120572
119894= 1 V = 119898 lowast 1Mbps (for
Scenario 2) Results demonstrate that the complexity of FPmethod deployed for resource allocation in Scenarios 1 and2 is exponential in size of the problem (which correspondsto the findings reported in [31]) and is comparable to thecomplexities of other techniques (UBA and DPC)
18 Mobile Information Systems
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
080020 090070050 060 100000 030010 040120572i
10
20
30
40
50
60
70
80
90
100
110
Dela
y fo
r PU
s (m
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
040030 090000 080060010 020 050 100070120572i
005
010
015
020
025
030
035
040
045
050
Loss
for P
Us (
)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
030020 040 090010 060 070 080 100000 050120572i
Figure 7 Mean throughput packet delay and loss for the PUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
Figure 2 shows the fairness of different methods calcu-lated according to Jainrsquos equation [38] as
119865PU =
(sum119894isinI 119903119875119894)
2
119899 sdot sum119894isinI 1199032
119875119894
119865SU =
(sum119895isinJ 119903119878119895)
2
119898 sdot sum119895isinJ 1199032
119878119895
119865 =
(sum119894isinI 119903119875119894 + sum119895isinJ 119903119878119895)
2
(119899 + 119898) sdot (sum119894isinI 1199032
119875119894+ sum119895isinJ 1199032
119878119895)
(45)
where 119865PU 119865SU and 119865 stand for Jainrsquos index of fairness forthe PUs SUs and all of the users respectively 119903
119875119894 119903119878119895
arethe mean throughputs for PU
119894and SU
119895 respectively Results
have been gathered for 119899 = 100 PUs 119898 = 100 SUs average
Mobile Information Systems 19
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
410
420
430
440
450
460
470
480
490
500
510Th
roug
hput
for S
Us (
kbits
s)
010 020 080 090050 060 070030 100000 040120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
15
20
25
30
35
40
45
50
Dela
y fo
r SU
s (m
s)
070 090030 040 050 080000 020010 100060120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
007
009
011
013
015
017
019
021
023
Loss
for S
Us (
)
080070 090020 050 060030 100040010000120572i
Figure 8 Mean throughput packet delay and loss for the SUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
SNR = 0 dB and target buffer size for the PUs calculatedaccording to (38a) (Scenarios 1 and 2) with different settingsof 120572119894and V in Scenario 2
It follows from these graphs that the fairness index amongall of the users (denoted as 119865) is higher in Scenario 2 with120572119894= 1 and lower in Scenario 1 and Scenario 2 with 120572
119894= 0
Such results are rather expectable in Scenario 1 and Scenario2 with 120572
119894= 0 the SUs are served for free on a best-effort
basis whereas the PUs enjoy full QoS guarantees Hence thenetwork resources are shared nonequally between the PUs
and the SUs with most of the RBs allocated to the PUs andthe rest of the bandwidth distributed among the SUs Onthe other hand the fairness index for the PUs and SUs (ie119865PU and 119865SU) is rather high in both scenarios with differentsettings of 120572
119894and V which indicates that the users of the same
type are treated equally during resource allocation
43 Simulation Results in Scenario 1 Let us evaluate theperformance of a resource allocation algorithm in Scenario1 in terms of mean throughput packet end-to-end delay and
20 Mobile Information Systems
MBC
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
20
30
40
50
60
70
80
90
Dela
y fo
r PU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
005
010
015
020
025
030
035
040
045
Loss
for P
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 9 Mean throughput packet delay and loss for the PUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
loss for different user types Figures 3ndash6 show results obtainedin simulations with 119899 = 100 PUs and average SNR = 0 dBResults demonstrate that aUBA scheme has the largest packetdelay and loss and the lowest throughput for both the PUs andthe SUs A poor performance of this scheme is explained asfollows
(i) QoS protection of PUs is not considered in UBAHence the throughput delay and loss are the samefor PUs and SUs
(ii) Buffer sizes of individual users are not consideredin resource allocation and therefore the QoS for
Mobile Information Systems 21
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
30
50
70
90
110
130
Dela
y fo
r SU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
000
010
020
030
040
050
060
Loss
for S
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
different users varies significantly (since differentusers have different traffic demands)
(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer
size and therefore there is no need to maximize theirtransmission rate and spend the network resources
Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mobile Information Systems 13
UBADPCGBC
NBCMBCABC
780
800
820
840
860
880
900
920
940
960Th
roug
hput
for P
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r PU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for P
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
Figure 3 Mean throughput packet delay and loss for PUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
the wireless channels between the eNB and the users Henceat the moment preceding the bandwidthpower allocation itis rather difficult to estimate the service capacity of a systemNevertheless it is possible to find the average service capacityand to determine the upper and lower bounds on servicecapacity of the eNB in the UL and DL directions such that
119877min le sum119894isinI119903119875119894(119905) asymp 119877ave le 119877max (39)
where119877min119877ave and119877max are the lower bound upper boundand average service capacity of the eNB respectively
In our case the upper bound on service capacity of theeNB is given by
119877max = 120596120595119861 log (1 + 119892 (SNRmax) sdot SNRmax) (40a)
where SNRmax is the maximal possible SNR value
The lower bound on service capacity of eNB is
119877min = 120596120595119861 log (1 + 119892 (SNRmin) sdot SNRmin) (40b)
where SNRmin is the minimal possible SNR valueThe average service capacity of the eNB equals
119877ave = 120596120595119861 log (1 + 119892 (SNRave) sdot SNRave) (40c)
where SNRave is the average SNR valueIf SNR information is available then the values SNRmax
SNRmin and SNRave can be set as
SNRmax = max119894isinI
SNR119894 (41a)
14 Mobile Information Systems
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r SU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for S
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
Figure 4 Mean throughput packet delay and loss for SUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
SNRmin = min119894isinI
SNR119894 (41b)
SNRave =1
119899
sum
119894isinISNR119894 (41c)
Otherwise (ie if SNR information is not available) thevalues are set arbitrarily
Now we can identify the situation when constraints (5)and (12) cannot be satisfied For this we should perform thefollowing test For Scenario 1 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus 119871
119894) (42)
then constraint (5) is feasible Otherwise condition (5)cannot be satisfiedHence all the SUs receive zero allocations
andwe assign the bandwidthpower resources only to the PUsby solving the following optimization problem
minimize max119894isinI
lceil119902119875119894+ 119886119875119894minus 119903119875119894(b119875 p119875)rceil+
(43a)
subject to 119903119875119894(b119875 p119875) le 119902119875119894+ 119886119875119894 forall119894 isin I (43b)
sum
119894isinI119887119875119894le 119861 (43c)
119887119875119894isin Z+ forall119894 isin I (43d)
119901119875119894le 119875119875119894 forall119894 isin I (43e)
119901119875119894ge 0 forall119894 isin I (43f)
Mobile Information Systems 15
725
750
775
800
825
850
875
900
925
950Th
roug
hput
for P
Us (
kbits
s)
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
10
20
30
40
50
60
70
Dela
y fo
r PU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Loss
for P
Us (
)
0
005
01
015
02
025
03
035
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Figure 5 Mean throughput packet delay and loss for PUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
for the UL direction For the DL directions constraint (43e)should be replaced by
sum
119894isinI119901119875119894le 119875eNB (43g)
For Scenario 2 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus (1 + 120572
119894) 119871119894) (44)
then constraint (12) is feasible Otherwise inequality (12)cannot be satisfied and the bandwidthpower resources areassigned only to the PUs (according to (43a)ndash(43g)) whereasthe SUs receive zero allocations
4 Performance Evaluation
41 Simulation Model A simulation model of the networkconsisting of one eNB 119899 PUs and 119898 SUs randomly locatedin a service area with 3 km radius has been developed upona standard LTE platform using the OPNET package [35]Thebandwidth of the eNB equals 119861 = 50RBs (which is equivalentto 10MHz) The slot duration in the algorithm equals 119879
119904=
1msThemaximal number of iterations in FP algorithm is set119870 = 200Themaximal transmission power of the eNB equals119875eNB = 46 dBm and the maximal transmission power of eachPUSU equals 119875
1198751= sdot sdot sdot = 119875
119875119899= 1198751198781= sdot sdot sdot = 119875
119878119898= 23 dBm
Other simulation settings of the model are listed in Table 2(all the parameters are based on LTE specifications [36])
16 Mobile Information Systems
Table 2 Simulation parameters of the model
Parameter ValueRadio network model
Pass loss 119871 = 40log10119877 + 30log
10119891 + 49 119877 distance (km) 119891
carrier frequency (Hz)
Shadow fading Log-normal shadow fading with a standard deviation of1012 dB for outdoorindoor users
Penetration loss The average building penetration loss is 12 dB with astandard deviation of 8 dB
Multipath fading Spatial Channel Model (SCM) Suburban macroUE velocity 0 kmsTransmitterreceiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver noise figure 5 dBThermal noise density minus174 dBmHzCableconnectorcombiner losses 2 dB
Physical profileOperation mode FDDCyclic prefix type Normal (7 symbols per slot)Evolved packet core (EPC) bearer definitions 348 kbits (nonguaranteed bit rate)Subcarrier spacing 15 kHz
Admission control parametersPhysical downlink control channel (PDCCH) symbols per subframe 3UL loading factor 1DL loading factor 1Inactive bearer timeout 20 sec
Buffer status report parametersPeriodic timer 5 subframesRetransmission timer 2560 subframes
L1L2 control parametersReserved size 2 RBsCyclic shifts 6Starting RB preserver for Format 1 messages 0Allocation periodicity 5 subframes
Random access (RA) parametersNumber of preambles 64Preamble format Format 0 (1-subframe long)Number of RA resources per frame 4Preamble retransmission limit 5 subframesRA response timer 5 subframesContention resolution timer 40 subframes
HARQ parametersMaximal number of retransmissions 3 (UL and DL)HARQ retransmission timer 8 subframes (UL and DL)Maximal number of HARQ processes 8 per UE (UL and DL)
A radio model of the network corresponds to the require-ments of ITU-T Recommendation M1225
The algorithms proposed in the paper are denoted asfollows
(i) GBC (greedy buffer Control) where the target buffersize equals 0 for all the PUs
(ii) NBC (nongreedy buffer control) with the target buffersize calculated according to (37a) and (37b)
(iii) MBC (Minimal Buffer Control) with 119879 = 10 slots andthe target buffer size given by (38a)
(iv) ABC (Average Buffer Control) with 119879 = 10 slots andthe target buffer size equaling (38b)
Two previously proposed schemes used to benchmark theperformance of the algorithms proposed in this paper are
(i) UBA (Utility Based Allocation) presented in [11]where the network resources (bandwidth and trans-mission power) are allocated to the UL channels tomaximize the total transmission rate of the userssubject to the capacity and transmission power con-straints
Mobile Information Systems 17
0 10 20 30 40 50 60 70 80Average SNR (dB)
UBADPCGBC
NBCMBCABC
30
35
40
45
50
55
60
65
70
Dela
y fo
r SU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
012
015
018
021
024
027
03
033
Loss
for S
Us (
)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
250
300
350
400
450
500Th
roug
hput
for S
Us (
kbits
s)
Figure 6 Mean throughput packet delay and loss for SUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
(ii) DPC (Delay Power Control) derived in [5] whichis used to balance the transmission delay againsttransmission power in wireless channels between theeNB and the users
We also gather simulation results for a proposed resourceallocation approach in Scenario 2 with different settings ofthe parameters120572
119894and V and benchmark its performancewith
the performance of the algorithm in Scenario 1All algorithms are simulated using identical settings
The data traffic in simulations is represented by voice overInternet Protocol (VoIP) video and Hypertext TransferProtocol (HTTP) applications mixed in proportion 2 3 5using the models defined in [37]
42 Complexity and Fairness Issues Let us first evaluatethe complexity and the fairness of resource allocation indifferent algorithms Figure 1 shows the average numberof iterations before convergence for UBA DPC and theproposed algorithms in Scenario 1 (denoted as MBC) andScenario 2 gathered in simulations with 119899 = 100 PUs andaverage SNR = 0 dB Note that the target buffer size for thePUs is calculated according to (38a) with T = 10 slots (inScenarios 1 and 2) and 120572
119894= 1 V = 119898 lowast 1Mbps (for
Scenario 2) Results demonstrate that the complexity of FPmethod deployed for resource allocation in Scenarios 1 and2 is exponential in size of the problem (which correspondsto the findings reported in [31]) and is comparable to thecomplexities of other techniques (UBA and DPC)
18 Mobile Information Systems
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
080020 090070050 060 100000 030010 040120572i
10
20
30
40
50
60
70
80
90
100
110
Dela
y fo
r PU
s (m
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
040030 090000 080060010 020 050 100070120572i
005
010
015
020
025
030
035
040
045
050
Loss
for P
Us (
)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
030020 040 090010 060 070 080 100000 050120572i
Figure 7 Mean throughput packet delay and loss for the PUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
Figure 2 shows the fairness of different methods calcu-lated according to Jainrsquos equation [38] as
119865PU =
(sum119894isinI 119903119875119894)
2
119899 sdot sum119894isinI 1199032
119875119894
119865SU =
(sum119895isinJ 119903119878119895)
2
119898 sdot sum119895isinJ 1199032
119878119895
119865 =
(sum119894isinI 119903119875119894 + sum119895isinJ 119903119878119895)
2
(119899 + 119898) sdot (sum119894isinI 1199032
119875119894+ sum119895isinJ 1199032
119878119895)
(45)
where 119865PU 119865SU and 119865 stand for Jainrsquos index of fairness forthe PUs SUs and all of the users respectively 119903
119875119894 119903119878119895
arethe mean throughputs for PU
119894and SU
119895 respectively Results
have been gathered for 119899 = 100 PUs 119898 = 100 SUs average
Mobile Information Systems 19
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
410
420
430
440
450
460
470
480
490
500
510Th
roug
hput
for S
Us (
kbits
s)
010 020 080 090050 060 070030 100000 040120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
15
20
25
30
35
40
45
50
Dela
y fo
r SU
s (m
s)
070 090030 040 050 080000 020010 100060120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
007
009
011
013
015
017
019
021
023
Loss
for S
Us (
)
080070 090020 050 060030 100040010000120572i
Figure 8 Mean throughput packet delay and loss for the SUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
SNR = 0 dB and target buffer size for the PUs calculatedaccording to (38a) (Scenarios 1 and 2) with different settingsof 120572119894and V in Scenario 2
It follows from these graphs that the fairness index amongall of the users (denoted as 119865) is higher in Scenario 2 with120572119894= 1 and lower in Scenario 1 and Scenario 2 with 120572
119894= 0
Such results are rather expectable in Scenario 1 and Scenario2 with 120572
119894= 0 the SUs are served for free on a best-effort
basis whereas the PUs enjoy full QoS guarantees Hence thenetwork resources are shared nonequally between the PUs
and the SUs with most of the RBs allocated to the PUs andthe rest of the bandwidth distributed among the SUs Onthe other hand the fairness index for the PUs and SUs (ie119865PU and 119865SU) is rather high in both scenarios with differentsettings of 120572
119894and V which indicates that the users of the same
type are treated equally during resource allocation
43 Simulation Results in Scenario 1 Let us evaluate theperformance of a resource allocation algorithm in Scenario1 in terms of mean throughput packet end-to-end delay and
20 Mobile Information Systems
MBC
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
20
30
40
50
60
70
80
90
Dela
y fo
r PU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
005
010
015
020
025
030
035
040
045
Loss
for P
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 9 Mean throughput packet delay and loss for the PUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
loss for different user types Figures 3ndash6 show results obtainedin simulations with 119899 = 100 PUs and average SNR = 0 dBResults demonstrate that aUBA scheme has the largest packetdelay and loss and the lowest throughput for both the PUs andthe SUs A poor performance of this scheme is explained asfollows
(i) QoS protection of PUs is not considered in UBAHence the throughput delay and loss are the samefor PUs and SUs
(ii) Buffer sizes of individual users are not consideredin resource allocation and therefore the QoS for
Mobile Information Systems 21
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
30
50
70
90
110
130
Dela
y fo
r SU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
000
010
020
030
040
050
060
Loss
for S
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
different users varies significantly (since differentusers have different traffic demands)
(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer
size and therefore there is no need to maximize theirtransmission rate and spend the network resources
Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
14 Mobile Information Systems
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
10
30
50
70
90
110
130
150
170
Dela
y fo
r SU
s (m
s)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
0
01
02
03
04
05
06
07
08
Loss
for S
Us (
)
10 20 30 40 50 60 70 80 90 1000Number of SUs m
UBADPCGBC
NBCMBCABC
Figure 4 Mean throughput packet delay and loss for SUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB
SNRmin = min119894isinI
SNR119894 (41b)
SNRave =1
119899
sum
119894isinISNR119894 (41c)
Otherwise (ie if SNR information is not available) thevalues are set arbitrarily
Now we can identify the situation when constraints (5)and (12) cannot be satisfied For this we should perform thefollowing test For Scenario 1 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus 119871
119894) (42)
then constraint (5) is feasible Otherwise condition (5)cannot be satisfiedHence all the SUs receive zero allocations
andwe assign the bandwidthpower resources only to the PUsby solving the following optimization problem
minimize max119894isinI
lceil119902119875119894+ 119886119875119894minus 119903119875119894(b119875 p119875)rceil+
(43a)
subject to 119903119875119894(b119875 p119875) le 119902119875119894+ 119886119875119894 forall119894 isin I (43b)
sum
119894isinI119887119875119894le 119861 (43c)
119887119875119894isin Z+ forall119894 isin I (43d)
119901119875119894le 119875119875119894 forall119894 isin I (43e)
119901119875119894ge 0 forall119894 isin I (43f)
Mobile Information Systems 15
725
750
775
800
825
850
875
900
925
950Th
roug
hput
for P
Us (
kbits
s)
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
10
20
30
40
50
60
70
Dela
y fo
r PU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Loss
for P
Us (
)
0
005
01
015
02
025
03
035
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Figure 5 Mean throughput packet delay and loss for PUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
for the UL direction For the DL directions constraint (43e)should be replaced by
sum
119894isinI119901119875119894le 119875eNB (43g)
For Scenario 2 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus (1 + 120572
119894) 119871119894) (44)
then constraint (12) is feasible Otherwise inequality (12)cannot be satisfied and the bandwidthpower resources areassigned only to the PUs (according to (43a)ndash(43g)) whereasthe SUs receive zero allocations
4 Performance Evaluation
41 Simulation Model A simulation model of the networkconsisting of one eNB 119899 PUs and 119898 SUs randomly locatedin a service area with 3 km radius has been developed upona standard LTE platform using the OPNET package [35]Thebandwidth of the eNB equals 119861 = 50RBs (which is equivalentto 10MHz) The slot duration in the algorithm equals 119879
119904=
1msThemaximal number of iterations in FP algorithm is set119870 = 200Themaximal transmission power of the eNB equals119875eNB = 46 dBm and the maximal transmission power of eachPUSU equals 119875
1198751= sdot sdot sdot = 119875
119875119899= 1198751198781= sdot sdot sdot = 119875
119878119898= 23 dBm
Other simulation settings of the model are listed in Table 2(all the parameters are based on LTE specifications [36])
16 Mobile Information Systems
Table 2 Simulation parameters of the model
Parameter ValueRadio network model
Pass loss 119871 = 40log10119877 + 30log
10119891 + 49 119877 distance (km) 119891
carrier frequency (Hz)
Shadow fading Log-normal shadow fading with a standard deviation of1012 dB for outdoorindoor users
Penetration loss The average building penetration loss is 12 dB with astandard deviation of 8 dB
Multipath fading Spatial Channel Model (SCM) Suburban macroUE velocity 0 kmsTransmitterreceiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver noise figure 5 dBThermal noise density minus174 dBmHzCableconnectorcombiner losses 2 dB
Physical profileOperation mode FDDCyclic prefix type Normal (7 symbols per slot)Evolved packet core (EPC) bearer definitions 348 kbits (nonguaranteed bit rate)Subcarrier spacing 15 kHz
Admission control parametersPhysical downlink control channel (PDCCH) symbols per subframe 3UL loading factor 1DL loading factor 1Inactive bearer timeout 20 sec
Buffer status report parametersPeriodic timer 5 subframesRetransmission timer 2560 subframes
L1L2 control parametersReserved size 2 RBsCyclic shifts 6Starting RB preserver for Format 1 messages 0Allocation periodicity 5 subframes
Random access (RA) parametersNumber of preambles 64Preamble format Format 0 (1-subframe long)Number of RA resources per frame 4Preamble retransmission limit 5 subframesRA response timer 5 subframesContention resolution timer 40 subframes
HARQ parametersMaximal number of retransmissions 3 (UL and DL)HARQ retransmission timer 8 subframes (UL and DL)Maximal number of HARQ processes 8 per UE (UL and DL)
A radio model of the network corresponds to the require-ments of ITU-T Recommendation M1225
The algorithms proposed in the paper are denoted asfollows
(i) GBC (greedy buffer Control) where the target buffersize equals 0 for all the PUs
(ii) NBC (nongreedy buffer control) with the target buffersize calculated according to (37a) and (37b)
(iii) MBC (Minimal Buffer Control) with 119879 = 10 slots andthe target buffer size given by (38a)
(iv) ABC (Average Buffer Control) with 119879 = 10 slots andthe target buffer size equaling (38b)
Two previously proposed schemes used to benchmark theperformance of the algorithms proposed in this paper are
(i) UBA (Utility Based Allocation) presented in [11]where the network resources (bandwidth and trans-mission power) are allocated to the UL channels tomaximize the total transmission rate of the userssubject to the capacity and transmission power con-straints
Mobile Information Systems 17
0 10 20 30 40 50 60 70 80Average SNR (dB)
UBADPCGBC
NBCMBCABC
30
35
40
45
50
55
60
65
70
Dela
y fo
r SU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
012
015
018
021
024
027
03
033
Loss
for S
Us (
)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
250
300
350
400
450
500Th
roug
hput
for S
Us (
kbits
s)
Figure 6 Mean throughput packet delay and loss for SUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
(ii) DPC (Delay Power Control) derived in [5] whichis used to balance the transmission delay againsttransmission power in wireless channels between theeNB and the users
We also gather simulation results for a proposed resourceallocation approach in Scenario 2 with different settings ofthe parameters120572
119894and V and benchmark its performancewith
the performance of the algorithm in Scenario 1All algorithms are simulated using identical settings
The data traffic in simulations is represented by voice overInternet Protocol (VoIP) video and Hypertext TransferProtocol (HTTP) applications mixed in proportion 2 3 5using the models defined in [37]
42 Complexity and Fairness Issues Let us first evaluatethe complexity and the fairness of resource allocation indifferent algorithms Figure 1 shows the average numberof iterations before convergence for UBA DPC and theproposed algorithms in Scenario 1 (denoted as MBC) andScenario 2 gathered in simulations with 119899 = 100 PUs andaverage SNR = 0 dB Note that the target buffer size for thePUs is calculated according to (38a) with T = 10 slots (inScenarios 1 and 2) and 120572
119894= 1 V = 119898 lowast 1Mbps (for
Scenario 2) Results demonstrate that the complexity of FPmethod deployed for resource allocation in Scenarios 1 and2 is exponential in size of the problem (which correspondsto the findings reported in [31]) and is comparable to thecomplexities of other techniques (UBA and DPC)
18 Mobile Information Systems
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
080020 090070050 060 100000 030010 040120572i
10
20
30
40
50
60
70
80
90
100
110
Dela
y fo
r PU
s (m
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
040030 090000 080060010 020 050 100070120572i
005
010
015
020
025
030
035
040
045
050
Loss
for P
Us (
)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
030020 040 090010 060 070 080 100000 050120572i
Figure 7 Mean throughput packet delay and loss for the PUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
Figure 2 shows the fairness of different methods calcu-lated according to Jainrsquos equation [38] as
119865PU =
(sum119894isinI 119903119875119894)
2
119899 sdot sum119894isinI 1199032
119875119894
119865SU =
(sum119895isinJ 119903119878119895)
2
119898 sdot sum119895isinJ 1199032
119878119895
119865 =
(sum119894isinI 119903119875119894 + sum119895isinJ 119903119878119895)
2
(119899 + 119898) sdot (sum119894isinI 1199032
119875119894+ sum119895isinJ 1199032
119878119895)
(45)
where 119865PU 119865SU and 119865 stand for Jainrsquos index of fairness forthe PUs SUs and all of the users respectively 119903
119875119894 119903119878119895
arethe mean throughputs for PU
119894and SU
119895 respectively Results
have been gathered for 119899 = 100 PUs 119898 = 100 SUs average
Mobile Information Systems 19
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
410
420
430
440
450
460
470
480
490
500
510Th
roug
hput
for S
Us (
kbits
s)
010 020 080 090050 060 070030 100000 040120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
15
20
25
30
35
40
45
50
Dela
y fo
r SU
s (m
s)
070 090030 040 050 080000 020010 100060120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
007
009
011
013
015
017
019
021
023
Loss
for S
Us (
)
080070 090020 050 060030 100040010000120572i
Figure 8 Mean throughput packet delay and loss for the SUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
SNR = 0 dB and target buffer size for the PUs calculatedaccording to (38a) (Scenarios 1 and 2) with different settingsof 120572119894and V in Scenario 2
It follows from these graphs that the fairness index amongall of the users (denoted as 119865) is higher in Scenario 2 with120572119894= 1 and lower in Scenario 1 and Scenario 2 with 120572
119894= 0
Such results are rather expectable in Scenario 1 and Scenario2 with 120572
119894= 0 the SUs are served for free on a best-effort
basis whereas the PUs enjoy full QoS guarantees Hence thenetwork resources are shared nonequally between the PUs
and the SUs with most of the RBs allocated to the PUs andthe rest of the bandwidth distributed among the SUs Onthe other hand the fairness index for the PUs and SUs (ie119865PU and 119865SU) is rather high in both scenarios with differentsettings of 120572
119894and V which indicates that the users of the same
type are treated equally during resource allocation
43 Simulation Results in Scenario 1 Let us evaluate theperformance of a resource allocation algorithm in Scenario1 in terms of mean throughput packet end-to-end delay and
20 Mobile Information Systems
MBC
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
20
30
40
50
60
70
80
90
Dela
y fo
r PU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
005
010
015
020
025
030
035
040
045
Loss
for P
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 9 Mean throughput packet delay and loss for the PUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
loss for different user types Figures 3ndash6 show results obtainedin simulations with 119899 = 100 PUs and average SNR = 0 dBResults demonstrate that aUBA scheme has the largest packetdelay and loss and the lowest throughput for both the PUs andthe SUs A poor performance of this scheme is explained asfollows
(i) QoS protection of PUs is not considered in UBAHence the throughput delay and loss are the samefor PUs and SUs
(ii) Buffer sizes of individual users are not consideredin resource allocation and therefore the QoS for
Mobile Information Systems 21
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
30
50
70
90
110
130
Dela
y fo
r SU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
000
010
020
030
040
050
060
Loss
for S
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
different users varies significantly (since differentusers have different traffic demands)
(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer
size and therefore there is no need to maximize theirtransmission rate and spend the network resources
Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mobile Information Systems 15
725
750
775
800
825
850
875
900
925
950Th
roug
hput
for P
Us (
kbits
s)
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
10
20
30
40
50
60
70
Dela
y fo
r PU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Loss
for P
Us (
)
0
005
01
015
02
025
03
035
200 5 10 15 25 30minus5minus10
Average SNR (dB)
UBADPCGBC
NBCMBCABC
Figure 5 Mean throughput packet delay and loss for PUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
for the UL direction For the DL directions constraint (43e)should be replaced by
sum
119894isinI119901119875119894le 119875eNB (43g)
For Scenario 2 if
119877min ge sum119894isinI(119902119875119894(119905) + 119886
119875119894(119905) minus (1 + 120572
119894) 119871119894) (44)
then constraint (12) is feasible Otherwise inequality (12)cannot be satisfied and the bandwidthpower resources areassigned only to the PUs (according to (43a)ndash(43g)) whereasthe SUs receive zero allocations
4 Performance Evaluation
41 Simulation Model A simulation model of the networkconsisting of one eNB 119899 PUs and 119898 SUs randomly locatedin a service area with 3 km radius has been developed upona standard LTE platform using the OPNET package [35]Thebandwidth of the eNB equals 119861 = 50RBs (which is equivalentto 10MHz) The slot duration in the algorithm equals 119879
119904=
1msThemaximal number of iterations in FP algorithm is set119870 = 200Themaximal transmission power of the eNB equals119875eNB = 46 dBm and the maximal transmission power of eachPUSU equals 119875
1198751= sdot sdot sdot = 119875
119875119899= 1198751198781= sdot sdot sdot = 119875
119878119898= 23 dBm
Other simulation settings of the model are listed in Table 2(all the parameters are based on LTE specifications [36])
16 Mobile Information Systems
Table 2 Simulation parameters of the model
Parameter ValueRadio network model
Pass loss 119871 = 40log10119877 + 30log
10119891 + 49 119877 distance (km) 119891
carrier frequency (Hz)
Shadow fading Log-normal shadow fading with a standard deviation of1012 dB for outdoorindoor users
Penetration loss The average building penetration loss is 12 dB with astandard deviation of 8 dB
Multipath fading Spatial Channel Model (SCM) Suburban macroUE velocity 0 kmsTransmitterreceiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver noise figure 5 dBThermal noise density minus174 dBmHzCableconnectorcombiner losses 2 dB
Physical profileOperation mode FDDCyclic prefix type Normal (7 symbols per slot)Evolved packet core (EPC) bearer definitions 348 kbits (nonguaranteed bit rate)Subcarrier spacing 15 kHz
Admission control parametersPhysical downlink control channel (PDCCH) symbols per subframe 3UL loading factor 1DL loading factor 1Inactive bearer timeout 20 sec
Buffer status report parametersPeriodic timer 5 subframesRetransmission timer 2560 subframes
L1L2 control parametersReserved size 2 RBsCyclic shifts 6Starting RB preserver for Format 1 messages 0Allocation periodicity 5 subframes
Random access (RA) parametersNumber of preambles 64Preamble format Format 0 (1-subframe long)Number of RA resources per frame 4Preamble retransmission limit 5 subframesRA response timer 5 subframesContention resolution timer 40 subframes
HARQ parametersMaximal number of retransmissions 3 (UL and DL)HARQ retransmission timer 8 subframes (UL and DL)Maximal number of HARQ processes 8 per UE (UL and DL)
A radio model of the network corresponds to the require-ments of ITU-T Recommendation M1225
The algorithms proposed in the paper are denoted asfollows
(i) GBC (greedy buffer Control) where the target buffersize equals 0 for all the PUs
(ii) NBC (nongreedy buffer control) with the target buffersize calculated according to (37a) and (37b)
(iii) MBC (Minimal Buffer Control) with 119879 = 10 slots andthe target buffer size given by (38a)
(iv) ABC (Average Buffer Control) with 119879 = 10 slots andthe target buffer size equaling (38b)
Two previously proposed schemes used to benchmark theperformance of the algorithms proposed in this paper are
(i) UBA (Utility Based Allocation) presented in [11]where the network resources (bandwidth and trans-mission power) are allocated to the UL channels tomaximize the total transmission rate of the userssubject to the capacity and transmission power con-straints
Mobile Information Systems 17
0 10 20 30 40 50 60 70 80Average SNR (dB)
UBADPCGBC
NBCMBCABC
30
35
40
45
50
55
60
65
70
Dela
y fo
r SU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
012
015
018
021
024
027
03
033
Loss
for S
Us (
)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
250
300
350
400
450
500Th
roug
hput
for S
Us (
kbits
s)
Figure 6 Mean throughput packet delay and loss for SUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
(ii) DPC (Delay Power Control) derived in [5] whichis used to balance the transmission delay againsttransmission power in wireless channels between theeNB and the users
We also gather simulation results for a proposed resourceallocation approach in Scenario 2 with different settings ofthe parameters120572
119894and V and benchmark its performancewith
the performance of the algorithm in Scenario 1All algorithms are simulated using identical settings
The data traffic in simulations is represented by voice overInternet Protocol (VoIP) video and Hypertext TransferProtocol (HTTP) applications mixed in proportion 2 3 5using the models defined in [37]
42 Complexity and Fairness Issues Let us first evaluatethe complexity and the fairness of resource allocation indifferent algorithms Figure 1 shows the average numberof iterations before convergence for UBA DPC and theproposed algorithms in Scenario 1 (denoted as MBC) andScenario 2 gathered in simulations with 119899 = 100 PUs andaverage SNR = 0 dB Note that the target buffer size for thePUs is calculated according to (38a) with T = 10 slots (inScenarios 1 and 2) and 120572
119894= 1 V = 119898 lowast 1Mbps (for
Scenario 2) Results demonstrate that the complexity of FPmethod deployed for resource allocation in Scenarios 1 and2 is exponential in size of the problem (which correspondsto the findings reported in [31]) and is comparable to thecomplexities of other techniques (UBA and DPC)
18 Mobile Information Systems
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
080020 090070050 060 100000 030010 040120572i
10
20
30
40
50
60
70
80
90
100
110
Dela
y fo
r PU
s (m
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
040030 090000 080060010 020 050 100070120572i
005
010
015
020
025
030
035
040
045
050
Loss
for P
Us (
)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
030020 040 090010 060 070 080 100000 050120572i
Figure 7 Mean throughput packet delay and loss for the PUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
Figure 2 shows the fairness of different methods calcu-lated according to Jainrsquos equation [38] as
119865PU =
(sum119894isinI 119903119875119894)
2
119899 sdot sum119894isinI 1199032
119875119894
119865SU =
(sum119895isinJ 119903119878119895)
2
119898 sdot sum119895isinJ 1199032
119878119895
119865 =
(sum119894isinI 119903119875119894 + sum119895isinJ 119903119878119895)
2
(119899 + 119898) sdot (sum119894isinI 1199032
119875119894+ sum119895isinJ 1199032
119878119895)
(45)
where 119865PU 119865SU and 119865 stand for Jainrsquos index of fairness forthe PUs SUs and all of the users respectively 119903
119875119894 119903119878119895
arethe mean throughputs for PU
119894and SU
119895 respectively Results
have been gathered for 119899 = 100 PUs 119898 = 100 SUs average
Mobile Information Systems 19
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
410
420
430
440
450
460
470
480
490
500
510Th
roug
hput
for S
Us (
kbits
s)
010 020 080 090050 060 070030 100000 040120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
15
20
25
30
35
40
45
50
Dela
y fo
r SU
s (m
s)
070 090030 040 050 080000 020010 100060120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
007
009
011
013
015
017
019
021
023
Loss
for S
Us (
)
080070 090020 050 060030 100040010000120572i
Figure 8 Mean throughput packet delay and loss for the SUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
SNR = 0 dB and target buffer size for the PUs calculatedaccording to (38a) (Scenarios 1 and 2) with different settingsof 120572119894and V in Scenario 2
It follows from these graphs that the fairness index amongall of the users (denoted as 119865) is higher in Scenario 2 with120572119894= 1 and lower in Scenario 1 and Scenario 2 with 120572
119894= 0
Such results are rather expectable in Scenario 1 and Scenario2 with 120572
119894= 0 the SUs are served for free on a best-effort
basis whereas the PUs enjoy full QoS guarantees Hence thenetwork resources are shared nonequally between the PUs
and the SUs with most of the RBs allocated to the PUs andthe rest of the bandwidth distributed among the SUs Onthe other hand the fairness index for the PUs and SUs (ie119865PU and 119865SU) is rather high in both scenarios with differentsettings of 120572
119894and V which indicates that the users of the same
type are treated equally during resource allocation
43 Simulation Results in Scenario 1 Let us evaluate theperformance of a resource allocation algorithm in Scenario1 in terms of mean throughput packet end-to-end delay and
20 Mobile Information Systems
MBC
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
20
30
40
50
60
70
80
90
Dela
y fo
r PU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
005
010
015
020
025
030
035
040
045
Loss
for P
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 9 Mean throughput packet delay and loss for the PUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
loss for different user types Figures 3ndash6 show results obtainedin simulations with 119899 = 100 PUs and average SNR = 0 dBResults demonstrate that aUBA scheme has the largest packetdelay and loss and the lowest throughput for both the PUs andthe SUs A poor performance of this scheme is explained asfollows
(i) QoS protection of PUs is not considered in UBAHence the throughput delay and loss are the samefor PUs and SUs
(ii) Buffer sizes of individual users are not consideredin resource allocation and therefore the QoS for
Mobile Information Systems 21
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
30
50
70
90
110
130
Dela
y fo
r SU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
000
010
020
030
040
050
060
Loss
for S
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
different users varies significantly (since differentusers have different traffic demands)
(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer
size and therefore there is no need to maximize theirtransmission rate and spend the network resources
Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
16 Mobile Information Systems
Table 2 Simulation parameters of the model
Parameter ValueRadio network model
Pass loss 119871 = 40log10119877 + 30log
10119891 + 49 119877 distance (km) 119891
carrier frequency (Hz)
Shadow fading Log-normal shadow fading with a standard deviation of1012 dB for outdoorindoor users
Penetration loss The average building penetration loss is 12 dB with astandard deviation of 8 dB
Multipath fading Spatial Channel Model (SCM) Suburban macroUE velocity 0 kmsTransmitterreceiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver noise figure 5 dBThermal noise density minus174 dBmHzCableconnectorcombiner losses 2 dB
Physical profileOperation mode FDDCyclic prefix type Normal (7 symbols per slot)Evolved packet core (EPC) bearer definitions 348 kbits (nonguaranteed bit rate)Subcarrier spacing 15 kHz
Admission control parametersPhysical downlink control channel (PDCCH) symbols per subframe 3UL loading factor 1DL loading factor 1Inactive bearer timeout 20 sec
Buffer status report parametersPeriodic timer 5 subframesRetransmission timer 2560 subframes
L1L2 control parametersReserved size 2 RBsCyclic shifts 6Starting RB preserver for Format 1 messages 0Allocation periodicity 5 subframes
Random access (RA) parametersNumber of preambles 64Preamble format Format 0 (1-subframe long)Number of RA resources per frame 4Preamble retransmission limit 5 subframesRA response timer 5 subframesContention resolution timer 40 subframes
HARQ parametersMaximal number of retransmissions 3 (UL and DL)HARQ retransmission timer 8 subframes (UL and DL)Maximal number of HARQ processes 8 per UE (UL and DL)
A radio model of the network corresponds to the require-ments of ITU-T Recommendation M1225
The algorithms proposed in the paper are denoted asfollows
(i) GBC (greedy buffer Control) where the target buffersize equals 0 for all the PUs
(ii) NBC (nongreedy buffer control) with the target buffersize calculated according to (37a) and (37b)
(iii) MBC (Minimal Buffer Control) with 119879 = 10 slots andthe target buffer size given by (38a)
(iv) ABC (Average Buffer Control) with 119879 = 10 slots andthe target buffer size equaling (38b)
Two previously proposed schemes used to benchmark theperformance of the algorithms proposed in this paper are
(i) UBA (Utility Based Allocation) presented in [11]where the network resources (bandwidth and trans-mission power) are allocated to the UL channels tomaximize the total transmission rate of the userssubject to the capacity and transmission power con-straints
Mobile Information Systems 17
0 10 20 30 40 50 60 70 80Average SNR (dB)
UBADPCGBC
NBCMBCABC
30
35
40
45
50
55
60
65
70
Dela
y fo
r SU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
012
015
018
021
024
027
03
033
Loss
for S
Us (
)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
250
300
350
400
450
500Th
roug
hput
for S
Us (
kbits
s)
Figure 6 Mean throughput packet delay and loss for SUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
(ii) DPC (Delay Power Control) derived in [5] whichis used to balance the transmission delay againsttransmission power in wireless channels between theeNB and the users
We also gather simulation results for a proposed resourceallocation approach in Scenario 2 with different settings ofthe parameters120572
119894and V and benchmark its performancewith
the performance of the algorithm in Scenario 1All algorithms are simulated using identical settings
The data traffic in simulations is represented by voice overInternet Protocol (VoIP) video and Hypertext TransferProtocol (HTTP) applications mixed in proportion 2 3 5using the models defined in [37]
42 Complexity and Fairness Issues Let us first evaluatethe complexity and the fairness of resource allocation indifferent algorithms Figure 1 shows the average numberof iterations before convergence for UBA DPC and theproposed algorithms in Scenario 1 (denoted as MBC) andScenario 2 gathered in simulations with 119899 = 100 PUs andaverage SNR = 0 dB Note that the target buffer size for thePUs is calculated according to (38a) with T = 10 slots (inScenarios 1 and 2) and 120572
119894= 1 V = 119898 lowast 1Mbps (for
Scenario 2) Results demonstrate that the complexity of FPmethod deployed for resource allocation in Scenarios 1 and2 is exponential in size of the problem (which correspondsto the findings reported in [31]) and is comparable to thecomplexities of other techniques (UBA and DPC)
18 Mobile Information Systems
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
080020 090070050 060 100000 030010 040120572i
10
20
30
40
50
60
70
80
90
100
110
Dela
y fo
r PU
s (m
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
040030 090000 080060010 020 050 100070120572i
005
010
015
020
025
030
035
040
045
050
Loss
for P
Us (
)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
030020 040 090010 060 070 080 100000 050120572i
Figure 7 Mean throughput packet delay and loss for the PUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
Figure 2 shows the fairness of different methods calcu-lated according to Jainrsquos equation [38] as
119865PU =
(sum119894isinI 119903119875119894)
2
119899 sdot sum119894isinI 1199032
119875119894
119865SU =
(sum119895isinJ 119903119878119895)
2
119898 sdot sum119895isinJ 1199032
119878119895
119865 =
(sum119894isinI 119903119875119894 + sum119895isinJ 119903119878119895)
2
(119899 + 119898) sdot (sum119894isinI 1199032
119875119894+ sum119895isinJ 1199032
119878119895)
(45)
where 119865PU 119865SU and 119865 stand for Jainrsquos index of fairness forthe PUs SUs and all of the users respectively 119903
119875119894 119903119878119895
arethe mean throughputs for PU
119894and SU
119895 respectively Results
have been gathered for 119899 = 100 PUs 119898 = 100 SUs average
Mobile Information Systems 19
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
410
420
430
440
450
460
470
480
490
500
510Th
roug
hput
for S
Us (
kbits
s)
010 020 080 090050 060 070030 100000 040120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
15
20
25
30
35
40
45
50
Dela
y fo
r SU
s (m
s)
070 090030 040 050 080000 020010 100060120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
007
009
011
013
015
017
019
021
023
Loss
for S
Us (
)
080070 090020 050 060030 100040010000120572i
Figure 8 Mean throughput packet delay and loss for the SUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
SNR = 0 dB and target buffer size for the PUs calculatedaccording to (38a) (Scenarios 1 and 2) with different settingsof 120572119894and V in Scenario 2
It follows from these graphs that the fairness index amongall of the users (denoted as 119865) is higher in Scenario 2 with120572119894= 1 and lower in Scenario 1 and Scenario 2 with 120572
119894= 0
Such results are rather expectable in Scenario 1 and Scenario2 with 120572
119894= 0 the SUs are served for free on a best-effort
basis whereas the PUs enjoy full QoS guarantees Hence thenetwork resources are shared nonequally between the PUs
and the SUs with most of the RBs allocated to the PUs andthe rest of the bandwidth distributed among the SUs Onthe other hand the fairness index for the PUs and SUs (ie119865PU and 119865SU) is rather high in both scenarios with differentsettings of 120572
119894and V which indicates that the users of the same
type are treated equally during resource allocation
43 Simulation Results in Scenario 1 Let us evaluate theperformance of a resource allocation algorithm in Scenario1 in terms of mean throughput packet end-to-end delay and
20 Mobile Information Systems
MBC
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
20
30
40
50
60
70
80
90
Dela
y fo
r PU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
005
010
015
020
025
030
035
040
045
Loss
for P
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 9 Mean throughput packet delay and loss for the PUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
loss for different user types Figures 3ndash6 show results obtainedin simulations with 119899 = 100 PUs and average SNR = 0 dBResults demonstrate that aUBA scheme has the largest packetdelay and loss and the lowest throughput for both the PUs andthe SUs A poor performance of this scheme is explained asfollows
(i) QoS protection of PUs is not considered in UBAHence the throughput delay and loss are the samefor PUs and SUs
(ii) Buffer sizes of individual users are not consideredin resource allocation and therefore the QoS for
Mobile Information Systems 21
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
30
50
70
90
110
130
Dela
y fo
r SU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
000
010
020
030
040
050
060
Loss
for S
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
different users varies significantly (since differentusers have different traffic demands)
(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer
size and therefore there is no need to maximize theirtransmission rate and spend the network resources
Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mobile Information Systems 17
0 10 20 30 40 50 60 70 80Average SNR (dB)
UBADPCGBC
NBCMBCABC
30
35
40
45
50
55
60
65
70
Dela
y fo
r SU
s (m
s)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
012
015
018
021
024
027
03
033
Loss
for S
Us (
)
250 5 10 15 20 30minus10 minus5
Average SNR (dB)
UBADPCGBC
NBCMBCABC
250
300
350
400
450
500Th
roug
hput
for S
Us (
kbits
s)
Figure 6 Mean throughput packet delay and loss for SUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB
(ii) DPC (Delay Power Control) derived in [5] whichis used to balance the transmission delay againsttransmission power in wireless channels between theeNB and the users
We also gather simulation results for a proposed resourceallocation approach in Scenario 2 with different settings ofthe parameters120572
119894and V and benchmark its performancewith
the performance of the algorithm in Scenario 1All algorithms are simulated using identical settings
The data traffic in simulations is represented by voice overInternet Protocol (VoIP) video and Hypertext TransferProtocol (HTTP) applications mixed in proportion 2 3 5using the models defined in [37]
42 Complexity and Fairness Issues Let us first evaluatethe complexity and the fairness of resource allocation indifferent algorithms Figure 1 shows the average numberof iterations before convergence for UBA DPC and theproposed algorithms in Scenario 1 (denoted as MBC) andScenario 2 gathered in simulations with 119899 = 100 PUs andaverage SNR = 0 dB Note that the target buffer size for thePUs is calculated according to (38a) with T = 10 slots (inScenarios 1 and 2) and 120572
119894= 1 V = 119898 lowast 1Mbps (for
Scenario 2) Results demonstrate that the complexity of FPmethod deployed for resource allocation in Scenarios 1 and2 is exponential in size of the problem (which correspondsto the findings reported in [31]) and is comparable to thecomplexities of other techniques (UBA and DPC)
18 Mobile Information Systems
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
080020 090070050 060 100000 030010 040120572i
10
20
30
40
50
60
70
80
90
100
110
Dela
y fo
r PU
s (m
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
040030 090000 080060010 020 050 100070120572i
005
010
015
020
025
030
035
040
045
050
Loss
for P
Us (
)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
030020 040 090010 060 070 080 100000 050120572i
Figure 7 Mean throughput packet delay and loss for the PUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
Figure 2 shows the fairness of different methods calcu-lated according to Jainrsquos equation [38] as
119865PU =
(sum119894isinI 119903119875119894)
2
119899 sdot sum119894isinI 1199032
119875119894
119865SU =
(sum119895isinJ 119903119878119895)
2
119898 sdot sum119895isinJ 1199032
119878119895
119865 =
(sum119894isinI 119903119875119894 + sum119895isinJ 119903119878119895)
2
(119899 + 119898) sdot (sum119894isinI 1199032
119875119894+ sum119895isinJ 1199032
119878119895)
(45)
where 119865PU 119865SU and 119865 stand for Jainrsquos index of fairness forthe PUs SUs and all of the users respectively 119903
119875119894 119903119878119895
arethe mean throughputs for PU
119894and SU
119895 respectively Results
have been gathered for 119899 = 100 PUs 119898 = 100 SUs average
Mobile Information Systems 19
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
410
420
430
440
450
460
470
480
490
500
510Th
roug
hput
for S
Us (
kbits
s)
010 020 080 090050 060 070030 100000 040120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
15
20
25
30
35
40
45
50
Dela
y fo
r SU
s (m
s)
070 090030 040 050 080000 020010 100060120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
007
009
011
013
015
017
019
021
023
Loss
for S
Us (
)
080070 090020 050 060030 100040010000120572i
Figure 8 Mean throughput packet delay and loss for the SUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
SNR = 0 dB and target buffer size for the PUs calculatedaccording to (38a) (Scenarios 1 and 2) with different settingsof 120572119894and V in Scenario 2
It follows from these graphs that the fairness index amongall of the users (denoted as 119865) is higher in Scenario 2 with120572119894= 1 and lower in Scenario 1 and Scenario 2 with 120572
119894= 0
Such results are rather expectable in Scenario 1 and Scenario2 with 120572
119894= 0 the SUs are served for free on a best-effort
basis whereas the PUs enjoy full QoS guarantees Hence thenetwork resources are shared nonequally between the PUs
and the SUs with most of the RBs allocated to the PUs andthe rest of the bandwidth distributed among the SUs Onthe other hand the fairness index for the PUs and SUs (ie119865PU and 119865SU) is rather high in both scenarios with differentsettings of 120572
119894and V which indicates that the users of the same
type are treated equally during resource allocation
43 Simulation Results in Scenario 1 Let us evaluate theperformance of a resource allocation algorithm in Scenario1 in terms of mean throughput packet end-to-end delay and
20 Mobile Information Systems
MBC
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
20
30
40
50
60
70
80
90
Dela
y fo
r PU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
005
010
015
020
025
030
035
040
045
Loss
for P
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 9 Mean throughput packet delay and loss for the PUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
loss for different user types Figures 3ndash6 show results obtainedin simulations with 119899 = 100 PUs and average SNR = 0 dBResults demonstrate that aUBA scheme has the largest packetdelay and loss and the lowest throughput for both the PUs andthe SUs A poor performance of this scheme is explained asfollows
(i) QoS protection of PUs is not considered in UBAHence the throughput delay and loss are the samefor PUs and SUs
(ii) Buffer sizes of individual users are not consideredin resource allocation and therefore the QoS for
Mobile Information Systems 21
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
30
50
70
90
110
130
Dela
y fo
r SU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
000
010
020
030
040
050
060
Loss
for S
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
different users varies significantly (since differentusers have different traffic demands)
(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer
size and therefore there is no need to maximize theirtransmission rate and spend the network resources
Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
18 Mobile Information Systems
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
080020 090070050 060 100000 030010 040120572i
10
20
30
40
50
60
70
80
90
100
110
Dela
y fo
r PU
s (m
s)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
040030 090000 080060010 020 050 100070120572i
005
010
015
020
025
030
035
040
045
050
Loss
for P
Us (
)
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
030020 040 090010 060 070 080 100000 050120572i
Figure 7 Mean throughput packet delay and loss for the PUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
Figure 2 shows the fairness of different methods calcu-lated according to Jainrsquos equation [38] as
119865PU =
(sum119894isinI 119903119875119894)
2
119899 sdot sum119894isinI 1199032
119875119894
119865SU =
(sum119895isinJ 119903119878119895)
2
119898 sdot sum119895isinJ 1199032
119878119895
119865 =
(sum119894isinI 119903119875119894 + sum119895isinJ 119903119878119895)
2
(119899 + 119898) sdot (sum119894isinI 1199032
119875119894+ sum119895isinJ 1199032
119878119895)
(45)
where 119865PU 119865SU and 119865 stand for Jainrsquos index of fairness forthe PUs SUs and all of the users respectively 119903
119875119894 119903119878119895
arethe mean throughputs for PU
119894and SU
119895 respectively Results
have been gathered for 119899 = 100 PUs 119898 = 100 SUs average
Mobile Information Systems 19
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
410
420
430
440
450
460
470
480
490
500
510Th
roug
hput
for S
Us (
kbits
s)
010 020 080 090050 060 070030 100000 040120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
15
20
25
30
35
40
45
50
Dela
y fo
r SU
s (m
s)
070 090030 040 050 080000 020010 100060120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
007
009
011
013
015
017
019
021
023
Loss
for S
Us (
)
080070 090020 050 060030 100040010000120572i
Figure 8 Mean throughput packet delay and loss for the SUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
SNR = 0 dB and target buffer size for the PUs calculatedaccording to (38a) (Scenarios 1 and 2) with different settingsof 120572119894and V in Scenario 2
It follows from these graphs that the fairness index amongall of the users (denoted as 119865) is higher in Scenario 2 with120572119894= 1 and lower in Scenario 1 and Scenario 2 with 120572
119894= 0
Such results are rather expectable in Scenario 1 and Scenario2 with 120572
119894= 0 the SUs are served for free on a best-effort
basis whereas the PUs enjoy full QoS guarantees Hence thenetwork resources are shared nonequally between the PUs
and the SUs with most of the RBs allocated to the PUs andthe rest of the bandwidth distributed among the SUs Onthe other hand the fairness index for the PUs and SUs (ie119865PU and 119865SU) is rather high in both scenarios with differentsettings of 120572
119894and V which indicates that the users of the same
type are treated equally during resource allocation
43 Simulation Results in Scenario 1 Let us evaluate theperformance of a resource allocation algorithm in Scenario1 in terms of mean throughput packet end-to-end delay and
20 Mobile Information Systems
MBC
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
20
30
40
50
60
70
80
90
Dela
y fo
r PU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
005
010
015
020
025
030
035
040
045
Loss
for P
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 9 Mean throughput packet delay and loss for the PUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
loss for different user types Figures 3ndash6 show results obtainedin simulations with 119899 = 100 PUs and average SNR = 0 dBResults demonstrate that aUBA scheme has the largest packetdelay and loss and the lowest throughput for both the PUs andthe SUs A poor performance of this scheme is explained asfollows
(i) QoS protection of PUs is not considered in UBAHence the throughput delay and loss are the samefor PUs and SUs
(ii) Buffer sizes of individual users are not consideredin resource allocation and therefore the QoS for
Mobile Information Systems 21
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
30
50
70
90
110
130
Dela
y fo
r SU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
000
010
020
030
040
050
060
Loss
for S
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
different users varies significantly (since differentusers have different traffic demands)
(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer
size and therefore there is no need to maximize theirtransmission rate and spend the network resources
Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mobile Information Systems 19
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
410
420
430
440
450
460
470
480
490
500
510Th
roug
hput
for S
Us (
kbits
s)
010 020 080 090050 060 070030 100000 040120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
15
20
25
30
35
40
45
50
Dela
y fo
r SU
s (m
s)
070 090030 040 050 080000 020010 100060120572i
v = 0
v = m lowast 1kbpsv = m lowast 10kbps
v = m lowast 100 kbpsv = m lowast 1MbpsMBC
007
009
011
013
015
017
019
021
023
Loss
for S
Us (
)
080070 090020 050 060030 100040010000120572i
Figure 8 Mean throughput packet delay and loss for the SUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average
SNR = 0 dB
SNR = 0 dB and target buffer size for the PUs calculatedaccording to (38a) (Scenarios 1 and 2) with different settingsof 120572119894and V in Scenario 2
It follows from these graphs that the fairness index amongall of the users (denoted as 119865) is higher in Scenario 2 with120572119894= 1 and lower in Scenario 1 and Scenario 2 with 120572
119894= 0
Such results are rather expectable in Scenario 1 and Scenario2 with 120572
119894= 0 the SUs are served for free on a best-effort
basis whereas the PUs enjoy full QoS guarantees Hence thenetwork resources are shared nonequally between the PUs
and the SUs with most of the RBs allocated to the PUs andthe rest of the bandwidth distributed among the SUs Onthe other hand the fairness index for the PUs and SUs (ie119865PU and 119865SU) is rather high in both scenarios with differentsettings of 120572
119894and V which indicates that the users of the same
type are treated equally during resource allocation
43 Simulation Results in Scenario 1 Let us evaluate theperformance of a resource allocation algorithm in Scenario1 in terms of mean throughput packet end-to-end delay and
20 Mobile Information Systems
MBC
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
20
30
40
50
60
70
80
90
Dela
y fo
r PU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
005
010
015
020
025
030
035
040
045
Loss
for P
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 9 Mean throughput packet delay and loss for the PUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
loss for different user types Figures 3ndash6 show results obtainedin simulations with 119899 = 100 PUs and average SNR = 0 dBResults demonstrate that aUBA scheme has the largest packetdelay and loss and the lowest throughput for both the PUs andthe SUs A poor performance of this scheme is explained asfollows
(i) QoS protection of PUs is not considered in UBAHence the throughput delay and loss are the samefor PUs and SUs
(ii) Buffer sizes of individual users are not consideredin resource allocation and therefore the QoS for
Mobile Information Systems 21
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
30
50
70
90
110
130
Dela
y fo
r SU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
000
010
020
030
040
050
060
Loss
for S
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
different users varies significantly (since differentusers have different traffic demands)
(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer
size and therefore there is no need to maximize theirtransmission rate and spend the network resources
Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
20 Mobile Information Systems
MBC
915
920
925
930
935
940
945
950Th
roug
hput
for P
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
20
30
40
50
60
70
80
90
Dela
y fo
r PU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
005
010
015
020
025
030
035
040
045
Loss
for P
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 9 Mean throughput packet delay and loss for the PUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
loss for different user types Figures 3ndash6 show results obtainedin simulations with 119899 = 100 PUs and average SNR = 0 dBResults demonstrate that aUBA scheme has the largest packetdelay and loss and the lowest throughput for both the PUs andthe SUs A poor performance of this scheme is explained asfollows
(i) QoS protection of PUs is not considered in UBAHence the throughput delay and loss are the samefor PUs and SUs
(ii) Buffer sizes of individual users are not consideredin resource allocation and therefore the QoS for
Mobile Information Systems 21
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
30
50
70
90
110
130
Dela
y fo
r SU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
000
010
020
030
040
050
060
Loss
for S
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
different users varies significantly (since differentusers have different traffic demands)
(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer
size and therefore there is no need to maximize theirtransmission rate and spend the network resources
Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mobile Information Systems 21
0
100
200
300
400
500
600
700
800
900
1000Th
roug
hput
for S
Us (
kbits
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
10
30
50
70
90
110
130
Dela
y fo
r SU
s (m
s)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
000
010
020
030
040
050
060
Loss
for S
Us (
)
20 40 60 80 1000Number of SUs m
MBC120572i = 0 v = 0
120572i = 1 v = 0
120572i = 0 v = m lowast 1Mbps
120572i = 1 v = m lowast 1Mbps
Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB
different users varies significantly (since differentusers have different traffic demands)
(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer
size and therefore there is no need to maximize theirtransmission rate and spend the network resources
Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
22 Mobile Information Systems
channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC
GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays
The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)
44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572
119894and V and the target buffer size of the PUs
calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB
Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572
119894and V The
parameter 120572119894has negative impact on service performance for
the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572
119894 which
leads to decreased throughput and increased delay and lossfor these users
We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves
45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572
119894and V in Scenario 2
Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB
Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572
119894= 0 because in this case the
PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572
119894=
1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources
5 Conclusion
Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002
[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008
[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007
[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011
[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999
[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009
[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012
[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mobile Information Systems 23
networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011
[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011
[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009
[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011
[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008
[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012
[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007
[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011
[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008
[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011
[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952
[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961
[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007
[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008
[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978
[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000
[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006
[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001
[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003
[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013
[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012
[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014
[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009
[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004
[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988
[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000
[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS
36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report
httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf
[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014