research article an energy-efficient scheme for multirelay...

Research ArticleAn Energy-Efficient Scheme for Multirelay CooperativeNetworks with Energy Harvesting

Dingcheng Yang1 Chuanqi Zhu1 Lin Xiao1 Xiaomei Shen2 and Tiankui Zhang2

1 Information Engineering School Nanchang University Nanchang 330031 China2Beijing University of Posts and Telecommunications Beijing China

Correspondence should be addressed to Lin Xiao xiaolinncueducn

Received 16 June 2016 Revised 23 October 2016 Accepted 20 November 2016

Academic Editor Konstantinos Demestichas

Copyright copy 2016 Dingcheng Yang et alThis is an open access article distributed under theCreativeCommonsAttributionLicensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This study investigates an energy-efficient scheme in multirelay cooperative networks with energy harvesting where multiplesessions need to communicate with each other via the relay node A two-step optimal method is proposed which maximizes thesystem energy efficiency while taking into account the receiver circuit energy consumption Firstly the optimal power allocation forrelay nodes is determined to maximize the system throughput this is based on directional water-filling algorithm Secondly usingquantum particle swarm optimization (QPSO) a joint relay node selection and session grouping optimization is proposed Withthis algorithm sessions can be classified into multiple groups that are assisted by the specific relay node with the maximum energyefficiency This approach leads to a better global optimization in searching ability and efficiency Simulation results show that theproposed scheme can improve the energy efficiency effectively compared with direct transmission and opportunistic relay-selectedcooperative transmission

1 Introduction

With the rapid growth of wireless communications it isimportant to consider the costs in energy usage This isespecially true in cooperative networks where nodes are pow-ered by batteries with finite capacities as energy efficiency iscritical because it affects the operation time of the network[1] Hence improving the energy efficiency for cooperativenetworks is essential to mitigate the limited energy availablein nodes Therefore this gives us a good motivation toinvestigate the energy efficiency in cooperative networks

Network-coded cooperation schemes are considered asa promising technology to improve energy efficiency andnetwork throughput [2] Network coding nodes combinemultiple input data into one output stream to reduce thenumber of transmission time slots However the receivercircuit power consumption when network coding is used hasnot been rigorously considered before an omission that isaddressed in this paper

Moreover energy harvesting is a promising techniquethat can be used in relay nodes to increase flexibility andreduce the energy charge it can bring more energy efficiency

for wireless networks [3] Most of the existing studies focuson power allocation schemes for relay nodes in a scenariowithmultiple unicast sessions However when using networkcoding the network coding noise and receiver circuit powerconsumption increase as the size of session groups increasesHence there is a need to study how to perform relay nodeselection and session grouping for energy-efficient multirelaycooperative networks and that is the topic of this paper

11 Related Work Research about network-coded coopera-tive networks to improve network throughput is consideredin [4ndash8] In [3] the concept of network coding noise whichhinders the performance of the overall network was firstintroduced In [5] the authors analyzed the origin of thenoise by studying signal aggregation at relay nodes and signalextraction at destination nodes In [6] two novel closed-formpower allocation scheme was proposed to reduce networkcoding noise in two-unicast wireless systems Based on [6] ajoint group assignment and power allocation algorithm werestudied in [7] this aims to reduce network coding noise ina multiunicast cooperative network Furthermore the relay

Hindawi Publishing CorporationMobile Information SystemsVolume 2016 Article ID 5618935 10 pageshttpdxdoiorg10115520165618935

2 Mobile Information Systems

selection and session grouping problem was investigated in[8] as session grouping can effectively reduce network codingnoise However in all of these works the circuit energyconsumption with network coding was not considered

To achieve better tradeoff between network throughputand power consumption the metric energy efficiency is usedin [9ndash11] In [9] the authors studied the energy-efficientrelay selection and power allocation problem for a two-way relay channel based on network coding Paper [10]presented an opportunistic listening scheme to promoteenergy efficiency for network-coded cooperative networks intwo-unicast sessions Paper [11] proposed an energy-efficientmulticast scheme with network coding

Moreover energy harvesting technologies for coopera-tive networks have been investigated in [12ndash17] and theserepresent a promising approach for powering nodes In [12]an opportunistic wireless information and energy transferrelaying scheme was proposed by Lagrangian optimalityReference [13] used the directional water-filling algorithm tomaximize the sum-rate

In cooperative relay networks with energy harvestingthe relay nodes selected and the choice of power allocationscheme have a great impact on the system performance In[14] finite energy storage was considered in relay nodes anda relay selection scheme was proposed based on finite-stateMarkov chain In [15 16] the source nodes and relay nodeswere considered as energy harvesting nodes and then thesystem throughput was maximized by optimizing both relayselection and power allocation

Another line of work on joint wireless energy and infor-mation transmission in relay networks is simultaneous wire-less information and power transfer (SWIPT) Researchershave focused on improving energy efficiency and a partic-ularly relevant piece of work is [17] To maximize the totalenergy efficiency the authors proposed a joint relay selectionand resource allocation scheme for SWIPT relay networkswith multiple source nodes and destination nodes pairs andenergy harvesting relay nodes

Improving the energy efficiency in relay networks isof critical importance for resolving the energy shortage ofnodes In the literature [14ndash17] the energy arrival timeand the amount of harvested energy are known prior totransmission However in real systems the amount of theharvested energy is affected by many factors such as weatherand channel conditions so it is necessary to consider atransmission scheme that can efficiently use the harvestedenergy from random energy sources

12 Contributions and Organization In this paper we focuson a multirelay cooperative network where relay nodes arepowered by random energy sources Unlike previous worksour study considers network coding finite energy storageand energy harvesting The aim of this paper is to optimizeenergy efficiency in multirelay cooperative networks withenergy harvesting In [18] we have proposed an energy-efficient session grouping scheme in a single relay network-coded cooperative network In this work we extend ourprevious work to a multirelay cooperative network andconsider the energy harvesting technology

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Figure 1 Multirelay cooperative network model

Our contributions are concluded in three aspects

(i) The receiver circuit power consumptionwith networkcoding is analyzed

(ii) An optimal power allocation for relay nodes is pro-posed based on the directional water-filling algo-rithm

(iii) An energy-efficient relay selection and session group-ing scheme is proposed based on the quantumparticleswarm optimization (QPSO)

The rest of this paper is organized as follows Section 2presents the network model including the throughput modeland power consuming model Section 3 studies the optimalpower allocation scheme and jointly optimizing multirelayselection and session grouping scheme Section 4 shows thenumerical results and analysis for the proposed schemeSection 5 is the conclusion of this paper

2 Network Model

As is depicted in Figure 1 we consider a network-codedcooperative networkwhich consists of119873 sessions and119870 relaynodes in a square with dimensions 119863 times 119863 In this model weassume that the relay nodes operate in amplify-and-forward(AF) mode and use orthogonal channels Sessions that selectthe same node share one channel and transmit data undertime division multiple access (TDMA) Moreover the relaynodes can harvest energy from random energy sources suchas wind energy and solar energy

21 Total Throughput In cooperative relaying networksthere are three transmission schemes (i) direct transmission(ii) opportunistic relay-selected cooperative transmissionand (iii) network-coded cooperative transmissionThe trans-mitting power of relay nodes is not constant since the randomenergy arrivals in the relay nodes

In network-coded cooperative networks sessions in agroup are assumed to be relayed in equal power119875119898119903119896 is defined

Mobile Information Systems 3

as the transmit power of relay node 119903119896 for group 119898 Theamplification factor 120572119898119903119896 for 119903119896 is expressed as

10038161003816100381610038161003816120572119898119903119896 100381610038161003816100381610038162 = 11987511989811990311989610038161003816100381610038161198661199031198961198981003816100381610038161003816 1205902119903119896 + sum119904119897isin119866119903119896119898 119875119904119897 10038161003816100381610038161003816ℎ119904119897119903119896 100381610038161003816100381610038162 (1)

where 119866119903119896119898 denotes the set of sessions in group 119898 for 119903119896 |119866119903119896119898|is the cardinality of 119866119903119896119898 and 119875119904119897 captures the transmit powerof source node 119904119897

Under network-coded cooperative networks there exitsnetwork coding noise (NC noise) at each destination nodewhen extracting desired data from the combined data Weassume that a session (119904119899 119889119899) is in a group119866119903119896119898 so theNCnoise119911NC119889119899 at 119889119899 is expressed as

119911NC119889119899 = 119911119889119899 + 119904119897 =119904119899sum119904119897isin119866119903119896119898

120572119903119896ℎ119903119896119889119899119911119903119896 minus 119904119897 =119904119899sum119904119897isin119866119903119896119898

120572119903119896ℎ119903119896119889119899ℎ119904119897119903119896ℎ119904119897119889119899 119911119889119899 (2)

where 119911119889119899 and 119911119903119896 are the Gaussian noise at 119889119899 and 119903119896respectively and ℎ119906V denotes the channel gain between node119906 and node V

Suppose that the channel between all nodes followsa simplified channel model that combines the distance-dependent signal attenuation and long term shadowing withloss exponent 120572 gt 2 Thus ℎ119906V can be expressed as ℎ119906V =119906minusVminus120572 where 119906minusV represents the distance between node119906 and node V and 120572 is the channel loss exponent From (2)the variance of the NC noise at 119889119899 is shown as

1205902119889NC119899

= 1205902119889119899 + (10038161003816100381610038161198661199031198961198981003816100381610038161003816 minus 1) (120572119898119903119896ℎ119903119896119889119899)2 1205902119903119896+ 1205902119889119899 119904119897 =119904119899sum119904119897isin119866119903119896119898

(120572119898119903119896ℎ119904119897119903119896ℎ119903119896119889119899ℎ119904119897119889119899 )2 (3)

A session has the option to select a relay node fromdifferent available relay nodes in our network In additioneach session may use at most one relay node We assume that119873 sessions are sorted into119872 groups each session belongs toonly one group For notational simplicity 1198661199031198960 is defined asthe direct transmission group by using the channel of 119903119896 Weconsider data transmission for each group (|119866119903119896119898| sessions) ina time frame 119879 which is equally divided into |119866119903119896119898| + 1 timeslots For the first |119866119903119896119898| time slots source nodes transmit dataone by one while the relay node and each destination nodekeep receiving data from all source nodes At the last timeslot 119903119896 transmits the combined data which is received by eachdestination node to extract desired data 119905119899 is defined as thetime duration of each session then we have

119905119899 = 119879sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot1003816100381610038161003816119866119903119896119898100381610038161003816100381610038161003816100381610038161198661199031198961198981003816100381610038161003816 + 1 (4)

Thus the throughput for a session (119904119899 119889119899) is shown as

119877NC (119904119899 119903119896 119866119903119896119898) = 119905119899 sdot 119882 sdot 119868NC (119904119899 119903119896 119866119903119896119898)119879= 119882sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 times

1003816100381610038161003816119866119903119896119898100381610038161003816100381610038161003816100381610038161198661199031198961198981003816100381610038161003816 + 1times 119868NC (119904119899 119903119896 119866119903119896119898)

(5)

where (119904119899 119889119899) isin 119866119903119896119898 and 119882 is the bandwidth of each relaynode 119868NC(119904119899 119903119896 119866119903119896119898) is the mutual information for a session(119904119899 119889119899) it is expressed as

119868NC (119904119899 119903119896 119866119903119896119898) = log2(1 + 120574119904119899119889119899+ 12057411990411989911990311989612057411990311989611988911989910038161003816100381610038161198661199031198961198981003816100381610038161003816 (1205902119889NC

119899

1205902119889119899) + 120574119903119896119889119899 + (1205902

119889NC119899

1205902119889119899)sum119904119897isin119866119903119896119898 120574119904119897119903119896)

(6)

where 120574119904119899119889119899 = (1198751199041198991205902119889119899)|ℎ119904119899119889119899 |2 120574119904119899119903119896 = (1198751199041198991205902119903119896)|ℎ119904119899119903119896 |2 and120574119903119896119889119899 = (1198751199031198961205902119889119899)|ℎ119903119896119889119899 |2 From (5) and (6) the throughput fora session (119904119899 119889119899) under network-coded cooperative transmis-sion scheme is

119877NC (119904119899 119903119896 119889119899) = 119882sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 times1003816100381610038161003816119866119903119896119898100381610038161003816100381610038161003816100381610038161198661199031198961198981003816100381610038161003816 + 1 times log2(1

+ 120574119904119899119889119899+ 12057411990411989911990311989612057411990311989611988911989910038161003816100381610038161198661199031198961198981003816100381610038161003816 (1205902119889NC

119899

1205902119889119899) + 120574119903119896119889119899 + (1205902

119889NC119899

1205902119889119899)sum119904119897isin119866119903119896119898 120574119904119897119903119896)

(7)

Similar to our previous work for opportunistic coopera-tive communication scheme and network-coded cooperativecommunication without grouping scheme throughput (7) isalso appropriate when |119866119903119896119898| = 1 and |119866119903119896119898| = 119873 respectively[18] Under direct transmission scheme the throughput for(119904119899 119889119899) is

119877119863 (119904119899 119903119896 119889119899) = 119882sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 times log (1 + 119904119899119889119899) (8)

22 Power Consumption In this part we derive the expres-sion of total power consumption in network-coded coopera-tive networks

We denote the transmission power for source nodes as119875119904 Assuming that the transmitting circuit power 119875ct andthe receiver circuit power 119875cr are the same for a group innetwork-coded cooperative networks with grouping schemethe destination nodes keep receiving data while the relaynode keeps receiving data except for the last slot Thereceiving time for each destination node in a group 119866119903119896119898 is

119905119889-cr = 119879sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot 10038161003816100381610038161198661199031198961198981003816100381610038161003816 (9)


Thus in a time frame 119879 the total receiver circuit energyconsumption at destination nodes is

119864119889 cr (119866119903119896119898) = 119905119889 cr119875cr 10038161003816100381610038161198661199031198961198981003816100381610038161003816 (10)

Let 119905119903-cr denote the receiving time of relay node 119903119896 for 119866119903119896119898then we have

119905119903-cr = 119879sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot10038161003816100381610038161198661199031198961198981003816100381610038161003816210038161003816100381610038161198661199031198961198981003816100381610038161003816 + 1 (11)

We assume that the transmission time 119905send of source nodesand relay nodes for 119866119903119896119898 are the same it is shown as

119905send = 119879sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot1003816100381610038161003816119866119903119896119898100381610038161003816100381610038161003816100381610038161198661199031198961198981003816100381610038161003816 + 1 (12)

Thus the total energy consumption for the source nodes andrelay nodes can be written as follows respectively

119864119904119905 (119866119903119896119898) = (119875119904 + 119875ct) sdot 119905send sdot 10038161003816100381610038161198661199031198961198981003816100381610038161003816 119864119903119896sum (119866119903119896119898) = (119875119898119903119896 + 119875ct) sdot 119905send + 119875cr sdot 119905119903cr (13)

Until now the total power consumption for transmitting 119866119903119896119898is

119875 (119866119903119896119898) = 119864119889 cr (119866119903119896119898) + 119864119904 119905 (119866119903119896119898) + 119864119903119896 sum (119866119903119896119898)119879 119898 ge 1 (14)

From (14) the total power consumption consists of threemain components source nodes relay nodes and destinationnodes From (11)ndash(13) 119875(119866119903119896119898) can be rewritten as follows

119875 (119866119903119896119898) = 1sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot10038161003816100381610038161198661199031198961198981003816100381610038161003816210038161003816100381610038161198661199031198961198981003816100381610038161003816 + 1

sdot (119875119904 + (1 + 110038161003816100381610038161198661199031198961198981003816100381610038161003816) 119875ct + (2 + 10038161003816100381610038161198661199031198961198981003816100381610038161003816) 119875cr + 11987511989811990311989610038161003816100381610038161198661199031198961198981003816100381610038161003816) (15)

For opportunistic cooperative communication schemeand network-coded cooperative communication withoutgrouping scheme the total receiver circuit power consump-tion for a group 119866119903119896119898 is obtained by substituting |119866119903119896119898| = 1 and|119866119903119896119898| = 119873 into (15) For the direct transmission group eachdestination node keeps receiving data for its time slot Hencethe power consumption of direct transmission group can beexpressed as

119875 (1198661199031198960 ) = 10038161003816100381610038161198661199031198960 1003816100381610038161003816sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot (119875cr + 119875119904 + 119875ct) (16)

Combining (15) and (16) the expression of total powerconsumption in network-coded cooperative networks is

119875total = 119870sum119896=1

119872minus1sum119898=0

119875 (119866119903119896119898) (17)

3 Joint Optimization of Relay Selection andSession Grouping

In this section we divide the energy efficiency problem intotwo subproblems the power allocation problem and theenergy-efficient transmission optimization problem For thefirst problem an energy allocation scheme is proposed basedon directional water-filling structure For the second prob-lem we use quantum particle swarm optimization (QPSO)and propose a new algorithm which jointly considers relayselection problem and session grouping based on the solutionof the first problem

31 Optimal Power Allocation The conventional water-fillingalgorithm is a useful technique in wireless communicationfor allocating power between different channels It impliesallocating more power to the channel with the higher SNRIn [19] a directional water-filling algorithm was introducedwhich considers the causality constraints on the energy usageIn this paper we solve the optimal power allocation problembased on directional water-filling

The relay nodes harvest energy from unpredictableenergy sources such as solar energy and wind energy whichgreatly depend on the conditions of the environment

We assume energy arrivals 1198641 1198642 119864119873 occur in thetime instants 1199051 1199052 119905119873 by a deadline 119879 the duration ofeach slot is 119871119899 = 119905119899 minus 119905119899minus1 Let 1199050 = 0 for simplicity Thetransmission rates are affected by the incoming energy Theobjective is to maximize the throughput by optimizing powerallocation for relay nodes

It is assumed that the transmit power of each relayis constant within each slot Each relay node is equippedwith an energy receiver The harvested energy is stored in arechargeable battery Thus the energy causality constraintsare obtained as follows

119899sum119899=1

119871119899119875119899 le 119899minus1sum119899=0

119864119894 119899 = 1 2 119873 + 1 (18)

119899sum119899=0

119864119899 minus 119899sum119899=1

119871119899119875119899 le 119864max 119899 = 1 119873 (19)

where 119875119899 denotes the transmit power of relay nodes duringslot 119871119899 and 119864max is the storage capacity of the battery atrelay nodes It is also assumed that 1198640 is the initial batteryenergy and 1198640 gt 0 Then the optimization problem can beformulated as

max119875119899ge0

119873+1sum119899=1

1198821198711198992 log (1 + 119875119899)st

119899sum119899=1

119871119899119875119899 le 119899minus1sum119899=0

119864119899 119899 = 1 2 119873 + 1119899sum119899=0

119864119899 minus 119899sum119899=1

119871119899119875119899 le 119864max 119899 = 1 119873(20)

Since the objective function in (20) is not convex con-straint (18) and constraint (19) are linear in 119875119899 which are


convex functions Hence the above optimization problem isa convex optimization problem We define the Lagrangianfunction as follows

120589 = 119873+1sum119899=1

1198821198711198992 log (1 + 119875119899)minus 119873+1sum119899=1

120591119899( 119899sum119899=1

119871119899119875119899 minus 119899minus1sum119899=0

119864119899) (21)

where 120591119899 is the Lagrangian multipliers and 120591119899 gt 0 Additionalcomplimentary slackness conditions can be expressed asfollows

120591119899( 119899sum119899=1

119871119899119875119899 minus 119899minus1sum119899=0

119864119899) = 0 119899 = 1 2 119873 (22)

120578119899 ( 119899sum119899=0

119864119899 minus 119899sum119899=1

119871119899119875119899 minus 119864max) = 0 119899 = 1 2 119873 (23)

Since the constraint is satisfied with equality increasing119875119899 will increase the objective function Then the optimaltransmit power during each slot can be obtained by applyingthe KKT optimality conditions

119875lowast119899 = 1sum119873+1119895=119899 120591119899 minus sum119873119895=119899 120578119899 minus 1 119899 = 1 119873 (24)

and 119875lowast119873+1 = 1120591119873+1 minus 1 119875lowast119899 is unique which satisfiessum119899119899=1 119871119899119875119899 = sum119899minus1119899=0 119864119899When 119864max = infin since constraints in (19) and slackness

conditions in (23) are satisfied from (24) the optimal power119875lowast119899 is monotonically increasing 119875lowast119899+1 ge 119875lowast119899 The resultsindicate that energy can be spread to the future for operatingoptimally When the constraint in (18) is not satisfied withequality (sum119897119899=1 119871119899119875119899 lt sum119897minus1119899=0 119864119899) then 120591119897 = 0 thus 119875lowast119897 = 119875lowast119897+1It shows that the energy is utilized for relay nodes not onlyin the current slot but also in future slots When 119875lowast119899 lt 119875lowast119899+1it means that the total energy is used for current slot and noenergy is used in the future

As proven before the harvested energy can only be usedin the future which means our algorithm allows energy toonly flow to the right To solve this problem we propose anoptimal power allocation based on directional water-filling

It is assumed that the optimal energy at time instants1199051 1199052 119905119873 is denoted by 1198641199051 1198641199052 119864119905119873 and is obtained

before the power allocation process The process of thealgorithm is then as follows

Step 1 Initialize the power allocation flag to 0 and let thealgorithm pointer point to the last slot 119905119873Step 2 Compare the energy level in 119905119873 with the energy levelin 119905119873minus1Step 3 No power allocation is performed when the energylevel in the current slot exceeds the previous slot

Step 4 If the energy level in the current slot is lower than theprevious slot allocate energy equally to both 119905119873 and 119905119873minus1 Setthe power allocation flag to 1 mark these two slots as 119905119873minus1and then the algorithm pointer points to 119905119873minus1Step 5 Point the algorithm pointer to the previous slot

Step 6 If the pointer reaches 1199051 and the power allocation flagis 1 go to Step 2 if the point reaches 1199051 and the flag is 0 stopand output 119875lowast119899 as the optimal power allocation otherwise goto Step 332 Multirelay Selection and Session Grouping Energy effi-ciency is defined as the ratio of network throughput to totalpower consumption Note that (7) (8) and (17) are thefunctions of119866119903119896119898 It is essential to consider how to put sessionsinto different groups and select a relay for each group Wedefine the session grouping results as Θ isin 119862119870times119873times119872 Θ119903119896119898119899indicates whether a session belongs to 119866119903119896119898

Θ119903119896 119898119899 = 1 (119904119899 119889119899) isin 1198661199031198961198980 otherwise (25)

A session (119904119899 119889119899) can be in at most one group thus

119896=119870119898=119872minus1sum119896=1119898=0

Θ119903119896119898119899 = 1 (26)

The optimization target of session grouping is to maxi-mize the energy efficiency in our networkmodelWe combine(7) (8) and (17) and formulate the optimization problem as

max EE = sum119873119899=1sum119870119896=1Θ119903119896 0119899 119877119863 (119904119899 119889119899) + sum119873119899=1sum119870119896=1sum119872minus1119898=1 Θ119903119896119898119899 119877NC (119904119899 119903119896 119866119903119896119898)sum119870119896=1sum119872minus1119898=0 119875 (119866119903119896119898)st 119866119903119896119898 = (119904119899 119889119899) forall119899 Θ119903119896 119898119899 = 1119872minus1sum119898=0

Θ119903119896 119898119899 = 1 (forall119899 119904119899 isin 119866119903119896119898)Θ119903119896 119898119899 isin 0 1 (1 le 119899 le 119873 0 le 119898 le 119872)

(27)


Obviously the optimization problem in (27) is a general ldquo0-1rdquoprogramming problem However this is a nonlinear problemthat can be solved only by exhaustive search Since eachsource node is expected to transmit data to its destinationnode from 119870 available channels either with or without theassistance of a relay node the complexity of exhaustive searchis

119862exhaustive = (2119872119870)119873 (28)

From (28) the complexity increases exponential with thenumber of sessions which is intolerable when the numberof sessions is large To solve this problem a joint relayselection and session grouping scheme is proposed based onQPSO

QPSO is a novel multiagent optimization system mod-ified by PSO that is inspired by the social behavior ofagents Each agent called quantum particle files in a 2N-dimensional space according to the historical experiences ofitself and of colleagues 2N represents the dimension of theoptimization problem [20 21]

We define the position of the 119895th quantum particle as

L119895 = [997888U997888V] = [[1205831198951 1205831198952 sdot sdot sdot 1205831198951198731205761198951 1205761198952 sdot sdot sdot 120576119895119873]] (29)

where 120583119895119899 represents the relay number of session (119904119899 119889119899) and120576119895119899 represents the group number of session (119904119899 119889119899) In QPSOalgorithm 120583119895119899 and 120576119895119899 are mapped into quantum particlersquos bitposition which can be expressed as

119909119895119899 = 119896min + 120583119895119899 (119896max minus 119896min) 119910119895119899 = 119898min + 120576119895119899 (119898max minus 119898min) (30)

where 119896max and 119896min are the upper bound and lower boundof the relay node number respectively Similarly 119898max and119898min express the upper bound and lower bound of the groupnumber

From (30) the quantum particlersquos bit position is in thespace of [1 119870] times [0119872] Therefore (29) can be simplified as

[997888119883997888119884] = [[1199091198951 1199091198952 sdot sdot sdot 1199091198951198731199101198951 1199101198952 sdot sdot sdot 119910119895119873]] (31)

We use the integral function round(sdot) to find the optimalΘ119903119896 119898119899 Thus the expression of Θ119903119896 119898119899 is shown as

Θ119903119896119898119899=

1 if (round (119909119895119899) = 119896 round (119910119895119899) = 119898) 0 otherwise

(32)

We set the objective function in (27) as the fitnessfunction The local optimal bit position of the 119895th quantumparticle is

[997888P997888Q] = [[1199011198951 1199011198952 1199011198953 1199011198954 sdot sdot sdot 1199011198951198731199021198951 1199021198952 1199021198953 1199021198954 sdot sdot sdot 119902119895119873]] (33)

The global optimal bit position of the whole quantum particlepopulation is

[[997888P119892997888Q119892]] = [[

1199011198921 1199011198922 1199011198923 1199011198924 sdot sdot sdot 1199011198921198731199021198921 1199021198922 1199021198923 1199021198924 sdot sdot sdot 119902119892119873]] (34)

In this proposed algorithmwe consider the generation in twodimensions The quantum rotation angles are calculated by

120579119894+1119895119899 = 1198901 (119901119894119895119899 minus 120583119894119895119899) + 1198902 (119901119894119892119899 minus 120583119894119895119899) 120593119894+1119895119899 = 1198904 (119902119894119895119899 minus 120576119894119895119899) + 1198905 (119902119894119892119899 minus 120576119894119895119899) (35)

where 1198901 and 1198902 express the relative important degree of997888P and997888P119892 and the updating process of the quantum particle can beexpressed as

120583119894+1119895119899 = radic1 minus (120583119894119895119899)2 if (119901119894119895119899 = 120583119894119895119899 = 119901119894119892119899 1198903 lt 1198881) 100381610038161003816100381610038161003816100381610038161003816120583119894119895119899 cos 120579119894119895119899 minus radic1 minus (120583119894119895119899)2 sin 120579119894119895119899100381610038161003816100381610038161003816100381610038161003816 others

120576119894+1119895119899 = radic1 minus (120576119894119895119899)2 if (119902119894119895119899 = 120576119894119895119899 = 119902119894119892119899 1198906 lt 1198882) 100381610038161003816100381610038161003816100381610038161003816120576119894119895119899 cos120593119894119895119899 minus radic1 minus (120576119894119895119899)2 sin120593119894119895119899100381610038161003816100381610038161003816100381610038161003816 others

(36)


where 1198903 and 1198906 are uniform random number between 0 and1 and 1198881 and 1198882 are mutation probabilities between 0 and 1119873

Assumption 1 The power allocation process has finished

Assumption 2 All the channel state information (CSI) is apriori known

Therefore the process of QPSO algorithm is given in thefollowing steps

Step 1 Initialize quantum particle population including thequantum particlesrsquo bit positions 119871119895 and the local optimal bitpositions Calculate the fitness of each quantum particle andrecord the global optimal bit position from (27)

Step 2 Update the rotation angle for each quantum particlefrom (35) Update the bit positions for each quantum particlefrom (36)

Step 3 Calculate the fitness of all quantum particles based onupdated positions

Step 4 Update the local optimal quantum position for eachquantum particle and the global optimal quantum position

Step 5 If it reaches the predefined value of the maximumgeneration stop the process output the global optimalquantum position and map it into the final transmissionstrategy by (30) (31) and (32) if not go to Step 34 Numerical Results

In this section we show the simulation results to evaluate theperformance of our proposed approachAs shown in Figure 1we consider our simulation within a 1000 times 1000m2 squarearea We consider a network randomly consisting of 50ndash200sessions and 5ndash50 relays For all network instances we assumethat the transmission power of each source node is 1W andthat the channel bandwidth is 22MHz The loss exponent 120572is 4 We assume that the white Gaussian noise at all nodes hasa variance of 10minus10W [8] The circuit power for each node ischosen as 110mW For QPSO we set the maximal generationas 200 ℎ = 20 1198901 = 015 1198902 = 02 1198904 = 06 1198905 = 071198881 = 1(500119870) and 1198882 = 1(1000119872) Each result is obtainedfrom averaging over 50 realizations Simulation parametersare provided in Table 1

41 System Performance of Relay Node Selection and SessionGrouping First we consider the system performance of relaynode selection and session grouping We analyze the energyefficiency total throughput and power consumption versusthe number of sessions The traditional direct transmission(DT) and opportunistic relay-selected cooperative transmis-sion (CR) are used to provide performance reference for ourproposed (NC) scheme In addition power allocations arepreoptimized in DT CR and NC

In CR and NC the source node 119878119899 can exploit a relaynode based on the energy level at relay node and channel state

Table 1 Simulation parameters

Parameters ValueNumber of sessions 50ndash200Number of relay nodes 5ndash50Distribution area 1000 times 1000m2Channel bandwidth 22MHzLoss exponent 4Transmit power of source node 1WCircuit power 110mWWhite Gaussian noise 1 times 10minus10WNumber of quantum particles 20Maximal generation 200Rotating factor of 120579 1198901 = 015 1198902 = 02Rotating factor of 120593 1198904 = 06 1198905 = 07Mutation probability 1198881 = 1(500119870)1198882 = 1(1000119872)

NCDTCR

100 150 20050Number of sessions (N)

07

08

09

1

11

12

13

14Th

roug

hput

(bit

sH

z)

Figure 2 Throughput for three transmission schemes

information (CSI) when it sends data to its destination nodeSince the bandwidths of different schemes may be differentthe performance is measured in bitsHz

Figure 2 shows that the proposed scheme outperformsother two schemes apparently Increasing number of sessionswill increase the possibility of sessions being a reasonablegroup As the number of sessions increases the averagethroughput of our scheme increases as well However in a bignumber regime the average throughput is saturated This isbecause the increasing NC noise will affect the throughput

Figure 3 is the average power consumption of each trans-mission scheme It shows that DT consumes the most power


NCDTCR


95

10

105

11

115

12

125

13

135

Aver

age p

ower

(Js

)

Figure 3 Average power consumption for three transmissionschemes

The reason is that this scheme is transmitting the maximumnumber of sessions by occupying all possible channels toimprove the energy efficiency This figure also indicates thatthe average power of CR transmission is the minimum Itis because better cooperative relay nodes are selected tomaximize the energy efficiency Unlike CR transmission thecircuit energy consumption is considered in our schemeThefigure indicates that NC performs better than DT

Figure 4 shows the energy efficiency of different trans-mission schemes It is observed that our proposed schemeachieves a higher energy efficiency than the other twoschemes This is because both the CSI and the energy levelof relay nodes are considered in our scheme

42 System Performance of Power Allocation Next we showthe performance of power allocation for relay nodes InFigure 5 the proposed scheme is validated Our approachalways outperforms the NC transmission without powerallocation for relay nodes In Figure 5(a) when the numberof sessions 119873 increases the throughput performance gapbecomes larger because the efficient power allocation assuresuniform distribution Figure 5(b) presents the average powerconsumption versus the number of sessions With increasingnumber of sessions the power is continually increasing inboth schemes As shown in the figure the power allocationscheme costs more power consumption than non-powerallocation scheme since higher throughput will consumemore power In Figure 5(c) the energy efficiency of powerallocation scheme is superior to that of non-power allocationscheme The energy efficiency begins to converge when thenumber of sessions becomes large since the existence ofNC noise could diminish the advantage of optimal powerallocation

NCDTCR

10

12

14

16

18

20

22

24

Ener

gy effi

cien

cy (M

bitJ

)


Figure 4 Energy efficiency for three transmission schemes

5 Conclusion

In this paper we studied the energy efficiency problem inmultiple relay cooperative networks with energy harvestingThe energy efficiency is taken as the classic network through-put per power allocation In the optimization problemnetwork coding noise and receiver circuit power consump-tion were considered This problem can be decomposedinto a power allocation problem and an energy-efficienttransmission optimization problemWe solved the first prob-lem by proposing a time-power allocation algorithm basedon directional water-filling algorithm The second problemwas solved by jointly considering relay selection schemeand session grouping based on quantum particle swarmoptimization Numerical results verified that the proposedtransmission scheme effectively improved energy efficiencycomparedwith direct transmission scheme and opportunisticcooperative transmission scheme

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was partly supported by the National Natural Sci-ence Foundation of China (61461029 and 61561032) theNatu-ral Science Foundation of Jiangxi Province (20114ACE0020020161BAB202043 20151BBE50054 and 20153BCB23020)China Postdoctoral Science Foundation Funded Project


With power allocation-NCWithout power allocation-NC

1

105

11

115

12

125

13

135

14

145Th

roug

hput

(bit

sH

z)


(a)


10

105

11

115

12

125

Aver

age p

ower

(Js

)


(b)



20

205

21

215

22

225

23

235

24

245

Ener

gy effi

cien

cy (M

bitJ

)

(c)

Figure 5 System performance of the policy with power allocation for relay nodes

(no 2015T80692) and Graduate Student Innovation SpecialFunds of Nanchang University (cx2016264)

References

[1] R Madan N B Mehta A F Molisch and J Zhang ldquoEnergy-efficient cooperative relaying over fading channels with simplerelay selectionrdquo IEEETransactions onWireless Communicationsvol 7 no 8 pp 3013ndash3025 2008

[2] A Nosratinia T E Hunter and A Hedayat ldquoCooperativecommunication in wireless networksrdquo IEEE CommunicationsMagazine vol 42 no 10 pp 74ndash80 2004

[3] Z Zhang Y Li K Huang and C Liang ldquoEnergy efficiencyanalysis of energy harvesting relay-aided cooperative networksrdquoin Proceedings of the 13th International Symposium on Modelingand Optimization in Mobile Ad Hoc and Wireless Networks(WiOpt rsquo15) pp 1ndash7 IEEE Mumbai India May 2015

[4] S Sharma Y Shi J Liu Y T Hou and S Kompella ldquoIsnetwork coding always good for cooperative communicationsrdquoin Proceedings of the IEEE INFOCOM pp 1ndash9 San Diego CAUSA March 2010

[5] S Sharma Y Shi J Liu Y THou S Kompella and S FMidkiffldquoNetwork coding in cooperative communications friend orfoerdquo IEEE Transactions on Mobile Computing vol 11 no 7 pp1073ndash1085 2012


[6] Z Mobini P Sadeghi and S Zokaei ldquoNetwork coding noisereduction via relay power allocation in a two-unicast wirelesssystemrdquo in Proceedings of the IEEE 22nd International Sympo-sium on Personal Indoor and Mobile Radio Communications(PIMRC rsquo11) pp 1459ndash1464 IEEE Toronto Canada September2011

[7] Z Mobini P Sadeghi M Khabbazian and S Zokaei ldquoPowerallocation and group assignment for reducing network codingnoise in multi-unicast wireless systemsrdquo IEEE Transactions onVehicular Technology vol 61 no 8 pp 3615ndash3629 2012

[8] S Sharma Y Shi Y T Hou H D Sherali and S KompellaldquoJoint optimization of session grouping and relay node selectionfor network-coded cooperative communicationsrdquo IEEE Trans-actions onMobile Computing vol 13 no 9 pp 2028ndash2041 2014

[9] M Zhou Q Cui R Jantti and X Tao ldquoEnergy-efficient relayselection and power allocation for two-way relay channel withanalog network codingrdquo IEEE Communications Letters vol 16no 6 pp 816ndash819 2012

[10] K Xiao Y Zhang G Feng X Duan J Zhu andZ Liu ldquoeCOPEenergy efficient network coding scheme in multi-rate wirelessnetworksrdquo in Proceedings of the IEEE Wireless Communicationsand Networking Conference Workshops (WCNCW rsquo13) pp 18ndash23 Shanghai China April 2013

[11] G Zhang and Y Li ldquoCooperative multicast transmission strat-egy for energy-efficient dynamic network codingrdquo in Proceed-ings of the IEEE International Conference on CommunicationsWorkshops (ICC rsquo13) pp 479ndash483 IEEE Budapest HungaryJune 2013

[12] H Wang W Wang and Z Zhang ldquoOpportunistic wirelessinformation and energy transfer for sustainable cooperativerelayingrdquo in Proceedings of the IEEE International Conference onCommunications (ICC rsquo15) pp 160ndash165 London UK June 2015

[13] K Tutuncuoglu and A Yener ldquoCooperative energy harvestingcommunications with relaying and energy sharingrdquo in Proceed-ings of the IEEE Information Theory Workshop (ITW rsquo13) IEEEAngeles Calif USA September 2013

[14] K H Liu ldquoPerformance analysis of relay selection for cooper-ative relays based on wireless power transfer with finite energystoragerdquo IEEE Transactions on Vehicular Technology vol 65 no7 pp 5110ndash5121 2016

[15] I Ahmed A Ikhlef R Schober and R K Mallik ldquoJoint powerallocation and relay selection in energy harvesting AF relaysystemsrdquo IEEE Wireless Communications Letters vol 2 no 2pp 239ndash242 2013

[16] N Zhao R Chai Q Hu and J Zhang ldquoEnergy efficiencyoptimization based joint relay selection and resource allocationfor SWIPT relay networksrdquo in Proceedings of the 10th Interna-tional Conference on Communications and Networking in China(ChinaCom rsquo15) pp 503ndash508 Shanghai China August 2015

[17] N Zhao R Chai Q Hu and J-K Zhang ldquoEnergy efficiencyoptimization based joint relay selection and resource allocationfor SWIPT relay networksrdquo in Proceedings of the 10th Interna-tional Conference on Communications and Networking in China(ChinaCom rsquo15) pp 503ndash508 Shanghai China August 2015

[18] X Shen T Zhang Z Zeng and X Lin ldquoEnergy efficient sessiongrouping scheme in network-coded cooperative communica-tionsrdquo in Proceedings of the 10th International Conference onCommunications and Networking in China (ChinaCom rsquo15) pp158ndash162 Shanghai China August 2015

[19] O Ozel K Tutuncuoglu J Yang S Ulukus and A YenerldquoTransmission with energy harvesting nodes in fading wireless

channels optimal policiesrdquo IEEE Journal on Selected Areas inCommunications vol 29 no 8 pp 1732ndash1743 2011

[20] J Cao T Zhang Z Zeng Y Chen and K K Chai ldquoMulti-relayselection schemes based on evolutionary algorithm in cooper-ative relay networksrdquo International Journal of CommunicationSystems vol 27 no 4 pp 571ndash591 2014

[21] T Zhang J Cao Z Zeng and D Liu ldquoJoint relay selection andspectrum allocation scheme in cooperative relay networksrdquo inProceedings of the 79th IEEE Vehicular Technology Conference(VTC rsquo14) pp 1ndash6 IEEE Seoul Republic of Korea May 2014

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selection and session grouping problem was investigated in[8] as session grouping can effectively reduce network codingnoise However in all of these works the circuit energyconsumption with network coding was not considered

To achieve better tradeoff between network throughputand power consumption the metric energy efficiency is usedin [9ndash11] In [9] the authors studied the energy-efficientrelay selection and power allocation problem for a two-way relay channel based on network coding Paper [10]presented an opportunistic listening scheme to promoteenergy efficiency for network-coded cooperative networks intwo-unicast sessions Paper [11] proposed an energy-efficientmulticast scheme with network coding

Moreover energy harvesting technologies for coopera-tive networks have been investigated in [12ndash17] and theserepresent a promising approach for powering nodes In [12]an opportunistic wireless information and energy transferrelaying scheme was proposed by Lagrangian optimalityReference [13] used the directional water-filling algorithm tomaximize the sum-rate

In cooperative relay networks with energy harvestingthe relay nodes selected and the choice of power allocationscheme have a great impact on the system performance In[14] finite energy storage was considered in relay nodes anda relay selection scheme was proposed based on finite-stateMarkov chain In [15 16] the source nodes and relay nodeswere considered as energy harvesting nodes and then thesystem throughput was maximized by optimizing both relayselection and power allocation

Another line of work on joint wireless energy and infor-mation transmission in relay networks is simultaneous wire-less information and power transfer (SWIPT) Researchershave focused on improving energy efficiency and a partic-ularly relevant piece of work is [17] To maximize the totalenergy efficiency the authors proposed a joint relay selectionand resource allocation scheme for SWIPT relay networkswith multiple source nodes and destination nodes pairs andenergy harvesting relay nodes

Improving the energy efficiency in relay networks isof critical importance for resolving the energy shortage ofnodes In the literature [14ndash17] the energy arrival timeand the amount of harvested energy are known prior totransmission However in real systems the amount of theharvested energy is affected by many factors such as weatherand channel conditions so it is necessary to consider atransmission scheme that can efficiently use the harvestedenergy from random energy sources

12 Contributions and Organization In this paper we focuson a multirelay cooperative network where relay nodes arepowered by random energy sources Unlike previous worksour study considers network coding finite energy storageand energy harvesting The aim of this paper is to optimizeenergy efficiency in multirelay cooperative networks withenergy harvesting In [18] we have proposed an energy-efficient session grouping scheme in a single relay network-coded cooperative network In this work we extend ourprevious work to a multirelay cooperative network andconsider the energy harvesting technology

s1

d1

s2

d2

s3

d3

s4d4

s5

d5

s6

d6

s7

d7

s8

d8

r1

r2

r3

100 200 300 400 500 600 700 800 900 10000Meters

0

100

200

300

400

500

600

700

800

900

1000

Met

ers

Figure 1 Multirelay cooperative network model

Our contributions are concluded in three aspects

(i) The receiver circuit power consumptionwith networkcoding is analyzed

(ii) An optimal power allocation for relay nodes is pro-posed based on the directional water-filling algo-rithm

(iii) An energy-efficient relay selection and session group-ing scheme is proposed based on the quantumparticleswarm optimization (QPSO)

The rest of this paper is organized as follows Section 2presents the network model including the throughput modeland power consuming model Section 3 studies the optimalpower allocation scheme and jointly optimizing multirelayselection and session grouping scheme Section 4 shows thenumerical results and analysis for the proposed schemeSection 5 is the conclusion of this paper

2 Network Model

As is depicted in Figure 1 we consider a network-codedcooperative networkwhich consists of119873 sessions and119870 relaynodes in a square with dimensions 119863 times 119863 In this model weassume that the relay nodes operate in amplify-and-forward(AF) mode and use orthogonal channels Sessions that selectthe same node share one channel and transmit data undertime division multiple access (TDMA) Moreover the relaynodes can harvest energy from random energy sources suchas wind energy and solar energy

21 Total Throughput In cooperative relaying networksthere are three transmission schemes (i) direct transmission(ii) opportunistic relay-selected cooperative transmissionand (iii) network-coded cooperative transmissionThe trans-mitting power of relay nodes is not constant since the randomenergy arrivals in the relay nodes

In network-coded cooperative networks sessions in agroup are assumed to be relayed in equal power119875119898119903119896 is defined



10038161003816100381610038161003816120572119898119903119896 100381610038161003816100381610038162 = 11987511989811990311989610038161003816100381610038161198661199031198961198981003816100381610038161003816 1205902119903119896 + sum119904119897isin119866119903119896119898 119875119904119897 10038161003816100381610038161003816ℎ119904119897119903119896 100381610038161003816100381610038162 (1)



119911NC119889119899 = 119911119889119899 + 119904119897 =119904119899sum119904119897isin119866119903119896119898

120572119903119896ℎ119903119896119889119899119911119903119896 minus 119904119897 =119904119899sum119904119897isin119866119903119896119898

120572119903119896ℎ119903119896119889119899ℎ119904119897119903119896ℎ119904119897119889119899 119911119889119899 (2)



1205902119889NC119899

= 1205902119889119899 + (10038161003816100381610038161198661199031198961198981003816100381610038161003816 minus 1) (120572119898119903119896ℎ119903119896119889119899)2 1205902119903119896+ 1205902119889119899 119904119897 =119904119899sum119904119897isin119866119903119896119898

(120572119898119903119896ℎ119904119897119903119896ℎ119903119896119889119899ℎ119904119897119889119899 )2 (3)


119905119899 = 119879sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot1003816100381610038161003816119866119903119896119898100381610038161003816100381610038161003816100381610038161198661199031198961198981003816100381610038161003816 + 1 (4)



1003816100381610038161003816119866119903119896119898100381610038161003816100381610038161003816100381610038161198661199031198961198981003816100381610038161003816 + 1times 119868NC (119904119899 119903119896 119866119903119896119898)

(5)


119868NC (119904119899 119903119896 119866119903119896119898) = log2(1 + 120574119904119899119889119899+ 12057411990411989911990311989612057411990311989611988911989910038161003816100381610038161198661199031198961198981003816100381610038161003816 (1205902119889NC

119899

1205902119889119899) + 120574119903119896119889119899 + (1205902

119889NC119899

1205902119889119899)sum119904119897isin119866119903119896119898 120574119904119897119903119896)

(6)



+ 120574119904119899119889119899+ 12057411990411989911990311989612057411990311989611988911989910038161003816100381610038161198661199031198961198981003816100381610038161003816 (1205902119889NC

119899

1205902119889119899) + 120574119903119896119889119899 + (1205902

119889NC119899

1205902119889119899)sum119904119897isin119866119903119896119898 120574119904119897119903119896)

(7)


119877119863 (119904119899 119903119896 119889119899) = 119882sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 times log (1 + 119904119899119889119899) (8)



119905119889-cr = 119879sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot 10038161003816100381610038161198661199031198961198981003816100381610038161003816 (9)



119864119889 cr (119866119903119896119898) = 119905119889 cr119875cr 10038161003816100381610038161198661199031198961198981003816100381610038161003816 (10)


119905119903-cr = 119879sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot10038161003816100381610038161198661199031198961198981003816100381610038161003816210038161003816100381610038161198661199031198961198981003816100381610038161003816 + 1 (11)


119905send = 119879sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot1003816100381610038161003816119866119903119896119898100381610038161003816100381610038161003816100381610038161198661199031198961198981003816100381610038161003816 + 1 (12)




119875 (119866119903119896119898) = 119864119889 cr (119866119903119896119898) + 119864119904 119905 (119866119903119896119898) + 119864119903119896 sum (119866119903119896119898)119879 119898 ge 1 (14)


119875 (119866119903119896119898) = 1sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot10038161003816100381610038161198661199031198961198981003816100381610038161003816210038161003816100381610038161198661199031198961198981003816100381610038161003816 + 1

sdot (119875119904 + (1 + 110038161003816100381610038161198661199031198961198981003816100381610038161003816) 119875ct + (2 + 10038161003816100381610038161198661199031198961198981003816100381610038161003816) 119875cr + 11987511989811990311989610038161003816100381610038161198661199031198961198981003816100381610038161003816) (15)


119875 (1198661199031198960 ) = 10038161003816100381610038161198661199031198960 1003816100381610038161003816sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot (119875cr + 119875119904 + 119875ct) (16)


119875total = 119870sum119896=1

119872minus1sum119898=0

119875 (119866119903119896119898) (17)







119899sum119899=1

119871119899119875119899 le 119899minus1sum119899=0

119864119894 119899 = 1 2 119873 + 1 (18)

119899sum119899=0

119864119899 minus 119899sum119899=1

119871119899119875119899 le 119864max 119899 = 1 119873 (19)


max119875119899ge0

119873+1sum119899=1

1198821198711198992 log (1 + 119875119899)st

119899sum119899=1

119871119899119875119899 le 119899minus1sum119899=0

119864119899 119899 = 1 2 119873 + 1119899sum119899=0

119864119899 minus 119899sum119899=1

119871119899119875119899 le 119864max 119899 = 1 119873(20)




120589 = 119873+1sum119899=1

1198821198711198992 log (1 + 119875119899)minus 119873+1sum119899=1

120591119899( 119899sum119899=1

119871119899119875119899 minus 119899minus1sum119899=0

119864119899) (21)


120591119899( 119899sum119899=1

119871119899119875119899 minus 119899minus1sum119899=0

119864119899) = 0 119899 = 1 2 119873 (22)

120578119899 ( 119899sum119899=0

119864119899 minus 119899sum119899=1

119871119899119875119899 minus 119864max) = 0 119899 = 1 2 119873 (23)











Θ119903119896 119898119899 = 1 (119904119899 119889119899) isin 1198661199031198961198980 otherwise (25)


119896=119870119898=119872minus1sum119896=1119898=0

Θ119903119896119898119899 = 1 (26)




(27)



119862exhaustive = (2119872119870)119873 (28)











Θ119903119896119898119899=


(32)




[[997888P119892997888Q119892]] = [[







(36)
















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5 Conclusion


Competing Interests


Acknowledgments




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Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





10038161003816100381610038161003816120572119898119903119896 100381610038161003816100381610038162 = 11987511989811990311989610038161003816100381610038161198661199031198961198981003816100381610038161003816 1205902119903119896 + sum119904119897isin119866119903119896119898 119875119904119897 10038161003816100381610038161003816ℎ119904119897119903119896 100381610038161003816100381610038162 (1)



119911NC119889119899 = 119911119889119899 + 119904119897 =119904119899sum119904119897isin119866119903119896119898

120572119903119896ℎ119903119896119889119899119911119903119896 minus 119904119897 =119904119899sum119904119897isin119866119903119896119898

120572119903119896ℎ119903119896119889119899ℎ119904119897119903119896ℎ119904119897119889119899 119911119889119899 (2)



1205902119889NC119899

= 1205902119889119899 + (10038161003816100381610038161198661199031198961198981003816100381610038161003816 minus 1) (120572119898119903119896ℎ119903119896119889119899)2 1205902119903119896+ 1205902119889119899 119904119897 =119904119899sum119904119897isin119866119903119896119898

(120572119898119903119896ℎ119904119897119903119896ℎ119903119896119889119899ℎ119904119897119889119899 )2 (3)


119905119899 = 119879sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot1003816100381610038161003816119866119903119896119898100381610038161003816100381610038161003816100381610038161198661199031198961198981003816100381610038161003816 + 1 (4)



1003816100381610038161003816119866119903119896119898100381610038161003816100381610038161003816100381610038161198661199031198961198981003816100381610038161003816 + 1times 119868NC (119904119899 119903119896 119866119903119896119898)

(5)


119868NC (119904119899 119903119896 119866119903119896119898) = log2(1 + 120574119904119899119889119899+ 12057411990411989911990311989612057411990311989611988911989910038161003816100381610038161198661199031198961198981003816100381610038161003816 (1205902119889NC

119899

1205902119889119899) + 120574119903119896119889119899 + (1205902

119889NC119899

1205902119889119899)sum119904119897isin119866119903119896119898 120574119904119897119903119896)

(6)



+ 120574119904119899119889119899+ 12057411990411989911990311989612057411990311989611988911989910038161003816100381610038161198661199031198961198981003816100381610038161003816 (1205902119889NC

119899

1205902119889119899) + 120574119903119896119889119899 + (1205902

119889NC119899

1205902119889119899)sum119904119897isin119866119903119896119898 120574119904119897119903119896)

(7)


119877119863 (119904119899 119903119896 119889119899) = 119882sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 times log (1 + 119904119899119889119899) (8)



119905119889-cr = 119879sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot 10038161003816100381610038161198661199031198961198981003816100381610038161003816 (9)



119864119889 cr (119866119903119896119898) = 119905119889 cr119875cr 10038161003816100381610038161198661199031198961198981003816100381610038161003816 (10)


119905119903-cr = 119879sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot10038161003816100381610038161198661199031198961198981003816100381610038161003816210038161003816100381610038161198661199031198961198981003816100381610038161003816 + 1 (11)


119905send = 119879sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot1003816100381610038161003816119866119903119896119898100381610038161003816100381610038161003816100381610038161198661199031198961198981003816100381610038161003816 + 1 (12)




119875 (119866119903119896119898) = 119864119889 cr (119866119903119896119898) + 119864119904 119905 (119866119903119896119898) + 119864119903119896 sum (119866119903119896119898)119879 119898 ge 1 (14)


119875 (119866119903119896119898) = 1sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot10038161003816100381610038161198661199031198961198981003816100381610038161003816210038161003816100381610038161198661199031198961198981003816100381610038161003816 + 1

sdot (119875119904 + (1 + 110038161003816100381610038161198661199031198961198981003816100381610038161003816) 119875ct + (2 + 10038161003816100381610038161198661199031198961198981003816100381610038161003816) 119875cr + 11987511989811990311989610038161003816100381610038161198661199031198961198981003816100381610038161003816) (15)


119875 (1198661199031198960 ) = 10038161003816100381610038161198661199031198960 1003816100381610038161003816sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot (119875cr + 119875119904 + 119875ct) (16)


119875total = 119870sum119896=1

119872minus1sum119898=0

119875 (119866119903119896119898) (17)







119899sum119899=1

119871119899119875119899 le 119899minus1sum119899=0

119864119894 119899 = 1 2 119873 + 1 (18)

119899sum119899=0

119864119899 minus 119899sum119899=1

119871119899119875119899 le 119864max 119899 = 1 119873 (19)


max119875119899ge0

119873+1sum119899=1

1198821198711198992 log (1 + 119875119899)st

119899sum119899=1

119871119899119875119899 le 119899minus1sum119899=0

119864119899 119899 = 1 2 119873 + 1119899sum119899=0

119864119899 minus 119899sum119899=1

119871119899119875119899 le 119864max 119899 = 1 119873(20)




120589 = 119873+1sum119899=1

1198821198711198992 log (1 + 119875119899)minus 119873+1sum119899=1

120591119899( 119899sum119899=1

119871119899119875119899 minus 119899minus1sum119899=0

119864119899) (21)


120591119899( 119899sum119899=1

119871119899119875119899 minus 119899minus1sum119899=0

119864119899) = 0 119899 = 1 2 119873 (22)

120578119899 ( 119899sum119899=0

119864119899 minus 119899sum119899=1

119871119899119875119899 minus 119864max) = 0 119899 = 1 2 119873 (23)











Θ119903119896 119898119899 = 1 (119904119899 119889119899) isin 1198661199031198961198980 otherwise (25)


119896=119870119898=119872minus1sum119896=1119898=0

Θ119903119896119898119899 = 1 (26)




(27)



119862exhaustive = (2119872119870)119873 (28)











Θ119903119896119898119899=


(32)




[[997888P119892997888Q119892]] = [[







(36)
















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5 Conclusion


Competing Interests


Acknowledgments




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References































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





119864119889 cr (119866119903119896119898) = 119905119889 cr119875cr 10038161003816100381610038161198661199031198961198981003816100381610038161003816 (10)


119905119903-cr = 119879sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot10038161003816100381610038161198661199031198961198981003816100381610038161003816210038161003816100381610038161198661199031198961198981003816100381610038161003816 + 1 (11)


119905send = 119879sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot1003816100381610038161003816119866119903119896119898100381610038161003816100381610038161003816100381610038161198661199031198961198981003816100381610038161003816 + 1 (12)




119875 (119866119903119896119898) = 119864119889 cr (119866119903119896119898) + 119864119904 119905 (119866119903119896119898) + 119864119903119896 sum (119866119903119896119898)119879 119898 ge 1 (14)


119875 (119866119903119896119898) = 1sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot10038161003816100381610038161198661199031198961198981003816100381610038161003816210038161003816100381610038161198661199031198961198981003816100381610038161003816 + 1

sdot (119875119904 + (1 + 110038161003816100381610038161198661199031198961198981003816100381610038161003816) 119875ct + (2 + 10038161003816100381610038161198661199031198961198981003816100381610038161003816) 119875cr + 11987511989811990311989610038161003816100381610038161198661199031198961198981003816100381610038161003816) (15)


119875 (1198661199031198960 ) = 10038161003816100381610038161198661199031198960 1003816100381610038161003816sum119872119898=0 10038161003816100381610038161198661199031198961198981003816100381610038161003816 sdot (119875cr + 119875119904 + 119875ct) (16)


119875total = 119870sum119896=1

119872minus1sum119898=0

119875 (119866119903119896119898) (17)







119899sum119899=1

119871119899119875119899 le 119899minus1sum119899=0

119864119894 119899 = 1 2 119873 + 1 (18)

119899sum119899=0

119864119899 minus 119899sum119899=1

119871119899119875119899 le 119864max 119899 = 1 119873 (19)


max119875119899ge0

119873+1sum119899=1

1198821198711198992 log (1 + 119875119899)st

119899sum119899=1

119871119899119875119899 le 119899minus1sum119899=0

119864119899 119899 = 1 2 119873 + 1119899sum119899=0

119864119899 minus 119899sum119899=1

119871119899119875119899 le 119864max 119899 = 1 119873(20)




120589 = 119873+1sum119899=1

1198821198711198992 log (1 + 119875119899)minus 119873+1sum119899=1

120591119899( 119899sum119899=1

119871119899119875119899 minus 119899minus1sum119899=0

119864119899) (21)


120591119899( 119899sum119899=1

119871119899119875119899 minus 119899minus1sum119899=0

119864119899) = 0 119899 = 1 2 119873 (22)

120578119899 ( 119899sum119899=0

119864119899 minus 119899sum119899=1

119871119899119875119899 minus 119864max) = 0 119899 = 1 2 119873 (23)











Θ119903119896 119898119899 = 1 (119904119899 119889119899) isin 1198661199031198961198980 otherwise (25)


119896=119870119898=119872minus1sum119896=1119898=0

Θ119903119896119898119899 = 1 (26)




(27)



119862exhaustive = (2119872119870)119873 (28)











Θ119903119896119898119899=


(32)




[[997888P119892997888Q119892]] = [[







(36)
















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5 Conclusion


Competing Interests


Acknowledgments




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References































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





120589 = 119873+1sum119899=1

1198821198711198992 log (1 + 119875119899)minus 119873+1sum119899=1

120591119899( 119899sum119899=1

119871119899119875119899 minus 119899minus1sum119899=0

119864119899) (21)


120591119899( 119899sum119899=1

119871119899119875119899 minus 119899minus1sum119899=0

119864119899) = 0 119899 = 1 2 119873 (22)

120578119899 ( 119899sum119899=0

119864119899 minus 119899sum119899=1

119871119899119875119899 minus 119864max) = 0 119899 = 1 2 119873 (23)











Θ119903119896 119898119899 = 1 (119904119899 119889119899) isin 1198661199031198961198980 otherwise (25)


119896=119870119898=119872minus1sum119896=1119898=0

Θ119903119896119898119899 = 1 (26)




(27)



119862exhaustive = (2119872119870)119873 (28)











Θ119903119896119898119899=


(32)




[[997888P119892997888Q119892]] = [[







(36)
















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5 Conclusion


Competing Interests


Acknowledgments




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References































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





119862exhaustive = (2119872119870)119873 (28)











Θ119903119896119898119899=


(32)




[[997888P119892997888Q119892]] = [[







(36)
















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5 Conclusion


Competing Interests


Acknowledgments




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References































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in


















NCDTCR


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5 Conclusion


Competing Interests


Acknowledgments




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References































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




NCDTCR


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5 Conclusion


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Acknowledgments




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References































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





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Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



research article an energy-efficient scheme for multirelay...

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