2.4_femto optimization power freq ilp han 2009

8/7/2019 2.4_Femto optimization power freq ILP Han 2009

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Optimization of Femtocell Network Congurationunder Interference Constraints

Kwanghun Han, Youngkyu Choi, Dongmyoung Kim, Minsoo Na, Sunghyun Choi, and Kiyoung Han School of Electrical Engineering and INMC, Seoul National University, Korea

WiMAX System Lab, Samsung Electronics, Suwon, KoreaInstitute of Network Technoloy, SK Telecom, Sungnam, Korea

Communication Lab, Samsung Electronics, Suwon, KoreaEmail: {khhan, ykchoi, dmkim }@mwnl.snu.ac.kr, [email protected], [email protected], [email protected]

Abstract Femto BS (Base Station) is emerging as a keytechnology to secure the coverage and capacity in indoor en-vironments. However, since the existing macrocell network isoverlaid on femtocell networks utilizing the same set of frequencychannels, femtocell networks can originate severe co-channelinterference to the macrocell network unless the femtocell net-

work is carefully congured. Therefore, according to a desirednetwork-wide objective, we optimize the femtocell network withconstraints such that the service connectivity with a femto BSis secured in the target indoor area while the signal emittedout of the building, playing as interference to the outdoor users,should be controlled with an appropriate strength in order notto interrupt the communication between macro BS and outdoorusers. Each optimization problem is formulated as a mixedinteger programming, and as the results, we obtain not onlythe transmit power and operational frequency channel of eachfemto BS, but also the optimal femto BS-to-user association pairat each geographical position.

I. INTRODUCTION

Femto BS (Base Station) is a small low-cost BS with ashort service range (i.e., 10 to 15 m), referred to as femtocell.It is typically designed to serve under 10 users in indoorenvironments such as small ofce and home. A femto BS istypically connected with a macrocell network via a broadbandwired connection, e.g., an IP (Internet Protocol) network overxDSL (x Digital Subscriber Line), or a dedicated backhaulnetwork. Today, it is strongly considered a practical candidatesolution to secure both the seamless indoor coverage and thehigh network capacity. The emerging IMT-advanced candidatesystems including 3GPP LTE-advanced and IEEE 802.16malso feature this femtocell technology [1][3].

Conventional outdoor BSs are referred to as macro BSs in

this paper. The functionality of femto BS is almost the sameas that of typical macro BS, while the price of femto BS canbe signicantly lower because (1) a femto BS is expected toserve a small number of users and (2) a relatively low transmitpower is enough to cover the service area. Such low cost of the hardware is expected to make the femtocell technology

0 This work is in part supported by Saumsung Electronics and the Ministryof Knowledge Economy, Korea, under the Information Technology ResearchCenter support program supervised by the Institute of Information TechnologyAdvancement (grant number IITA-2009-C1090-0902-0006).

widely accepted since femto BSs can be bought in the marketby users and easily installed in a plug-and-play manner.

However, as more and more femto BSs are deployed in agiven area, unless the femtocell network is properly optimized,the overall network capacity might be signicantly compro-

mised due to the co-channel interference. Besides, since theexisting macrocell network is assumed to be overlaid on fem-tocell networks utilizing the same set of operating frequencychannels, femtocell networks can originate severe co-channelinterference to the macrocell network if the conguration of afemtocell network is not carefully managed. In the meantime,a seamless coverage inside the target indoor area should bealso ensured. However, considering the expected huge numberof femto BSs, it is almost impossible to keep the network optimized via the manual setting by a human engineer as donein conventional cellular networks. Therefore, the femtocellnetwork is desired to be self-organizing such that the network conguration automatically keeps updated by being aware of

the network environmental changes, e.g., addition/deletion of neighboring femto BSs. Consequently, it is very important toaddress the problem how to optimize the femtocell network (specically, conguring the transmit power and frequencychannel of femto BS) in a systematic manner.

In the literature, there has been some related work, es-pecially, in the context of WLAN AP deployments [4][6].However, the considered problem is quite different from theWLAN AP deployment problems due mainly to the co-channel interference to/from macrocells. Moreover, none of the existing schemes deals with BS location determination,power control, frequency channel allocation, and user asso-ciation altogether , and with Shannons capacity directly asan optimization objective. We formulate joint optimizationproblems, which yield the transmit power, frequency channel,and deployment location for each femto BS along with thedesired femto BS-to-user association pair at each geographicalposition.

The rest of the paper is organized as follows: In Section II,we describe the system model. Section III formulates theoptimization problems, and then the performance results arediscussed in Section IV. We conclude the paper in Section Valong with the remark on our ongoing work.


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Fig. 1. Three simulation scenarios.

I I . S YSTEM M ODEL

A. Macrocell and Femtocell Networks

We assume WiBro, i.e., a Korean version of MobileWiMAX, for our system modeling and evaluation [7]. The

macrocell network is modeled by a conventional multi-cellhoneycomb structure. Each single macrocell is divided intothree sectors denoted by S0, S1, and S2 as shown in Fig. 1,and a sector labeled by S x (x = 0 , 1, 2) uses the (x + 1) thfrequency channel out of three available channels. Assumingthat both macrocell and femtocell networks are perfectlysynchronized, the macro BS plays as a downlink interfererto the users in a femtocell network.

The architecture of the femtocell-based enterprise network in consideration is illustrated in Fig. 2. A femtocell network is composed of a number of femto BSs and a WSM (Wire-less System Management) server, which is a network entityin charge of the optimization of femto BSs conguration.

The WSM server jointly optimizes the radio parameters of the femto BSs, e.g., transmit power and frequency channel,according to a given network-wide objective. Here, we assumethat the WSM server has no authority for conguring theradio parameters of macro BS, and hence, the interferencefrom macrocell network is an uncontrollable factor in theoptimization of the femtocell network. Throughout this paper,we assume that the WSM server has the knowledge of allthe required information, e.g., the channel gains between eachBS and users, required for the network optimization. How toacquire such information should be a separate research topic.

We assume that the building, within which the femtocellnetwork is deployed, is a rectangular parallelepiped with aside length of W building as its rst oor plan is illustrated inFig. 3, and has three oors as shown in Fig. 2. We assumethat all the indoor users are associated with one of femtoBSs, and all the outdoor users are served by macro BSs.Based on these assumptions, we consider the outdoor regionsurrounding the building with the width of W street / 2 to assessthe impact of the interference from the femtocell network onthe signal quality, e.g., SINR (Signal to Interference plus NoiseRatio), experienced by outdoor users. We assume that thenine equidistant candidate locations, where femto BSs can be

Fig. 2. Femtocell network architecture.

installed, exist on each oor of the building as shown in Fig. 3,and the indices of candidate locations at the same horizontalposition on each oor are labeled as x/y/z , where x, y, and zare the index of the 1st, 2nd, and 3rd oors candidate location,respectively.

B. TPs (Testing Points)

In order to evaluate the performance of the target area, i.e.,the indoor and outdoor regions, in a mathematically efcientmanner, we consider the notion of TP (Testing Point), whichis used to measure a continuous object via quantization. Thetarget area can be divided into many square grids and a TPis located at the center of each grid. A particular metricvalue corresponding to a TP represents the metric at all theother points within the square grid, which the TP belongsto. For instance, the channel gain between a femto BS anda user is represented by the channel gain between the TPsof two grids, which the femto BS and the user belong to,respectively. Specically, we use the term of internal TP(ITP) and external TP (ETP) to differentiate the indoor users

from the outdoor users since different constraints need to beconsidered depending on the location of a user. Throughoutthe rest of the paper, we consider that the SINR at everyITP should be at least 3 dB to meet the requirement forthe indoor coverage, and the degradation of SINR due to theoverall interference from the femtocell network observed atevery ETP should not be larger than 1 dB.

C. Antenna and Channel Models

Macro BSs are assumed to use directional antennas forsectorization. The antenna gain, A (in dBi), is given as afunction of the angle between a given location of interestand the predened reference direction.

A () = min 12

3dB

2, Am , 180 180,

where Am is 20 dBi and 3dB is 70 degrees. On the otherhand, both femto BSs and users are assumed to use an omni-directional antenna, whose gain amounts to 2 and 1 dBi,respectively. Different channel models are considered depend-ing on the point-to-point link of particular interest since theindoor channel characteristic is quite different from that of outdoor channel. More specically, we consider four different


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this objective as an initial step thanks to the linear formulationeasiness.

Now we express the constraints mathematically one afteranother. First, we assume that at most M ( |A| ) femto BSscan be deployed and each femto BS uses only one frequencychannel due to the assumption of no sectorization:

aA f F

zaf M, (C1)

f F

zaf 1, a A. (C2)

In addition, there exist both minimum and maximum boundfor transmit power:

C zaf paf zaf , a A, f F , (C3)

where C P min /P max . P min and P max are the minimumand maximum transmit powers of a femto BS, respectively. Anormalized power paf is 0 if zaf is 0, and paf ranges fromC to 1, otherwise. Accordingly, if a femto BS should not bedeployed at the location a , zaf for all f F are set to zero.After the optimization problem is solved, the actual transmitpower P af of femto BS a is determined by paf P max .

Assuming that each ITP corresponds to a user, any user isallowed to associate with only one femto BS in one frequencychannel:

aA f F

x jaf = 1 , j J i , (C4)

f F

x jaf 1, j J i , a A, (C5)

x jaf zaf , j J i , a A, f F . (C6)

In order to guarantee the coverage, we need to maintainboth SNR and SINR of ITPs over the predened threshold.First, the SNR constraint with a threshold is formulated asfollows:

Inf (1 x jaf ) + gjaf P max paf N 0 +

eEgjef P Macro

, j J i , a A, f F

(C7)

where Inf is a virtually innite value; N 0 is the backgroundnoise power; and

eEgjef P Macro is the total interference power

from macro BSs. The SNR constraint is valid only for ITP j ,which is associated with femto BS a using frequency channelf , namely, x jaf = 1 . Note that if x jaf = 1 , it also holdsthat zaf = 1 by (C7). For this purpose, Inf (1 x jaf ) isintroduced because (C8) can be safely ignored unless x jaf is1. This technique is frequently used during our formulation.Denitely, it can be transformed to the linear inequalityconstraint 1 for MIP:

Inf x jaf gjaf P max paf Inf N 0 +eE

gjef P Macro .

1 Other fractional constraints can be transformed to a linear form, similarly.

(a) Incorrect region: Intersection of afne functions.

(b) Correct region: Union of afne functions by selection tech-nique.

Fig. 4. Linear approximation of log(x ) .

While the SNR constraint looks unnecessary if the SINR con-

straint is also considered, we deliberately add this constraintto reduce the solving time by shrinking the solution set.Next, we consider the SINR constraint of ITP. Compared

with the above SNR constraint, it additionally considers thecochannel interference from other femto BSs as follows:

Inf (1 x jaf ) + gjaf P max paf N 0 +

eEgjef P Macro +

bA\ agjbf P max pbf

,

j J i , a A, f F , (C8)

where is the SINR threshold for the coverage guarantee.Another major concern is minimizing the impact of the

interference from femtocell network on the outdoor users, who

are connected to macro BSs. To meet this requirement, werestrict the SINR degradation at each ETP j under 1 dB:

maxeE

gjef P Macro + Inf (1 yjf )

N 0 +eE

gjef P Macro +aA

gjaf P max paf j ,

E E\ argmaxeE

gjef P Macro , j J e , f F , (C9)

where j is the minimum bound of the SINR at ETP jexperienced after the deployment of femtocell network. Sincethe original SINR at ETP j can be precomputed, j can bealso predetermined such that j (dB) is equal to the originalSINR (dB) minus 1 dB. Note that ETP j is assumed to be

attached to macro BS argmaxeE gjef P Macro . Since the SINR

constraint is valid only for the single frequency channel usedby the sector, which is associated by ETP j , Inf (1 yjf ) isintroduced to safely ignore the SINR constraint if yjf = 0 .To ensure that yjf = 1 for a certain frequency channel, anadditional constraint for auxiliary variable yjf is consideredas follows:

f F

yjf = 1 , j J e . (C10)


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Finally, the MaxPwr problem is formulated as follows:

maxaA f F

paf

s.t.C1, C2, C3, C4, C5, C6, C7, C8, C9, C10.

As addressed previously, the MaxPwr problem does not nec-essarily maximize the inbuilding capacity since the impact of cochannel interference from other femto BSs is not reectedto the objective. For this reason, we consider the MaxCapproblem in the next section.

B. MaxCap Problem

The achievable capacity at an ITP is given by Shannoncapacity, i.e., log2(1 + SINR ), and hence we need to incor-porate this equation to the objective function to address theinbuilding capacity optimization. However, since log functionis nonlinear, it is impossible to directly deal with it viaMIP. Alternatively, we take the approach to approximate thenonlinear Shannon capacity equation into piecewise linearfunctions, which can be managed by MIP.

To do so, we rst look at the characteristic of Shannoncapacity assuming that ITP j is associated with femto BS a :

log2 (1 + SINR )

= log N 0 +eE

gjef P Macro +bA

gjbf P max P bf

log N 0 +eE

gjef P Macro +bA\ a

gjbf P max P bf .

As seen above, Shannon capacity is decomposed into log and

log function, which takes the sum of linear variables as theinput. Therefore, if we can approximate the log and log intolinear functions, Shannon capacity is also approximated intolinear functions. Fortunately, log is a concave function, whichcan be easily approximated as the sum of piecewise afnefunctions:

an x + bn log(x) an x + bn + ,

where n is an index variable and is a positive value.Specically, the parameters of each line and the number of lines can be adjusted according to the required precision. Byusing this approximation technique, we can represent log partof Shannon capacity at ITP j as follows:

S j cn N 0 +eE

gjef P Macro +bA

gjbf P max P bf

+ dn + Inf (1 x jaf ) + W, j J i , a A, f F , n,(C11)

where S j is a real variable which delegates the intersectionregion of the afne functions; cn and dn are approximationparameters; and W is the offset value to make S j positive.Inf (1 x jaf ) term is for a selection technique.

(a) Before the deployment of femtocell network.

(b) After the deployment of femtocell network.

Fig. 5. Spatial distribution of SINR illustrated by using colormap at1st/2nd/3rd oors. Each rectangle corresponds to a oor, and the boundaryregion of the left-most rectangle represents the street region right next to thebuilding.

While log(x) can be directly approximated through simpleintersection, log(x) cannot be done as shown in Fig. 4(a),but can be approximated by getting the union region as shownin Fig. 4(b). To do so, we need to select a proper afne functiondepending on domain x. More specically, we will add thevirtual innite value to the other afne functions except theproper afne function to safely ignore them. Accordingly, wetake the selection technique again, and hence, an indicatorvariable vjn is introduced to choose the proper afne function,which gives the biggest value for a given input. Finally, weobtain the inequality conditions given as follows:

Q j cn N 0 +eE

gjef P Macro +bA\ a

gjbf P max P bf

dn + Inf (2 vjn x jaf ) + W, j J i , a A, f F , n,(C12)

where W is the offset used to make Q j positive. A constraintfor vjn is also required:

nN

vjn = 1 , j J i . (C13)

Finally, we can dene the MaxCap problem as follows:

maxjJ i

(S j + Q j )

s.t.C1, C2, C3, C4, C5, C6, C7,

C8, C9, C10, C11, C12, C13.

The MaxCap problem directly addresses the improvementof inbuilding SINR, and hence, it effectively optimizes thefemtocell network from the viewpoint of the site performance.


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Fig. 6. The CDF of SINR, when the building is located at L#1.

TABLE IISOLUTIONS OF M AX PWR AND M AX CAP OPTIMIZATION PROBLEMS ,

WHEN THE BUILDING IS LOCATED AT L#1

BSindex

MaxPwr MaxCapFreq. Ch. Power (mW) Freq. Ch. Power (mW)

2 3 0.01 3 0.084 1 0.01 1 0.066 2 0.01 2 0.018 2 0.01 2 0.05

11 3 0.01 1 0.0113 1 0.02 1 0.0815 2 0.03 2 0.0217 2 0.01 2 0.0120 3 0.13 3 0.0522 1 0.18 1 0.6424 3 0.05 2 0.0126 2 0.13 2 0.04

IV. P ERFORMANCE E VALUATION

In this section, we compare both the MaxPwr and MaxCapproblems. Note that no other algorithms in the literaturecan satisfy all the constraints in consideration, so they arenot compared. We are interested in the overall performanceimprovement of the target inbuilding area and the overallperformance degradation of outdoor region. As a result, weexpect to obtain the theoretical performance bound of thefemtocell deployment optimization with the proposed objec-tives. For this purpose, we evaluate the cumulative distributionfunction (CDF) of the SINR measured at all the grids. 2 TheSINR at an outdoor grid is dened as the maximum SINR,which can be observed from one of macro BSs, assumingthat the user selects the BS to associate with according tothe maximum SINR policy. Without femtocell network, theSINR at any inbuilding grid is determined exactly in the samemanner as the outdoor SINR. When the femtocell network is employed, the SINR at each inbuilding grid is dened asthe maximum SINR, which can be observed from one of femto BSs, assuming that the indoor user also follows themaximum SINR policy for its association. From the CDF of

2 The grid size for SINR measurement is not necessarily equal to that usedto build TPs since it has nothing to do with the problem complexity.

SINR, we can obtain various interesting information, e.g., theprobability of coverage hole due to SINR outage, the statisticsof transmission rate, the performance degradation of outdoorusers due to the interference from femtocell network.

For the numerical analysis, we use CPLEX as the MIPsolver [9]. We consider two-tier cellular environment for themacro network as presented in Section II and the cell radiusis assumed 800 m. The transmit power P Macro of macro BS isxed to 20 W and the maximum transmit power P max of femtoBS is assumed 100 mW. We consider that the building sizeW building = 50 m and street size W street = 30 m, respectively.

We consider three building location cases, where a buildingin cell 0 is located at different positions within the same cell,i.e., L#1, L#2, and L#3 indicated in Fig. 1. The reason why weconsider these three cases is that each position holds distinctivefeatures of interference originating from macro BSs: in thecase of L#1, the signals from sector 1 of cell 0, sector 2 of cell 0 and sector 0 of cell 2 are almost of the same strengths,and hence, it is likely that whatever a frequency channel ischosen, the outdoor users operating at that frequency channel

would be found in the vicinity of the building. In the case of L#2, the signal levels both from sectors 1 and 2 of cell 0 arerelatively stronger than that from sector 0 of cell 2, and thestrengths of two signals are almost the same. Therefore, it ishighly probable that there is no outdoor user using frequencychannel 1. For L#3, the signal level from sector 0 of cell 0 isthe strongest one, and hence, most outdoor users around thebuilding will operate in frequency channel 1.

Among these three locations, we present the results obtainedonly for L#1 and L#2. The major difference between L#2 andL#3 cases is whether the number of frequency channels, whichare mainly used by the outdoor users around the building,is 2 or 1. Note that, at building location L#3, the degree of

freedom in determining the radio parameters of femto BS willincrease, since the constraint, i.e., limiting the interference onthe outdoor users, is easily satised if a frequency channeldominantly used by the outdoor users is avoided by femtoBSs.

For our evaluation, we exclude the decision problem of thelocation of femto BSs, which is less relevant to our majorinterest, namely, an automatic radio parameter congurationof femto BSs. To do so, we x M = 12 such that the fourlocations at each oor are considered including the locationindices, i.e., 2, 4, 6, 8, 11, 13, 15, 17, 20, 22, 24, and 26. Forother location indices a , zaf is xed to zero for all f F . Forthe evaluation of MaxPwr and MaxCap problems, we placean ITPs on each of 2-by-2 m grids, which cover the wholeinbuilding region.

Fig. 5 shows the effect of femtocell network congured byMaxCap optimization via illustrating the spatial distribution of SINR when the building is located at L#1. While the entireindoor region of the building experiences SINR under 5 dBbefore deploying the femtocell network due to the heavypenetration loss of the signal from macro BSs, the femtocellnetwork is observed to boost up the SINR of the whole indoorarea to over 3 dB. Looking at the color of the street region


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Fig. 7. The CDF of SINR, when the building is located at L#2.

TABLE IIISOLUTIONS OF M AX PWR AND M AX CAP OPTIMIZATION PROBLEMS ,

WHEN THE BUILDING IS LOCATED AT L#2

BSindex

MaxPwr MaxCapFreq. Ch. Power (mW) Freq. Ch. Power (mW)

2 3 0.01 1 100

4 1 0.01 1 0.016 1 20.11 1 0.018 2 0.22 2 0.04

11 3 0.03 3 0.0813 1 0.01 2 0.0115 1 100 2 0.0117 3 0.01 1 0.0420 1 60.97 1 0.0122 1 59.95 1 0.0624 1 100 2 0.0126 1 60.98 1 14.74

surrounding the 1st oor, we see that there is no signicantdegradation in the SINR the outdoor users experience due to

the deployment of the femtocell network.The solutions given by MaxPwr and MaxCap optimization

at L#1 are listed in Table II. The transmit power value (in mW)is rounded off to the second decimal place. Both solutionsexploit all the frequency channels because all the frequencychannels are used by the outdoor users near the building.That is, if any femto BSs in any frequency channel use largetransmission power values, the SINR constraints of some ETPswill not be satised. Consequently, all the femto BSs use smalltransmission power values for both MaxPwr and MaxCap.Fig. 6 shows that the SINR of the indoor region is dramaticallyimproved by both optimizations. Indeed, the SINR degradationat the outdoor region is observed be to less than 1 dB, whichwas given as the requirement. Interestingly, we can observethat MaxCap improves the region with the low-to-mid SINR(less than 15 dB) more efciently than MaxPwr optimization.

The solutions given by MaxPwr and MaxCap optimizationat L#2 are listed in Table III. The CDF of the SINR is alsodepicted in Fig. 7. For both cases, some femto BSs operatingin frequency channel 1 use large transmission power values,since all the outdoor users on the street use either frequencychannel 2 or 3 to satisfy their QoS requirements since sectors 1

and 2 use frequency channels 2 and 3, respectively. Comparedwith the previous case, the most noteworthy observation fromFig. 7 is that the gap of the indoor SINR performance betweenMaxPwr and MaxCap is quite remarkable. This phenomenoncan be explained as follows: from the discussion about theimplication according to the building location, we can inferthat it plays more strictly at L#1 than at L#2 the constraintthat the SINR degradation of the outdoor users should belimited. Therefore, MaxPwr optimization at L#2 can havemore chances to increase the transmit power of femto BSwithout violating the constraints. However, as we discussed thelimitation of MaxPwr optimization earlier in its formulation,the higher transmit power of the entire BSs does not neces-sarily yield the network-wide conguration optimized fromthe SINR perspective. Indeed, Table III shows that MaxPwroptimization congures relatively high transmit power to thefemto BS indices including 20, 22, 24, and 26, which arelocated at the same oor.

V. C ONCLUSION

We formulated the femtocell network optimization problemswith constraints on the inbuilding coverage and the interfer-ence given to the outdoor users for two different objectives.The MaxPwr and MaxCap problems aim to maximize thecapacity of the target indoor area by maximizing the sum of femto BSs transmit power and by maximizing the sum of ap-proximated cell capacity respectively. Through the numericalresults based on a widely used channel model, we veried thebenet of the femtocell network and analyzed the solutionsobtained for each optimization objective. Our results showthe theoretical performance bound by network optimization insuch an environment. As future work, we plan to develop lowcomplexity algorithms and tackle the network-wide throughput

optimization problem considering the intracell and network-wide fairness policy.

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2.4_femto optimization power freq ilp han 2009

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