The 18th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'07)

LIMITED DOWNLINK NETWORK COORDINATION IN CELLULAR NETWORKS

Federico BoccardiBell Labs, Alcatel-Lucent

Swindon, UK

ABSTRACT

We investigate the downlink throughput of cellular systemswhere groups of M antennas- either co-located or spatiallydistributed- transmit to a subset of a total population ofK >M users in a coherent, coordinated fashion in order to miti-gate intercell interference. We consider two types of coordi-nation: the capacity-achieving technique based on dirty papercoding (DPC), and a simpler technique based on zero-forcing(ZF) beamforming with per-antenna power constraints. Duringa given frame, a scheduler chooses the subset of the K usersin order to maximize the weighted sum rate, where the weightsare based on the proportional-fair scheduling algorithm. Weconsider the weighted average sum throughput among K usersper cell in a multi-cell network where coordination is limitedto a neighborhood ofM antennas. Consequently, the perfor-mance ofboth systems is limited by interference from antennasthat are outside of the M coordinated antennas. Compared toa 12-sector baseline which uses the same number of antennasper cell site, the throughput of ZF and DPC achieve respectivegains of 1.5 and 1.75.

I INTRODUCTION

In conventional cellular networks, the throughput is limitedby co-channel interference, either from within a cell (intra-cell interference) or from nearby cells (intercell interference).Downlink intracell interference can be eliminated by orthog-onal channel allocation, for example through OFDMA. Inter-cell interference can be reduced in several ways, for exam-ple through frequency planning, soft handoff, or beamformingmultiple antennas. While these techniques reduce the interfer-ence, intercell interference in theory can be completely elim-inated by coherently coordinating the transmission of signalsacross base stations in the entire network. Each user's signal istransmitted simultaneously from multiple base station antennas(possibly spatially distributed), and the signals are weightedand pre-processed so that intercell interference is mitigated orcompletely eliminated [1].Due to the complexity required to coordinate transmission

over an entire network, we focus on downlink coordinationover a limited subset of the network. We consider dirty papercoding (DPC), a capacity-achieving technique for the broad-cast channel [2], and a simpler zero-forcing (ZF) beamformingalgorithm which uses linear weighting and conventional single-user channel coding. Under ZF, multiple non-interfering beamsare generated to serve multiple users simultaneously. Moti-vated by practical considerations that often require individualpower amplifiers for each transmit antennas, we impose a per-antenna power constraint on the transmit powers. Under thisconstraint, power allocation for ZF was shown to be a con-

Howard HuangBell Labs, Alcatel-LucentCrawford Hill, NJ, USA

vex optimization, and its sum-rate throughput performance wasshown to be optimal as the number of users increases asymp-totically [3]. We assume a high-speed backhaul for transferringcoherent channel knowledge and user data among the coordi-nating bases. The effects of delay or channel estimation er-ror are not considered here but should be investigated in futurework.

Previous work in this area has studied the performance ofDPC and ZF under the condition of equal rate service for non-outage users during each frame [1]. This requirement is suit-able for equal-rate circuit-based applications. In this paper, weconsider the context of a scheduled packet-data system wherethe goal is to maximize the weighted sum rate of the users dur-ing each frame. Our methodology is an extension of the pro-portional fair scheduling (PFS) algorithm to a system wheremultiple users can be served during each frame.

The paper is organized as follows. In Section II we give thesystem model. In Section III we describe the system architec-ture, transmission technique, and system simulation methodol-ogy for the two precoding schemes, ZF and DPC. In Section IVwe discuss the baseline sectorized system. In Section V we thepresent the scheduling methodology used for all three trans-mission options, and in Section VI we discuss the simulationresults.

II SYSTEM MODEL

We consider a cellular system of N = 19 hexagonal cellswhere a center cell is surrounded by two rings of cells. Weevaluate the throughput performance of the central cell in thepresence of interference caused by the 18 surrounding cells.For the precoding systems, let M be the number of coordi-nated antennas. For the sectorization cases, let M = 1 be thenumber of antennas per sector. The placement of the antennasis described later. Let K be the number of single-antenna usersper cell, and let hl m be the channel response between the mthantenna (m 1,.. M) of the Ith cell (I = 1, . . ., N) and thekth user (k 1, . . ., K) of the central cell:

hkm k3km kA(Om) [dim 'd0] pkmF (1)

where 13m is the Rayleigh fading, /31mk V C(O, 1), A(0 m)is the antenna element response as a function of the directionfrom the mth antenna ofthe Ith cell to the kth user in the centralcell, dl m is the distance between the mth antenna ofthe Ith celland the kth user of the central cell, do is the reference distancedefined as the distance between the cell center and its vertex, nis the pathloss coefficient, and Pim is the lognormal shadowingbetween the mth antenna of the Ith cell and the kth user.

The variable F is the reference SNR defined as the SNR mea-sured at the cell vertex assuming a single antenna at the cell

1-4244-1144-0/07/$25.00(02007 IEEE

The 18th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'07)

center transmits at full power, accounting only for the pathloss.This parameter conveniently captures the effects of transmitpower, cable losses, thermal noise power and other link-relatedparameters. For example, for a conventional macrocellular sys-tem with a 2 km base-to-base distance and with a 30 watt am-plifier transmitting in 1MHz bandwidth, the reference SNR isF = 18dB [4]. If instead we use a 3 watt amplifier and keep theother parameters the same, the reference SNR would be F =

8dB. Alternatively, we could have kept the transmit power thesame (30 watts) and increased the bandwidth by a factor of 10(to 10MHz) to obtain F = 8dB.We model the element response as an inverted parabola that

is parameterized by the 3 dB beamwidth O3dB and the sidelobepower A, measured in dB:

A(0,m) dB= -min{12(01 m/03dB)2, As} (2)

where 0 C [-7,7] is the direction of user k with respect tothe broadside direction of the mth antenna of the Ith cell. Thedifferent antenna array parameters considered in this work aresummarized in Table 1, but we leave the discussion of theseparameters for Sections A and A.

[TXscheme J M [ Antennaarray | 03dB | A,3 sectors 1 none (70/ 180)7F 20 dB12 sectors 1 none (17.5/180)7w 26 dBZF centr. 12 circular (90/180)w7 20 dBZF distr. 12 linear (70/180)w7 20 dBDPC centr. 12 circular (90/180)w7 20 dBDPC distr. 12 linear (70/ 180)w7 20 dB

Table 1: Antenna parameters.

We assume that antennas are coordinated in clusters ofMantennas, and each cluster served K single-antenna users. Let-ting I 1 be the index of the target cluster, the discrete-timecomplex baseband received signal by the kth user served bythis this cluster is

N

Yk=hkx1+Zhxl+nk, k 1,...,K (3)1=2

where hk = [hk1,... hlm] is the channel vector betweenthe antenna array of this cluster and its kth user, h =[hl 1, ... . h$M] is the channel vector from the Ith interferingcluster, xi CmX 1 is the signal vector transmitted by the Ithcluster, nk - CN(O, 1) is the complex additive white Gaussiannoise at the kth user, M is the number of antennas per coordi-nating cluster and K is the number of users served per cluster.We assume that each cluster perfectly knows the channel stateinformation of only its users. On a given symbol period, eachbase I serves a subset of users S' C {1, ... , K}. Under a per-antenna average power constraint, the transmitted signal mustsatisfy

E[Xl 2 <pl T=1m=1,...,M (4)

III PRECODING WITH FULL CSI AT THE BASE STATION

In this section we consider two precoding schemes that requirefull channel state information (CSI) at the transmitter side.The focus is on the zero-forcing (ZF) beamformer with a per-antenna power constraint. The well-known dirty paper coding(DPC) scheme with a sum power constraint is also consideredas benchmark.

A System architecture

For both ZF and DPC, coordinated transmission occurs overa cluster of M antennas. As shown below in Figure 1, theantennas for a given cluster are either co-located or spatiallydistributed depending the type of coordination.

* Centralized coordination. The cluster consists of a circu-lar array ofM = 12 co-located antennas. The grey areain Figure 1 indicates that coordination occurs among eachset ofM antennas. The antennas are located at the "half-hour" points of an analog clock with sufficient elementspacing so that the independent Rayleigh fading assump-tion is justified. We model the element response using (2),with 03dB = w/2 and A, = 20 dB, where each antenna'sboresight direction corresponds to its radial direction withrespect to the array's center. Users experience interferencefrom other cells; therefore users at the cell edge will ex-perience the most interference. The CSI is shared amongM co-located antennas.

* Distributed coordination. The M = 12 coordinated an-tennas are spatially distributed in 3 groups of 4 antennas,where each group is associated with a different cell site.In Figure 1, the three groups on the corners of the greyarea are coordinated. Each group is a linear array consist-ing of directional elements pointing towards the center ofthe grey area. Note that the three groups that share a com-mon base are each associated with a different coordinationgroup. Ifwe were to label each coordination cluster witha different hexagon, these hexagons would tile the cellu-lar network. Note that in discussing simulations for thedistributed architecture, the notion of hexagonal cells isreplaced by the hexagonal coordination regions.

Each element has parameters with 03dB 707 andA, = 20 dB. The distributed architecture is similar tothe conventional 3-sector architecture, and the element pa-rameters as the same for the two cases. Because of non-ideal sidelobes, users near the sector border will experi-ence interference from adjacent sectors. The implementa-tion would be more difficult than for the centralized casesince CSI must be shared among spatially distributed an-tenna groups.

B Transmission schemes

1) ZF

where Pl is the power constraint for the mth antenna of the We now discuss the ZF transmission technique for a given clus-lth base station. ter of M coordinated antennas. Assuming a linear precoder

The 18th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'07)

DPC/ZF Distributed

(72 accounts for the intercell interference and that this interfer-ence is considered Gaussian. We describe how this interferenceis generated in the following subsection. Problem (7) is a con-vex problem which in general can be solved by using an interiorpoint method [5]. In general, in considering service to the com-plete population ofK users, we need to consider all possiblesets of users with cardinality lSl < min(M, K). Therefore theoverall optimization is a generalization of (7):

max R(S)SC{1..K}

iSI<min(M,K)

(8)

0

12 Sectors DPC/ZF Centralized

Figure 1: Antenna architectures for sectorized and precodingsystems. Shaded regions indicate antennas that are coordi-nated.

(beamformer) is used, the transmitted signal for the central basestation can be written as

x= G(S)u, (5)

where G(S) C CMXlSI is the beamforming matrix for theusers in set S and u = [u1, . . ., uIsI]T is the vector of in-formation bearing signals. Note that in defining u, the user

indices have been rearranged so the users chosen for servicecorrespond to the first S indices.

Ifwe use ZF beamforming, the beamforming matrix is cho-sen such that H(S)G(S) = IISI, where H(S) C CISlXMis obtained by extracting the appropriate rows of H =

[hT ... hc1JT, and Il is the TST-by- Sl identity matrix. As-suming ISI < M, the ZF matrix can be chosen to be thepseudo-inverse of H(S),

G (S) = HH(S) [H(S)HH(S)] -l. (6)

Letting ak be the quality of service (QoS) weight for the kthuser, for a given set of users S (S < M), the problem offinding the optimum user power allocations which maximizethe weighted sum rate under ZF beamforming subject to per-

antenna power constraints can be formalized as:

R(S)

subject to

max gIakVVk,k= L 11

k=l

(7)

Vk>0, k =,..., S

jlgmk 2Vk<<Pm, mT=l,...,M

where Ymk is the (m, k)th element of G(S), or' is the thermalnoise plus interference variance and where the power constraintfollows from (5) and (4). The QoS weights are generated by a

scheduler described in Section V. We emphasize that the term

Solving (8) optimally requires a brute force search over all pos-sible sets S of 1, 2, ... ,M users. The number of sets to con-

sider is min( M) (KKs!!, so the complexity of this searchbecomes unacceptably high for large K. We therefore use

a suboptimum but efficient greedy algorithm for large K de-scribed in [6] (see also [7]) for selecting a subset of users

SC {1,... , K} to serve.

2) DPC

As with ZF, we are interested in deriving the expression forthe maximum weighted sum rate achievable by K users in thecenter cell in the presence of intercell interference or2 receivedby the kth user. Defining

(9)

and Heq = EH, for each given channel matrix Heq 1, the max-imum throughput is achieved by Dirty-Paper Coding (DPC)[8]:

C(Heq, P) = max log det (I + HH diag(v)Heq) (10)

where maximization is over v C R K such that Eiqi < P,P = E Pm and Pm is the power constraint on the mth antenna.The convex maximization in (10) can be solved by the simpleiterative algorithm of [9]. Let RDPC (P) be the rate regionachieved by DPC. To determine the optimum throughput whena scheduler is used, it is necessary to determine the point R*on the boundary of the rate region that achieves the maximumweighted rate sum for a given set of QoS weights

R* = argmax aR subjectto R C RDPC(P) (11)R

where a [= ,... ,l aK] is the vector of QoS weights. In [10]an algorithm is proposed to optimally solve (11) by exploitingthe duality with the uplink channel [8].

C Simulation methodologyIn this subsection, we describe the simulation methodology fordetermining the throughput for both ZF and DPC, where thethroughput is defined as the average sum rate of the K users.

1Note that the achievable rate region of the downlink transmission definedby the channel matrix H and the noise variances [ .I K] is the same of

the one of the downlink transmission defined by the channel E and the noisevariances [1, ,1].

0

3 Sectors

E = diag [I /g2 .... . I/g2 ]1 K

The 18th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'07)

We describe a methodology that assumes M-antenna coordina-tion is applied throughout the entire network. However, insteadof having to run a multicell simulation where coordination oc-curs in each hexagonal coordination region, we propose a muchsimpler procedure that requires coordination to be simulated inonly the center coordination region. This procedure occurs inmultiple rounds. To simplify the discussion, we use the term"cell" to refer to the hexagonal coordination region.

For the first round, consider a single isolated cell. In otherwords, we assume there is no intercell interference, and (71 =

... = (JK = 1. We randomly drop K users with a spatiallyuniform distribution in this region. For each user, we also gen-erate a shadow fading realization. We fix the user location andshadow fading realizations for F frames. Over these F frames,we generate i.i.d Rayleigh fading realizations for each frameand determine the maximum weighted sum rate according toeither (8) or (11). The generation of QoS weights is describedin Section V, and the mean rate of each user is calculated aftera steady state has been reached after F/2 frames. At the end ofF frames, we generate a new set of user positions and shadowfadings, and the procedure is repeated for a total of D sets ofF frames. The sum average rate metric is simply the sum ofthe K users' mean rates. For each frame after steady state, werecord the transmit covariance; therefore we collect a total ofDF/2 transmit covariances corresponding to the steady stateperformance.On successive rounds, we account for the effects of intercell

interference. For a given frame, we account for this interfer-ence by assigning to each cell a random member from the setof DF'2 transmit covariances from the previous round. In do-ing so, we treat each interfering cell as if it was an isolated cellserving K users as in the first round. Then for the kth user inthe center cell, we can compute the total thermal noise plus in-terference variance Ok based on the transmit covariances fromthe interfering cells and channel realizations for this user. Thesum average rate and transmit covariances for the center cellcan be computed as before.

This procedure should be repeated for successive rounds un-til the statistics of the interference are stabilized. However, inour simulations, two rounds are sufficient for stabilization.

IV SECTORIZATION

In this section we consider a sectorized system, where thereis single antenna in each sector, and there are either 3 or 12sectors per cell.

A System architectureFor the case of 3 sectors, the response of each element is givenby (2) with O3dB = 70 7 and Am = 20 dB. For the case of12 sectors, the response is narrower, and the sidelobe power is6dB lower: O3dB 187 it and Am = 26 dB.

B Transmission scheme

Transmission for the sectorized systems is assumed to be coor-dinated in the sense that the scheduled transmission among sec-

ber of users per sector is large, then coordinated transmissionwould not have much advantage over the conventional trans-mission technique where each sector operates autonomously.However, ifthe number ofusers per sector is smaller, then thereare some gains over autonomous transmission.Each sector is assumed to transmit at full power, and each

user measures its received signal power from all sectors. Eachuser feeds back its vector of received signal powers, so eachbase can compute the SINRs of all users associated with itssectors. The problem is to determine the optimum allocationof users to sectors in order to maximize the weighted sum rateamong users in a cell. We let s be the N5 x 1 sector allocationvector, where s(i), i = 1, . . . , N, indicates the user allocatedto the ith sector and N, is the number of sectors, and let tYs (k)the SINR of the kth user under the sector allocation s. The op-

timal sector allocation is given by the solution of the followingproblem

Ns

In general, solving (12) requires a brute force search over allpossible sets of N, users. The number of set to consider is

K!T!, so the complexity of this search becomes unaccept-

(K-N,

ably high for large K. We therefore use a suboptimal greedyalgorithm which is analogous to the one presented in SectionIII.

C Simulation methodologyThe central cell throughput is evaluated using a similar method-ology as for the ZF and DPC case. However, we need only a

single round to evaluate the throughput, because the effect ofthe multicell interference is accounted for in the SINR expres-

sion (12).

V SCHEDULING METHOLOGY

In this section, we describe how to generate the quality ofservice (QoS) weights V1 ,... , CK used in calculating theweighted sum rate metric used by all transmission techniques.For a given set ofQoS weights, recall that DPC numerically de-termines the optimal subset of users to be served. On the otherhand, both ZF and sectorization rely on a greedy algorithm forchoosing the subset of users.

For the weight calculation we use the proportional fairscheduling (PFS) algorithm [11]: the users are scheduled bytaking into account the ratio between the instantaneous achiev-able rate and the average rate. Indeed, the QoS weight ak forthe kth user is the reciprocal of the user's average windowedrate (note that the instantaneous achievable rate term in (7),(10) and (12) is given by log(.)). In other words, if we letRk (f ) be the average rate of the kth user on frame f, thenthe average rate on next frame is updated using a sliding win-dow average based on a forgetting factor -y: Rk (f + 1) =

(1 '-y)Rsk(f) + -yR k(f ), where Rk(f) is the rate received

by user k during frame f. This value is zero if the user is

tors with co-located antennas is performed jointly. If the num- not served. The QoS weight is SiMPIY ak(f) = 1IRk(f).

The 18th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'07)

Note that in general, we do not include the frame index f forthe QoS weight. The QoS weight for the kth user is initial-ized using an estimate of its average achievable rate Rk (1)

log(1 + [dmin/do] -'F , where dmin is the distance fromthe user to the closest base antenna.

The PFS algorithm is applicable for scheduling the singlebest user out ofK users during a frame. It ensures fairness inthe sense that over the long term, each user gets served a frac-tion 1/K of the frames. It is also optimal in the sense that itmaximizes the sum log of user rates. Our scheduler is moregeneral in that multiple users could be served during a frame.It is reasonable to use the average rate reciprocal as the QoSweight since the same fairness mechanisms at work in PFS ap-ply here. Namely, users that have been starved will have higherQoS weights, and users that have been served recently will havelower QoS weights. In Section VI, we show empirically thatthese mechanisms provide fairness; however, analytic optimal-ity of this scheduler for multiuser service has not been shown.

VI SIMULATION RESULTS

We simulate a cellular system consisting a central cell and tworings of surrounding cells, each with K = 20 users. For theDPC and ZF the transmitter perfectly knows the channel stateinformation; for the sectorized system, the transmitter onlyknows the SINR of the users. We assume a pathloss coeffi-cient n = 4, shadowing with standard deviation 8dB, F = 100frames per user drop, D = 10 drops, forgetting factor -y = 0.1.

In Figure 2 we compare DPC, ZF and sectorized system (3and 12 sectors) in terms of sum-rate vs reference SNR, wherethe reference SNR is defined as the average SNR in a vertex ofthe cell. We note that the centralized system architecture per-

40DPC centralized

35 -O- DPC distributed --- ---

ZF centralizedZF distributed - A

30 12 sectors0 3 sectors

E2

..

10-

_- ------------------------------. ...

-20 -15 -10 -5 0 5 10 15 20reference SNR [dB]

Figure 2: Comparison between DPC, ZF and sectorized system(3 and 12 sectors) in terms of sum-rate vs reference SNR.

forms better than the distributed system architecture for bothDPC and ZF. This is due to the fact that the interference be-tween sectors of the co-located linear arrays for the distributedarchitecture is more detrimental than the intercell interference

for the centralized architecture. When the centralized archi-tecture is used, compared to a baseline sectorized system with12 (3) sectors, the interference-limited throughput of the ZFand DPC are respectively a factor 1.5 (3.5) and 1.75 (4) higher.Note that as K increases, the performance gain ofthe 12-sectorsystem versus the 3-sector system approaches 4, as one mightexpect due to the linear throughput gain of sectorization.

VII CONCLUSIONS

We have studied the potential improvement in downlinkthroughput of cellular systems using limited network coordi-nation to mitigate intercell interference. We studied ZF andDPC precoding techniques under distributed and centralizedarchitectures. For either precoding technique, the centralizedarchitecture performs uniformly better over the range of pow-ers considered. DPC and ZF provide respective gains of up to1.75 and 1.5 over the 12-sector baseline and gains of up to 4.5and 3.5 over the 3-sector baseline. Sectorization using 12 sec-tors is a cost-efficient technique for improving the performanceof a conventional 3-sector system. Additional throughput gainscan be achieved under ideal conditions using limited networkcoordination under the centralized architecture. However, theimpact of practical considerations such as imperfect channelknowledge at the transmitter should be studied.

ACKNOWLEDGEMENT

This work has been partly supported by the IST project10273 10 MEMBRANE.

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