multicell coordinated scheduling with multiuser zf beamforming

Multicell Coordinated Scheduling with MultiuserZF Beamforming

Min Li, Chunshan LiuDepartment of Engineering

Macquarie UniversitySydney, Australia

{min.li, chunshan.liu}@mq.edu.au

Iain B. CollingsComputational Informatics

CSIROSydney, Australia

[email protected]

Stephen V. HanlyDepartment of Engineering

Macquarie UniversitySydney, Australia

[email protected]

Abstract—We investigate a coordinated scheduling problem ina two-cell network where in each cell, two users are scheduledfor simultaneous communication. Zero-forcing (ZF) beamformingis employed at each base station to suppress both intra- andinter-cell interference. The coordinated scheduling/beamformingproblem is formulated as finding proper scheduling decisionsand hence beamformers across the network such that a weightedsum-throughput is maximized. We propose three distributedscheduling policies that only require local data and local channelstate information at each cell, and consume much less computa-tion and communication overhead than the global optimizationapproach via exhaustive search. The proposed policies illustratethe complexity-performance tradeoff for the coordinated system.Nevertheless, numerical results show that at all levels of complex-ity, the proposed policies perform close to the global optimizationapproach with ZF beamforming and outperform the scheme withmatched filtering beamforming even with global coordination.

I. INTRODUCTION

Coordinated multipoint transmission (CoMP) is consideredas one of the key candidate techniques to improve the cell-edgeuser performance and increase the overall system capacity inthe LTE and LTE-Advanced wireless mobile networks [1]–[3]. Various forms of CoMP have been considered in bothacademia and industry. Perhaps the most common one is thejoint transmission (JT) [3] (or network MIMO [4]), in whichmultiple base stations (BSs) are allowed to serve one remoteuser equipment (UE) simultaneously over the same resource.Since the BSs form a virtual antenna array for transmission,in theory, a significant capacity gain can be obtained from theJT-based CoMP. However, great challenges arise in practicaldeployments of JT, due to the requirements of large-capacityand low-latency backhaul for sharing data and disseminatingchannel state information (CSI) among the engaged BSs.

Coordinated scheduling/beamforming (CS/CB) emerges asanother CoMP architecture with relatively low complexity. Inthe CS/CB-based CoMP, each UE is communicating only withthe BS in its anchor cell, but the transmission is facilitated withan exchange of control information among the coordinatedBSs. Such coordination consumes far less backhaul resourcesthan those for sharing data and CSI in JT. Hence, the CS/CB isvery competitive compared to the JT from this practical pointof view.

In this work, we focus on the CS/CB-based CoMP withthe aim of developing low-complexity multicell coordinated

scheduling policies. Related CS/CB studies can be found in[5]–[9]. Reference [5] addressed the CB problem for a two-cellnetwork, where inter-cell interference is allowed but subject tosignal-to-interference-and-noise-ratio targets for a fixed set ofUEs in each cell. Assuming that each UE is associated witha static precoding codebook, [6] proposed a joint beam/UEselection mechanism by exploring feedback information fromUEs, which includes not only each UE’s preferred precodingmatrix index (PMI) for its serving cell but also the worstcompanion PMIs for one or more interfering cells. Allowingto switch between either matched filter (MF) or zero-forcing(ZF) beamforming, [7] put forth a low-complexity algorithmto select the best users and beamforming strategies acrossmultiple cells. While [6], [7] focused on the CS/CB with singleuser scheduled in each cell, [8] and [9] studied the CS/CBwith multiple users scheduled within each cell under randombeamforming and optimization-based linear beamforming, re-spectively.

Along the line of [8], [9], we study the CS/CB with multipleusers scheduled within each cell. ZF beamforming is adoptedto mitigate both intra- and inter-cell interference. Specifically,we consider a coordinated two-cell network, where each BShas sufficient number of antennas to accommodate two UEs forsimultaneous communication in its cell. Each BS has data onlyfor the UEs it serves and knows the channels originating fromitself to the UEs in the network. Under such local data and CSIassumptions, we formulate a CS/CB problem on how to alignscheduling decisions and beamformers across the cluster withthe objective of maximizing the weighted sum-throughput. TheCS/CB problem is a combinatorial problem, and finding theoptimal scheduling decision requires a gathering of network-wide CSI and an exhaustive search. Such a global optimizationapproach involves not only tremendous backhaul resourcesfor CSI passing but also expensive searching computation. Toreduce the cost, we propose three low-complexity distributedCS/CB policies. These policies involve semiorthogonal userselection [10] at the initial stage followed by different levels ofmessage passing for coordination between the cells. Numericalresults confirm the effectiveness of the proposed policiesand illustrate the complexity-performance tradeoff for thecoordinated system.

Notation: Boldface uppercase letters and boldface lowercase

IEEE ICC 2014 - Wireless Communications Symposium

978-1-4799-2003-7/14/$31.00 ©2014 IEEE 5017

letters are used to denote matrices and vectors, respectively,e.g., A is a matrix and a is a vector. Notation (·)† rep-resents the conjugate transpose. CN (0, σ2) denotes a zero-mean circularly-symmetric complex Gaussian distribution withvariance σ2. E(·) denotes the expectation operation, while tr(·)denotes the trace operation. ∥a∥ stands for the l2 norm ofvector a and IM is an M ×M identity matrix.

II. SYSTEM MODEL AND PROBLEM FORMULATION

A. System Model

We consider a two-cell downlink network, where the BSsperform coordinated transmission to the UEs over the samefrequency resource. As shown in Fig. 1, each cell consistsof one M -antenna BS and K uniformly distributed single-antenna UEs. Each UE is served by the BS in its anchor cell,and each BS only has the data information intended for itsserving UEs. With regards to channel knowledge, each BSknows the channels originating from itself to all UEs acrossthe two cells, but it is oblivious of the channels originatingfrom the other BS. A finite-capacity backhaul link connectsthe BSs so as to allow a certain level of information exchangebetween them. Due to the capacity limitation, the backhaulresource is mainly used for coordination information exchangebut not for any data information sharing between the BSs.

Transmission time is slotted, and within each slot, two outof K UEs in each cell are co-scheduled for communication.For notational convenience, we denote the BS in cell i as BSi, the kth UE in cell i as UE ki and the collection of activeUE indices in cell i as Ai. Thus, we have Ai ⊂ {1, ...,K}with |Ai| = 2, for i = 1, 2. Let uki ∼ CN (0, 1) be the datasymbol intended for UE ki in cell i, and let unit-norm vectorwki ∈ CM×1 be a linear beamformer associated with symboluki . Then the transmitted signal vector at BS i is given by

xi =∑

ki∈Ai

wki

√Pkiuki , (1)

where Pki denotes the transmission power allocated for UE ki,subject to a per-BS average power constraint as tr(E[xix

†i ]) =∑

ki∈AiPki ≤ P . The received signal at UE ki is then given

by

yki=√αi,ki

βi,kih†i,ki

xi︸︷︷︸intra−cell signal

+√αi,ki

βi,kih†i,ki

xi︸︷︷︸inter−cell interference

+ zki︸︷︷︸noise

, (2)

where notation i denotes the complement of i with respectto the set {1, 2}; αj,ki is the distance-dependent path lossfrom BS j to UE ki, while βj,ki

is the corresponding log-normal random shadowing, i.e., the quantity 10 log10(βj,ki) isGaussian distributed with zero-mean and standard deviation ofσshad; hj,ki ∈ CM×1 stands for the small-scale fading channelbetween BS j and UE ki, with i.i.d. entries ∼ CN (0, 1); andzki ∼ CN (0, N0) is the random noise at UE ki.

We now focus on the scenario where the BSs adopt a ZFlinear beamforming strategy. The number of antenna at eachBS is assumed to be large enough, e.g., M ≥ 4, so as toaccommodate both perfect intra- and inter-cell interferencenullings based on the local data and CSI at the BSs. In

BS 1

BS 2

Backhaul

UEs

Fig. 1. A two-cell cellular network with CS/CB.

particular, supposing that the BSs know each other’s activeUE indices, the unit-norm ZF beamformer wki for UE kiis then chosen by BS i from the null space of channels{hi,A1∪A2\ki

}. The receiving signal-to-noise ratio (SNR) at

UE ki is thus given by

SNRki = αi,kiβi,kiPki

∣∣∣h†i,ki

wki

∣∣∣2/N0. (3)

The corresponding instantaneous achievable rate Rki is char-acterized as Rki = log2 (1 + SNRki) under the assumptionthat UE ki has knowledge of the path loss, shadowing coeffi-cients and the small-scale fading channels connected to itself.

B. Problem Formulation

In the system described, it is clear that the exact beam-former generation at one cell is coupled with the schedulingdecision in the other cell. Therefore, the transmission mustbe coordinated in a way that aligns scheduling decisionsand beamformers across the two cells with the objective ofminimizing interference and maximizing useful signal strengthtowards their co-scheduled UEs. To this end, we formulate aCS/CB problem that maximizes the weighted sum-throughputunder some fairness constraints on UEs as follows:

P : maxA1×A2,

Ai⊂{1,...,K},|Ai|=2

R =2∑

i=1

∑ki∈Ai

wkiRki , (4)

where wki is the weight coefficient associated with UE ki.When calculating rates {Rki}, optimal allocations {Pki} arefound independently at the BSs by a modified water-fillingthat takes the weights into account [11]:

Pki =

(λwki −

1

γki

)+

, (5)

where (x)+ denotes max{x, 0}, γki is defined as

γki = αi,kiβi,ki

∣∣∣h†i,ki

wki

∣∣∣2/N0, (6)

and the water level λ is chosen to satisfy∑ki∈Ai

Pki = P, for i = 1, 2. (7)


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Different choices of weight coefficients in the problem mayreflect different fairness among UEs in the system. With focuson proportional fairness criterion [12], we assume that eachcoefficient wki at a time slot evolves as the reciprocal of itspast average throughput according to

wki(t+ 1) =1

Rki(t+ 1)

, (8)

with

Rki (t+ 1) =

{ (1− 1

T

)Rki (t) +

1T Rki (t) , if ki ∈ Ai(t)(

1− 1T

)Rki (t) , otherwise,

and T is a constant denoting the smoothing window size. Foreach slot t, we wish to determine the optimal scheduling UEsin each cell such that the weighted sum-throughput of (4) ismaximized.

C. Discussions

The CS/CB problem P is a combinatorial problem. Astraightforward approach to solve P is to perform a searchover all possible joint combinations of scheduling UEs acrossthe network and identify the optimal one that leads to themaximum objective. Despite its conceptual simplicity andoptimality, such an exhaustive method has obvious drawbacks.First, it is a global optimization approach and relies on acentral processing unit that is able to collect the network-wide CSIs and weight coefficients. This unit could be eitheran additional entity (e.g., a cloud) or one of the BSs inthe network. However, the information aggregation processrequires such a tremendous amount of capacity resources thatit will be beyond the capacity of the backhaul infrastructure.Second, this approach has a searching space of size

(K2

)2,

and thus it is not computationally feasible for even moderateto large K (e.g., K = 100). Motivated by these issues, we areinterested in developing some low-complexity algorithms thatoffer no significant performance loss and can be implementedin a distributed manner with limited message passing.

III. DISTRIBUTED POLICIES WITH MESSAGE PASSING

In this section, we propose several distributed policies tosolve the problem. As we shall see shortly, these policiesillustrate the tradeoff between complexity and performance.

A. Distributed Coordinated Scheduling (DCS) with SelectiveUser-Index Passing: A Simple Policy

The first policy we considered can be viewed as a sim-ple application of the Semiorthogonal User Selection (SUS)algorithm, which is developed for the single-cell broadcastcommunication under ZF beamforming [10]. As indicated byits name, the SUS algorithm constructs a scheduling user setthat has channels semiorthogonal to one another and withrelatively large gains. Without fairness constraint, the SUS isshown to be optimal in the sense that it achieves both themultiplexing gain and the multiuser diversity gain in the limitof large number of homogeneous UEs in a single cell [10].

Turning to the two-cell network studied here, one mightenvision that each cell could first form the scheduling user set

Ai independently based on the SUS algorithm, and then passthe selected active UE indices onto each other via backhaul inorder to generate appropriate ZF beamformers.

In the following, we summarize the SUS algorithm ac-counting for the path loss and shadowing coefficients that aremissing in the original description in [10].

Step 1: Ki,1 = {1, . . . ,K}, Ai = ∅, i = 1, 2; j = 1; N = 2.Step 2: For each ki ∈ Ki,j , compute gi,ki , the component

of user channel√

αi,kiβi,kihi,ki orthogonal to the subspacespanned by {gi,(1), . . . ,gi,(j−1)} as

gi,ki =√αi,kiβi,ki

(IM −

∑j−1

l=1

gi,(l)g†i,(l)∥∥gi,(l)

∥∥2)hi,ki , (9)

where when j = 1, gi,ki =√αi,kiβi,kihi,ki .

Step 3: The BS i schedules its jth UE as follows:

πi(j) = arg maxki∈Ki,j

wki(t) log2

(1 +

P

2∥gi,ki∥

2

),

Ai ← Ai

∪πi(j),gi,(j) ← gi,πi(j). (10)

Step 4: If |Ai| < N , the BS i then forms a new set Ki,j+1

consisting of UE channels semiorthogonal to gi,(j) as

Ki,j+1 =

ki ∈ Ki,j\πi(j),

∣∣∣√αi,kiβi,kih†i,ki

gi,(j)

∣∣∣∥∥√αi,kiβi,kihi,ki

∥∥ ∥∥gi,(j)

∥∥ < ϵ

,

(11)

sets j = j+1 and goes to Step 2; otherwise, the UE selectionprocess terminates. In (11), ϵ ∈ (0, 1] is a design parameterthat specifies the maximum correlation allowed.

This distributed policy possesses a searching complexity of∑2j=1 |Ki,j |, which is at most (2K − 1) at each BS, for the

SUS algorithm, and it involves only two UE indices exchangebetween the BSs along each direction. The policy is apparentlysimple, but it lacks optimality since it fails to account for theinter-cell interference in the user selection. It might happenthat the cells have to devote significant amount of power tonulling the inter-cell interference with only a small portion lefttowards its scheduled UEs. This would certainly degrade thesystem performance.

B. DCS with Selective User-Index Passing: An EnhancedPolicy

We now improve the simple policy by allowing moreinformation exchange between the BSs. The enhanced policyworks as follows.

First, each BS independently forms a scheduled candidatelist Ci that consists of K ′ UEs (with 2 < K ′ ≪ K) based onthe SUS algorithm. This can be done via Step 1-4 previouslydescribed with Ci and N = K ′ in lieu of Ai and N = 2,respectively. Next, one of the BSs, e.g., BS i, forwards itscandidate list Ci to the other BS i via the backhaul link. Wecall BS i and BS i the follower and leader BS, respectively.For fairness, the two BSs rotate to serve as a leader from onetime slot to another. Knowing the shortlists of both cells, theleader BS turns to search the best scheduling combination that


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TABLE ICOMPLEXITY COMPARISON

Policy searching space user-index passing CSI passing1 2(2K − 1) 4 -

DCS-ZF-2 SUS : 2

∑K′−1j=0 (K − j) K′ + 4 -

3 P1/P2 :(K′2

)22K′ + 4 vectors: 2K′; scalars: 4K′

GOS-ZF P :(K2

)24 vectors: 2K; scalars: 4K

maximizes its own weighted throughput based on its local CSI.In other words, it tries to find the optimal scheduling decisionA∗

1×A∗2 of the following subproblem of the original problem:

P1 : maxA1×A2,

A1⊂C1,A2⊂C2,|A1|=|A2|=2

Ri =∑

ki∈Ai

wkiRki

, (12)

and then informs the follower BS about the decision. TheZF beamformers are then generated at each cell based on thescheduling decision across the two cells.

This enhanced policy improves the previous policy througha partial coordination at the leader BS via (12). The com-plexity of the SUS algorithm at each BS is

∑K′

j=1 |Ki,j | ≤∑K′−1j=0 (K − j), while the searching space to solve problem

P1 is(K′

2

)2. Note that when K ′ << K, the searching

space is significantly reduced compared with that for theoriginal problem P . The information exchange involved in theenhanced policy is (K ′ + 4) UE indices in total.

C. DCS with Selective Joint User-Index and CSI Passing

While having only user-index information exchange be-tween the BSs can accommodate partial coordination at onecell, one might expect that passing CSIs along with userindices may provide further benefits. We now develop a thirdpolicy that involves CSI passing as well.

As done in our second policy, we allow each BS to createa shortlist of scheduled UEs based on the SUS algorithm. Wealso distinguish the leader and the follower BS, and assumeBS i to be the leader at the current time slot. Then the leaderactions first and passes its list Ci to the follower. Given theside information, the follower BS i is able to form a set

Hi =

{hi,k1∪k2 ∪ αi,k1∪k2 ∪ βi,k1∪k2 ,

k1 ∪ k2 ∈ C1 × C2

}(13)

that contains all the CSIs from itself to the UEs in thecandidate lists. The follower then pass the CSI set Hi, alongwith the weights {wki , ki ∈ Ci}, onto the leader BS so thatthe latter can search the best scheduling combination over thecandidate lists that maximizes the total weighted throughput.In other words, the following subproblem of the originalproblem P is solved at the leader:

P2 : maxA1×A2,

A1⊂C1,A2⊂C2|A1|=|A2|=2

R =2∑

j=1

∑kj∈Aj

wkjRkj

. (14)

The corresponding optimal solution A∗1 × A∗

2 is forwardedback to the follower BS, based on which appropriate ZFbeamformers are generated at each BS for transmission.

By leveraging the additional CSIs, an enhanced coordinationthat benefits both cells is performed in this policy. The userselection complexity and searching space for the subproblemremain the same as the second policy. But it requires morebackhaul resources to transmit the selective CSIs and weights.

We summarize the complexity of different policies proposedin Table I, where we label the first, second and third poli-cy as DCS-ZF-{1, 2, 3}, respectively, and label the globallyoptimized scheduling (where one of the BSs serves as thecentral processor) as GOS-ZF. It is clear that the GOS-ZF hasthe highest complexity, while for the distributed policies, thecomplexity increases progressively from the first to the lastone.

Remark 1: In the third policy, note that the selective CSIsare assumed to be perfectly conveyed from the follower BSto the leader BS via the backhaul link. In reality, this couldbe problematic due to the finite-capacity constraint on thebackhaul. To alleviate this issue, the follower BS may quantizeits CSIs at some finite rate and forward the quantizationindices to the leader BS, which in turn recovers and uses suchquantized CSIs to perform the CS/CB optimization.

For example, to deal with the small-scale fading vectors,a common approach is to quantize the channel direction ofeach vector hi,kj = hi,kj/

∥∥hi,kj

∥∥ and the channel normg(hi,kj ) =

∥∥hi,kj

∥∥ separately. In particular, assume that acodebook CBi of unit norm vectors of size 2B

CBi = {ci,1, . . . , ci,2B} (15)

is predefined and shared between the BSs. The follower BSfirst quantizes each hi,kj as hi,kj = ci,li,kj

according to theminimum distance criterion [13], [14]

li,kj = arg max1≤n≤2B

∣∣∣h†i,kj

ci,n

∣∣∣ , (16)

and then reports the index li,kj to the leader BS. The realchannel norm, as well as the path loss, shadowing and weights,can be instead represented in a finite number of bits via thestandard scalar quantization techniques, see, e.g., [15] and thereferences therein.

IV. NUMERICAL RESULTS

In this section, we investigate the performance of the pro-posed scheduling policies in a two-cell network. The system


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−5 0 5 10 15 20 25 305

10

15

20

25

30

35

40

45

50

55

Cell edge SNR (dB)

Avera

ge s

um

−th

roughput(

bps/H

Z)

GOS−ZF

DCS−ZF−1

GOS−MF

DS−MF

Fig. 2. Sum-throughput comparison: some baseline schemes.

0 5 10 15 20 25 3010

15

20

25

30

35

40

45

50

55

Cell edge SNR (dB)

Avera

ge s

um

−th

roughput(

bps/H

Z)

GOS−ZF

DCS−ZF−3 (K’=4)




DCS−ZF−1

Fig. 3. Sum-throughput comparison: the distributed polices proposed.

parameters follow from a typical LTE deployment. Specifical-ly, the cell radius is r = 1.4 km and the total bandwidth is10 MHZ. We consider 100 random network realizations, inwhich 10 UEs are randomly generated and uniformly droppedin each cell. The BS’s total transmit power is set to be 46 dBmover the total bandwidth. The distance-dependent path loss ismodeled as: 10 log10(αj,ki) = −(128.1 + 37.6 log10(dj,ki))dB, where dj,ki is in km and denotes the distance betweenBS j and UE ki in cell i. The standard deviation of thelog-normal shadowing σshad = 10 dB. For the small-scalefading, Rayleigh fading channels are independently generatedfor each UE at each time slot. The weight updating parameterT = 100. For a fixed network topology, 200 transmission slotsare simulated.

0 1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Individual UE Rate (bps/HZ)

CD

F

DCS−ZF−1





GOS−ZF

Fig. 4. User rate distribution (cell-edge SNR = 10 dB).

For the purpose of comparison, the performances of thefollowing baseline schemes are also evaluated:

• Distributed Scheduling under Matched Filter beamform-ing (DS-MF): each cell independently schedules its twoUEs based on the SUS algorithm and transmits via MFbeamforming without any coordination between cells;

• Globally Optimized Scheduling under Matched Filterbeamforming (GOS-MF): an exhaustive search is per-formed across the two cells to determine the best schedul-ing decision under MF beamforming.

Fig. 2 plots the average sum-throughput as a function ofcell-edge received SNR under the baseline schemes, the DCS-ZF-1 and the GOS-ZF. It is seen that the simple DCS-ZF-1with minimum amount of coordination outperforms the MFbeamforming transmissions even with full coordination for avery wide range of SNR, e.g., from 5 dB to 30 dB in theexample. But compared to the GOS-ZF, the DCS-ZF-1 stillsuffers a relatively large rate loss, roughly 7 bps/HZ in theexample.

Fig. 3 plots the average sum-throughput for the otherpolicies proposed. The second policy (DCS-ZF-2) improvesupon the DCS-ZF-1, while the third policy (DCS-ZF-3) is thebest and performs close to the GOS-ZF when K ′ = 4. As touser fairness, Fig. 4 illustrates the cumulative distributions ofUE individual rates under different policies with the referencecell-edge SNR fixed at 10 dB. It can be seen that the enhancedpolicies achieve almost the same level of fairness as the GOS-ZF.

We have also investigated the impact of quantization of CSIson the sum-throughput in the third policy. In particular, in theinformation set passed from the follower to the leader, eachchannel direction is independently quantized using the randomvector quantization (RVQ) codebook [13] with B = 4 or 8bits, while the channel norm, path loss, shadowing and weightsare left unquantized. The resulting performance is shown inFig. 5, where we label it as DCS-ZF-3-QCDI (with K ′ = 4).It is seen that with 4-bit RVQ, the coarsely conveyed CDIs


5021

0 5 10 15 20 25 3010

15

20

25

30

35

40

45

50

55

Cell edge SNR (dB)

Avera

ge s

um

−th

roughput(

bps/H

Z)

GOS−ZF


DCS−ZF−3−QCDI (K’=4, RVQ, 8bits)

DCS−ZF−3−QCDI (K’=4, RVQ, 4bits)


Fig. 5. Impact of passing QCDI.

do not improve the scheduling decision: The third policy failsto provide any benefits over the second one. But with 8-bitRVQ, the leader can learn and leverage finer CDIs, yielding anaverage throughput close to the case with perfect CSI passing.

V. CONCLUDING REMARKS

In this work, we have focused on a coordinated two-cell downlink network, where spatial multiplexing via ZFbeamforming is deployed in each cell. With only local dataand local CSI at each cell, we have addressed the key issueon how to align scheduling decisions and beamformers acrossthe two cells with the goal of maximizing the sum-throughputunder proportional fairness constraint. Realizing that a globalexhaustive-search approach is not computationally feasible ingeneral, we have proposed three low-complexity policies thatcan be implemented in a distributed manner with differentlevels of message passing. Numerical results confirm theeffectiveness of the proposed policies and shed light on thepractical system design. The three policies proposed naturallyfit into systems where different levels of coordination maytake place depending on the amount of backhaul resourcesavailable between BSs.

It is remarked that the policies proposed here are applicableto any coordinated systems in conjunction with other typesof linear beamformers, such as regularized ZF and signal-to-leakage-plus-noise-ratio based beamforming [16]. In addition,the distributed policies proposed can also be generalized to acoordinated network with more than two cells, and this is leftfor future work.

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[3] A. Osseiran, J. F. Monserrat, and W. Mohr, Mobile and WirelessCommunications for IMT-advanced and Beyond. Wiley.com, 2011.

[4] D. Gesbert, S. Hanly, H. Huang, S. Shamai, O. Simeone, and W. Yu,“Multi-cell MIMO cooperative networks: A new look at interference,”IEEE Journal on Selected Areas in Communications, vol. 28, no. 9, pp.1380–1408, 2010.

[5] R. Zakhour and S. V. Hanly, “Base station cooperation on the downlink:Large system analysis,” IEEE Trans. Inf. Theory, vol. 58, no. 4, pp.2079–2106, 2012.

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[12] P. Viswanath, D. N. C. Tse, and R. Laroia, “Opportunistic beamformingusing dumb antennas,” IEEE Trans. Inf. Theory, vol. 48, no. 6, pp. 1277–1294, 2002.

[13] N. Jindal, “MIMO broadcast channels with finite-rate feedback,” IEEETrans. Inf. Theory, vol. 52, no. 11, pp. 5045–5060, 2006.

[14] T. Yoo, N. Jindal, and A. Goldsmith, “Multi-antenna downlink channelswith limited feedback and user selection,” IEEE J. Sel. Areas Commun.,vol. 25, no. 7, pp. 1478–1491, 2007.

[15] D. J. Love, R. W. Heath, V. K. N. Lau, D. Gesbert, B. D. Rao, andM. Andrews, “An overview of limited feedback in wireless commu-nication systems,” IEEE J. Sel. Areas Commun., vol. 26, no. 8, pp.1341–1365, 2008.

[16] W. L. Ho, Q. S. Quek, S. Sun, and R. W. Heath, “Decentralized pre-coding for multicell MIMO downlink,” IEEE Trans. Wireless Commun.,vol. 10, no. 6, pp. 1798–1809, 2011.


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