idea for pilot contamincation

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An Overview of Massive MIMO: Benefits andChallenges

Lu Lu, Geoffrey Ye Li, A. Lee Swindlehurst, Alexei Ashikhmin, and Rui Zhang

Abstract—Massive multiple-input multiple-output (MIMO)wireless communications refers to the idea equipping cellular basestations (BSs) with a very large number of antennas, and has beenshown to potentially allow for orders of magnitude improvementin spectral and energy efficiency using relatively simple (linear)processing. In this article, we present a comprehensive overviewof state-of-the-art research on the topic, which has recentlyattracted considerable attention. We begin with an informationtheoretic analysis to illustrate the conjectured advantages ofmassive MIMO, and then we address implementation issuesrelated to channel estimation, detection and precoding schemes.We particularly focus on the potential impact of pilot contam-ination caused by the use of non-orthogonal pilot sequences byusers in adjacent cells. We also analyze the energy efficiencyachieved by massive MIMO systems, and demonstrate how thedegrees of freedom provided by massive MIMO systems enableefficient single-carrier transmission. Finally, the challenges andopportunities associated with implementing massive MIMO infuture wireless communications systems are discussed.

Index Terms—Massive MIMO systems, spectral efficiency,energy efficiency, time-division duplexing (TDD), channel esti-mation, precoding and detection, pilot contamination, orthogonalfrequency division multiplexing (OFDM), single-carrier transmis-sion

I. INTRODUCTION

Multiple-input multiple-output (MIMO) technology hasbeen widely studied during the last two decades and applied tomany wireless standards since it can significantly improve thecapacity and reliability of wireless systems. While initial workon the problem focused on point-to-point MIMO links wheretwo devices with multiple antennas communicate with eachother, focus has shifted in recent years to more practical multi-user MIMO (MU-MIMO) systems, where typically a basestation (BS) with multiple antennas simultaneously serves aset of single-antenna users and the multiplexing gain can beshared by all users. In this way, expensive equipment is onlyneeded on the BS end of the link, and the user terminals

Copyright (c) 2013 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to [email protected] received on September 30, 2013; revised on December 30, 2013and March 26, 2014; accepted on March 28, 2014. The editor coordinatingthe review of this paper and approving it for publication was F. Pereira.

L. Lu and G. Y. Li are with the School of Electrical and ComputerEngineering, Georgia Institute of Technology, Atlanta, GA 30332 USA(email: {lulu, liye}@ece.gatech.edu). A. Lee Swindlehurst is with the HenrySamueli School of Engineering, University of California, Irvine, CA, USA(email: [email protected] ). Alexei Ashikhmin is with the Communicationsand Statistical Sciences Department, Bell Laboratories, Lucent Technologies,Murray Hill, NJ, USA (email: [email protected]). Rui Zhang is withthe Department of Electrical and Computer Engineering, National Universityof Singapore, Singapore (email: [email protected]).

...

...

...

...

Fig. 1. Illustration of Massive MU-MIMO systems.

can be relatively cheap single-antenna devices. Furthermore,due to multi-user diversity, the performance of MU-MIMOsystems is generally less sensitive to the propagation envi-ronment than in the point-to-point MIMO case. As a result,MU-MIMO has become an integral part of communicationsstandards, such as 802.11 (WiFi), 802.16 (WiMAX), LTE,and is progressively being deployed throughout the world. Formost MIMO implementations, the BS typically employs onlya few (i.e., fewer than 10) antennas, and the correspondingimprovement in spectral efficiency, while important, is stillrelatively modest.

In a recent effort to achieve more dramatic gains as wellas to simplify the required signal processing, massive MIMOsystems or large-scale antenna systems (LSAS) have beenproposed in [1], [2], where each BS is equipped with orders ofmagnitude more antennas, e.g., 100 or more. A massive MU-MIMO network is depicted in Fig. 1. Asymptotic argumentsbased on random matrix theory [2] demonstrate that the effectsof uncorrelated noise and small-scale fading are eliminated,the number of users per cell are independent of the size ofthe cell, and the required transmitted energy per bit vanishesas the number of antennas in a MIMO cell grows to infinity.Furthermore, simple linear signal processing approaches, suchas matched-filter (MF) precoding/detection, can be used inmassive MIMO systems to achieve these advantages.

It is shown in [2] that under realistic propagation as-sumptions, MF-based non-cooperative massive MIMO sys-tems could in principle achieve a data rate of 17 Mb/s foreach of 40 users in a 20 MHz channel in both the uplink(reverse link) and downlink (forward link) directions, with anaverage throughput of 730 Mb/s per cell and an overall spectralefficiency of 26.5 bps/Hz. Since the number of antennas atthe BS is typically assumed to be significantly larger than thenumber of users, a large number of degrees of freedom areavailable and can be used to shape the transmitted signals



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in a hardware-friendly way or to null interference [3]. Tomake such a system practical, algorithms for massive MIMOsystems are required to keep the complexity low.

Another advantage of massive MIMO lies in its potentialenergy efficiency compared to a corresponding single-antennasystem. It is shown in [4] that each single-antenna user ina massive MIMO system can scale down its transmit powerproportional to the number of antennas at the BS with perfectchannel state information (CSI) or to the square root of thenumber of BS antennas with imperfect CSI, to get the sameperformance as a corresponding single-input single-output(SISO) system. This leads to higher energy efficiency and isvery important for future wireless networks where excessiveenergy consumption is a growing concern [5], [6]. On theother hand, if adequate transmit power is available, then amassive MIMO system could significantly extend the rangeof operation compared with a single antenna system. Eventhough the conclusions in [4] ignore the power consumptionof the radio front-end, massive MIMO is still a promisingcandidate for improving energy-efficiency of future networks.

The observations described above have recently sparked aflurry of research activities aimed at understanding the signalprocessing and information theoretic ramifications of massiveMIMO system designs. In [7], massive MIMO systems arereviewed from various perspectives, including fundamentalinformation theoretical gains, antenna and propagation aspects,and transceiver design. A follow-up tutorial [8] briefly dis-cusses recent work. In this paper, we provide a more compre-hensive and detailed overview of state-of-the-art research onthis topic. In Section II, the opportunities of massive MIMOsystems are viewed from an information theoretic perspective.Issues on channel estimation and signal detection are thendiscussed in Section III, and transmit precoding schemes arepresented in Section IV. Besides the MF precoder/detector,other linear schemes such as minimum mean-squared error(MMSE) and zero-forcing (ZF) precoders/detectors are dis-cussed based on either single-cell processing or multi-cellcoordinated processing. In Section V, the so-called pilot con-tamination effect, caused by employing non-orthogonal pilotsequences at different users in different cells, is discussed indetail. The energy efficiency of massive MIMO systems is thenanalyzed in Section VI. Instead of using orthogonal frequencydivision multiplexing (OFDM) as in most MU-MIMO imple-mentations today, the possibility of single-carrier modulationfor massive MIMO systems is discussed in Section VII.Finally, the challenges and potentials related to applicationsof massive MIMO in future wireless communications areidentified in Section VIII and conclusions are provided inSection IX.

Notation: Boldface lower and upper case symbols representvectors and matrices, respectively. The transpose, conjugate,and Hermitian transpose operators are denoted by (·)T, (·)∗,and (·)H, respectively. The Moore-Penrose pseudoinverse op-erator is denoted by (·)†. The determinant and trace operatorsare denoted by det(·) and Tr(·), respectively. The norm of avector is denoted by || · ||, and a� b means a is much greaterthan b.

II. FROM REGULAR TO MASSIVE MIMO

In this section, the advantages of massive MIMO systemsare reviewed from an information theoretic point of view. Westart with point-to-point MIMO systems to reveal the potentialopportunities that arise by equipping the terminals with a largenumber of antennas, and then we discuss the performance ofMU-MIMO systems, where multiple single-antenna users arecommunicating with a BS equipped with a large number ofantennas. Most results in this section are based on [7], [9],and [10].

A. Point-to-Point MIMO

We consider a point-to-point MIMO transmission first,where the transmitter and the receiver are equipped withNt and Nr antennas, respectively. We focus on the narrow-band time-invariant channel with a deterministic and constantchannel matrix H ∈ CNr×Nt . OFDM-based schemes arenormally used to convert a frequency-selective wide-bandchannel into multiple parallel flat-fading narrow-band channels[11].

The received signal vector, y ∈ CNr×1, can be expressed as

y =√ρHx + n, (1)

where x ∈ CNt×1 is the transmit signal vector and n ∈ CNr×1

represents noise and interference. We focus on the case thatthe total power of the transmit signal is normalized, i.e.,E{||x||2} = 1, and the noise is zero-mean circularly sym-metric complex Gaussian with an identity covariance matrixI. With these assumptions, the scalar ρ is the transmit power.

If we assume independent and identically distributed (i.i.d.)Gaussian transmit signals and that perfect CSI is available atthe receiver, the instantaneous achievable rate can be expressedas

C = log2 det

(I +

ρ

NtHHH

)bits/s/Hz. (2)

When the propagation coefficients in the channel matrix H arenormalized as Tr(HHH) ≈ NtNr, upper and lower boundson the capacity are derived in [7] with the help of Jensen’sinequality:

log2 (1 + ρNr) ≤ C ≤ min(Nt, Nr) log2

(1+

ρmax(Nt, Nr)

Nt

).

(3)The actual achievable rate depends on the distribution

of the singular values of HHH. Among all channels withthe same normalization, those whose singular values are allequal achieve the highest rate, i.e., the upper bound in (3),while those with only one non-zero singular value have thelowest rate, i.e., the lower bound in (3). The best case canbe approached in the limit by a scenario where all of thepropagation coefficients in the channel matrix are i.i.d., whilethe worst case corresponds for example to a scenario withline-of-sight (LOS) propagation.

Next we discuss two extreme cases, where either the numberof transmit or the number of receive antennas goes to infinity.

1) Nt � Nr and Nt →∞: When the number of transmitantennas goes to infinity while the number of receive antennas



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is constant, i.e., Nt � Nr, Nt → ∞, the row vectors of Hare asymptotically orthogonal, and hence we have

(HHH)

Nt≈ INr . (4)

In this case, the achievable rate in (2) can be approximated as

C ≈ Nr log2(1 + ρ) bits/s/Hz, (5)

which achieves the upper bound in (3).

2) Nr � Nt and Nr → ∞: Using similar derivations asin Case 1), we have

C ≈ Nt log2(1 +ρNrNt

) bits/s/Hz, (6)

which achieves the upper bound in (3) as well.The results in (5) and (6) show the advantages of equipping

the arrays in a MIMO link with a large number of antennas.Note that the above discussion depends on the assumptionthat the row or the column vectors of H are asymptoticallyorthogonal, which is an optimistic assumption regarding thepropagation coefficients. The multiplexing gain disappears inLOS propagation environments, as shown in [7].

B. Multi-User MIMO

MU-MIMO systems can obtain the promising multiplexinggain of massive point-to-point MIMO systems while eliminat-ing problems due to unfavorable propagation environments.

Consider a MU-MIMO system with L cells, where eachcell has K served single-antenna users and one BS with Nantennas. Denote the channel coefficient from the k-th userin the l-th cell to the n-th antenna of the i-th BS as hi,k,l,n,which is equal to a complex small-scale fading factor times anamplitude factor that accounts for geometric attenuation andlarge-scale fading:

hi,k,l,n = gi,k,l,n√di,k,l, (7)

where gi,k,l,n and di,k,l represent complex small-scale fadingand large-scale fading coefficients, respectively. The small-scale fading coefficients are assumed to be different fordifferent users or for different antennas at each BS whilethe large-scale fading coefficients are the same for differentantennas at the same BS, but are user-dependent. Then, thechannel matrix from all K users in the l-th cell to the i-th BScan be expressed as

Hi,l =

hi,1,l,1 · · · hi,K,l,1

.... . .

...hi,1,l,N · · · hi,K,l,N

= Gi,lD1/2i,l , (8)

where

Gi,l =

gi,1,l,1 · · · gi,K,l,1

.... . .

...gi,1,l,N · · · gi,K,l,N

, (9)

Di,l =

di,1,l

. . .

di,K,l

. (10)

Consider a single-cell (L = 1) MU-MIMO system with Ksingle-antenna users and a BS with N antennas. For simplicity,the cell and the BS indices are dropped when single-cellsystems are considered.

1) Uplink: For uplink signal transmission, the receivedsignal vector at a single BS, which we denote by yu ∈ CN×1,has the same expression as in (1):

yu =√ρuHxu + nu, (11)

where xu ∈ CK×1 is the signal vector from all users,H ∈ CN×K is the uplink channel matrix defined in (8) bydropping the cell and the BS indices, nu ∈ CN×1 is a zero-mean noise vector with complex Gaussian distribution andidentity covariance matrix, and ρu is the uplink transmit power.The transmitted symbol from the k-th user, xuk , is the k-thelement of xu = [xu1 , ..., x

uK ]T with E[|xuk |2] = 1.

Based on the assumption that the small-scale fading coeffi-cients for different users are independent, the column channelvectors from different users are asymptotically orthogonal asthe number of antennas at the BS, N , grows to infinity [2].Then, we have

HHH = D1/2GHGD1/2 ≈ ND1/2IKD1/2 = ND. (12)

A detailed discussion of this result can be found in [9]. Basedon the result in (12), the overall achievable rate of all usersbecomes

C = log2 det(I + ρuHHH)

≈ log2 det(I +NρuD)

=

K∑k=1

log2(1 +Nρudk) bits/s/Hz. (13)

In the following, we show that simple MF processing at theBS can achieve the capacity in (13). When MF processing isused, the BS processes the signal vector by multiplying theconjugate-transpose of the channel, as

HHyu = HH(√ρuHxu + nu)

≈ N√ρuDxu + HHnu, (14)

where (12) is used. Note that the channel vectors are asymp-totically orthogonal when the number of antennas at the BSgrows to infinity. Therefore, HH does not color the noise.Since D is a diagonal matrix, the MF processing separates thesignals from different users into different streams and there isasymptotically no inter-user interference. The signal transmis-sions from each user can thus be treated as if originating froma SISO channel. From (14), the signal-to-noise ratio (SNR) forthe k-th user is Nρudk. Consequently, the rate achievable byusing MF is the same as the limit in (13), which implies thatsimple MF processing at the BS is optimal when the numberof antennas at the BS, N , grows to infinity.

2) Downlink: Denote yd ∈ CK×1 as the received signalvector at all K users. For most prior work in massive MIMO,



4

time-division duplexing (TDD) mode is assumed as discussedin Section III-A, where the downlink channel is the transposeof the uplink channel matrix. Then, the received signal vectorcan be expressed as

yd =√ρdH

Txd + nd, (15)

where xd ∈ CN×1 is the signal vector transmitted by the BS,nd ∈ CK×1 is additive noise defined as before, and ρd is thetransmit power of the downlink. To normalize the transmitpower, we assume E{||xd||2} = 1.

As we see in Section III, the BS usually has CSI correspond-ing to all users based on uplink pilot transmission. Therefore, itis possible for the BS to perform power allocation to maximizethe sum transmission rate. With power allocation, the sumcapacity for the system is [10]

C = maxP

log2 det(IN + ρdHPHH)

≈ maxP

log2 det(IK + ρdNPD) bits/s/Hz, (16)

where (12) is used and P is a positive diagonal matrix withthe power allocations (p1, ..., pK) as its diagonal elements and∑Kk=1 pk = 1.If the MF precoder is used, the transmitted signal vector is

xd = H∗D−1/2P1/2sd, (17)

where sd ∈ CK×1 is the source information vector. Then, thereceived signal vector at all K users is

yd =√ρdH

TH∗D−1/2P1/2sd + nd

≈ √ρdND1/2P1/2sd + nd, (18)

where the second line of (18) is for the case when the numberof antennas at the BS, N , grows to infinity, and (12) isused. Since P and D are both diagonal matrices, the signaltransmission from the BS to each user can be treated asif originating from a SISO transmission, and again, inter-user interference has been suppressed. The overall achievabledata rate in (18) can be maximized by appropriate choice ofthe power allocation as in (16), which demonstrates that thecapacity can be achieved using the simple MF precoder.

Above, we have shown that based on the favorable propaga-tion assumption of (12), the simple MF precoder/detector canachieve the capacity of a massive MU-MIMO system whenthe number of antennas at the BS, N , is much larger than thenumber of users, K, and grows to infinity, i.e., N � K andN →∞. The results for another scenario that both the numberof antennas at the BS and the number of users grow largewhile their ratio is bounded, i.e., N/K = c as N,K → ∞,where c is a constant, are different. The detailed results forboth scenarios are discussed in the following sections.

III. CHANNEL ESTIMATION AND SIGNAL DETECTION

In this section, channel estimation and signal detection at theBS are discussed. We first discuss channel estimation methodsfor massive MIMO and explain why TDD mode is usuallyassumed. Then, both linear and non-linear signal detectionmethods are presented.

Uplink pilot

BS ProcessingDownlink data

Uplink data

Fig. 2. Multi-User MIMO TDD protocol

A. Channel Estimation

For regular MIMO systems, multi-user precoding in thedownlink and detection in the uplink require CSI at theBS. The resource, time or frequency, required for channelestimation in a MIMO system is proportional to the numberof the transmit antennas and is independent of the number ofthe receive antennas.

If FDD is used, that is, uplink and downlink use differentfrequency bands, the CSI corresponding to the uplink anddownlink is different. Channel estimation for the uplink isdone at the BS by letting all users send different pilotsequences. The time required for uplink pilot transmission isindependent of the number of antennas at the BS. However, toget CSI for the downlink channel in FDD systems, a two-stageprocedure is required. The BS first transmits pilot symbols toall users, and then all users feed back estimated CSI (partialor complete) for the downlink channels to the BS. The timerequired to transmit the downlink pilot symbols is proportionalto the number of antennas at the BS. As the number of BS an-tennas grows large, the traditional downlink channel estimationstrategy for FDD systems becomes infeasible. For example,consider a 1ms × 100kHz channel coherence interval, whichcan support transmission of 100 complex symbols. When thereare 100 antennas at the BS, the whole coherence interval willbe used for downlink training if orthogonal pilot waveformsare used for channels to each antenna, while there is no symbolleft for data transmission.

Fortunately, the channel estimation strategy in TDD systemscan be utilized to solve the problem. Based on the assumptionof channel reciprocity, only CSI for the uplink needs to beestimated. In [12], a TDD protocol, shown in Fig. 2, wasproposed. According to this protocol, all the users in all thecells first synchronously send uplink data signals. Next, theusers send pilot sequences. BSs use these pilot sequencesto estimate CSI to the users located in their cells. Then,BSs use the estimated CSI to detect the uplink data and togenerate beamforming vectors for downlink data transmission.However, due to the limited channel coherence time, the pilotsequences employed by users in neighboring cells may nolonger be orthogonal to those within the cell, leading to apilot contamination problem [2], which will be discussed indetail in Section V.

Linear MMSE based channel estimation is commonly used,which can provide near-optimal performance with low com-plexity. Besides MMSE estimation, a compressive sensing-based channel estimation approach is proposed in [13], whichexploits the fact that the degrees of freedom of the physical



5

channel matrix are much smaller than the number of freeparameters. To improve the spectral efficiency of the system, atime-frequency training sequence design is developed in [14].The proposed structure achieves the benefits of both time- andfrequency-domain estimation while avoiding their individualdrawbacks.

B. Signal Detection

Linear signal detectors with low complexity, such as the MF,ZF, and MMSE detectors, are practical candidates for massiveMIMO systems. They can asymptotically achieve capacity asthe number of antennas at the BS is large enough comparedto the number of users and the channel vectors from differentusers are independent [2], [7]. The performance of massiveMIMO systems based on various linear receivers has beenstudied from various perspectives [15]–[18]. A performancecomparison between the MMSE and the MF receivers inrealistic system settings is provided in [15]. It shows thatthe MMSE receiver can achieve the same performance asthe MF receiver with fewer antennas, especially when thereexists inter-cell interference. The scenario with a bounded ratioof the number of antennas to the number of users has beeninvestigated in [16] and [17] for the MMSE and ZF receivers,respectively. In [16], an expression for the asymptotic signal-to-interference-plus-noise-ratio (SINR) of the MMSE receiverfor a single-cell system with a bounded ratio of the numberof antennas to the number of users is obtained. Two types ofMMSE receivers are considered: the optimal MMSE receivertaking different transmit power levels from different users intoaccount and a suboptimal MMSE receiver assuming equaltransmit power. In [17], the exact data rate, symbol-errorrate, and outage performance of the ZF receivers are derived.Besides centralized MIMO systems, the sum rate of the ZFreceivers in distributed MIMO systems is also analyzed andlower and upper bounds on the sum rate are derived in [18].A rough calculation of the complexity order for the ZF andMMSE receivers is O(NK +NK2 +K3) [7].

In addition to linear detection methods, non-linear detectioncan also be used to achieve better performance at the costof higher computational complexity. Complexity reduction fornon-linear detectors in massive MIMO systems is the keyissue, and some work has been done on this topic. In [19],a block-iterative generalized decision feedback equalizer (BI-GDFE) is proposed, and its asymptotic SINR performance isevaluated. The complexity order of the proposed BI-GDFEis O((NK +N2K +N3)Niter), where Niter is the numberof iterations. For random MIMO channels, the proposed BI-GDFE can approach the single-user MF bound within only afew iterations even if the number of antennas is large. Com-plexity reduction schemes for the existing local neighborhoodsearch, including likelihood ascent search (LAS) [20], [21] andtabu search (TS) [22], are presented. LAS-based detection in[21] can achieve a better bit-error rate with the same orderof complexity as traditional LAS. The layered TS method in[22] performs detection in a layered manner and works wellin large MIMO systems with low complexity, which has thecomplexity order as O(((N+Ntabu)Nneighbor+NK)Niter+

NK2 + K3), where Ntabu and Nneighbor are the maximumnumber of entries and the number of neighboring vectorsused by the algorithm. Low-complexity graph-based schemesare proposed in [23] and [24]. In [23], a low-complexityreceiver based on cooperative particle swarm optimization andfactor-graph data detection is investigated. To obtain goodfeatures from both the local neighborhood search algorithmand the factor-graph based belief propagation (BP) algorithm,a hybrid reactive TS-BP approach is developed in [24]. It canachieve near-optimal performance with low complexity forsignals with high-order modulation. Moreover, the element-based lattice-reduction (LR) algorithms in [25] can providebetter performance than other LR approaches with lowercomplexity. Some other detection related work can be foundin [26]–[28].

IV. PRECODING

In this section, precoding at the BS is discussed. We first dis-cuss basic precoding methods and then extend the discussionto multi-cell precoding. Finally, some practical issues relatedto precoding are discussed.

For regular MIMO systems, both non-linear and linearprecoding techniques can be used. Compared with linearprecoding methods, non-linear methods, such as dirty-paper-coding (DPC) [29], vector perturbation (VP) [30] and lattice-aided methods [31], have better performance albeit with higherimplementation complexity. However, with an increase in thenumber of antennas at the BS, linear precoders, such as MFand ZF, are shown to be near-optimal [2], [7]. Thus, it is morepractical to use low-complexity linear precoding techniques inmassive MIMO systems. Therefore, we mainly focus on linearprecoding techniques in this section.

A. Basic Precoding

Basic precoding methods include MF and ZF. When MF isused, the transmit signal from the BS can be expressed as

xMFd =

1√α

(HT)Hsd =1√α

H∗sd, (19)

where α is a power normalization factor. The impact ofnormalization techniques is discussed in [32], which showsthat vector normalization is better for ZF while matrix nor-malization is better for MF.

When ZF is used, the transmit signal from the BS can beexpressed as

xZFd =1√α

(HT)†sd =1√α

H∗(HTH∗)−1sd. (20)

For regularized ZF (RZF), a diagonal loading factor is addedprior to the inversion of the matrix HTH∗, and the transmitsignal at the BS is expressed as

xRZFd =1√α

H∗(HTH∗ + δI)−1sd, (21)

where δ > 0 is the regularization factor, and can be optimizedbased on the design requirements. The RZF precoder becomesthe ZF precoder as δ → 0, and becomes the MF precoder asδ →∞.



6

The performance of (R)ZF precoding for a single-cellmassive MIMO system is analyzed in [33] when the numberof antennas at the BS, N , is much larger than the number ofusers, K, and grows to infinity, i.e., N � K and N → ∞.The analysis is based on estimated CSI, where the estimatedchannel matrix, H, is used instead of the accurate channelmatrix H, in (20) and (21). A lower bound on the sum rate forthe ZF precoder is derived. The ZF precoder outperforms MFin the high spectral efficiency region while MF is better in thelow spectral efficiency region. The computational complexityof these precoders is discussed in [33] as well. To reachmaximum spectral efficiency, the ZF precoder requires lesscomputation than the MF precoder, a surprising result basedon the fact that fewer users are served for the ZF precoder atpeak spectral efficiency. Note that the user selection problemmay become more complex as the number of users grows.

Besides the scenario where the number of antennas at theBS is much larger than the number of users, another scenariois investigated in [34]–[36] where both the number of antennasat the BS and the number of users grow large while their ratiois bounded, i.e., N/K = c as N,K → ∞, where c is aconstant. In this setup, ZF precoding achieves an SNR thattends to the optimal SNR for an interference-free system withN −K transmit antennas when N,K →∞ [7]. With perfectCSI, the asymptotic SINR performance of RZF precoding isderived in [34], which depends on the user-to-antenna ratio,K/N , the regularization parameter, δ, and the SNR. In [35],the analysis is extended to take the transmit correlation intoaccount. With an estimated channel matrix, H, the equivalentdeterministic SINRs for ZF and RZF precoding are derived in[36], where a tight approximation is derived even for systemswith a finite number of BS antennas.

B. Multi-Cell Precoding

Linear precoders can also be used in multi-cell massiveMIMO systems, where cooperating BSs are designed to jointlyserve users in different cells [37]. Depending on the overheadof the information exchange among the BSs, there are threescenarios: single-cell processing, coordinated beamforming,and network MIMO multi-cell processing. Single-cell process-ing is based on the assumption that BSs only have channelinformation for users in their own cells and no informationabout users in other cells. Coordinated beamforming exploitschannel information from a BS to users of all cells. Thenetwork MIMO multi-cell processing concept is based on fullcooperation among BSs, where not only channel informationbut also data are globally shared. Among the above threescenarios, single-cell processing can avoid the informationexchange overhead, but it cannot mitigate inter-cell interfer-ence. Based on the single-cell processing assumption, theRZF precoder can achieve performance similar to MF withfewer antennas [15]. Processing based on network MIMOprovides the best performance but has the highest infor-mation exchange overhead [38]–[40]. The network-MIMO-based scheme proposed in [40] can achieve the performancelimit with one order of magnitude fewer BS antennas thansingle-cell processing [2]. As discussed below, coordinated

beamforming can obtain a tradeoff between performance andthe overhead of information exchange [41].

Compared with regular MIMO systems, the use of coordi-nated beamforming with massive MIMO is considerably moredifficult; with a large number of BS antennas, it becomes moreand more impractical to share instantaneous CSI among theBSs. Therefore, different schemes based on sharing statisticalCSI are investigated. Scenarios where the number of antennasat the BS is much larger than the number of users, N � K,where their ratio is bounded, N/K = c as N,K → ∞, areboth studied. For the first scenario, a beamformer is designedto minimize total transmit power across all BS’s in [42].Random matrix theory is utilized to obtain an asymptoticallyoptimal distributed beamformer. A two-layer precoding ap-proach is proposed in [43] to relax the requirement that oneBS should get full CSI for its own cell, where the BS onlyneeds to estimate the channels within the subspace determinedby the outer precoder. Thus, the proposed scheme also reducesthe number of pilot symbols required for channel estimationin addition to the overhead due to information exchange. Forthe second scenario, a min-max-fair coordination beamformeris proposed in [44], [45], which exploits a nested ZF structureto recursively solve a series of min-max fairness problemsof decreasing dimension. To further reduce the informationexchange overhead for power allocation updating, the schemeproposed in [46] maximizes the minimum weighted SINR ofthe users.

Distributed MIMO based on limited CSI exchange is inves-tigated in [47], where the proposed linear Hermitian precodingin each cell uses only CSI for its own cell and the large-scalefading coefficients of users in other cells. The performanceloss due to the use of limited CSI is negligible compared tothe case with full CSI exchange. Thus, the design can be usedto reduce the information exchange overhead, especially formassive MIMO systems.

Note that for the coordinated schemes in [42]–[47], howto obtain the required CSI is not taken into account. Theanalysis is based on the assumption that the required CSI,either instantaneous or statistical, is already known at the BSs.In [48], [49], and [50], the problem of multi-cell precodinghas been considered in more general and realistic settings. Inparticular, channel estimation error and pilot contamination areexplicitly taken into account. These results will be discussedin Section V.

C. Practical Considerations

The precoding designs in [51]–[53] take practical antennaarray structures into account. To build a large array in practice,the use of non-linear but power-efficient radio-frequency (RF)front-end amplifiers is preferred. To avoid signal distortion,the transmit signals are required to have a low peak-to-average-power-ratio (PAPR). A precoding method based onper-antenna constant envelope constraints is developed toreduce the PAPR of the transmit signal in [51], [52]. Comparedto the average-only transmit power constraint, extra transmitpower is required to achieve a desired rate with per-antennapower constraints [54], [55]. However, precoding with such



7

constraints facilitates the use of power-efficient amplifiers,leading to improvement in the power efficiency of the entiresystem. Instead of considering precoding only, a frameworkbased on joint precoding, modulation, and PAPR reductionis proposed in [56]. The approach described in [56] haslow PAPR and enables the use of low-cost RF amplifiers.Moreover, a comprehensive performance analysis regardingthe use of large and dense antenna arrays is provided in [53].

Since the computational complexity of the precoder increas-es with the number of antennas at the BS, low-complexityprecoding methods are necessary. A low-complexity normdescent search precoder is proposed in [57] for systems witha large number of antennas, whose bit-error rate curves dropexponentially with SNR. A low-complexity method based onmatrix inversion is proposed in [58] to decrease the compu-tational complexity of the ZF and the MMSE precoders. Ingeneral, the design of low-complexity precoders is critical formassive MIMO systems.

V. PILOT CONTAMINATION

As we have discussed in Section III-A, only TDD is likelyto be employed with massive MIMO systems due to the highoverhead and complexity associated with channel estimationand channel sharing under FDD. As shown in Fig. 2, for TDD-based massive MIMO transmission systems, pilot sequencesare transmitted from users in the uplink to estimate channels.Let ψk,l = (ψ

[1]k,l, . . . , ψ

[τ ]k,l)

T be the pilot sequence of user kin cell l, where τ denotes the length of the pilot sequence.Though it is not necessary, it is convenient to assume that|ψ[j]k,l| = 1 and we use this assumption in what follows. Ideally,

the pilot sequences employed by users within the same celland in the neighboring cells should be orthogonal, that is

ψHk,lψj,l′ = δ[k − j]δ[l − l′], (22)

where δ[.] is defined as

δ[n] =

{1 n = 0

0 otherwise(23)

In this case, a BS can obtain uncontaminated estimation of thechannel vectors in the sense that they are not correlated to thechannel vectors of other users.

However, the number of orthogonal pilot sequences with agiven period and bandwidth is limited, which in turn limits thenumber of users that can be served [2]. In order to handle moreusers, nonorthogonal pilot sequences are used in neighboringcells. Thus for some different k, j, l, and l′, we may have

ψHk,lψj,l′ 6= 0. (24)

As a result, the estimate of the channel vector to a userbecomes correlated with the channel vectors of the userswith non-orthogonal pilot sequences. Below, we consider thepilot contamination issue in more details and discuss possiblemethods for its mitigation.

A. Pilot Contamination EffectThere are many schemes for assigning pilot sequences to

users in different cells. One simple scheme is to reuse the same

... ...

(a) Uplink Transmission

Cell iCell l

...

Cell j

... ...

(b) Downlink Transmission

Cell iCell l

...

Cell j

Fig. 3. Illustration of pilot contamination concept.

set of orthogonal pilot sequences, say ψ1, . . . ,ψK , in all cells.This means that the k-th user in any cell will be assigned thepilot sequence ψk. Identical pilot sequences assigned to usersin neighboring cells will interfere with each other causingpilot contamination. This situation is shown in Fig. 3. Onlyusers with the same pilot sequence ψk are shown. Duringdownlink transmission, this results in the BS beamformingsignals not only to its own users, but also to users in theneighboring cells, and therefore creates a strong source ofdirectional interference.. This interference, unlike the intra-cell interference, will not disappear as the number of BSantennas increases. A similar effect occurs during the uplinktransmission.

Consider a system with L cells. Each cell is assumed tohave K single-antenna users and a BS with N antennas, whereN � K. For purposes of illustration, we assume that all Lcells use the same set of K pilot sequences, represented bythe τ × K orthogonal matrix Φ = (ψ1, ...,ψK) satisfyingΦHΦ = τI. Assume further that the pilot transmission fromdifferent cells is synchronized, as in Fig. 3(a). The receivedsignal matrix at the i-th BS, Yp

i ∈ CN×τ , can be expressedas

Ypi =√ρp

L∑l=1

Hi,lΦT + Np

i , (25)

where Hi,l ∈ CN×K , defined in (8), is the channel matrix fromall K users in the l-th cell to the i-th BS. The k-th column ofHi,l, denoted by hi,k,l, is the channel vector from the k-th userin the l-th cell to the i-th BS. Np

i ∈ CN×τ is the noise matrixat the i-th BS during the pilot transmission phase, whoseentries are i.i.d. circular complex Gaussian random variableswith zero-mean and unit variance, and ρp is the pilot transmitpower.

To estimate the channel, the i-th BS projects its receivedsignal on Φ∗ to get sufficient statistics for estimating Hi,i



8

[59]. From (25), the resulting estimated channel matrix is

Hi,i =1√ρpτ

YpiΦ∗

= Hi,i +∑l 6=i

Hi,l +1√ρpτ

NpiΦ∗, (26)

where we have used ΦHΦ = τI. The k-th column, hi,k,i, ofHi,i is the estimate of the channel vector, hi,k,i. From (26),we have that the estimate, hi,k,i, is a linear combination of thechannel vectors, hi,k,l, l = 1, . . . , L, of the users in differentcells with the same pilot sequence. In [2], this phenomenon isreferred to as pilot contamination.

In a MIMO system with no pilot contamination, the channelestimation and precoding can be completely decoupled fromeach other. In the case of pilot contamination this is notthe right approach. Because of the pilot contamination, theestimated channel vector in any cell is a linear combination ofchannel vectors of users in other cells that use the same pilotsequence. In [60], an MMSE-based precoding is proposed thattakes this particular form of the estimated channel vector intoaccount and attempts to minimize i) the sum of squares oferrors for users located in cell l; and ii) the sum of squaresof interferences for users located in other cells. MMSE-based precoding provides significant improvement comparedwith traditional precoding methods like ZF, single-cell MMSEprecoding from [61], and others.

Consider now the uplink data transmission stage after chan-nel estimation. The received signal at the i-th BS is

yui =√ρu

L∑l=1

K∑k=1

hi,k,lxuk,l + nui , (27)

where xuk,l is the symbol from the k-th user in the l-th celland nui is the additive noise vector during uplink transmission.When the MF detector is used, the BS processes the signalvector by multiplying with the conjugate-transpose of thechannel estimate. Thus the detected symbol from the k-th userof the i-th cell, xuk,i, is

xuk,i =(hi,k,i

)Hyui

=(

L∑l=1

hi,k,l + vi)H(√ρu

L∑l=1

K∑k=1

hi,k,lxuk,l + nui ), (28)

where vi is the i-th column of 1√ρpτ

NpiΦ∗ in (26).

From (28) and (12), as the number of BS antennas growslarge, i.e. N →∞, the SINR of the k-th user in the i-th celltends to the following limit [2]

SINRuk,i =d2i,k,i∑

l 6=i d2i,k,l

, (29)

where di,k,l is the large-scale channel fading coefficient in (7).From (29), the SINR depends only on the large-scale fadingfactors of the channels while the small-scale fading factorsand noise are averaged out. Moreover, from (26), when non-orthogonal pilot sequences are used in different cells, the BScannot distinguish among the channel vectors from its own

cell to channels from other cells. Furthermore, the SINR limitdue to pilot contamination will not disappear as the numberof antennas increases. Similar results hold for the ZF or theMMSE detectors.

The pilot contamination affects the downlink transmissionas well, as shown in Fig. 3(b). For the downlink, the powervaries from one coherent interval to another if (26) is useddirectly as beamforming vectors. Thus, a normalized versionfor the beamforming vectors is commonly proposed in [62].Let the MF beamforming vector from the i-th BS to the k-thuser in the i-th cell be

wdk,i =

hi,k,i

||hi,k,i||=

hi,k,i

αk,i√N, (30)

where the scalar αk,i =||hi,k,i||√

Nis a normalization factor.

Then the i-th BS transmits a N -dimensional vector

xdi =

K∑k=1

wdk,is

dk,i, (31)

where sdk,i is the source symbol for the k-th user in the i-thcell. The received signal at the k-th user of the i-th cell is

ydk,i =√ρd

L∑l=1

hTl,k,i

K∑k′=1

(wdk′ ,l

)∗sdk′ ,l

+ ndk,i, (32)

where ndk,i is the additive noise. Based on a derivation similarto that for the uplink, the downlink SINR of the k-th user inthe i-th cell, as N →∞, tends to [62]

SINRdk,i =d2i,k,i/α

2k,i∑

l 6=i d2l,k,i/α

2k,l

, (33)

where

α2k,l =

L∑j=1

dl,k,j +1

ρpτ. (34)

The expression in (33) is slightly different from that in [2],[7] due to the normalization for the MF precoder.

Besides the normalization factor, the statistical propertiesof the interference terms in (29) and (33) are different. In theuplink, interference comes from the users with the same pilotsequence as the k-th user in the j-th cell. The denominatorin (29) depends on the distances from these interfering usersto the j-th BS. In the downlink, interference comes fromthe neighboring BSs that transmit using contaminated channelestimates. The denominator in (33) depends on the distancesfrom the neighboring BSs to the k-th user in the j-th cell.Moreover, the coefficients in the denominator of (29) can betreated as independent parameters while the coefficients inthe denominator of (33) are all correlated. To see this, it isenough to note that distances from the k-th user in the i-thcell to the neighboring cells, say the l-th, the j-th and the m-thcells, almost precisely determine the coordinates of the user,and therefore also determine the distances to other cells. Eventhough the statistical properties are different for the uplink anddownlink, the dissimilarities have little impact on performance[2], [62].



9

Since it is an important issue that limits the performanceof multi-cell massive MIMO systems, the pilot contaminationeffect under different scenarios is investigated in several papers[15], [63]–[65]. To demonstrate how the SINR changes withthe number of antennas at the BS, the SINR convergencerate is derived in [63]. From (29) and (33), a massive MIMOsystem with strong pilot contamination obviously has a lowerperformance limit than one with weak pilot contamination.However, it reaches the (lower) performance limit with fewerantennas at the BS. In [64], the sum rate lower bound is derivedwhen pilot contamination is present. The impact of morepractical channel models on pilot contamination is analyzedin [65]. The model takes the correlation of channels corre-sponding to different users into account and is also suitable forenvironments without rich scattering. Using general channelmodels and practical precoders/detecors and taking the pilotcontamination effect into account, it is demonstrated in [15]that the RZF/MMSE precoder/detector can perform as well asthe MF precoder/detector with almost one order of magnitudefewer antennas when the number of antennas at the BS is notextremely large compared to the number of users in each cell.

The impact of pilot contamination when the number ofantennas at the BS and the number of users grow to infinitywhile maintaining a fixed ratio is studied in [66], [67]. Inparticular, performance limits based on MF and MMSE filtersare derived in [66], [67], and the asymptotic SINR in bothcases depends on both pilot contamination and interferenceaveraging. The difference is that the MMSE filter can obtainan interference suppression gain, leading to higher asymptoticSINR performance. When the ratio of the number of usersand the number of antennas at the BS tends to zero, similarSINR results as in (29) and (33) can be obtained where onlythe pilot contamination effect appears in the asymptotic SINRexpression.

B. Mitigating Pilot Contamination

Several methods have been developed to mitigate the pilotcontamination effect. We introduce some of them here.

1) Protocol-based Methods: One way to reduce the effectis through frequency reuse or reducing the number of servedusers that use non-orthogonal pilot sequences [2], [68]. Forsome specific cases, the performance can be improved [68],but in general, frequency reuse may make little difference sincefewer users are served simultaneously even though the SINRsfor specific users increase [2].

In the transmission protocol proposed in [2], all userstransmit pilot sequences synchronously, as shown in Fig. 2.In order to mitigate the pilot contamination, a scheme basedon a time-shifted (asynchronous) protocol is proposed in [69],[70] and [62]. The basic idea is to partition cells into severalgroups A1, ..., AΓ and to use a time-shifted protocol in eachgroup. An example of this approach with Γ = 3 is shownin Fig. 4. While the users from group A1 transmit pilots, theBSs from A2 transmit downlink data signals. This avoids pilotcontamination among users from A1 and A2. At the same timethe BSs from A1 have to estimate their channel vectors inthe presence of downlink signals transmitted by the BSs from

A2 and A3. Since downlink transmit power, ρd, is usuallysignificantly higher than that of pilot sequences, ρp, it is nota priori clear that this approach provides any gain. From [70]and [62], as N →∞, the uplink and downlink SINRs tend tothe following limits,

SINRuk,i =d2i,k,i∑

j∈Aγ ,j 6=i d2i,k,j

, (35)

and,

SINRdk,i =d2i,k,i/α

2k,i∑

j∈Aγ ,j 6=i d2l,k,i/α

2k,l

. (36)

From these expressions, only users from the same group createinterference to each other. This leads to better performancecompared to (29) and (33). This scheme yields the same SINRsas the scheme with frequency reuse Γ while still allowing useof the entire band in all cells. Instead of using the same uplinkand downlink transmit powers, ρu and ρd, optimized individualpowers, ρuk,l and ρdk,l, can be used for each user. It is shown in[62] that power allocation can substantially improve the SINRcompared with (29) and (33).

Uplink pilot

BS ProcessingDownlink data

Uplink data

Group 1

Group 2

Group 3

Fig. 4. Time-shifted pilot scheme with Γ = 3.

2) Precoding Methods: A distributed single-cell precodingmethod is proposed in [60]. According to this method, theprecoding matrix at one BS is designed to minimize the sumof the squared error of its own users and interference to theusers in all other cells. The distributed single-cell precodingmethod is shown to provide better performance than traditionalsingle-cell ZF precoding.

The precoding methods based on multi-cell cooperation in[38] and [39] can mitigate the pilot contamination effect.However, the information exchange overhead required amongthe BSs increases with the number of antennas. Therefore,these methods are only feasible for MIMO systems with alimited number of antennas.

To obtain the benefit of cooperation while limiting theinformation exchange overhead, a pilot contamination pre-coding (PCP) method is proposed in [48]. PCP is based ontwo assumptions that the source signals for all users in allcells are accessible at each BS and that large-scale fadingcoefficients, di,k,l, are accessible to all BS’s or a network hub.Due to pilot contamination, the channel estimate, hi,k,i, is alinear combination of the channel vectors hi,k,l, l = 1, . . . , Lfrom (26). Instead of mitigating interference caused by thiscontaminated estimate, each BS uses the pilot contaminationfor transmitting information to all users in the network as



10

described below.In order to transmit information to the k-th users of all cells,

the i-th BS transmits signal

sdk,i =

L∑l=1

ai,k,lsdk,l, (37)

instead of the source symbol sdk,i. The coefficients ai,k,l arecalled PCP coefficients. They are computed as a function of thelarge-scale fading coefficients dj,k,l. The choice ai,k,l = δ[i−l]corresponds to the case of no PCP. Note that N -dimensionalMF beamforming vectors, wd

k,i, are computed exactly asin (30), that is completely locally without any cooperationbetween BSs. Uplink PCP is formulated similarly.

If the PCP coefficients ai,k,l are computed using the ZFcriterion proposed in [48], it is referred as ZF-PCP. ZF-PCP allows one to simultaneously remove the additive noiseand inter-cell interference. Thus, ZF-PCP theoretically yieldsinfinite SINRs, SINRdk,i =∞, as N →∞.

It is interesting to note, however, that ZF PCP does not givegood results for finite values of N . From [48] that for finiteN , we have

SINRdk,l =Nρdρuτ

∣∣∣∑Lj=1 dj,k,laj,k,l

∣∣∣2T1 +N · T2

, (38)

where

T1=

L∑j=1

K∑n=1

(1

L+ ρddj,k,l

)(1 + ρdτ

L∑s=1

dj,n,s

)L∑u=1

|aj,n,u|2

(39)and

T2 = ρdρuτ∑u6=l

∣∣∣∣∣∣L∑j=1

dj,k,laj,k,u

∣∣∣∣∣∣2

. (40)

When the coefficients ai,k,l are numerically optimized todirectly maximize SINRdk,l in (38), the approach is referredas optimal PCP.

The expression in (38) allows one to conduct Monte-Carlosimulation of massive MIMO systems in a very simple fashion,by simply generating random large-scale fading coefficientsdi,k,l. Fig.5 shows the cumulative distribution function (CDFs)of user rates for different PCPs. The user downlink rates arecomputed as log2(1+SINRdk,l). The network consists of L = 7wrapped around cells. The number of BS antennas is N = 64and the number of users in each cell is K = 10. One cansee that ZF-PCP has significantly worse performance than noPCP scenario. Computations show that only at N exceeding106, ZF-PCP starts giving some gain over no-PCP. However,PCP with numerically optimized coefficients provides a verylarge improvement over no-PCP scenario. In particular, at theoutage probability 5%, optimal PCP provides 7500-fold gainin terms of downlink user rates.

3) AOA-based Methods: As shown in [71]–[73], underrealistic channel models, some users with identical or non-orthogonal pilot sequences may have no interference with eachother. According to the multipath channel model for linearantenna arrays, the channel vectors from the k-th user in the

10−6

10−4

10−2

100

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Rate: bits/channel use

CD

F

Optimized PCPZF PCPNo PCP

5% outage

Fig. 5. CDF of downlink user rates for different PCP algorithms

l-th cell to the i-th BS have the form [74]

hi,k,l =1

Θ

Θ∑θ=1

a(φ)ηi,k,l, (41)

where Θ is the number of paths, ηi,k,l ∼ CN (0, σ2i,k,l) is

independent of the path index θ, σ2i,k,l is the user’s average

path loss, and a(φ) is the steering vector. For a uniform lineararray, the steering vector can be expressed as

a(φ) =

1

e−j2πDλ cos(φ)

...

e−j2π(N−1)D

λ cos(φ)

, (42)

where D is the antenna spacing, λ is the wavelength ofthe carrier, and φ is a random angle-of-arrival (AOA) withprobability density function (PDF), f(φ). In [71]–[73], it isshown that users with mutually non-overlapping AOA PDFshardly contaminate each other even if they use the samepilot sequence. A coordinated scheme for assigning identicalpilot sequences only to users of this type is developed in[73]. This scheme achieves a significant reduction in inter-cell interference and a corresponding increase in uplink anddownlink SINRs.

4) Blind Methods: The blind methods based on subspacepartitioning in [75]–[77] can also mitigate pilot contamination.In [75], an eigenvalue-decomposition-based (EVD) channelestimation and iterative least-square with projection (ILSP)estimation of channel vectors is proposed. The EVD-basedestimation is based on the assumption that the channel vectorsfrom different users are orthogonal. This assumption allowsone to estimate channel vectors using the statistics of thereceived data. The multiplicative scalar ambiguity inherentto this type of estimation can be resolved by using mutuallyorthogonal cell pilot sequences assigned to the network cells.

This approach can be summarized as follows. During theuplink transmission, the users first transmit data signals and



11

then cell pilot sequences. The estimation consists of thefollowing steps:Step 1: The covariance matrix of the received signal is esti-

mated by

Ryul= E[yul (yul )H ] ≈ Ryul

=1

T

T∑t=1

yul [t](yul [t])H ,

(43)where yul [t] is the received signal by the l-th BS attime t defined in (27).

Step 2: A N × K matrix Ul is found, whose k-th colum-n is the eigenvector of Ryul

corresponding to theeigenvalue that is closest to the quantity, Nρudl,l,k.Furthermore, with the help of the pilot sequences,an estimate Ξl, of the multiplicative matrix, Ξl isoabtained [75].

Step 3: The estimate Gl,l = UlΞl is calculated.The ILSP estimation is based on the idea of joint iterativeestimation of the channel vectors and transmitted data. LetXl be the K × T matrix composed of the T consecutivelytransmitted signals of the K users from the l-th cell, Xbe the set of all possible Xl, and Yl be correspondingmatrix of received symbols. Let H(0)

l,l be an initial estimateof Hl,l, obtained for example with help from the EVD-basedestimation. Then ILSP consists of a multiple repetitions of thefollowing steps:

Step 1: X(i)l = arg maxXl∈X || 1

ρuH

(i−1)H

l,l Yl −Xl||,Step 2: H

(i)l,l = 1

ρuYlX

(i)H

l , i = i+ 1.

In [76], [77], a blind pilot decontamination scheme isproposed for systems with a power-controlled handoff strategy,and this scheme can separate the interference subspace fromthe desired signal subspace, resulting in no pilot contamina-tion. Other precoding and detection schemes that require lessCSI, such as the Hermitian precoding method in [47], can helpreduce pilot contamination as well.

VI. ENERGY EFFICIENCY

Besides spectral efficiency, massive MIMO technology canimprove power efficiency as well [78]. In this section, we firstpresent the power scaling law for massive MIMO systems andthen discuss the spectral and energy efficiency tradeoff.

The power scaling law for massive MU-MIMO systems hasbeen derived in [4]. As before, consider uplink transmission ina single-cell system with K single-antenna users, a BS with Nantennas where N � K. The channel vectors from differentusers are uncorrelated. In this scenario, linear detectors [2],[7], such as MF, ZF and MMSE, are good enough. Based on[4] and (14), for the MF detector with perfect CSI at the BS,the ergodic achievable uplink data rate for the k-th user whenthe number of BS antennas, N , goes to infinity is

Ruk ≈ log2(1 +Ndkρu) bits/s/Hz. (44)

For comparison, the data rate for a user with transmit powerρu through a SISO link with large-scale fading coefficient dkonly is

Ru,SISOk = log2(1 + dkρu) bits/s/Hz. (45)

From (44) and (45), when N is large, the performance of a userwith transmit power ρu/N in the MU-MIMO system with Nantennas at the BS is the same as a SISO system with transmitpower ρu without small-scale fading. Consequently, the powercan be scaled down by N times for one user when perfectCSI is available at the BS. Moreover, the spectral efficiencyincreases by a factor of K in serving K users simultaneously.

The results based on imperfect CSI at the BS are somewhatdifferent. Based on [4], when an MMSE channel estimate isobtained during the pilot transmission phase and is used foruplink data detection, the ergodic achievable rate for the k-thuser based on the MF detector is

Ruk,I ≈ log2(1 + τNd2kρ

2u) bits/s/Hz (46)

as N → ∞, where τ is the length of the pilot sequence andthe pilot power satisfies ρp = τρu. From (45) and (46), therate of a user with transmit power ρu/

√N in the MU-MIMO

system with N BS antennas is asymptotically the same asthe performance under SISO transmission with transmit powerτdkρ

2u without small-scale fading. Thus, the transmit power

of one user can be scaled down by 1/√N to get the same

performance. Similar results for ZF and MMSE receivers forboth perfect and imperfect CSI are also obtained in [4].

In addition to the single-cell scenario, the power scaling lawis still valid for multi-cell systems; that is, one user can scaledown the transmit power proportional to 1/N or 1/

√N based

on perfect and imperfect CSI, respectively, to get the sameperformance as in the SISO case [4]. Note that this result stillholds even with pilot contamination [4].

Energy efficiency is defined as the ratio of the spectralefficiency and the transmit power. The tradeoff for the uplinkis studied in [4]. With perfect CSI, the energy efficiencydecreases as the spectral efficiency increases. However, adifferent result is obtained if imperfect CSI is available. In thelow transmit power region, energy efficiency increases withthe spectral efficiency, while with high transmit power, energyefficiency decreases as the spectral efficiency increases. Thetradeoff for the downlink is discussed in [33]. Compared to theMF precoder, ZF can provide better performance in scenarioswith high spectral efficiency and low energy efficiency, whilethe converse holds for scenarios with high energy efficiencyand low spectral efficiency.

Circuit power consumption is not considered in [4], [33].When the circuit power is considered, the question of howto perform antenna selection to improve energy efficiency isinvestigated in [79] and [80]. In [79], RF chain selection forconfigurations both with and without CSI is studied to maxi-mize spectral efficiency for a given total power consumptionconstraint. It is shown that for a MISO case without CSI,the optimal number of RF chains is about half the maximumnumber of RF chains that can be supported by the powerbudget. In [80], mutual information based on antenna selectionis derived, and the variance of the mutual information is foundto decrease as the number of antennas increases. This workalso shows that in order to maximize the energy efficiency, allantennas should be used if the circuit power can be ignoredcompared to the transmit power while only a subset of theantennas should be chosen if the circuit power is comparable



12

to the transmit power.

VII. SINGLE-CARRIER TRANSMISSION

Existing results for massive MIMO systems mainly focuson flat fading channels, which would imply that OFDM isassumed for wide-band frequency-selective channels. OFDMdecomposes the wideband channel into a set of narrow-bandflat fading subchannels so that techniques for flat fadingchannels can be used. However, a significant drawback ofOFDM signals is their high PAPR, which can result in lowpower amplifier efficiency. Moreover, to deal with intersymbolinterference (ISI), a cyclic-prefix (CP) is inserted in the time-domain, which decreases the spectral and power efficiency.The computational burden for calculating the discrete Fouriertransform (DFT) for OFDM modulation and demodulationincreases with the number of antennas as well. As an alterna-tive, single-carrier transmission has been studied for massiveMIMO systems [81], which can reduce complexity incurred bythe DFT. Furthermore, single-carrier transmission has a lowerPAPR than OFDM. Note that, regardless of whether single-carrier or OFDM modulation is used, the methods in [51], [52]for frequency flat channels and in [82] for frequency selectivechannels can be used to shape the samples transmitted by eachantenna to have constant envelope.

For a frequency-selective single-cell MU-MISO downlinkchannel, the channel between the n-th transmit antenna tothe k-th user can be modeled as a finite impulse responsefilter with Θ taps, where the channel coefficient for tap θ,hk,n[θ], has the same form as in (7), where the small-scaleand large-scale fading components are denoted as gk,n[θ] anddk[θ], respectively. It is assumed that the small-scale fadingcoefficients remain the same for each block of M symbols andthe large-scale fading coefficients are fixed during the entiretransmission. Denote xd[t] ∈ CN×1 as the transmit signalvector from the BS at time t. Then, the received signal vectorat time t combined together for all K users can be expressedas

yd[t] =√ρd

Θ−1∑θ=0

HT[θ]xd[t− θ] + nd[t]

=√ρd

Θ−1∑θ=0

D1/2[θ]GT[θ]xd[t− θ] + nd[t], (47)

where nd[t] =[nd1[t], ..., ndK [t]

]T ∈ CK×1 is additive whiteGaussian noise at all users and H[θ] = (hk,n[θ])K,Nk,n=1 is anN ×K channel matrix for channel tap θ.

To suppress multi-user interference and ISI, the followingprecoder has been proposed in [81]:

xd[t] =

√1

NK

Θ−1∑θ=0

H∗[θ]sd[t+ θ], (48)

where sd[t] is the information symbol vector at time t, eachof whose elements represents an information symbol for agiven user, and the scalar

√1NK is for power normalization.

The proposed precoder in (48) takes the time-inverse andcomplex-conjugated image of the channel impulse response

0 10 20 30 40 50 60 70 80 90 10010

−4

10−3

10−2

10−1

100

antenna number, M

SE

R

exponential channel model, κ = 0, MFexponential channel model, κ = 0, MMSEexponential channel model, κ = 1, MFexponential channel model, κ = 1, MMSETU channel model, κ = 0, MFTU channel model, κ = 0, MMSETU channel model, κ = 1, MFTU channel model, κ = 1, MMSE

Fig. 6. SER performance of the uplink single carrier transmission.

and has a form similar to MF. It is shown in [81] thatmulti-user interference and ISI can be efficiently suppressedwith low total transmit-power-to-receiver-noise ratio, leadingto near-optimal sum rate performance independent of thechannel power delay profile. The proposed precoder can alsoachieve an array power gain proportional to the number of BSantennas.

For the uplink transmission, the operation can be treated asa dual process of the downlink transmission. MF and MMSEdetectors can be used for signal detection. The symbol-error-rate (SER) performance with quadrature-phase-shift-keying(QPSK) modulation for the exponential channel model andTU channel model with 20 taps is shown in Fig. 6, whereSNR is −5dB. A LOS path is considered for the first arrivalpath and the strength of the LOS component is determinedby the Rician factor, κ. In general, the SER performance forexponential channel models is a little better than that for theTU channel model and the MMSE receiver performs betterthan the MF receiver.

Besides the work in [81], there are some discussions aboutsingle-carrier transmission in massive MIMO systems in [56]and [83]. To validate the potentials of single-carrier transmis-sion in massive MIMO systems, further investigation is neededin more general and complicated scenarios.

VIII. CHALLENGES AND POTENTIALS

To make massive MIMO systems a reality, there are stillmany issues that need to be studied and addressed. Some ofthese challenges are discussed below.

A. Basic Issues

1) Propagation Models: Most existing work on massiveMIMO is based on the premise that as the number of an-tennas grows, the individual user channels are still spatiallyuncorrelated and their channel vectors asymptotically becomepairwise orthogonal under favorable propagation conditions.Theoretical studies of massive MIMO typically assume i.i.d.complex Gaussian (Rayleigh fading) conditions [2], [4], whichis hard to justify in some situations. A number of experimentalstudies with multiple antenna arrays have been performed at2.6 GHz [84]–[86] by employing antennas in small cylindrical



13

or large linear arrays with 128 or 112 elements, respectively,and have led to several interesting observations. From [86],the real antenna correlation coefficients are significantly largerthan would be expected under i.i.d. channel assumptions.Furthermore, very highly correlated channel vectors cannotbe rendered orthogonal by increasing the number of anten-nas. This suggests that user scheduling should be a criticalcomponent of massive MIMO systems and is much moreimportant than in regular MIMO implementation where morecomplicated signal processing can be used to separate spatiallycorrelated users. From [85], there is significant performancedegradation in the case of closely spaced users with a LOSpath to the BS for different system settings; instead ofachieving 80-90% of the optimum dirty paper coding bound,performance drops to about 55%. Nevertheless, both sets ofstudies have concluded that despite significant differencesbetween the ideal i.i.d. assumption and the measured channels,a large fraction of the theoretical performance gains of largeantenna arrays can in practice still be achieved.

2) TDD and FDD modes: As discussed earlier in SectionIII, research on massive MIMO systems is normally based onthe TDD transmission mode due to channel estimation andfeedback issues. There are several possible ways to enableFDD mode in massive MIMO systems. One way is to designefficient precoding methods based on partial CSI [87] or evenno CSI. Another way is to use the idea of compressed sensingto reduce the feedback overhead [13], [88]. At the BS, theantennas are usually correlated when placing so many antennasin a finite area. The correlation among channel responsesfrom different antennas indicates that we do not need CSI foreach individual antenna. Instead, the CSI can be compressedfirst and then only the necessary information is fed back.The BS can reconstruct the CSI according to the receivedinformation. In this way, the overhead for CSI feedback canbe greatly reduced. Moreover, even though the uplink anddownlink are allocated with different frequencies, they arenot always independent of each other. Several strategies usechannel reciprocity in FDD systems [89]. Frequency correctionalgorithms are needed to achieve channel reciprocity in FDDsystems. Several frequency correction algorithms, such asfrequency correction based on direction of arrival, covariancematrix, and spatio-temporal correlation, have been discussedand compared in [89]. To utilize it in massive MIMO systems,more investigation is needed.

3) Modulation: To construct a BS with a large number ofantennas, low-cost power-efficient RF amplifiers are necessary,and problems with high PAPR can impede good performancefor OFDM [56]. As discussed in Section VII, single-carriertransmission is able to achieve near-optimal sum-rate perfor-mance at low-transmit-power-to-receiver-noise-power ratios,without requiring equalization at the receiver and multi-userresource allocation. Whether this is possible for more generaland complicated scenarios needs further investigation.

4) Pilot Contamination: In a typical multi-cell massiveMIMO system, users from neighboring cells may use non-orthogonal pilots. The reason for this is very simple — thenumber of orthogonal pilots is smaller than the number ofusers. The use of non-orthogonal pilots results in the pilot

contamination problem. Pilot contamination causes directedinter-cell interference, which, unlike other sources of inter-ferences, grows together with the number of BS antennasand significantly damages the system performance. Variouschannel estimation, precoding, and cooperation methods havebeen proposed to resolve this issue. However, more efficientmethods with good performance, low complexity, and limitedor zero cooperation between BSs are worth more intensivestudy.

5) Hardware Impairments: Only limited work has beendone on the impact of hardware impairments on massiveMIMO systems. Initial studies in [90], [91] have shown thathardware effects can lead to channel estimation error anda capacity ceiling even though a high array gain can stillbe achieved with an increase in the number of antennas atthe BS. The user side impairment is more severe comparedto the BS side. Fortunately, the pilot contamination issue inthe non-ideal case is actually easier to mitigate compared tothe ideal case [91]. Some other initial work has studied theimpact of phase noise [92], [93], per-antenna power constraints[51], [52], mutual coupling [94] and hybrid analog/digitalbeamforming architectures [53], [95], but they are only limitedto signal processing models rather than actual transceiverimplementations. For massive MIMO to become a reality,more studies on the topic are desired.

6) Antenna Arrays: There are several practical issues re-garding antenna arrays that are relevant to massive MIMOsystems. One concerns the configuration and deployment ofthe arrays. In [96], a massive MIMO system is proposed whereantennas are placed in a 2D grid. Moreover, 3D and distributedarray structures are candidates as well. The second issue is themutual coupling effect among antenna elements. The mutualcoupling effect can be ignored only when the antennas arewell separated from each other. For massive MIMO systems,antennas may be compactly arranged, and, the coupling issuecannot be ignored [97]. Finally, the increased hardware andcomputational costs due to the use of very large antennaarrays should be considered. To reduce cost while maintain-ing performance, an electromagnetic lens antenna (ELA) isproposed in [98], [99], integrated to a large antenna array.The proposed ELA can provide spatial multipath separationand energy focusing functions, which can be exploited toimprove the performance of massive MIMO and/or reduce itsimplementation cost and complexity. In general, issues relatedto array design and implementation are critical for massiveMIMO systems.

B. Application Issues

The use of massive MIMO in wireless networks has thepotential to achieve dramatic improvements in capacity andenergy efficiency. It also fits very well with applicationsinvolving heterogeneous networks and millimeter wave com-munications, among many others.

1) Heterogeneous Networks: In heterogeneous networks(HetNets), low-cost small cells referred to as pico- or femto-cells are flexibly deployed in order to provide dense coverageand ubiquitous high throughput. The use of massive MIMO



14

in coordination with HetNets in order to provide improvedinterference management and energy efficiency is an importantfuture research direction.

Interference management among coexisting massive MIMOsystems and small cells is a critical issue. It is importantthat a macro-cell BS with a large number of antennas beable to communicate with its own macro-cell users withoutinterfering with users in small cells. A precoding method basedon reversed TDD is proposed in [100] to address this issue. Inthis approach, the macro-cell BS estimates the null space tothe small cells during their downlink transmission and thenprojects its downlink data transmission into the null spaceof the small cells, generating interference-free transmission.A similar idea has also been proposed before in [101] forcognitive radio networks. However, by employing a largenumber of antennas at the macro-cell BS, higher degrees offreedom can be used to improve system performance.

Energy efficiency issues in massive MIMO systems withHetNets are addressed in [102], [103]. The energy efficiencyof massive MIMO systems and HetNets are compared in [102]under the assumption that a given area is covered either by amassive MIMO system or a certain number of small cells.From [102], when the number of cells is large, HetNets aremore energy efficient than a corresponding massive MIMOsystem, but otherwise a massive MIMO system is better. Inother settings, users may be simultaneously served by botha massive MIMO BS and small cell BS’s. A beamformingmethod to minimize consumed power under given rate require-ments in such a scenario is proposed in [103] when perfectCSI is available and interference coordination is used. Basedon the results in [103], it is usually optimal to assign one BSper user even though users could be served by several BS’s.

To deploy small cells, a high-capacity and easily accessiblebackhaul network is required. The use of massive MIMO BSsfor wireless backhaul is proposed in [104]. Additional workis necessary to make such an approach more practical.

2) Millimeter Waves: Another technology for achievingdramatic improvement in capacity and spectral efficiency iscommunications over millimeter wave (MMW) bands aroundor above 30 GHz, where the spectrum is less crowded andavailable bandwidths are broader. MMW technology fits wellwith massive MIMO and HetNet technology. An encouragingfactor is the apparent symbiosis among these three concepts:smaller cell sizes are attractive for operation at MMW fre-quencies where RF path loss is significantly higher, the shorterwavelength associated with higher frequencies is appealing formassive MIMO designs since the size of the antenna array andassociated electronics is reduced, and the large beamforminggain achievable with a very large number of antennas canextend coverage to help overcome the high MMW path loss.

A very thorough MMW measurement campaign has beencompleted in New York City at 28 GHz and in Austin,Texas, at 38 GHz [105]. Using directional horn antennas forthe data collection, the experiments established operationalranges in both outdoor and indoor environments, and providedmeasurements of path loss exponent, penetration loss throughdifferent types of windows and walls, delay spread, number ofresolvable multipaths, and reflection coefficients. The results in

[105] are promising for MMW MIMO systems, but many im-portant questions remain. For example, propagation at MMWfrequencies does not obey a Rayleigh-fading model, it tends tobe LOS or near-LOS. This obviously has important implica-tions for the achievable spatial multiplexing gain. Furthermore,the use of MMW frequencies means higher Doppler shifts fora given velocity, and hence potentially shorter coherence times.However, there are two mitigating factors that compensate forthis. First, as mentioned above, millimeter-wave systems willprimarily be used for relatively short-range applications (e.g.,femto- and pico-cells) due to the increased path loss relative tocurrent systems that operate near 2-3 GHz. Consequently, themobility of users in such systems will be relatively low, andwe can expect that the order-of-magnitude increase in carrierfrequency will likely be accompanied by a correspondingorder-of-magnitude decrease in user velocity. Second, theability of massive MIMO implementations to achieve verynarrow spatial selectivity (e.g., “pencil” beams) coupled with(near-)LOS propagation will result in a significant reduction indelay spread, and hence a corresponding increase in coherencebandwidth. Together, these factors should lead to systems thatdo not require a significant increase in channel update rates,but additional work is needed to confirm this conjecture.

IX. CONCLUSIONS

In this article, we have comprehensively described massiveMIMO systems from several different perspectives. By equip-ping a BS with a large number of antennas, spectral and energyefficiency can be dramatically improved. However, to makethe benefits of massive MIMO a reality, significant additionalresearch is needed on a number of issues, including channelcorrelation, hardware implementations and impairments, inter-ference management, and modulation.

ACKNOWLEDGEMENTS

The authors would like to thank Prof. David Gesbert withEURECOM for valuable comments and suggestions to im-prove the quality of this article. The authors would also liketo thank Mr. Yinsheng Liu with Beijing Jiaotong Universityfor plots.

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Lu Lu (S’09) received her B.S.E degree and M.S.Edegree from the University of Electronic Science andTechnology of China (UESTC), Chengdu, China,in 2007 and 2010, respectively. She then got herlicentiate degree from Royal Institute of Technology(KTH) in 2011. She is currently working toward thePh.D. degree with the School of Electrical and Com-puter Engineering, Georgia Institute of Technology,Atlanta, GA, USA. Her research interests includeMIMO, cooperative communications, and cognitiveradio networks. She is a co-recipient of the Best

Paper Award at ICCCN 2011, Maui, Hawaii.

Geoffrey Ye Li (S’93-M’95-SM’97-F’06) receivedhis B.S.E. and M.S.E. degrees in 1983 and 1986,respectively, from the Department of Wireless En-gineering, Nanjing Institute of Technology, Nan-jing, China, and his Ph.D. degree in 1994 fromthe Department of Electrical Engineering, AuburnUniversity, Alabama.

He was a Teaching Assistant and then a Lecturerwith Southeast University, Nanjing, China, from1986 to 1991, a Research and Teaching Assistantwith Auburn University, Alabama, from 1991 to

1994, and a Post-Doctoral Research Associate with the University of Marylandat College Park, Maryland, from 1994 to 1996. He was with AT&T Labs -Research at Red Bank, New Jersey, as a Senior and then a Principal TechnicalStaff Member from 1996 to 2000. Since 2000, he has been with the School ofElectrical and Computer Engineering at the Georgia Institute of Technologyas an Associate Professor and then a Full Professor. He is also holdingthe Cheung Kong Scholar title at the University of Electronic Science andTechnology of China since March 2006.

His general research interests include statistical signal processing andcommunications, with emphasis on cross-layer optimization for spectral- andenergy-efficient networks, cognitive radios and opportunistic spectrum access,and practical issues in LTE systems. In these areas, he has published over300 refereed journal and conference papers in addition to 25 granted patents.His publications have been cited over 15,000 times from Google Citationsand he is listed as a highly cited researcher by Thomson Reuters. He hasbeen involved in editorial activities in more than 10 technical journals for theIEEE Communications and Signal Processing Societies. He organized andchaired many international conferences, including technical program vice-chair of IEEE ICC’03, technical program co-chair of IEEE SPAWC’11, andgeneral chair of IEEE GlobalSIP’14. He has been awarded IEEE Fellowfor his contributions to signal processing for wireless communications since2006. He won the Stephen O. Rice Prize Paper Award in 2010 and the WTCWireless Recognition Award in 2013 from the IEEE Communications Society.He also received the James Evans Avant Garde Award in 2013 from the IEEEVehicular Technology Society.

A. Lee Swindlehurst (S’83-M’84-SM’99-F’04) re-ceived the B.S., summa cum laude, and M.S. degreesin Electrical Engineering from Brigham Young Uni-versity, Provo, Utah, in 1985 and 1986, respectively,and the PhD degree in Electrical Engineering fromStanford University in 1991. From 1986-1990, hewas employed at ESL, Inc., of Sunnyvale, CA,where he was involved in the design of algorithmsand architectures for several radar and sonar signalprocessing systems. He was on the faculty of theDepartment of Electrical and Computer Engineering

at Brigham Young University from 1990-2007, where he was a Full Professorand served as Department Chair from 2003-2006. During 1996-1997, heheld a joint appointment as a visiting scholar at both Uppsala University,Uppsala, Sweden, and at the Royal Institute of Technology, Stockholm,Sweden. From 2006-07, he was on leave working as Vice President ofResearch for ArrayComm LLC in San Jose, California. He is currently theAssociate Dean for Research and Graduate Studies in the Henry SamueliSchool of Engineering and a Professor of the Electrical Engineering andComputer Science Department at the University of California Irvine. Hisresearch interests include sensor array signal processing for radar and wirelesscommunications, detection and estimation theory, and system identification,and he has over 240 publications in these areas.

Dr. Swindlehurst is a Fellow of the IEEE, a past Secretary of the IEEESignal Processing Society, past Editor-in-Chief of the IEEE Journal ofSelected Topics in Signal Processing, and past member of the Editorial Boardsfor the EURASIP Journal on Wireless Communications and Networking, IEEESignal Processing Magazine, and the IEEE Transactions on Signal Processing.He is a recipient of several paper awards: the 2000 IEEE W. R. G. Baker PrizePaper Award, the 2006 and 2010 IEEE Signal Processing Society’s Best PaperAwards, the 2006 IEEE Communications Society Stephen O. Rice Prize inthe Field of Communication Theory, and is co-author of a paper that receivedthe IEEE Signal Processing Society Young Author Best Paper Award in 2001.



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Alexei Ashikhmin (M’00-SM’08) is a researchscientist in the Communications and Statistical Sci-ences Department of Bell Labs, Murray Hill, NewJersey. Alexei Ashikhmin’s research interests includecommunications theory, large scale antenna arrays,classical and quantum information theory, and thetheory of error correcting codes. From 2003 to2006, and from 2011 to 2014 Dr. Ashikhmin servedas an Associate Editor for IEEE Transactions onInformation Theory.

In 2004 Dr. Ashikhmin received S. O. Rice Awardfor the 2004 best paper of IEEE Transactions on Communications. In 2002,2010, and 2011 Dr. Ashikhmin received Bell Laboratories President Awardsfor breakthrough research in wired and wireless communication projects.

In 2005-2007 Alexei Ashikhmin was an adjunct professor at ColumbiaUniversity. He taught courses “Error Correcting Code” and “CommunicationsTheory”.

Rui Zhang (S’00-M’07) received the B.Eng. (First-Class Hons.) and M.Eng. degrees from the Na-tional University of Singapore in 2000 and 2001,respectively, and the Ph.D. degree from the Stan-ford University, Stanford, CA USA, in 2007, all inelectrical engineering. Since 2007, he has workedwith the Institute for Infocomm Research, A-STAR,Singapore, where he is now a Senior Research Sci-entist. Since 2010, he has joined the Department ofElectrical and Computer Engineering of the NationalUniversity of Singapore as an Assistant Professor.

His current research interests include multiuser MIMO, cognitive radio,cooperative communication, energy efficient and energy harvesting wirelesscommunication, wireless information and power transfer, smart grid, andoptimization theory.

Dr. Zhang has authored/coauthored over 180 internationally refereed journaland conference papers. He was the co-recipient of the Best Paper Awardfrom the IEEE PIMRC in 2005. He was the recipient of the 6th IEEEComSoc Asia-Pacific Best Young Researcher Award in 2010, and the YoungInvestigator Award of the National University of Singapore in 2011. He isnow an elected member of IEEE Signal Processing Society SPCOM and SAMTechnical Committees, and an editor for the IEEE Transactions on WirelessCommunications and the IEEE Transactions on Signal Processing.

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