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Massive MIMO in the UL/DL of cellular networks: How many antennas do we need?
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
, 2013
"... We consider the uplink (UL) and downlink (DL) of noncooperative multicellular timedivision duplexing (TDD) systems, assuming that the number N of antennas per base station (BS) and the number K of user terminals (UTs) per cell are large. Our system model accounts for channel estimation, pilot con ..."
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Cited by 109 (13 self)
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We consider the uplink (UL) and downlink (DL) of noncooperative multicellular timedivision duplexing (TDD) systems, assuming that the number N of antennas per base station (BS) and the number K of user terminals (UTs) per cell are large. Our system model accounts for channel estimation, pilot contamination, and an arbitrary path loss and antenna correlation for each link. We derive approximations of achievable rates with several linear precoders and detectors which are proven to be asymptotically tight, but accurate for realistic system dimensions, as shown by simulations. It is known from previous work assuming uncorrelated channels, that as N →∞while K is fixed, the system performance is limited by pilot contamination, the simplest precoders/detectors, i.e., eigenbeamforming (BF) and matched filter (MF), are optimal, and the transmit power can be made arbitrarily small. We analyze to which extent these conclusions hold in the more realistic setting where N is not extremely large compared to K. In particular, we derive how many antennas per UT are needed to achieve η % of the ultimate performance limit with infinitely many antennas and how many more antennas are needed with MF and BF to achieve the performance of minimum meansquare error (MMSE) detection and regularized zeroforcing (RZF), respectively.
Joint spatial division and multiplexing: Opportunistic beamforming and user grouping,” arXiv preprint arXiv:1305.7252
, 2013
"... Joint Spatial Division and Multiplexing (JSDM) is a recently proposed scheme to enable massive MIMO like gains and simplified system operations for Frequency Division Duplexing (FDD) systems. The key idea lies in partitioning the users into groups with approximately similar covariances, and use a tw ..."
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Cited by 17 (4 self)
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Joint Spatial Division and Multiplexing (JSDM) is a recently proposed scheme to enable massive MIMO like gains and simplified system operations for Frequency Division Duplexing (FDD) systems. The key idea lies in partitioning the users into groups with approximately similar covariances, and use a two stage downlink beamforming: a prebeamformer that depends on the channel covariances and minimizes interference across groups and a multiuser MIMO precoder for the effective channel after prebeamforming, to counteract interference within a group. We first focus on the regime of a fixed number of antennas and large number of users, and show that opportunistic beamforming with user selection yields significant gain, and thus, channel correlation may yield a capacity improvement over the uncorrelated “isotropic ” channel result of [1]. We prove that in the presence of different correlations among groups, a block diagonalization approach for the design of prebeamformers achieves the optimal sumrate scaling, albeit with a constant gap from the upper bound. Next, we consider the regime of large number of antennas and users, where user selection does not provide significant gain. In the presence of a large number of antennas, the design of prebeamformers reduces to choosing the columns of a Discrete Fourier Transform matrix based on the angles of arrival and angular spreads of the user channel covariance, when the base station (BS) is equipped with a uniform linear antenna array. Motivated by this result, we propose a simplified user grouping algorithm to cluster users into groups when the number
Degrees of Freedom of the Network MIMO Channel With Distributed CSI
, 2013
"... Abstract—In this work, we discuss the joint precoding with finite rate feedback in the socalled network MIMO where the TXs share the knowledge of the data symbols to be transmitted. We introduce a distributed channel state information (DCSI) model where each TX has its own local estimate of the ove ..."
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Cited by 16 (6 self)
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Abstract—In this work, we discuss the joint precoding with finite rate feedback in the socalled network MIMO where the TXs share the knowledge of the data symbols to be transmitted. We introduce a distributed channel state information (DCSI) model where each TX has its own local estimate of the overall multiuser MIMO channel and must make a precoding decision solely based on the available local CSI. We refer to this channel as the DCSIMIMO channel and the precoding problem as distributed precoding. We extend to the DCSI setting the work from Jindal in [1] for the conventional MIMO Broadcast Channel (BC) in which the number of Degrees of Freedom (DoFs) achieved by Zero Forcing (ZF) was derived as a function of the scaling in the logarithm of the SignaltoNoise Ratio (SNR) of the number of quantizing bits. Particularly, we show the seemingly pessimistic result that the number of DoFs at each user is limited by the worst CSI across all users and across all TXs. This is in contrast to the conventional MIMO BC where the number of DoFs at one user is solely dependent on the quality of the estimation of his own feedback. Consequently, we provide precoding schemes improving on the achieved number of DoFs. For the twouser case, the derived novel precoder achieves a number of DoFs limited by the best CSI accuracy across the TXs instead of the worst with conventional ZF. We also advocate the use of hierarchical quantization of the CSI, for which we show that considerable gains are possible. Finally, we use the previous analysis to derive the DoFs optimal allocation of the feedback bits to the various TXs under a constraint on the size of the aggregate feedback in the network, in the case where conventional ZF is used.
The Multicell Multiuser MIMO Uplink with Very Large Antenna Arrays and a FiniteDimensional Channel
, 2013
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An overview of massive MIMO: Benefits and challenges
 IEEE J. SEL. TOPICS SIGNAL PROCESS
, 2014
"... Massive multipleinput multipleoutput (MIMO) wireless communications refers to the idea equipping cellular base stations (BSs) with a very large number of antennas, and has been shown to potentially allow for orders of magnitude improvement in spectral and energy efficiency using relatively simple ..."
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Cited by 12 (4 self)
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Massive multipleinput multipleoutput (MIMO) wireless communications refers to the idea equipping cellular base stations (BSs) with a very large number of antennas, and has been shown to potentially allow for orders of magnitude improvement in spectral and energy efficiency using relatively simple (linear) processing. In this paper, we present a comprehensive overview of stateoftheart research on the topic, which has recently attracted considerable attention. We begin with an information theoretic analysis to illustrate the conjectured advantages of massive MIMO, and then we address implementation issues related to channel estimation, detection and precoding schemes. We particularly focus on the potential impact of pilot contamination caused by the use of nonorthogonal pilot sequences by users in adjacent cells. We also analyze the energy efficiency achieved by massive MIMO systems, and demonstrate how the degrees of freedom provided by massive MIMO systems enable efficient singlecarrier transmission. Finally, the challenges and opportunities associated with implementing massive MIMO in future wireless communications systems are discussed.
Joint beamforming and power control in coordinated multicell: Maxmin duality, effective network and large system transition
 IEEE TRANS. WIRELESS COMMUN
, 2013
"... This paper studies joint beamforming and power control in a coordinated multicell downlink system that serves multiple users per cell to maximize the minimum weighted signaltointerferenceplusnoise ratio. The optimal solution and distributed algorithm with geometrically fast convergence rate are ..."
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Cited by 8 (1 self)
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This paper studies joint beamforming and power control in a coordinated multicell downlink system that serves multiple users per cell to maximize the minimum weighted signaltointerferenceplusnoise ratio. The optimal solution and distributed algorithm with geometrically fast convergence rate are derived by employing the nonlinear PerronFrobenius theory and the multicell network duality. The iterative algorithm, though operating in a distributed manner, still requires instantaneous power update within the coordinated cluster through the backhaul. The backhaul information exchange and message passing may become prohibitive with increasing number of transmit antennas and increasing number of users. In order to derive asymptotically optimal solution, random matrix theory is leveraged to design a distributed algorithm that only requires statistical information. The advantage of our approach is that there is no instantaneous power update through backhaul. Moreover, by using nonlinear PerronFrobenius theory and random matrix theory, an effective primal network and an effective dual network are proposed to characterize and interpret the asymptotic solution.
NEMOx: Scalable Network MIMO for Wireless Networks
 In Proc. ACM Int. Conf. Mobile Computing and Networking (MobiCom
, 2013
"... Network MIMO (netMIMO) has potential for significantly enhancing the capacity of wireless networks with tight coordination of access points (APs) to serve multiple users concurrently. Existing schemes realize netMIMO by integrating distributed APs into one “giant ” MIMO but do not scale well owing ..."
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Cited by 6 (2 self)
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Network MIMO (netMIMO) has potential for significantly enhancing the capacity of wireless networks with tight coordination of access points (APs) to serve multiple users concurrently. Existing schemes realize netMIMO by integrating distributed APs into one “giant ” MIMO but do not scale well owing to their global synchronization requirement and overhead in sharing data between APs. To remedy this limitation, we propose a novel system, NEMOx, that realizes netMIMO downlink transmission for largescale wireless networks. NEMOx organizes a network into practicalsize clusters, each containing multiple distributed APs (dAPs) that opportunistically synchronize with each other for netMIMO downlink transmission. Intercluster interference is managed with a decentralized channelaccess algorithm, which is designed to balance between the dAPs ’ cooperation gain and spatial reuse—a unique tradeoff in netMIMO. Within each cluster, NEMOx optimizes the power budgeting among dAPs and the set of users to serve, ensuring fairness and effective cancellation of crosstalk interference. We have implemented and evaluated a prototype of NEMOx in a software radio testbed, demonstrating its throughput scalability and multiple folds of performance gain over current wireless LAN architecture and alternative netMIMO schemes.
Scalable Synchronization and Reciprocity Calibration for Distributed Multiuser MIMO
"... MIMO) is a promising wireless network architecture that combines the advantages of “massive MIMO ” and “small cells. ” It consists of several Access Points (APs) connected to a central server via a wired backhaul network and acting as a large distributed antenna system. We focus on the downlink, wh ..."
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Cited by 5 (3 self)
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MIMO) is a promising wireless network architecture that combines the advantages of “massive MIMO ” and “small cells. ” It consists of several Access Points (APs) connected to a central server via a wired backhaul network and acting as a large distributed antenna system. We focus on the downlink, which is both more demanding in terms of traffic and more challenging in terms of implementation than the uplink. In order to enable multiuser joint precoding of the downlink signals, channel state information at the transmitter side is required. We consider Time Division Duplex (TDD), where the downlink channels can be learned from the user uplink pilot signals, thanks to channel reciprocity. Furthermore, coherent multiuser joint precoding is possible only if the APs maintain a sufficiently accurate relative timing and phase synchronization. AP synchronization and TDD reciprocity calibration are two key problems to be solved in order to enable distributed MUMIMO downlink. In this paper, we propose novel overtheair synchronization and calibration protocols that scale well with the network size. The proposed schemes can be applied to networks formed by a large number of APs, each of which is driven by an inexpensive 802.11grade clock and has a standard RF frontend, not explicitly designed to be reciprocal. Our protocols can incorporate, as a building block, any suitable timing and frequency estimator. Here we revisit the problem of joint ML timing and frequency estimation and use the corresponding CramerRao bound to evaluate the performance of the synchronization protocol. Overall, the proposed synchronization and calibration schemes are shown to achieve sufficient accuracy for satisfactory distributed MUMIMO performance. Index Terms—Distributed multiuser MIMO downlink, cooperative small cells, synchronization, TDD calibration. I.