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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
Large System Analysis of the Energy Consumption Distribution in MultiUser MIMO Systems with Mobility
, 2015
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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.
Joint power and antenna selection optimization in large distributed MIMO networks
, 2013
"... Large multipleinput multipleoutput (MIMO) networks promise high energy efficiency, i.e., much less power is required to achieve the same capacity compared to the conventional MIMO networks if perfect channel state information (CSI) is available at the transmitter. However, in such networks, huge o ..."
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Cited by 7 (0 self)
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Large multipleinput multipleoutput (MIMO) networks promise high energy efficiency, i.e., much less power is required to achieve the same capacity compared to the conventional MIMO networks if perfect channel state information (CSI) is available at the transmitter. However, in such networks, huge overhead is required to obtain full CSI especially for FrequencyDivision Duplex (FDD) systems. To reduce overhead, we propose a downlink antenna selection scheme, which selects S antennas from M> S transmit antennas based on the large scale fading to serve K ≤ S users in large distributed MIMO networks employing regularized zeroforcing (RZF) precoding. In particular, we study the joint optimization of antenna selection, regularization factor, and power allocation to maximize the average weighted sumrate. This is a mixed combinatorial and nonconvex problem whose objective and constraints have no closedform expressions. We apply random matrix theory to derive asymptotically accurate expressions for the objective and constraints. As such, the joint optimization problem is decomposed into subproblems, each of which is solved by an efficient algorithm. In addition, we derive structural solutions for some special cases and show that the capacity of very large distributed MIMO networks scales as O (KlogM) when M → ∞ with K,S fixed. Simulations show that the proposed scheme achieves significant performance gain over various baselines.
Large system analysis of cooperative multicell downlink transmission via regularized channel inversion with imperfect CSIT
 IEEE Trans. Wireless Commun
, 2013
"... Abstract—In this paper, we analyze the ergodic sumrate of a multicell downlink system with base station (BS) cooperation using regularized zeroforcing (RZF) precoding. Our model assumes that the channels between BSs and users have independent spatial correlations and imperfect channel state info ..."
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Cited by 7 (0 self)
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Abstract—In this paper, we analyze the ergodic sumrate of a multicell downlink system with base station (BS) cooperation using regularized zeroforcing (RZF) precoding. Our model assumes that the channels between BSs and users have independent spatial correlations and imperfect channel state information at the transmitter (CSIT) is available. Our derivations are based on large dimensional random matrix theory (RMT) under the assumption that the numbers of antennas at the BS and users approach to infinity with some fixed ratios. In particular, a deterministic equivalent expression of the ergodic sumrate is obtained and is instrumental in getting insight about the joint operations of BSs, which leads to an efficient method to find the asymptoticoptimal regularization parameter for the RZF. In another application, we use the deterministic channel rate to study the optimal feedback bit allocation among the BSs for maximizing the ergodic sumrate, subject to a total number of feedback bits constraint. By inspecting the properties of the allocation, we further propose a scheme to greatly reduce the search space for optimization. Simulation results demonstrate that the ergodic sumrates achievable by a subspace search provides comparable results to those by an exhaustive search under various typical settings. Index Terms—Large dimensional RMT, multicell cooperation, regularized zeroforcing, feedback bit allocation. I.
Optimal linear precoding in multiuser MIMO systems: A large system analysis
 in Proceedings of Globecom 2014
, 2014
"... Abstract—We consider the downlink of a singlecell multiuser MIMO system in which the base station makes use of N antennas to communicate with K singleantenna user equipments (UEs) randomly positioned in the coverage area. In particular, we focus on the problem of designing the optimal linear prec ..."
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Cited by 7 (4 self)
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Abstract—We consider the downlink of a singlecell multiuser MIMO system in which the base station makes use of N antennas to communicate with K singleantenna user equipments (UEs) randomly positioned in the coverage area. In particular, we focus on the problem of designing the optimal linear precoding for minimizing the total power consumption while satisfying a set of target signaltointerferenceplusnoise ratios (SINRs). To gain insights into the structure of the optimal solution and reduce the computational complexity for its evaluation, we analyze the asymptotic regime where N and K grow large with a given ratio and make use of recent results from large system analysis to compute the asymptotic solution. Then, we concentrate on the asymptotically design of heuristic linear precoding techniques. Interestingly, it turns out that the regularized zeroforcing (RZF) precoder is equivalent to the optimal one when the ratio between the SINR requirement and the average channel attenuation is the same for all UEs. If this condition does not hold true but only the same SINR constraint is imposed for all UEs, then the RZF can be modified to still achieve optimality if statistical information of the UE positions is available at the BS. Numerical results are used to evaluate the performance gap in the finite system regime and to make comparisons among the precoding techniques. I.
Massive MIMO and InterTier Interference Coordination
"... Abstract—We study the performance of a twotier system where a large number of small cells is deployed under a macrocellular “umbrella”. The macrocellular tier provides coverage and handles mobile users, while the small cell tier provides high rate locally to nomadic users. While the standard appr ..."
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Cited by 7 (2 self)
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Abstract—We study the performance of a twotier system where a large number of small cells is deployed under a macrocellular “umbrella”. The macrocellular tier provides coverage and handles mobile users, while the small cell tier provides high rate locally to nomadic users. While the standard approach consists of operating the two tiers in different frequency bands, for various reasons (e.g., lack of licensed spectrum), it may be useful to operate both tiers in the whole available spectrum. Hence, we consider schemes for intertier interference coordination that do not assume any explicit data or channel state information sharing between tiers. In particular, we consider cochannel TDD and reverse TDD schemes, when the macro (tier1) base station has a very large number of antennas and the tier2 base stations have a moderately large number of antennas. We show that by exploiting the spatial directionality of the channel vectors, very efficient intertier interference management can be obtained with relatively low complexity. Our approach consists of a sort of “spatial blanking ” of certain angleofdeparture of the tier1 base station at given scheduled timefrequency slots, in order to create transmission opportunities for the corresponding tier2 small cells. In particular, such “spatial blanking ” is significantly more efficient than isotropic slot blanking (enhanced InterCell Interference Coordination, eICIC) currently proposed in LTE standardization. I.
Linear precoding for broadcast channels with confidential messages under transmitside channel correlation
 IEEE Comms. Letters
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