Random Beamforming over Correlated Fading Channels

We study a multiple-input multiple-output (MIMO) multiple access channel (MAC) from several multi-antenna transmitters to a multi-antenna receiver. The fading channels between the transmitters and the receiver are modeled by random matrices, composed of independent column vectors with zero mean and different covariance matrices. Each transmitter is assumed to send multiple data streams with a random precoding matrix extracted from a Haar-distributed matrix. For this general channel model, we derive deterministic approximations of the normalized mutual information, the normalized sum-rate with minimum-mean-square-error (MMSE) detection and the signal-to-interference-plus-noise-ratio (SINR) of the MMSE decoder, which become arbitrarily tight as all system parameters grow infinitely large at the same speed. In addition, we derive the asymptotically optimal power allocation under individual or sum-power constraints. Our results allow us to tackle the problem of optimal stream control in interference channels which would be intractable in any finite setting. Numerical results corroborate our analysis and verify its accuracy for realistic system dimensions. Moreover, the techniques applied in this paper constitute a novel contribution to the field of large random matrix theory and could be used to study even more involved channel models.Comment: 35 pages, 5 figure

Power Allocation Games in Wireless Networks of Multi-antenna Terminals

We consider wireless networks that can be modeled by multiple access channels in which all the terminals are equipped with multiple antennas. The propagation model used to account for the effects of transmit and receive antenna correlations is the unitary-invariant-unitary model, which is one of the most general models available in the literature. In this context, we introduce and analyze two resource allocation games. In both games, the mobile stations selfishly choose their power allocation policies in order to maximize their individual uplink transmission rates; in particular they can ignore some specified centralized policies. In the first game considered, the base station implements successive interference cancellation (SIC) and each mobile station chooses his best space-time power allocation scheme; here, a coordination mechanism is used to indicate to the users the order in which the receiver applies SIC. In the second framework, the base station is assumed to implement single-user decoding. For these two games a thorough analysis of the Nash equilibrium is provided: the existence and uniqueness issues are addressed; the corresponding power allocation policies are determined by exploiting random matrix theory; the sum-rate efficiency of the equilibrium is studied analytically in the low and high signal-to-noise ratio regimes and by simulations in more typical scenarios. Simulations show that, in particular, the sum-rate efficiency is high for the type of systems investigated and the performance loss due to the use of the proposed suboptimum coordination mechanism is very small

Large System Analysis of Linear Precoding in Correlated MISO Broadcast Channels under Limited Feedback

In this paper, we study the sum rate performance of zero-forcing (ZF) and regularized ZF (RZF) precoding in large MISO broadcast systems under the assumptions of imperfect channel state information at the transmitter and per-user channel transmit correlation. Our analysis assumes that the number of transmit antennas $M$ and the number of single-antenna users $K$ are large while their ratio remains bounded. We derive deterministic approximations of the empirical signal-to-interference plus noise ratio (SINR) at the receivers, which are tight as $M,K\to\infty$. In the course of this derivation, the per-user channel correlation model requires the development of a novel deterministic equivalent of the empirical Stieltjes transform of large dimensional random matrices with generalized variance profile. The deterministic SINR approximations enable us to solve various practical optimization problems. Under sum rate maximization, we derive (i) for RZF the optimal regularization parameter, (ii) for ZF the optimal number of users, (iii) for ZF and RZF the optimal power allocation scheme and (iv) the optimal amount of feedback in large FDD/TDD multi-user systems. Numerical simulations suggest that the deterministic approximations are accurate even for small $M,K$.Comment: submitted to IEEE Transactions on Information Theor

Distributed Linear Precoding and User Selection in Coordinated Multicell Systems

In this manuscript we tackle the problem of semi-distributed user selection with distributed linear precoding for sum rate maximization in multiuser multicell systems. A set of adjacent base stations (BS) form a cluster in order to perform coordinated transmission to cell-edge users, and coordination is carried out through a central processing unit (CU). However, the message exchange between BSs and the CU is limited to scheduling control signaling and no user data or channel state information (CSI) exchange is allowed. In the considered multicell coordinated approach, each BS has its own set of cell-edge users and transmits only to one intended user while interference to non-intended users at other BSs is suppressed by signal steering (precoding). We use two distributed linear precoding schemes, Distributed Zero Forcing (DZF) and Distributed Virtual Signal-to-Interference-plus-Noise Ratio (DVSINR). Considering multiple users per cell and the backhaul limitations, the BSs rely on local CSI to solve the user selection problem. First we investigate how the signal-to-noise-ratio (SNR) regime and the number of antennas at the BSs affect the effective channel gain (the magnitude of the channels after precoding) and its relationship with multiuser diversity. Considering that user selection must be based on the type of implemented precoding, we develop metrics of compatibility (estimations of the effective channel gains) that can be computed from local CSI at each BS and reported to the CU for scheduling decisions. Based on such metrics, we design user selection algorithms that can find a set of users that potentially maximizes the sum rate. Numerical results show the effectiveness of the proposed metrics and algorithms for different configurations of users and antennas at the base stations.Comment: 12 pages, 6 figure

Decomposition by Successive Convex Approximation: A Unifying Approach for Linear Transceiver Design in Heterogeneous Networks

We study the downlink linear precoder design problem in a multi-cell dense heterogeneous network (HetNet). The problem is formulated as a general sum-utility maximization (SUM) problem, which includes as special cases many practical precoder design problems such as multi-cell coordinated linear precoding, full and partial per-cell coordinated multi-point transmission, zero-forcing precoding and joint BS clustering and beamforming/precoding. The SUM problem is difficult due to its non-convexity and the tight coupling of the users' precoders. In this paper we propose a novel convex approximation technique to approximate the original problem by a series of convex subproblems, each of which decomposes across all the cells. The convexity of the subproblems allows for efficient computation, while their decomposability leads to distributed implementation. {Our approach hinges upon the identification of certain key convexity properties of the sum-utility objective, which allows us to transform the problem into a form that can be solved using a popular algorithmic framework called BSUM (Block Successive Upper-Bound Minimization).} Simulation experiments show that the proposed framework is effective for solving interference management problems in large HetNet.Comment: Accepted by IEEE Transactions on Wireless Communicatio