On the Convergence of Massive MIMO Systems

In this paper we examine convergence properties of massive MIMO systems with the aim of determining the number of antennas required for massive MIMO gains. We consider three characteristics of a channel matrix and study their asymptotic behaviour. Furthermore, we derive ZF SNR and MF SINR for a scenario of unequal receive powers. In our results we include the effects of spatial correlation. We show that the rate of convergence of channel metrics is much slower than that of the ZF/MF precoder properties.Comment: 6 pages, 6 figures, ICC 201

Low-Complexity Precoding Design for Massive Multiuser MIMO Systems Using Approximate Message Passing

A practical challenge in the precoding design of massive multiuser multiple-input multiple-output (MIMO) systems is to facilitate hardware-friendly implementation. To achieve this, we propose a low peak-to-average power ratio (PAPR) precoding based on an approximate message passing (AMP) algorithm to minimize multiuser interference (MUI) in massive multiuser MIMO systems. The proposed approach exhibits fast convergence and low complexity characteristics. Compared with a conventional constant-envelope precoding and an annulus-constrained precoding, simulation results demonstrate that the proposed AMP precoding is superior both in terms of computational complexity and average running time. In addition, the proposed AMP precoding exhibits a much desirable tradeoff between MUI suppression and PAPR reduction. These findings indicate that the proposed AMP precoding is a suitable candidate for hardware implementation, which is very appealing for massive MIMO systems

Gaussian Message Passing for Overloaded Massive MIMO-NOMA

This paper considers a low-complexity Gaussian Message Passing (GMP) scheme for a coded massive Multiple-Input Multiple-Output (MIMO) systems with Non-Orthogonal Multiple Access (massive MIMO-NOMA), in which a base station with $N_s$ antennas serves $N_u$ sources simultaneously in the same frequency. Both $N_u$ and $N_s$ are large numbers, and we consider the overloaded cases with $N_u>N_s$. The GMP for MIMO-NOMA is a message passing algorithm operating on a fully-connected loopy factor graph, which is well understood to fail to converge due to the correlation problem. In this paper, we utilize the large-scale property of the system to simplify the convergence analysis of the GMP under the overloaded condition. First, we prove that the \emph{variances} of the GMP definitely converge to the mean square error (MSE) of Linear Minimum Mean Square Error (LMMSE) multi-user detection. Secondly, the \emph{means} of the traditional GMP will fail to converge when $N_u/N_s< (\sqrt{2}-1)^{-2}\approx5.83$. Therefore, we propose and derive a new convergent GMP called scale-and-add GMP (SA-GMP), which always converges to the LMMSE multi-user detection performance for any $N_u/N_s>1$, and show that it has a faster convergence speed than the traditional GMP with the same complexity. Finally, numerical results are provided to verify the validity and accuracy of the theoretical results presented.Comment: Accepted by IEEE TWC, 16 pages, 11 figure

A Unified Successive Pseudo-Convex Approximation Framework

In this paper, we propose a successive pseudo-convex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems. The stationary points are obtained by solving a sequence of successively refined approximate problems, each of which is much easier to solve than the original problem. To achieve convergence, the approximate problem only needs to exhibit a weak form of convexity, namely, pseudo-convexity. We show that the proposed framework not only includes as special cases a number of existing methods, for example, the gradient method and the Jacobi algorithm, but also leads to new algorithms which enjoy easier implementation and faster convergence speed. We also propose a novel line search method for nondifferentiable optimization problems, which is carried out over a properly constructed differentiable function with the benefit of a simplified implementation as compared to state-of-the-art line search techniques that directly operate on the original nondifferentiable objective function. The advantages of the proposed algorithm are shown, both theoretically and numerically, by several example applications, namely, MIMO broadcast channel capacity computation, energy efficiency maximization in massive MIMO systems and LASSO in sparse signal recovery.Comment: submitted to IEEE Transactions on Signal Processing; original title: A Novel Iterative Convex Approximation Metho

Efficient low-complexity data detection for multiple-input multiple-output wireless communication systems

The tradeoff between the computational complexity and system performance in multipleinput multiple-output (MIMO) wireless communication systems is critical to practical applications. In this dissertation, we investigate efficient low-complexity data detection schemes from conventional small-scale to recent large-scale MIMO systems, with the targeted applications in terrestrial wireless communication systems, vehicular networks, and underwater acoustic communication systems. In the small-scale MIMO scenario, we study turbo equalization schemes for multipleinput multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) and multipleinput multiple-output single-carrier frequency division multiple access (MIMO SC-FDMA) systems. For the MIMO-OFDM system, we propose a soft-input soft-output sorted QR decomposition (SQRD) based turbo equalization scheme under imperfect channel estimation. We demonstrate the performance enhancement of the proposed scheme over the conventional minimum mean-square error (MMSE) based turbo equalization scheme in terms of system bit error rate (BER) and convergence performance. Furthermore, by jointly considering channel estimation error and the a priori information from the channel decoder, we develop low-complexity turbo equalization schemes conditioned on channel estimate for MIMO systems. Our proposed methods generalize the expressions used for MMSE and MMSE-SQRD based turbo equalizers, where the existing methods can be viewed as special cases. In addition, we extend the SQRD-based soft interference cancelation scheme to MIMO SC-FDMA systems where a multi-user MIMO scenario is considered. We show an improved system BER performance of the proposed turbo detection scheme over the conventional MMSE-based detection scheme. In the large-scale MIMO scenario, we focus on low-complexity detection schemes because computational complexity becomes critical issue for massive MIMO applications. We first propose an innovative approach of using the stair matrix in the development of massive MIMO detection schemes. We demonstrate the applicability of the stair matrix through the study of the convergence conditions. We then investigate the system performance and demonstrate that the convergence rate and the system BER are much improved over the diagonal matrix based approach with the same system configuration. We further investigate low-complexity and fast processing detection schemes for massive MIMO systems where a block diagonal matrix is utilized in the development. Using a parallel processing structure, the processing time can be much reduced. We investigate the convergence performance through both the probability that the convergence conditions are satisfied and the convergence rate, and evaluate the system performance in terms of computational complexity, system BER, and the overall processing time. Using our proposed approach, we extend the block Gauss-Seidel method to large-scale array signal detection in underwater acoustic (UWA) communications. By utilizing a recently proposed computational efficient statistic UWA channel model, we show that the proposed scheme can effectively approach the system performance of the original Gauss-Seidel method, but with much reduced processing delay

Accelerated Randomized Methods for Receiver Design in Extra-Large Scale MIMO Arrays

Recent interest has been cast on accelerated versions of the randomized Kaczmarz (RK) algorithm due to the increase in applications that consider sparse linear systems. In particular, considering the context of massive multiple-input-multiple-output (M-MIMO) communication systems, a low complexity naive RK-based receiver has recently been proposed. This method can take advantage of non-stationarities emerging from extra-large M-MIMO systems, but it performs poorly on highly spatially correlated channels. To address this problem, in this paper, we propose a new class of accelerated RK-based receiver designs, where convergence acceleration is based on the residual information. However, we show that the cost of obtaining this knowledge on an iteration basis is not worth it due to the lousy convergence effects caused by system and channel parameters. Inspired by this observation, we further propose a RK-based receiver with sampling without replacement, referred to as RK-RZF. This simple technique is more effective in performing signal detection under reduced complexity. Future works suggest advantage of RK-based receivers to improve current 5G commercial systems and solve the problem of signal detection in other paradigms beyond 5G.Comment: 11 pages, 4 figures, submitted to IEEE TV