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

Capacity-Achieving Iterative LMMSE Detection for MIMO-NOMA Systems

This paper considers a iterative Linear Minimum Mean Square Error (LMMSE) detection for the uplink Multiuser Multiple-Input and Multiple-Output (MU-MIMO) systems with Non-Orthogonal Multiple Access (NOMA). The iterative LMMSE detection greatly reduces the system computational complexity by departing the overall processing into many low-complexity distributed calculations. However, it is generally considered to be sub-optimal and achieves relatively poor performance. In this paper, we firstly present the matching conditions and area theorems for the iterative detection of the MIMO-NOMA systems. Based on the proposed matching conditions and area theorems, the achievable rate region of the iterative LMMSE detection is analysed. We prove that by properly design the iterative LMMSE detection, it can achieve (i) the optimal sum capacity of MU-MIMO systems, (ii) all the maximal extreme points in the capacity region of MU-MIMO system, and (iii) the whole capacity region of two-user MIMO systems.Comment: 6pages, 5 figures, accepted by IEEE ICC 2016, 23-27 May 2016, Kuala Lumpur, Malaysi

Message Passing in C-RAN: Joint User Activity and Signal Detection

In cloud radio access network (C-RAN), remote radio heads (RRHs) and users are uniformly distributed in a large area such that the channel matrix can be considered as sparse. Based on this phenomenon, RRHs only need to detect the relatively strong signals from nearby users and ignore the weak signals from far users, which is helpful to develop low-complexity detection algorithms without causing much performance loss. However, before detection, RRHs require to obtain the realtime user activity information by the dynamic grant procedure, which causes the enormous latency. To address this issue, in this paper, we consider a grant-free C-RAN system and propose a low-complexity Bernoulli-Gaussian message passing (BGMP) algorithm based on the sparsified channel, which jointly detects the user activity and signal. Since active users are assumed to transmit Gaussian signals at any time, the user activity can be regarded as a Bernoulli variable and the signals from all users obey a Bernoulli-Gaussian distribution. In the BGMP, the detection functions for signals are designed with respect to the Bernoulli-Gaussian variable. Numerical results demonstrate the robustness and effectivity of the BGMP. That is, for different sparsified channels, the BGMP can approach the mean-square error (MSE) of the genie-aided sparse minimum mean-square error (GA-SMMSE) which exactly knows the user activity information. Meanwhile, the fast convergence and strong recovery capability for user activity of the BGMP are also verified.Comment: Conference, 6 pages, 7 figures, accepted by IEEE Globecom 201