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

Receiver Architectures for MIMO-OFDM Based on a Combined VMP-SP Algorithm

Iterative information processing, either based on heuristics or analytical frameworks, has been shown to be a very powerful tool for the design of efficient, yet feasible, wireless receiver architectures. Within this context, algorithms performing message-passing on a probabilistic graph, such as the sum-product (SP) and variational message passing (VMP) algorithms, have become increasingly popular. In this contribution, we apply a combined VMP-SP message-passing technique to the design of receivers for MIMO-ODFM systems. The message-passing equations of the combined scheme can be obtained from the equations of the stationary points of a constrained region-based free energy approximation. When applied to a MIMO-OFDM probabilistic model, we obtain a generic receiver architecture performing iterative channel weight and noise precision estimation, equalization and data decoding. We show that this generic scheme can be particularized to a variety of different receiver structures, ranging from high-performance iterative structures to low complexity receivers. This allows for a flexible design of the signal processing specially tailored for the requirements of each specific application. The numerical assessment of our solutions, based on Monte Carlo simulations, corroborates the high performance of the proposed algorithms and their superiority to heuristic approaches

A Low-Complexity Double EP-based Detector for Iterative Detection and Decoding in MIMO

We propose a new iterative detection and decoding (IDD) algorithm for multiple-input multiple-output (MIMO) based on expectation propagation (EP) with application to massive MIMO scenarios. Two main results are presented. We first introduce EP to iteratively improve the Gaussian approximations of both the estimation of the posterior by the MIMO detector and the soft output of the channel decoder. With this novel approach, denoted by double-EP (DEP), the convergence is very much improved with a computational complexity just two times the one of the linear minimum mean square error (LMMSE) based IDD, as illustrated by the included experiments. Besides, as in the LMMSE MIMO detector, when the number of antennas increases, the computational cost of the matrix inversion operation required by the DEP becomes unaffordable. In this work we also develop approaches of DEP where the mean and the covariance matrix of the posterior are approximated by using the Gauss-Seidel and Neumann series methods, respectively. This low-complexity DEP detector has quadratic complexity in the number of antennas, as the low-complexity LMMSE techniques. Experimental results show that the new low-complexity DEP achieves the performance of the DEP as the ratio between the number of transmitting and receiving antennas decreasesProyectos Nacionales Españoles del Gobierno de España TEC2017-90093-C3-2-

Deep Learning Based on Orthogonal Approximate Message Passing for CP-Free OFDM

Channel estimation and signal detection are very challenging for an orthogonal frequency division multiplexing (OFDM) system without cyclic prefix (CP). In this article, deep learning based on orthogonal approximate message passing (DL-OAMP) is used to address these problems. The DL-OAMP receiver includes a channel estimation neural network (CE-Net) and a signal detection neural network based on OAMP, called OAMP-Net. The CE-Net is initialized by the least square channel estimation algorithm and refined by minimum mean-squared error (MMSE) neural network. The OAMP-Net is established by unfolding the iterative OAMP algorithm and adding some trainable parameters to improve the detection performance. The DL-OAMP receiver is with low complexity and can estimate time-varying channels with only a single training. Simulation results demonstrate that the bit-error rate (BER) of the proposed scheme is lower than those of competitive algorithms for high-order modulation.Comment: 5 pages, 4 figures, updated manuscript, International Conference on Acoustics, Speech and Signal Processing (ICASSP 2019). arXiv admin note: substantial text overlap with arXiv:1903.0476