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

Generalized Spatial Modulation in Large-Scale Multiuser MIMO Systems

Generalized spatial modulation (GSM) uses $n_t$ transmit antenna elements but fewer transmit radio frequency (RF) chains, $n_{rf}$. Spatial modulation (SM) and spatial multiplexing are special cases of GSM with $n_{rf}=1$ and $n_{rf}=n_t$, respectively. In GSM, in addition to conveying information bits through $n_{rf}$ conventional modulation symbols (for example, QAM), the indices of the $n_{rf}$ active transmit antennas also convey information bits. In this paper, we investigate {\em GSM for large-scale multiuser MIMO communications on the uplink}. Our contributions in this paper include: ($i$) an average bit error probability (ABEP) analysis for maximum-likelihood detection in multiuser GSM-MIMO on the uplink, where we derive an upper bound on the ABEP, and ($ii$) low-complexity algorithms for GSM-MIMO signal detection and channel estimation at the base station receiver based on message passing. The analytical upper bounds on the ABEP are found to be tight at moderate to high signal-to-noise ratios (SNR). The proposed receiver algorithms are found to scale very well in complexity while achieving near-optimal performance in large dimensions. Simulation results show that, for the same spectral efficiency, multiuser GSM-MIMO can outperform multiuser SM-MIMO as well as conventional multiuser MIMO, by about 2 to 9 dB at a bit error rate of $10^{-3}$. Such SNR gains in GSM-MIMO compared to SM-MIMO and conventional MIMO can be attributed to the fact that, because of a larger number of spatial index bits, GSM-MIMO can use a lower-order QAM alphabet which is more power efficient.Comment: IEEE Trans. on Wireless Communications, accepte

Channel Hardening-Exploiting Message Passing (CHEMP) Receiver in Large-Scale MIMO Systems

In this paper, we propose a MIMO receiver algorithm that exploits {\em channel hardening} that occurs in large MIMO channels. Channel hardening refers to the phenomenon where the off-diagonal terms of the ${\bf H}^H{\bf H}$ matrix become increasingly weaker compared to the diagonal terms as the size of the channel gain matrix ${\bf H}$ increases. Specifically, we propose a message passing detection (MPD) algorithm which works with the real-valued matched filtered received vector (whose signal term becomes ${\bf H}^T{\bf H}{\bf x}$, where ${\bf x}$ is the transmitted vector), and uses a Gaussian approximation on the off-diagonal terms of the ${\bf H}^T{\bf H}$ matrix. We also propose a simple estimation scheme which directly obtains an estimate of ${\bf H}^T{\bf H}$ (instead of an estimate of ${\bf H}$), which is used as an effective channel estimate in the MPD algorithm. We refer to this receiver as the {\em channel hardening-exploiting message passing (CHEMP)} receiver. The proposed CHEMP receiver achieves very good performance in large-scale MIMO systems (e.g., in systems with 16 to 128 uplink users and 128 base station antennas). For the considered large MIMO settings, the complexity of the proposed MPD algorithm is almost the same as or less than that of the minimum mean square error (MMSE) detection. This is because the MPD algorithm does not need a matrix inversion. It also achieves a significantly better performance compared to MMSE and other message passing detection algorithms using MMSE estimate of ${\bf H}$. We also present a convergence analysis of the proposed MPD algorithm. Further, we design optimized irregular low density parity check (LDPC) codes specific to the considered large MIMO channel and the CHEMP receiver through EXIT chart matching. The LDPC codes thus obtained achieve improved coded bit error rate performance compared to off-the-shelf irregular LDPC codes