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 variances of the GMP definitely converge to the mean square error (MSE) of Linear Minimum Mean Square Error (LMMSE) multi-user detection. Secondly, the means of the traditional GMP will fail to converge when N_u/N_s< (√(2)-1)^-2≈5.83. 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.