Gaussian Message Passing Iterative Detection for MIMO-NOMA Systems with Massive Access

This paper considers a low-complexity Gaussian Message Passing Iterative Detection (GMPID) algorithm for Multiple-Input Multiple-Output systems with Non-Orthogonal Multiple Access (MIMO-NOMA), in which a base station with Nᵣ antennas serves Nᵤ sources simultaneously. Both Nᵤ and Nᵣ are very large numbers and we consider the cases that Nᵤ>Nᵣ. The GMPID is based on a fully connected loopy graph, which is well understood to be not convergent in some cases. The large-scale property of the MIMO-NOMA is used to simplify the convergence analysis. Firstly, we prove that the variances of the GMPID definitely converge to that of Minimum Mean Square Error (MMSE) detection. Secondly, two sufficient conditions that the means of the GMPID converge to a higher MSE than that of the MMSE detection are proposed. However, the means of the GMPID may still not converge when Nᵤ/Nᵣ Nᵣ with a faster convergence speed. Finally, numerical results are provided to verify the validity of the proposed theoretical results.