Convergence analysis and assurance for Gaussian message passing iterative detector in massive MU-MIMO systems

This paper considers a low-complexity Gaussian message passing iterative detection (GMPID) algorithm for a massive multiuser multiple-input multiple-output (MU-MIMO) system, in which a base station with M antennas serves K Gaussian sources simultaneously. Both K and M are very large numbers, and we consider the cases that K<M. The GMPID is a message passing algorithm operating on a fully connected loopy graph, which is well understood to be non-convergent in some cases. As it is hard to analyze the GMPID directly, the large-scale property of the massive MU-MIMO is used to simplify the analysis. First, we prove that the variances of the GMPID definitely converge to the mean square error of minimum mean square error (mmse) detection. Second, we derive two sufficient conditions that make the means of the GMPID converge to those of the mmse detection. However, the means of GMPID may not converge when K/M≥ (√2-1)². Therefore, a modified GMPID called scale-and-add GMPID, which converges to the mmse detection in mean and variance for any K<M , and has a faster convergence speed than the GMPID, but has no higher complexity than the GMPID, is proposed. Finally, numerical results are provided to verify the validity and accuracy of the theoretical results.