Convergence Analysis and Assurance for Gaussian Message Passing Iterative Detector in Massive MU-MIMO Systems

TL;DR

This paper analyzes the convergence of a low-complexity Gaussian message passing algorithm for massive MU-MIMO systems, proving variance convergence, establishing conditions for mean convergence, and proposing an improved algorithm with faster convergence.

Contribution

It provides a theoretical convergence analysis of GMPID in massive MU-MIMO, introduces conditions for mean convergence, and proposes SA-GMPID with enhanced convergence properties.

Findings

GMPID variances converge to MMSE MSE

Conditions for GMPID mean convergence are established

SA-GMPID achieves faster convergence without increased complexity

Abstract

This paper considers a low-complexity Gaussian Message Passing Iterative Detection (GMPID) algorithm for 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 low-complexity message passing algorithm based on a fully connected loopy graph, which is well understood to be not convergent in some cases. As it is hard to analyse the GMPID directly, the large-scale property of the massive MU-MIMO is used to simplify the analysis. Firstly, we prove that the variances of the GMPID definitely converge to the mean square error of Minimum Mean Square Error (MMSE) detection. Secondly, we propose two sufficient conditions that the means of the GMPID converge to those of the MMSE detection. However, the means of GMPID may not converge when $ K/M\geq (\sqrt{2}-1)^2$. Therefore, a new convergent GMPID called SA-GMPID (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.