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This paper considers a low-complexity Gaussian Message Passing Iterative Detection (GMPID) method over a pairwise graph 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 large numbers and we consider the cases that K < M in this paper. The GMPID is a message passing algorithm based on a fully connected loopy graph, which is well known that it is not convergent in some cases. In this paper, we first analyse the convergence of GMPID. Two sufficient conditions that the GMPID converges to the Minimum Mean Square Error (MMSE) detection are proposed. However, the GMPID may still not converge when K/M > (√2 − l)2. Therefore, a new convergent GMPID with equally low complexity called SA-GMPID is proposed, which converges to the MMSE detection for any K < M with a faster convergence speed. Finally, numerical results are provided to verify the validity and accuracy of the proposed theoretical results.

A low-complexity Gaussian message passing iterative detector for massive MU-MIMO systems