  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 $K/M>(\sqrt{2}-1)^2$. 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.
