  In this paper, relaxed belief propagation (RBP) based detectors are proposed
for multiple-input multiple-out (MIMO) system. The factor graph is leveraged to
represent the MIMO channels, and based on which our algorithms are developed.
Unlike the existing complicated standard belief propagation (SBP) detector that
considers all the edges of the factor graph when updating messages, the
proposed RBP focuses on partial edges, which largely reduces computational
complexity. In particular, relax degree is introduced in to determine how many
edges to be selected, whereby RBP is a generalized edge selection based BP
method and SBP is a special case of RBP having the smallest relax degree.
Moreover, we propose a novel Gaussian approximation with feedback information
mechanism to enable the proposed RBP detector. In order to further improve the
detection performance, we also propose to cascade a minimum mean square error
(MMSE) detector before the RBP detector, from which pseudo priori information
is judiciously exploited. Convergence and complexity analyses, along with the
numerical simulation results, verify that the proposed RBP outperform other BP
methods having the similar complexity, and the MMSE cascaded RBP even
outperform SBP at the largest relax degree in large MIMO systems.
