Massive MIMO Detection Based on Belief Propagation in Spatially Correlated Channels

Belief Propagation (BP) is an iterative method to solve inference problems by passing messages in a factor graph. Due to its low complexity and near optimality, the BP algorithm and its variants have been widely applied to solve massive Multiple-Input Multiple-Output (MIMO) detection problems. However, it is worth noting that most of the existing works assume that the channels are spatially independently fading, in which scenario the BP iterations could converge to a fix point even there exist loops in the factor graph. Actually, the practical channels are spatially correlated fading due to the limited-scattering radio environment. Unfortunately, we found that the convergence performance of the BP iterations suffers severe degradation from the spatial correlation. Thus the main work of this paper is to improve the convergence performance of the BP iterations in the massive MIMO detection with the spatially correlated fading channels. In particular, we present two efficient methods, i.e., automatic damping and pre-processing. In the first method, a heuristic damping factor is calculated automatically in each BP iteration from the Kullback-Leibler divergence between the two successive messages, i.e., the current and the previous iterations, and then the calculated damping factor is used to smooth the messages (damping). In the second method, the channel matrices are first pre-processed by a de-correlation matrix, then followed by normal BP algorithms. The de-correlation can also be approximated by fast Fourier transform when the number of receive antennas is a large radix-2 number. The two methods can be used together, exhibiting superior performance over the conventional BP with both analytical spatially-correlated channel models and realistic measured channels in our simulation results.