Pair-wise Markov Random Fields Applied to the Design of Low Complexity MIMO Detectors

Pair-wise Markov random fields (MRF) are considered for application to the development of low complexity, iterative MIMO detection. Specifically, we consider two types of MRF, namely, the fully-connected and ring-type. For the edge potentials, we use the bivariate Gaussian function obtained by marginalizing the posterior joint probability density under the Gaussian assumption. Since the corresponding factor graphs are sparse, in the sense that the number of edges connected to a factor node (edge degree) is only 2, the computations are much easier than that of ML, which is similar to the belief propagation (BP), or sumproduct, algorithm that is run over the fully connected factor graph. The BER performances for non-Gaussian input are evaluated via simulation, and the results show the validity of the proposed algorithms. We also customize the algorithm for Gaussian input to obtain the Gaussian BP that is run over the two MRF and proves its convergence in mean to the linear MMSE estimates. The result lies on the same line of those in [16] and [24], but with differences in its graphical model and the message passing rule. Since the MAP estimator for the Gaussian input is equivalent to the linear MMSE estimator, it shows the optimality, in mean, of the scheme for Gaussian input.