  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 sum-product, 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.
