I. Introduction
Recently, the applications of message passing to receiver design have attracted much attention [1]. Belief propagation (BP) [2], [3] is especially efficient for discrete probabilistic or linear Gaussian models, but it induces high complexity in nonlinear models or models involving both continuous and discrete variables. Mean field (MF) [4] is suitable for continuous probabilistic conjugate-exponential models, but it may exhibit poor performance in some scenarios, e.g., when applied to multisignal summation structure [5]. Expectation propagation (EP) [6] can be regarded as an approximation of BP [7], where some beliefs are approximated by distributions in a specific exponential family. By exploiting their virtues while avoiding their drawbacks, BP, EP, and MF have been integrated carefully to design superior receivers with low complexity [5], [8] –[12]. In this work, we consider low-complexity hybrid message passing receiver design to achieve joint channel estimation and decoding for multiuser MIMO-OFDM systems.