  In this work, with combined belief propagation (BP), mean field (MF) and
expectation propagation (EP), an iterative receiver is designed for joint phase
noise (PN) estimation, equalization and decoding in a coded communication
system. The presence of the PN results in a nonlinear observation model.
Conventionally, the nonlinear model is directly linearized by using the
first-order Taylor approximation, e.g., in the state-of-the-art soft-input
extended Kalman smoothing approach (soft-in EKS). In this work, MF is used to
handle the factor due to the nonlinear model, and a second-order Taylor
approximation is used to achieve Gaussian approximation to the MF messages,
which is crucial to the low-complexity implementation of the receiver with BP
and EP. It turns out that our approximation is more effective than the direct
linearization in the soft-in EKS with similar complexity, leading to
significant performance improvement as demonstrated by simulation results.
