Variational bayesian perspectives on iterative detection in the presence of phase uncertainty

The problem of iterative detection/decoding of data symbols transmitted over an additive white Gaussian noise channel in the presence of phase uncertainty is addressed in this paper. By modeling the phase uncertainty either as an unknown deterministic variable/process or random variable/process with known a priori probability density function, a number of receiver algorithms with various amount of unoptimality have already been proposed to solve the problem. Contrary to the previous contributions, we look at the problem from the variational Bayesian perspective. In particular, efficient iterative joint estimation and detection schemes, based on the generic variational Bayesian (VB) framework, are derived for the constant phase model as well as for the dynamic phase model. In addition, the VB-based approach is related to the optimal noncoherent receiver and to the receiver obtained via the expectation-maximization (EM) algorithm.