Adaptive iterative detectors for phase-uncertain channels via variational bounding

The problem of iterative detection/decoding of data symbols transmitted over an additive white Gaussian noise (AWGN) channel in the presence of phase uncertainty is addressed in this paper. By modelling the phase uncertainty either as an unknown deterministic variable/process or random variable/ process with a known a priori probability density function, a number of non-Bayesian and Bayesian detection algorithms with various amount of suboptimality have been proposed in the literature to solve the problem. In this paper, a new set of suboptimal iterative detection algorithms is obtained by utilizing the variational bounding technique. Especially, applying the generic variational Bayesian (VB) framework, efficient iterative joint estimation and detection/decoding schemes are derived for the constant phase model as well as for the dynamic phase model. In addition, the relation of the VB-based approach to the optimal noncoherent receiver as well as to the classical approach via the expectation-maximization (EM) algorithm is provided. Performance of the proposed detectors in the presence of a strong dynamic phase noise is compared to the performance of the existing detectors. Furthermore, an incremental scheduling of the VB (or EM) algorithm is shown to reduce the overall complexity of the receiver.