Expectation Propagation and Transparent Propagation in Iterative Signal Estimation in the Presence of Impulsive Noise

Expectation Propagation (EP) and Transparent Propagation (TP) are employed in iterative estimation of correlated Gaussian samples in the presence of bursty impulsive noise, modeled as Markov Middleton class A. The proposed estimation strategy is based on a message-passing approach in which a Kalman Smoother and a Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm work in parallel. Due to the correlation between signal samples and correlation of channel states, the corresponding factor graph includes cycles. Therefore, the message passing approach should be implemented iteratively. Furthermore, the presence of Gaussian observations, continuous random variables, and impulsive noise states, discrete random variables, produces Gaussian mixtures. We utilize the variational inference techniques such as EP and TP to approximate the Gaussian mixtures and to avoid exponentially increasing complexity of messages. The performance of EP and TP based estimators are evaluated by using computer simulations. The results show a considerable improvement in performance brought about by the estimation strategy.