Estimation of Gaussian Processes in Markov-Middleton Impulsive Noise

This work addresses the estimation of Gaussian signals over power line channels which are impaired by impulsive noise. The Markov-Middleton model is used to describe the memory and the multi-interferer nature of the impulsive noise. The estimation of Gaussian samples has been obtained by using a message passing algorithm. The message passing approach involves estimation of the channel states, approximation of the Gaussian mixtures and estimation of the correlated Gaussian samples. Correlation of channel states and correlation of input samples results in a loopy factor graph. To implement message passing on a loopy factor graph, we divide the graph in two main parts that exchange their messages by using a parallel iterative schedule. The lower part detects the channel states using the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm and the upper part estimates the signal samples using a Kalman smoother. The proposed approach extensively reduces the complexity of the overall estimation process.