Bayesian Estimation of a Gaussian source in Middleton's Class-A Impulsive Noise

Abstract: The paper focuses on minimum mean square error (MMSE) Bayesian estimation for a Gaussian source impaired by additive Middleton's Class-A impulsive noise. In addition to the optimal Bayesian estimator, the paper considers also the soft-limiter and the blanker, which are two popular suboptimal estimators characterized by very low complexity. The MMSE-optimum thresholds for such suboptimal estimators are obtained by practical iterative algorithms with fast convergence. The paper derives also the optimal thresholds according to a maximum-SNR (MSNR) criterion, and establishes connections with the MMSE criterion. Furthermore, closed form analytic expressions are derived for the MSE and the SNR of all the suboptimal estimators, which perfectly match simulation results. Noteworthy, these results can be applied to characterize the receiving performance of any multicarrier system impaired by a Gaussian-mixture noise, such as asymmetric digital subscriber lines (ADSL) and power-line communications (PLC).