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This letter derives the minimum mean square error (MMSE) Bayesian estimator for a Gaussian source impaired by additive Middleton's Class-A impulsive noise. Additionally, as low-complex alternatives, the letter considers two popular suboptimal estimators, such as the soft-limiter and the blanker. The optimum MMSE thresholds for these suboptimal estimators are obtained by iteratively solving fixed point equations. The theoretical findings are corroborated by simulation results, which highlight the MSE performance penalty of the suboptimal estimators may be negligible with respect to the optimal Bayesian estimator (OBE). Noteworthy, the proposed estimators can be extended to any noise, or observation error, that can be modeled as a Gaussian-mixture.

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