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

Computer Science – Information Theory

Scientific paper

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30 pages, 16 figures, submitted to IEEE Trans. on Signal Processing

Scientific paper

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 order to reduce the implementation complexity associated with the expression of the optimum Bayesian estimator, the paper considers also two popular suboptimal estimators, which are the soft-limiter and the blanker. The optimum Bayesian thresholds for such suboptimal estimators are obtained by iteratively solving fixed point equations. Connections with the maximum SNR estimators are also established. Theoretical expressions for the MSE and the SNR of the suboptimal estimators are also derived, and the results confirmed by simulations. Noteworthy, the results can be applied to any noise characterized by a Gaussian mixture distribution.

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