  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).
