Maximum a-posteriori estimation in linear models with a random Gaussian model matrix: A Bayesian-EM approach

This paper considers the problem of Bayesian estimation of a Gaussian vector in a linear model with random Gaussian uncertainty in the mixing matrix. The maximum a-posteriori estimator is derived for this model using the Bayesian expectation-maximization. It is demonstrated that the solution forms an elegant and simple iteration which can be easily implemented. Finally, the estimator developed is considered in the context of near-Gaussian-digitally modulated signals under channel uncertainty, where it is shown that the MAP estimator outperforms the standard linear MMSE estimator in terms of mean square error (MSE) and bit error rate (BER).