Maximum A-Posteriori Estimation in Linear Models With a Gaussian Model Matrix

We consider the Bayesian inference of a random Gaussian vector in a linear model with a Gaussian model matrix. We derive the maximum a-posteriori (MAP) estimator for this model and show that it can be found using a simple line search over a unimodal function that can be efficiently evaluated. Next, we discuss the application of this estimator in the context of near-optimal detection of near-Gaussian-digitally modulated signals and demonstrate through simulations that the MAP estimator outperforms the standard linear MMSE estimator in terms of mean square error (MSE) and bit error rate (BER).