Conditional mean estimator for the Gramian matrix of complex Gaussian random variables [wireless communication linear pre-equalization application]

The problem of estimating and predicting the Gramian of a matrix (with rather general structure) of correlated complex Gaussian random variables is addressed. We propose its conditional mean estimator as the optimum Bayesian estimator for a quadratic risk function and present its mean square error (MSE) performance analysis. Numerical results for the example of linear pre-equalization in a wireless communications application show a significantly improved performance of the novel estimator compared to known approaches.