Mismatched MMSE estimation of multivariate Gaussian sources

The distortion increase in minimum mean-square error (MMSE) estimation of multivariate Gaussian sources is analyzed for the situation in which the statistics are mismatched, i.e., the covariance matrix is not perfectly known during the estimation process. First a deterministic mismatch model with an additive perturbation matrix is considered, for which we provide closed form expressions for the distortion excess caused by the mismatch. The mismatch study is then generalized by using random matrix theory tools which allow an asymptotic result for a broad class of perturbation matrices to be proved.