Optimal linear correction in LMMSE estimation using moments of the complex inverse Wishart distribution

The conventional linear minimum mean square error estimator (LMMSE) suffers a severe performance degradation whenever the sample size is comparable to the observation dimension. In order to tackle this problem, we propose an optimal linear correction of the conventional LMMSE, which minimizes the average mean square error (MSE) by using the moments of the complex inverse Wishart distribution. Numerical simulations highlight that the proposed estimator dramatically outperforms the conventional LMMSE in the small sample size regime.