A map based estimator for inverse complex covariance matricies

A novel approach to estimate (inverse) complex covariance matrices is proposed. By considering the class of unitary invariant estimators, the main challenge lies in estimating the underlying eigenvalues from sampled versions. By exploiting that the distribution of the sample eigenvalues can be derived in closed form, a Maximum A Posteriori (MAP) based scheme is then derived. The performance of the derived estimator is simulated and results indicate that the proposed scheme shows performance similar to one of the best estimators known to date. The main advantage lies in that the proposed solution only requires numerical optimization over a P-dimensional space where P is the size of the covariance matrix.