Statistical analysis of the covariance matrix MLE in K-distributed clutter

In the context of radar detection, the clutter covariance matrix estimation is an important point to design optimal detectors. While the Gaussian clutter case has been extensively studied, the new advances in radar technology show that non-Gaussian clutter models have to be considered. Among these models, the spherically invariant random vector modelling is particularly interesting since it includes the K-distributed clutter model, known to fit very well with experimental data. This is why recent results in the literature focus on this distribution. More precisely, the maximum likelihood estimator of a K-distributed clutter covariance matrix has already been derived. This paper proposes a complete statistical performance analysis of this estimator through its consistency and its unbiasedness at finite number of samples. Moreover, the closed-form expression of the true Cramér–Rao bound is derived for the K-distribution covariance matrix and the efficiency of the maximum likelihood estimator is emphasized by simulations.