Maximum likelihood covariance matrix estimation for complex elliptically symmetric distributions under mismatched conditions

• This paper deals with the ML estimation of scatter matrix of CES distributions.
• We consider mismatched model conditions, that is, hypothesized and the true model are different.
• The novelty of the paper is the derivation in closed form of the Huber limit for CES distributions.
• The paper is completed with the comparison of mismatched ML, matched ML estimators and CRLBs.

This paper deals with the maximum likelihood (ML) estimation of scatter matrix of complex elliptically symmetric (CES) distributed data when the hypothesized and the true model belong to the CES family but are different, then under mismatched model condition. Firstly, we derive the Huber limit, or sandwich matrix expression, for a generic CES model. Then, we compare the performance of mismatched and matched ML estimators to the Huber limit and to the Cramér–Rao lower bound (CRLB) in some relevant study cases.