ML estimate and CRLB of Covariance Matrix for Complex Elliptically Symmetric distribution

This paper derives the “constrained” maximum likelihood (ML) estimators and the Cramér-Rao Lower Bounds (CRLB) for the scatter matrix of Complex Elliptically Symmetric distributions and compares them in the particular cases of complex Gaussian, Generalized Gaussian (GG) and t-distributed observation vectors. Numerical results confirm the goodness of the ML estimators and the advantage of a constraint on the matrix trace for small data size.