Cramér-Rao Lower Bounds on Covariance Matrix Estimation for Complex Elliptically Symmetric Distributions

摘要

This paper introduces the Cramér-Rao Lower Bounds (CRLBs) for the scatter matrix of Complex Elliptically Symmetric distributions and compares them to the performance of the (constrained-)ML estimators 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 taking into proper account a constraint on the matrix trace for small data size. The work is completed with the comparison with the performance of Tyler's matrix estimator that shows a very robust behavior in almost all the analyzed cases and with the CRLBs for the Complex Angular Elliptical distributions, whose Tyler's estimator is the ML one.