Performance of high resolution frequencies estimation methods compared to the Cramer-Rao bounds

An explicit expression for the Cramer-Rao bounds (CRBs) and a calculation of the statistical perturbation of the covariance matrix due to additive noise are presented. The results are applied to a statistical efficiency analysis of the main frequency estimation methods based on eigenvalue decomposition. For the covariance matrix, in order to characterize the perturbation of the signal subspace, only the component of the perturbation of the eigenvectors orthogonal to the subspace is considered. This gives a simpler and more significant form of the error covariance. The treatment includes the cases of forward-backward and moving averages. The CRB and estimation variances are calculated in the presence of additive random noise, but for a given set of amplitudes characterized by their sample covariance matrix. This approach is more realistic for the evaluation of efficiency in the small-sample case