Hybrid lower bound via compression of the sampled CLR function

In this paper, a new class of hybrid lower bounds on the mean square-error of estimators is proposed. Derivation of the proposed class is performed by applying an integral transform on the centered likelihood-ratio (CLR) function. It is shown that the hybrid Cramer-Rao and Barankin bounds are the limits of convergent sequences of bounds, which are obtained from the proposed class using specific sequences of integral transform kernels. A new hybrid bound is derived from the proposed class using a sequence of integral transform kernels, which comprise a compression matrix of the sampled CLR function. In comparison with existing bounds, the proposed bound is computationally manageable and provides better prediction of the threshold region of the joint maximum-a posteriori probability maximum-likelihood estimator, in a single tone estimation scenario.