Refinement and derivation of statistical resolution limits for circular or rectilinear correlated sources in CES data models

Abstract

This paper analyzes the deterministic (DCRB) and the stochastic (SCRB) Cramér-Rao bound on direction-of-arrival (DOA) estimation for two equi-powered correlated complex circular or rectilinear sources affected by complex circular white noise in different complex elliptically symmetric (CES) data models. Beginning by decomposing these CRBs, into factors depending on signal and noise parameters, and on geometric parameters of the array, some new interpretable closed-form expressions are derived in particular scenarios. These expressions provide useful insight into the behavior of these CRB’s dependence on the correlation factor. Approximate closed-form expressions of these CRBs for small DOA separation are also derived. These results lead to new formulas for statistical resolution limit (SRL) based on the Smith criterion at which an unbiased DOA estimation algorithm can resolve two closely-spaced circular or rectilinear sources. These SCRB-derived formulas are much less optimistic than those which have so far been deduced only from the DCRB under the assumption of known sources.