Abstract
•General closed-form expressions of the deterministic Cramér Rao bound (DCRB), semiparametric DCRB, stochastic Cramér Rao bound (SCRB) and semiparametric SCRB for direction of arrival (DOA) estimation are given in complex elliptically symmetric (CES) data models.•Simple exact and asymptotic (for small DOA separation) interpretable closed-form expressions are presented for the DCRB and SCRB of the DOA for two equi-powered correlated known, arbitrary, circular or rectilinear sources in CES data models.•The dependence of these bounds on the magnitude and phase of the correlation is examined.•Using asymptotic expressions of DCRBs and SCRBs, interpretable closed-form expressions of Statistical Resolution Limit (SRL) based on Smith’s criterion are derived in different scenarios.•Comments to explain how different parameters impact the derived SRLs and how also the SRLs derived from the SCRBs are much less optimistic than those that have so far been deduced only from the DCRB under the assumption of known sources are discussed.
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.