The Hybrid CramÉr–Rao Bound on Broadside DOA Estimation of Extended Sources in Presence of Array Errors

In this correspondence we derive explicit expressions for the hybrid Cramer-Rao lower bound (HCRB) on the estimation accuracy of signal direction of arrival (DOA) from data collected by randomly perturbed arrays. The presence of a wavefront spatial decorrelation, which is modeled as a multiplicative correlated noise, has also been taken into account in the data model, since it is typical in those applications involving extended sources. In particular, we consider perturbations in sensor positions. Existing approaches to DOA HCRB calculation do not consider the presence of multiplicative noise and are referred to the assumption of small perturbations only, still not being worked out explicitly. Here, we assume that the impinging wavefronts are coming from broadside or more generally from a narrow DOA sector, allowing the explicit derivation of the HCRB for any variance of the sensor positioning errors in the line-of-sight direction. This scenario corresponds to the typical operative condition of remote sensing systems such as synthetic aperture radar (SAR) multibaseline interferometers, for which a few HCRB sample curves are reported.