Cramer-Rao bound analysis of wideband source localization and DOA estimation

In this paper, we derive the Cramer-Rao Bound(CRB) for wideband source localization and DOA estimation. The resulting CRB formula can be decomposed into two terms: one that depends on the signal characteristic and one that depends on the array geometry. For a uniformly spaced circular array(UCA), a concise analytical form of the CRB can be given by using some algebraic approximation. We further define a DOA beamwidth based on the resulting CRB formula. The DOA beamwidth can be used to design the sampling angular spacing for the Maximum-likelihood(ML) algorithm. For a randomly distributed array, we use an elliptical model to determine the largest and smallest effective beamwidth. The effective bearnwidth and the CRB analysis of source localization allow us to design an efficient. algorithm for the ML estimator. Finally, our simulation results of the Approximated Maximum Likelihood(AML) algorithm are demonstrated to match well to the CRB analysis at high SNR.