Performance bounds and statistical analysis of DOA estimation

The aim of this chapter is to provide a unified methodology to study the theoretical statistical performance of arbitrary DOA estimation and source number detection methods and to tackle the resolvability of closely space sources. A particular attention is given to the asymptotic distribution, mean and covariance of DOA estimates and to the Cramer Rao and asymptotically minimum variance bounds. To illustrate this general framework, several examples are detailed such as the conventional MUSIC algorithm, the MDL criterion and the angular resolution limit based on the detection theory. Furthermore robustness with respect to the Gaussian distribution, the independence and narrow band assumptions, and array modeling errors are also considered