Simple and accurate direction of arrival estimator in the case of imperfect spatial coherence

We consider the direction-finding problem in the imperfect spatial coherence case, i.e., when the amplitude and phase of the wavefront vary randomly along the array aperture. This phenomenon can originate from propagation through an inhomogeneous medium. It is also encountered in the case of spatially dispersed sources. We derive a fast and accurate estimator for the direction of arrival of a single source using a uniform linear array (ULA) of sensors. The estimator is based on a reduced statistic obtained from the subdiagonals of the covariance matrix of the array output. It only entails computing the Fourier transform of an (m-1)-length sequence where m is the number of array sensors. A theoretical analysis is carried out, and an expression for the asymptotic variance of the estimator is derived. Numerical simulations validate the theoretical results and show that the estimator has an accuracy very close to the Cramer-Rao bound.