Direction finding for a wavefront with imperfect spatial coherence

We consider the direction-of-arrival (DOA) problem for a wavefront whose amplitude and phase vary randomly along the array aperture. This phenomenon can for instance originate from propagation through an inhomogeneous medium. A simple and accurate DOA estimator is derived in the case of an uniform linear array of sensors. The estimator is based upon a reduced statistic obtained from the sub-diagonals 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 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 Cramér-Rao bound.