An analysis of ESPRIT under random sensor uncertainties

A general expression for the mean-square error (MSE) of the ESPRIT direction-of-arrival (DOA) estimation of narrowband far-field sources under random sensor perturbations is derived. Explicit solutions for the case of an arbitrary ESPRIT array geometry with one and two sources are given. Solutions for the case of a uniform linear array and arbitrary number of sources are found provided that the number of sensors is large. For this case, it is found that the MSE of ESPRIT with maximum aperture (i.e., maximum-overlapping subarrays) is lower than that of ESPRIT with nonoverlapping subarrays. A comparison with MUSIC suggests that the MSE for MUSIC is lower than that for ESPRIT. Furthermore, for the cases studied, it is shown that the MSE of ESPRIT depends only on sensor phase errors while that of MUSIC is dependent on both sensor grain and phase errors