Direction finding with nonuniform arrays via higher-order statistics

In array signal processing, it is shown that nonuniform arrays, such as minimum redundancy (MR) arrays or nonredundant arrays, may lead to significant improvement in performances. Unfortunately, a nonuniform array without matched sensor doublets cannot be employed in the covariance-based ESPRIT algorithm, which is known as one of the most popular high resolution eigenstructure techniques for direction-of-arrival (DOA) estimation and exhibits several advantages over another popular algorithm, the MUSIC algorithm, such as requiring no knowledge of the array geometry and less computations than MUSIC. In this paper we will show the requirement in ESPRIT that the array must be composed of sensor doublets, i.e., the array must be able to divided into two matched subarrays, can be easily removed by employing higher-order statistics (cumulants) instead of the original used second-order statistics (covariances) of the received data. Based on the proposed cumulant matrix pairs, a nonuniform array with L sensors can be used to resolve at least L DOA´s. Simulation results illustrate that the proposed cumulant matrices hold the inherent advantages of both the nonuniform arrays in improving performances and the cumulant-based techniques in suppressing spatially colored Gaussian noise effects.