Spatial power spectral density estimation using a Welch coprime sensor array processor

Abstract

A coprime sensor array (CSA) is a sparse array geometry that interleaves two spatially undersampled uniform linear arrays (ULAs) with coprime undersampling factors. The CSA product processor achieves an asymptotically unbiased spatial power spectral density (PSD) estimate using far fewer sensors than a conventional ULA beamformer, but at the expense of increased sidelobes and variance. Nonstationary underwater sonar environments often preclude increasing the number of snapshots required to achieve a desirable PSD variance. Bartlett's and Welch's methods improve PSD variance by O(K) at the expense of resolution without requiring additional snapshots by averaging uncorrelated PSD estimates obtained using K array segments. This paper proposes the Welch overlapping segment averaging product (WOSA-product) processor for coprime arrays to achieve unambiguous PSD estimates with desirable variance properties for passive direction of arrival estimation. The first two moments of the WOSA-product processor's spatial PSD estimate are derived in closed-form for spatially white Gaussian processes. Monte Carlo simulations verify the variance reduction predicted by the analytical derivation for white processes and planewave arrivals, and the effects of segment length on resolution, variance reduction, and peak sidelobe levels are discussed.