Spatial power spectral density estimation using a multitapered coprime sensor array minimum 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 Min processor achieves an asymptotically unbiased spatial power spectral density (PSD) estimate while approaching the variance of a ULA conventional beamformer. Nonstationary underwater sonar environments often preclude the number of snapshots required to achieve a desirable PSD variance. The multitaper method improves PSD variance by O(K) at the expense of resolution without additional snapshot cost by averaging uncorrelated PSD estimates obtained using a set of K orthogonal tapers. This paper proposes the multitapered Min processor to achieve unambiguous PSD estimates with desirable variance properties for passive beamforming scenarios. The probability density function and the first two moments of the MT-Min processor's PSD estimate are derived in closed-form for spatially white Gaussian processes. Simulations verify the variance reduction predicted by the analytical derivation for white processes and, by extension, for non-white processes. The multitaper method is then extended to an ad hoc mixture of Min and Product processors under constant noise plateau normalization that attenuates the spurious peaks occurring in the CSA PSD estimates in the presence of multiple planewave arrivals.