Spatial power spectral estimation using coprime sensor array with the min processor

Abstract

A coprime sensor array (CSA) commonly estimates the spatial power spectral density (PSD) of the observed signal by multiplying one conventionally beamformed subarray scanned response with the complex conjugate of the other [Vaidyanathan and Pal, 2011]. This product processor removes the CSA subarray spatial aliasing ambiguities, but has a peak sidelobe higher than the peak sidelobe of a fully populated uniform linear array (ULA) [Adhikari et al., 2014]. Moreover, the resulting spatial PSD estimate is not guaranteed positive semi-definite, and as a result, weak sources can be masked by the negative side lobes of strong interferers. This paper proposes choosing the minimum between the two CSA subarray periodograms at each bearing to resolve the spatial aliasing ambiguities. This min processor achieves lower peak sidelobe height and total sidelobe area than the product processor and preserves the PSD positive semi-definite characteristic. Closed-form expressions for the first two moments of the CSA min PSD estimator are available. Simulations and real data show that the min processor achieves a lower PSD estimate variance than the product processor while keeping the PSD estimate approximately unbiased. [Work supported by ONR BRC Program.]