Estimating the spatial spectra of Gaussian processes with co-prime sensor arrays

Abstract

A co-prime sensor array (CSA) is a nonuniform line array formed by interleaving two undersampled uniform line arrays. The CSA requires fewer sensors to span the same aperture as a densely sampled uniform line array (ULA), allowing the CSA to match the resolution of the ULA for direction of arrival estimation of narrowband planewaves. However, each CSA subarray suffers from aliasing, or grating lobes, due to the spatial undersampling. Vaidyanathan and Pal (2011) proved that if the subarray undersampling factors are co-prime, the aliasing can be unambiguously resolved by multiplying the spatial spectra of the subarrays. This product spatial spectra is the spatial cross-spectral density between the arrays, and is an estimate of the spatial power spectral density (PSD). In this talk, we extend the classic results of Jenkins and Watts (1968) on the periodogram PSD estimator for Gaussian processes to obtain the product processor's bias for spatially wide-sense stationary processes, and the processor's covariance for spatially white Gaussians. Additionally, we demonstrate that the CSA's product PSD estimate is not necessarily positive definite. Consequently, the CSA product spectrum may fail to detect weak signals in the presence of strong interferers. [Work supported by ONR BRC Program.]