Processor dependent bias of spatial spectral estimates from coprime sensor arrays.

Abstract

Coprime sensor arrays (CSAs) can estimate the directions of arrival of O(MN) narrowband plane wave sources using only O(M+N) sensors with the CSA product processor. Processing data from a finite aperture array effectively smears the true spatial power spectral density (PSD) with a kernel function determined by both the array geometry and the processing of the signals observed by the array. This paper examines the asymptotic behaviors of the kernel functions resulting from two different processors applied to a CSA sampling geometry in the limit of large aperture. The kernel functions of the product processed CSA and conventionally beamformed coprime sensor arrays (CBF CSA) are compared to the baseline of the kernel of a densely populated uniform line array (ULA) of similar aperture. At the limit of large aperture, the product processed CSA estimate is asymptotically unbiased like the ULA, while the CBF CSA estimate is not. The PSD estimates computed from the CSA processors are compared when spatially correlated Gaussian noise is an input to the array to highlight the bias issues.