Gaussian Source Detection and Spatial Spectral Estimation Using a Coprime Sensor Array With the Min Processor

Abstract

A coprime sensor array (CSA) interleaves two undersampled uniform linear arrays with coprime undersampling factors and has recently found broad applications in signal detection and estimation. CSAs commonly use the product processor by multiplying the scanned responses of two colinear subarrays to estimate the spatial power spectral density (PSD) of the received signal. This paper proposes a new CSA processor, the CSAmin processor, which chooses the minimum between the two CSA subarray periodograms at each bearing to estimate the spatial PSD. The proposed CSAmin processor resolves the CSA subarray spatial aliasing equally well as the product processor. For an extended aperture CSA, the CSAmin reduces the peak sidelobe height and total sidelobe area over the product processor for the same CSA geometry. Moreover, unlike the PSD estimate from the product processor, the PSD estimate from the CSAmin is guaranteed to be positive semidefinite. This paper derives the probability density function, the complementary cumulative distribution function (CCDF, or tail distribution), and the first two moments of the CSAmin PSD estimator in closed form for Gaussian sources in white Gaussian noise. Numerical simulations verify the derived CSAmin statistics and demonstrate that the CSAmin improves the performance over the product processor in detecting narrowband Gaussian sources in the presence of loud interferers and noise. The CSAmin spatial PSD estimate achieves lower variance than the product processor estimate, and keeps the PSD estimate unbiased for white Gaussian processes and asymptotically unbiased for nonwhite Gaussian processes.