Gaussian signal detection by coprime sensor arrays

Coprime sensor arrays (CSAs) achieve the resolution of a fully populated uniform linear array (ULA) with the same aperture using fewer sensors. The conventional CSA product beamformer suffers from a smaller array gain due to the reduced number of sensors. This paper derives that the conditional PDFs for detecting Gaussian signals in spatially white Gaussian noise with the CSA product processor are products of Bessel functions. The resulting ROCs are compared with those of the ULA energy detector for a conventional beamformer. The Bessel function CSA detection PDFs asymptotically converge to exponential distributions like the ULA detection PDFs, revealing that the detection gain of the nonlinear CSA processor is still proportional to the number of sensors. Monte Carlo simulations confirm the validity of the analytic results and the asymptotic approximations to the PDFs.