Gaussian signal detection by coprime sensor arrays

Abstract

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 prod uct beamformer suffers from a smaller array gain due to the reduced number of sensors. This paper derives that the condi tional 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 beam former. The Bessel function CSA detection PDFs asymptot ically converge to exponential distributions like the ULA de tection PDFs, revealing that the detection gain of the nonlin ear CSA processor is still proportional to the number of sen sors. Monte Carlo simulations confirm the validity of the an alytic results and the asymptotic approximations to the PDFs.

Detecting Gaussian Signals Using Coprime Sensor Arrays in Spatially Correlated Gaussian Noise

“…The subarrays share sensors, which inherently makes the subarray outputs correlated, even for the case of spatially white noise. The CSA pp output PDF is therefore characterized by the product of two dependent Rayleigh random variables [14], [49],…”

“…Adhikari and Buck assert the noise only correlation coefficient is negligible for large coprime factors M, N > 4 [14]. For white noise as the only input, the correlation coefficient reduces to ρ 0 (0) = 1/ √ MN.…”

“…For the ULA cbf and CSA cbf , the CBF operates on the full array aperture as a single coherent array, and the detector statistic is the power of the CBF output. For the CSA pp , the CBF processes each subarray separately, and the detector statistic is the magnitude of the product of these subarray outputs [14]. CBF is often used in detectors operating in unknown or varying spatially correlated noise environments due to its robustness to mismatch in array elements' locations, gains and phase responses [30].…”

“…Ref. [14] derived the conditional PDFs for the CSA pp detector for signals in spatially white noise, and found that the detection gain asymptotically converges to the number of sensors in the high SNR and large coprime factor limits. Refs.…”

Wideband source enumeration and direction-of-arrival estimation using sparse array periodogram averaging in low snapshot scenarios

“…Note that the proposed wideband source enumeration scheme applies in general to any sparse array geometry with a contiguous region in its difference co-array, such as coprime arrays and nested arrays [3] [4]. For demonstration purposes, we use a MRA with 6 sensors at locations [1,2,5,6,12,14]d. This array offers a contiguous coarray region spanning k ∈ [− 13,13].…”