Statistical characterization of coprime sensor arrays: Array gain vs. spatially correlated noise

Abstract

Sensor arrays suppress spatially-uncorrelated noise through conventional beamforming (CBF). Array Gain (AG) quantifies the SNR improvement at the CBF output compared to the sensor-level SNR. The AG for a CBF Uniform Line Array (ULA) in uncorrelated noise is the number of sensors. A Coprime Sensor Array (CSA) is a sparse array geometry interleaving two undersampled ULAs, multiplying the subarray CBF outputs to achieve the same resolution as a fully populated ULA of the same aperture using fewer sensors [Vaidyanathan & Pal, 2010]. The CSA product process AG in uncorrelated noise is asymptotically equal to the number of sensors for large input SNR [Adhikari & Buck, 2015]. This research derives the AGs for CSAs and ULAs using the traditional SNR definition and deflection statistics [Cox, 1973] for a spatial first-order autoregressive process. This process introduces spatial correlation and is a simple model for turbulent flow noise over a towed array. Although the CSA AG is lower than the ULA for uncorrelated noise, the CSA's AG degrades more slowly than the ULA's AG with increasing noise correlation, due to larger spacing in the CSA subarrays. The CSA is more robust to correlated noise than the ULA AG. [Funded by NUWC & ONR.]