Novel method for digital beamforming in co‐prime sensor arrays using product and min processors

Abstract

The co-prime sensor array (CSA), obtained by systematically combining two ULAs with increasing inter-sensor spacing, has been recently introduced as an effective sparse configuration in direction of arrival estimation and beamforming applications. Since the inter-sensor spacing is frequently greater than the one-half wavelength, the CSA has the drawback of generating grating lobes in passive beamforming. To mitigate this problem, the authors propose a novel method based on digital beamforming at sub-array level using product and min processors. In this study, the main goal is nulling the grating lobes with known directions using multiplication of virtual and real patterns. Hence, the angular location of the grating lobes in the CSA sub-arrays are analytically extracted and trimmed so that by using new strategies, the grating lobes of the considered sub-array removed by nulls of the other sub-array. The performance of the proposed method in the CSA with N = N 1 + N 2 -1 sensors is compared to a fully populated uniform linear array with M = N 1 N 2 physical sensors. The results of analytical expressions and simulations demonstrate that the power pattern obtained by the proposed method in the CSA is better than the previous methods, so-called product and min processors.