Passive beamforming in co-prime sensor arrays using NSCB method under original pattern perturbations minimization

Abstract

The co-prime sensor array (CSA), which is an effective sparse configuration, has the drawback of generating grating lobes in passive beamforming. To mitigate this problem, we propose a novel method based on null synthesis with cancellation beams (NSCBs) under original pattern perturbations minimization. In this paper we regard the grating lobes as interference signals with known directions. Firstly, the angular location of the grating lobes in the CSA subarrays are analytically extracted. Then, using the NSCBs method, the grating lobes of the subarrays nulled by adaptive weighting of the CSA elements. We have also shown that the original pattern perturbations minimization problem in mean square sense reduces to minimizing the perturbation of the array excitation. The proposed method will be formulated as a quadratic optimization problem, which can be efficiently solved using the method of Lagrange multipliers. The analytical and simulated results demonstrate that the power pattern obtained by the proposed method in the CSA, in terms of side lobe levels, peak side lobe ratio and integrated side lobe ratio, is better than the previous methods, so called product and min processors.