Robust Hybrid Algorithm of PSO and SOCP for Grating Lobe Suppression and against Array Manifold Mismatch

Abstract

Based on Particle Swarm Optimization (PSO) and Second-Order Cone Programming (SOCP) algorithm, this paper proposes a hybrid optimization method to suppress the grating lobes of sparse arrays and improve the robustness of array layout. With the peak side-lobe level (PSLL) as the objective function, the paper adopts the particle swarm optimization as a global optimization algorithm to optimize the elements’ positions, the convex optimization as a local optimization algorithm to optimize the elements’ weights. The effectiveness of the grating lobes suppression (as low as -32.13 dB) by this method is illustrated through its application to the sparse linear array when the actual steering vector is known. To enhance the robustness of the optimized array, a rebuilt robust convex optimization model is adopted in the optimization of both array excitations and layout. When the array manifold mismatch error is 1cm, the PSLL by the robust algorithm can be compressed to -27dB, compared to that of -24dB by the ordinary optimization. Results of a set of representative numerical experiments show that the algorithm proposed in this paper can obtain a more robust array layout and matched elements’ weight coefficients to avoid the huge degradation of the array pattern performance in the presence of array manifold mismatch errors. The good performance of pattern synthesis demonstrates the effectiveness of the proposed robust algorithm.