Synthesis of Modular Subarrayed Phased-Array With Shaped-Beams by Means of Sequential Convex Optimization

In this letter, an efficient method based on sequential convex optimization is proposed to synthesize modular subarrayed phased-arrays with shaped beams. The proposed method consists of two steps. In the first step, the subarray configuration with exact tiling is acquired through solving iterative convex optimization problems. To obtain the arrangement of subarrays with exact tiling, the binary vector sparsity problem is relaxed to be a reweighted
${{\boldsymbol{l}}_1}$
-norm minimization problem which can be solved efficiently by interior point method. In general, there are plenty of exact tiling configurations. To obtain the subarray configuration which is more conductive to radiating the target shaped-beam, the limiting conditions of the shaped-beam are added to the solution process of exact tiling. In the abovementioned solution process, the excitations of the subarrays can be obtained at the same time. However, due to the exact tiling constraints in the solution process, the obtained excitations are usually not the optimal solution for the obtained exact tiling configuration. Therefore, in the second step of the proposed method, the convex optimization method is used again to recompute the excitations of the modular subarrayed phased-array. Two numerical examples are implemented to verify the validity and reliability of the proposed method.