Multibeam Directivity Maximization for Overlapped Subarrayed Array via Alternate Convex Programming

The synthesis of an overlapped phased array with low sidelobe levels and high multibeam directivity is addressed using alternate convex programming. First, the beamforming and directivity expressions for the overlapped subarray are derived by defining both the subarray weight matrix and the superarray weight matrix. On this basis, a two-variable optimization problem is established and then decomposed into two single-variable subproblems. Next, the nonconvex constraints on directivity are relaxed and reformulated as linear constraints. Following these steps, satisfactory subarray weights and superarray weights can be obtained by alternatively solving the single-variable optimization problems using convex programming. The effectiveness of the proposed method is verified by comparison with state-of-the-art methods.