Synthesis of Irregular Phased Arrays Subject to Constraint on Directivity via Convex Optimization

The synthesis of irregular phased arrays subject to constraint on directivity is fulfilled by convex optimization. In particular, based on the membership between the antenna elements and subarrays, the dictionary matrix, the resulting sparse excitation vector, and the sparse binary vector are introduced to describe the array pattern and exact tiling of the aperture. Therefore, the synthesis of irregular phased arrays without overlaps and holes satisfying given maximum sidelobe level (SLL) and minimum directivity can be summarized as a mixed integer nonconvex programming problem, where both the subarray tiling configurations and the associated complex excitations are optimized simultaneously. To avoid the nonconvexities, some mathematical transformations in terms of directivity are implemented and the binary sparse vector is relaxed to be a real sparse vector by the minimization of the weighted l
₁
-norm. Consequently, the nonconvex problem is reduced to iterative convex optimization problems, where several convex optimization problems are included and can be efficiently solved using convex optimization solver. The excellent performances of the proposed method are verified by comparing with previously reported methods through several numerical examples.