Synthesis of Sparse Antenna Arrays Subject to Constraint on Directivity via Iterative Convex Optimization

An effective optimization method is proposed for the synthesis of sparse antenna arrays subject to constraint on directivity in this letter. Based on the framework of thinned arrays synthesis, a real-value mixed integer programming problem for the minimization of the number of elements under given maximum sidelobe level, scan range, and minimum directivity in a limited array aperture is established. In order to solve this problem efficiently, an iterative convex optimization method is proposed, where the strategies of weighted l
₁
-norm minimization and the polygonal expansion and contraction of the element position are integrated together organically. Owing to the adoption of such two strategies, both the search space regarding the element positions and the convergence speed can be controlled flexibly. Several representative numerical examples are presented in comparison with reported advanced methods to demonstrate the effectiveness of the proposed method.