Synthesis of Linear and Planar Arrays Via Sequential Convex Optimizations

In this paper, an iterative procedure for the synthesis of sparse arrays radiating focused beampattern is presented. The proposed approach provides a significant reduction in the complexity of the beam forming network, which is fulfilled by reducing the number of antenna elements in the array. An iterative scheme is used where the prescribed pattern response in the mainlobe is cast as a multi-convex problem at each step that the nonconvex lower bound constraint is relaxed while including a reweighted l
₁
-norm minimization based on the magnitudes of the elements. Thus, a sparse array with fewer elements (compared to other methods) and a better performance of beam pattern (e.g., narrower 3-dB beamwidth, lower maximum sidelobe level) is produced. The resulting sparse array is able to generate a steerable pencil beam, matching a given power mask and avoid to constraint the fitting of any a priori defined reference beam pattern. The practical array imperfections are also compensated in the optimization stage by using worst-case performance optimization technique. Examples concerning the design of linear and planar arrays show relevant savings of array elements with respect to conventional array techniques.