Efficient Pencil Beam Synthesis in 4-D Antenna Arrays Using an Iterative Convex Optimization Algorithm

A novel iterative convex optimization algorithm is proposed for the efficient synthesis of 4-D antenna arrays in this paper. A general nonconvex programming problem in terms of pencil beam synthesis at the center frequency and the suppression of multiple sidebands with different time schemes is first established. In order to decrease the nonconvexity with respect to equivalent excitations, the nonconvex programming problem is then decomposed into a convex optimization problem at the center frequency and a simplified nonconvex optimization problem at sidebands. Based on the optimized results at the center frequency, an iterative convex optimization algorithm that consists in solving a sequence of convex optimization problems is adopted to solve the nonconvex optimization problem efficiently. Because of the introduction of iterative idea and convex optimization, the proposed method achieves a good tradeoff between the optimization time and the optimality of the solution for the synthesis of 4-D antenna arrays of various scales. Numerical examples of uniformly or nonuniformly spaced 4-D antenna arrays are presented to demonstrate the excellent performance of the proposed algorithm in comparison with those of the previously reported methods.