Antenna Array Directivity Maximization With Sidelobe Level Constraints Using Convex Optimization

New methods for maximizing the directivities of the array antennas are proposed. First, the array pencil beam (PB) directivity maximization problems without or with sidelobe constraints are formulated as convex optimization problems, which are solved optimally to achieve better optimized directivity results, compared with traditional method with radiation intensity maximization only. Then, to deal with the nonconvexity in the wide beam (WB) directivity maximization problem, a novel iterative directivity optimization method based on Taylor expansion of the quadratic function is proposed, and the original nonconvex problem can be efficiently solved by the convex optimization methods in an iterative way. Finally, a two-stage iterative directivity maximization method is further proposed to deal with the sidelobe constraints in the WB directivity maximization problem. Two initial point schemes for the iterative algorithms are studied in detail with the performance comparisons. The two-stage algorithm can be used to yield very good results, even under very wide beamwidth and strict sidelobe constraint conditions. With the proposed methods, the array directivity maximization problems can be solved by the convex optimization methods in a very efficient way. Several representative examples are presented to demonstrate the excellent performance of the proposed methods.