Optimal Narrow Beam Low Sidelobe Synthesis for Arbitrary Arrays

The classical narrow main beam and low sidelobe synthesis problem is addressed and extended to arbitrary sidelobe envelopes in both one and two dimensional scenarios. The proposed approach allows also to handle arbitrary arrays. This extended basic synthesis problem is first rewritten as a convex optimization problem. This problem is then transformed into either a linear program or a second order cone program that can be solved efficiently by readily available software. The convex formulation is not strictly equivalent to the initial synthesis problem but arguments are given that establish that the obtained optimum is either identical or can be made as close as wanted to the desired one. Finally, numerical applications and a comparison with a classical solution are presented to both confirm the optimality of the solution and illustrate the potentialities of the proposed approach.