Sum and Difference Beams Synthesis for a Sparse Array with a Common Excitation Vector

A method was proposed for generating sum and difference beam patterns simultaneously in a sparse antenna array by utilizing a common excitation vector. This approach was motivated by the challenges in accurately estimating signal arrival direction and the intricate design of feeding network structures. This study formulates a nonconvex optimization problem based on the radiation performance of dual beams, incorporating a nonconvex mainlobe constraint for the sum beam and a nonconvex null depth constraint for the difference beam. The successive convex approximation algorithm is utilized to address these formulated problems. In order to overcome infeasible solutions arising from nonconvex constraints, slack variables are introduced to aid in the pursuit of feasible points. Simulation results demonstrate that the proposed algorithm improves the radiation performance of both sum and difference beam patterns with fewer antennas compared to other algorithms, thus confirming the advantages of the proposed approach.