Sum and difference patterns synthesis with common excitation amplitude

This paper focuses on the joint optimization problem of sum and difference patterns with common excitation amplitudes and separate excitation phases. The objective is to reduce the complexity of the antenna system while still maintaining a certain degree-of-freedom (DoF) in synthesizing dual-patterns. The problem is formulated with angular response and common excitation amplitude constraints, making it a nonconvex optimization problem. To address this, we introduce two groups of auxiliary variables to decouple the excitation vector from the complex nonconvex constraints. This allows the original problem to be effectively solved via alternately determining the closed-form solutions for several single-variable optimization subproblems. Additionally, our approach is extended to scenarios involving dynamic range ratio (DRR) reduction, aiming to lower the cost and difficulty of hardware implementation. Theoretical analysis and simulation results are provided to demonstrate that the proposed algorithm can converge to the Karush-Kuhn-Tucker points of the original problem. It is also observed that our approach is capable of generating desired dual-patterns with common excitation amplitudes, regardless of the presence or absence of DRR control.