Synthesis of Sparse Arrays With Discrete Phase Constraints via Mixed-Integer Programming

Synthesizing sparse arrays with discrete phase constraints is a critical problem in many applications. In this letter, we present a novel approach for synthesizing sparse arrays with discrete phase constraints using mixed-integer programming (MIP). The proposed approach optimizes both antenna positions and amplitude/phase excitations subject to the given discrete phase constraints. We show that our approach is flexible and can handle various practical constrains, such as minimum spacing constraints between elements, phase-only constraints in reconfigurable arrays. For each scenario, we obtain different MIP formulations, which can be solved using off-the-shelf solvers. Representative simulations are provided to demonstrate the effectiveness and superiority of the proposed method in sparse array synthesis.