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

• Published in: IEEE antennas and wireless propagation letters Vol. 23; no. 3; pp. 1030 - 1034
• Main Authors: Xia, Dongnan, Zhang, Xuejing
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Convex functions; Discrete phase constraint; Integer programming; Linear programming; Mixed integer; mixed-integer programming (MIP); Mutual coupling; phase-only reconfigurable array; Phased arrays; Programming; Quantization (signal); Radar antennas; sparse array synthesis; Sparse matrices; Synthesis
• ISSN: 1536-1225; 1548-5757
• DOI: 10.1109/LAWP.2023.3342143

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.