Convex Formulations for Antenna Array Pattern Optimization Through Linear, Quadratic, and Second-Order Cone Programming

Álvaro F. Vaquero () and Juan Córcoles
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Álvaro F. Vaquero: Department of Mathematics, Group of Signal Theory and Communications, Universidad de Oviedo, 33203 Gijón, Spain
Juan Córcoles: Applied Electromagnetics Group, Information Processing and Telecommunications Center, Escuela Técnica Superior de Ingenieros de Telecomunicación, Universidad Politécnica de Madrid, 28040 Madrid, Spain

Mathematics, 2025, vol. 13, issue 11, 1-25

Abstract: This work presents a comprehensive study on formulations for the radiation pattern design of antenna arrays through convex optimization techniques, with a focus on linear, quadratic, and second-order cone programming. The proposed approaches heavily rely on the construction of Hermitian forms to systematically build convex optimization problems for synthesizing desired beam patterns while including practical constraints such as sidelobe levels (SLLs), maximum directivity, and null placement. By formulating the radiation pattern synthesis problem through a convex formulation, global optimality and computational efficiency are ensured. The paper introduces the mathematical foundations of the proposed methodologies, detailing the structure and benefits of each convex optimization model. Numerical examples demonstrate the effectiveness of the proposed methodologies in achieving high-performance radiation patterns for circular and planar arrays. The results highlight trade-offs between formulation complexity and pattern performance across different optimization models, providing valuable insights for antenna array pattern synthesis. Overall, this work underscores the potential of convex optimization in antenna array pattern synthesis methodologies.

Keywords: array pattern optimization; convex optimization; linear programming; quadratic programming; second-order cone programming (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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