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

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 sys...

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Main Authors: Álvaro F. Vaquero, Juan Córcoles
Format: Article
Language:English
Published: MDPI AG 2025-05-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/11/1796
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author Álvaro F. Vaquero
Juan Córcoles
author_facet Álvaro F. Vaquero
Juan Córcoles
author_sort Álvaro F. Vaquero
collection DOAJ
description 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.
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spelling doaj-art-dff77e5f479b4684b9ba5e99d47a11e62025-08-20T03:11:32ZengMDPI AGMathematics2227-73902025-05-011311179610.3390/math13111796Convex Formulations for Antenna Array Pattern Optimization Through Linear, Quadratic, and Second-Order Cone ProgrammingÁlvaro F. Vaquero0Juan Córcoles1Department of Mathematics, Group of Signal Theory and Communications, Universidad de Oviedo, 33203 Gijón, SpainApplied Electromagnetics Group, Information Processing and Telecommunications Center, Escuela Técnica Superior de Ingenieros de Telecomunicación, Universidad Politécnica de Madrid, 28040 Madrid, SpainThis 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.https://www.mdpi.com/2227-7390/13/11/1796array pattern optimizationconvex optimizationlinear programmingquadratic programmingsecond-order cone programming
spellingShingle Álvaro F. Vaquero
Juan Córcoles
Convex Formulations for Antenna Array Pattern Optimization Through Linear, Quadratic, and Second-Order Cone Programming
Mathematics
array pattern optimization
convex optimization
linear programming
quadratic programming
second-order cone programming
title Convex Formulations for Antenna Array Pattern Optimization Through Linear, Quadratic, and Second-Order Cone Programming
title_full Convex Formulations for Antenna Array Pattern Optimization Through Linear, Quadratic, and Second-Order Cone Programming
title_fullStr Convex Formulations for Antenna Array Pattern Optimization Through Linear, Quadratic, and Second-Order Cone Programming
title_full_unstemmed Convex Formulations for Antenna Array Pattern Optimization Through Linear, Quadratic, and Second-Order Cone Programming
title_short Convex Formulations for Antenna Array Pattern Optimization Through Linear, Quadratic, and Second-Order Cone Programming
title_sort convex formulations for antenna array pattern optimization through linear quadratic and second order cone programming
topic array pattern optimization
convex optimization
linear programming
quadratic programming
second-order cone programming
url https://www.mdpi.com/2227-7390/13/11/1796
work_keys_str_mv AT alvarofvaquero convexformulationsforantennaarraypatternoptimizationthroughlinearquadraticandsecondorderconeprogramming
AT juancorcoles convexformulationsforantennaarraypatternoptimizationthroughlinearquadraticandsecondorderconeprogramming