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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MDPI AG
2025-05-01
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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. |
| format | Article |
| id | doaj-art-dff77e5f479b4684b9ba5e99d47a11e6 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| 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 |