Synthesis of Large Ultra-wideband Sparse Circular Planar Arrays Based on Rotationally Symmetric Structure
Abstract
:1. Introduction
2. Formulation and Algorithm
2.1. UWB Rotationally Symmetric Sparse Circular Planar Array Synthesis Problem
2.2. Modified Differential Evolution Algorithm (MDEA)
2.2.1. New Encoding Mechanism
2.2.2. Low-Dimensional Evolution Operators
- Mutation: For the individual , the candidate individual can be generated by using the following mutation operator:
- Crossover: In the new encoding mechanism, the variable dimension of the individual is always two. Faced with such a low-dimension individual, we should greatly exploit each dimension to enhance the local search ability of the proposed algorithm. Therefore, for the candidate individual and , a trial individual is generated by the following crossover operator:
- Replacement: When mutation and crossover operators are used, offspring individuals are generated to make up an offspring population To improve the global search ability of the proposed algorithm, each individual in the offspring population will randomly select an individual in the population to replace, and the generated new population is expressed as In particular, the minimum element spacing constraint is considered, thus we need to check the new population whether meets it. If meets this constraint, will compete with the original population .
- Selection: According to the UWB array synthesis problem concerned in this study, the fitness function is set as the PSL of the array pattern at the highest frequency. That is,
2.3. The Proposed MDEA Procedure
Algorithm 1 The proposed MDEA synthesis procedure for large UWB sparse planar array based on the rotationally symmetric structure |
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3. Numerical Experiments
3.1. UWB Sparse Planar Array with 600 Elements and 5:1 Bandwidth
3.2. 2000-Element Square Kilometer Array (SKA) Operating over 70 MHz to 450 MHz
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Liu, F.; Wen, P.; Zhang, C.; Wang, L.; Xu, K. Synthesis of Large Ultra-wideband Sparse Circular Planar Arrays Based on Rotationally Symmetric Structure. Electronics 2023, 12, 4833. https://doi.org/10.3390/electronics12234833
Liu F, Wen P, Zhang C, Wang L, Xu K. Synthesis of Large Ultra-wideband Sparse Circular Planar Arrays Based on Rotationally Symmetric Structure. Electronics. 2023; 12(23):4833. https://doi.org/10.3390/electronics12234833
Chicago/Turabian StyleLiu, Foxiang, Pin Wen, Chaoqun Zhang, Lei Wang, and Kaida Xu. 2023. "Synthesis of Large Ultra-wideband Sparse Circular Planar Arrays Based on Rotationally Symmetric Structure" Electronics 12, no. 23: 4833. https://doi.org/10.3390/electronics12234833
APA StyleLiu, F., Wen, P., Zhang, C., Wang, L., & Xu, K. (2023). Synthesis of Large Ultra-wideband Sparse Circular Planar Arrays Based on Rotationally Symmetric Structure. Electronics, 12(23), 4833. https://doi.org/10.3390/electronics12234833