一种嵌套K-means聚类的任意形状波束子阵划分方法

张清河; 李宇航; 沈钊阳; 文方青

doi:10.12263/DZXB.20231119

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一种嵌套K-means聚类的任意形状波束子阵划分方法

学术论文 | 更新时间：2025-12-08

- 一种嵌套K-means聚类的任意形状波束子阵划分方法
- A K-means-Based Nested Subarray Partition Method for Generating Arbitrary Shaped Beam Patterns
- 电子学报 2025年53卷第1期页码：119-127
- 作者机构：
  
  1.水电工程智能视觉监测湖北省重点实验室（三峡大学），湖北宜昌 443002
  2.三峡大学计算机与信息学院，湖北宜昌 443002
- 作者简介：
  
  [ "张清河男，1969年11月出生于湖北省当阳市.现为三峡大学计算机与信息学院教授、硕士生导师.主要研究方向为电磁散射与逆散射、微波成像、天线设计与综合、阵列信号处理等." ]
  [ "李宇航男，2000年6月出生于湖北省襄阳市.现为三峡大学计算机与信息学院硕士研究生.主要研究方向为子阵划分. E-mail: 1437567029@qq.com" ]
- 基金信息：
  
  国家自然科学基金(62371271)
- DOI：10.12263/DZXB.20231119
  中图分类号： TN91;
- 收稿：2023-12-01，
  
  修回：2024-07-14，
  
  纸质出版：2025-01-25
- 稿件说明：
移动端阅览
张清河, 李宇航, 沈钊阳, 等. 一种嵌套K-means聚类的任意形状波束子阵划分方法[J]. 电子学报, 2025, 53(01): 119-127.

ZHANG Qing-he, LI Yu-hang, SHEN Zhao-yang, et al. A K-means-Based Nested Subarray Partition Method for Generating Arbitrary Shaped Beam Patterns[J]. Acta Electronica Sinica, 2025, 53(01): 119-127.
张清河, 李宇航, 沈钊阳, 等. 一种嵌套K-means聚类的任意形状波束子阵划分方法[J]. 电子学报, 2025, 53(01): 119-127. DOI：10.12263/DZXB.20231119

ZHANG Qing-he, LI Yu-hang, SHEN Zhao-yang, et al. A K-means-Based Nested Subarray Partition Method for Generating Arbitrary Shaped Beam Patterns[J]. Acta Electronica Sinica, 2025, 53(01): 119-127. DOI：10.12263/DZXB.20231119

摘要

传统相控阵由于其高昂成本的限制，已经无法满足日益增长的广泛应用需求，而基于稀疏阵、子阵等技术的非传统相控阵技术则得到了广泛的关注和研究.如何有效地划分子阵，以及如何优化子阵的计算过程，是提高计算效率和性能的关键问题.本文提出一种融合群智能优化算法及聚类技术的嵌套迭代优化方法来解决任意形状波束子阵划分问题.该方法包含内、外两个嵌套循环迭代优化过程：（i）外循环采用群智能优化方法来实现用户定义任意方向图下的参考阵列，并利用谢昆诺夫多项式和基本代数理论分析得到多组不同的阵列单元复激励（由阵因子多项式分布在非谢昆诺夫单位圆上的根所决定）；（ii）内循环基于激励匹配策略，专注于通过K-means聚类方法实现阵列天线的最优子阵布局及相应的子阵复激励系数，并最终产生一个逼近参考阵列的波束方向图.通过与传统K-means聚类方法、粒子群优化方法在方向图逼近、激励匹配误差、模式匹配误差、阵列性能参数及计算效率等方面的比较，验证了所提方法的有效性.

Abstract

Traditional phased arrays

due to their high cost limitations

are no longer able to meet the growing demand for widespread applications. However

non-traditional phased array technologies based on sparse arrays

subarrays

and other technologies have received widespread attention and research. How to effectively draw molecular arrays and optimize the calculation process of sub arrays are key issues in improving computational efficiency and performance. This article proposes a nested iterative optimization method that integrates swarm intelligence optimization and clustering techniques to solve the problem of arbitrary shaped beam subarray partitioning. This method consists of two nested loop iterative optimization processes: (i) The outer loop uses swarm intelligence optimization method to achieve a reference array under any user-defined directional pattern

and analyzes multiple sets of different unit excitations (determined by the roots of the Shekunov polynomial distributed on a non unit circle) using Shekunov polynomial and basic algebraic theory; (ii) Based on the excitation matching strategy

the inner loop aims to achieve the optimal subarray layout and corresponding subarray excitation coefficients of the phased array through K-means clustering method

and ultimately generate a beam pattern that approximates the reference array. The effectiveness of the proposed method was verified by comparing it with traditional K-means clustering methods and particle swarm optimization methods in terms of pattern approximation

excitation matching error

pattern matching error

array performance parameters

and computational efficiency.

关键词

Keywords

references

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