Page 27 - 《应用声学》2024年第6期

第 43 卷 第 6 期 Vol. 43, No. 6
2024 年 11 月 Journal of Applied Acoustics November, 2024

⋄ 研究报告 ⋄

多项式结构恒定束宽波束形成器的高效

稀疏化设计 ∗

王晓楠 陈华伟 †

(南京航空航天大学电子信息工程学院 南京 211106)
摘要：针对传声器阵列多项式结构波束形成器实现复杂度偏大的问题，提出了一种基于交替方向乘子法的
多项式结构波束形成器稀疏化设计方法。该方法利用主瓣空间响应变化的优化准则以实现恒定束宽波束形
成器设计，并通过将原始的高维非凸问题转化为并行求解的低维凸优化子问题，有效提高了多项式结构波束
形成器的稀疏化效率。实验结果表明，与现有多项式结构波束形成器的稀疏化设计方法相比，所提方法在保
持良好的设计鲁棒性的同时具备了更优的恒定束宽性能。在优化效率方面，所提方法耗时仅为现有方法的
0.69%∼1.09%，并且获得了更高的抽头稀疏度。
关键词：传声器阵列；多项式结构波束形成器；恒定束宽；稀疏化设计；交替方向乘子法
中图法分类号: TN912.3 文献标识码: A 文章编号: 1000-310X(2024)06-1203-16
DOI: 10.11684/j.issn.1000-310X.2024.06.003

Efficient sparse design of polynomial beamformers with

constant-beamwidth

WANG Xiaonan CHEN Huawei

(College of Electronic and information Engineering, Nanjing University of Aeronautics and Astronautics,
Nanjing 211106, China)

Abstract: To address the issue of high computational complexity in implementing polynomial structure beam-
formers for microphone arrays, a sparse design method based on the alternating direction method of multipliers
is proposed. This method utilizes an optimization criterion that considers the mainlobe spatial response vari-
ation to achieve constant-beamwidth beamformer design, and by transforming the original high-dimensional
non-convex problem into parallel solvable low-dimensional convex subproblems, the efficiency of sparse design
for polynomial structure beamformers is significantly improved. Experimental results demonstrate that, com-
pared to existing sparse design methods for polynomial structure beamformers, the proposed method exhibits
better constant-beamwidth performance while maintaining good design robustness. In terms of optimization
efficiency, the proposed method only takes 0.69% to 1.09% of the time required by the existing methods, and
it achieves higher tap sparsity.
Keywords: Microphone arrays; Polynomial beamformers; Constant-beamwidth; Sparse design; Alternating
direction method of multipliers

2023-07-11 收稿; 2023-09-13 定稿
国家自然科学基金项目 (61971219)
∗
作者简介: 王晓楠 (1999– ), 女, 山东临沂人, 硕士研究生, 研究方向: 传感器阵列信号处理和声学信号处理。
通信作者 E-mail: hwchen@nuaa.edu.cn
†