基于差分共阵的降维高效欠定波达角估计

doi:10.12305/j.issn.1001-506X.2026.09.08

系统工程与电子技术 ›› 2026, Vol. 48 ›› Issue (9): 2949-2957.doi: 10.12305/j.issn.1001-506X.2026.09.08

• 传感器与信号处理 • 上一篇

基于差分共阵的降维高效欠定波达角估计

李享¹^,²(), 闫锋刚¹, 孟祥天¹, 曹丙霞¹(), 沙明辉³, 李占国³, 金铭¹

1. 哈尔滨工业大学（威海）信息科学与工程学院，山东威海 264209
2. 哈尔滨工业大学电子与信息工程学院，黑龙江哈尔滨 150001
3. 北京无线电测量研究所，北京 100854

收稿日期:2025-05-28 修回日期:2025-08-18 接受日期:2025-08-20 出版日期:2025-11-24 发布日期:2025-11-24
通讯作者: 曹丙霞 E-mail:lxlixiang_hit@163.com;cbxhit@163.com
作者简介:李　享（1994—），男，博士研究生，主要研究方向为阵列信号处理、阵列结构设计
闫锋刚（1982—），男，教授，博士，主要研究方向为雷达信号处理、反辐射制导
孟祥天（1994—），男，讲师，博士，主要研究方向为阵列信号处理、反辐射制导
沙明辉（1986—），男，研究员，博士，主要研究方向为雷达系统设计、雷达波形优化
李占国（1984—），男，高级工程师，博士，主要研究方向为电子对抗、技术侦察
金　铭（1968—），男，教授，博士，主要研究方向为雷达系统设计、阵列信号处理
基金资助:
国家自然科学基金（62171150）；泰山学者工程专项经费（tsqn202211087）；山东省自然科学基金（ZR2023MF091，ZR2024MF071，ZR2024QF068）；航空科学基金（2023Z037077002）资助课题

Efficient reduced-dimensional underdetermined direction-of-arrival estimation based on difference co-array

Xiang Li¹^,²(), Fenggang Yan¹, Xiangtian Meng¹, Bingxia Cao¹(), Minghui Sha³, Zhanguo Li³, Ming Jin¹

1. School of Information Science and Engineering，Harbin Institute of Technology （Weihai），Weihai 264209，China
2. School of Electronics and Information Engineering，Harbin Institute of Technology，Harbin 150001，China
3. Beijing Institute of Radio Measurement，Beijing 100854，China

Received:2025-05-28 Revised:2025-08-18 Accepted:2025-08-20 Online:2025-11-24 Published:2025-11-24
Contact: Bingxia Cao E-mail:lxlixiang_hit@163.com;cbxhit@163.com

摘要/Abstract

摘要：

针对大孔径稀疏阵列中差分共阵矩阵维度高而引发的计算效率低的问题，提出一种降维高自由度欠定高效波达角估计方法。首先，利用前后向平均方法构造差分共阵实值全对称矩阵，通过理论推导证明了该实值矩阵特征空间与两个降维矩阵特征空间的等效性。在此基础上，提出基于差分共阵的降维半域子空间分解算法，利用降维矩阵特征值分解实现子空间重构，并构造半域谱搜索函数实现欠定超分辨角度估计。理论分析表明，该方法在特征值分解和谱峰搜索过程中大幅降低了计算复杂度。仿真实验表明，所提方法不仅具有与经典空间平滑多重信号分类算法相近的估计精度，还显著提高了计算效率，有效解决了高维矩阵计算复杂度高的问题，为大规模稀疏阵列高效波达角估计提供了可行方案。

关键词: 欠定波达角估计, 稀疏阵列, 降维矩阵, 实值运算

Abstract:

To address the computational inefficiency caused by high-dimensional matrices of the difference co-array in sparse arrays with large apertures, an efficient reduced-dimensional underdetermined direction-of-arrival （DOA） estimation method with enhanced degrees of freedom is proposed. Firstly, a real-valued centrosymmetric difference co-array matrix is constructed using forward/backward averaging method. The equivalence between its eigenspace and those of two reduced-dimensional matrices is theoretically proven. Based on this, a reduced-dimensional half-domain subspace decomposition algorithm based on difference co-array is proposed, which achieves subspace reconstruction through eigenvalue decomposition of reduced-dimensional matrices and constructs a half-domain spectral search function to achieve underdetermined super-resolution angle estimation. Theoretical analysis demonstrates significant computational complexity reduction in both eigenvalue decomposition and spectral peak search stages. Simulation results indicate that the proposed method substantially improves computational efficiency and maintains similar estimation accuracy to conventional spatial smoothing multiple signal classification algorithms. This method addresses the issue of high computational complexity in large matrix, providing an efficient solution for DOA estimation in large sparse arrays.

Key words: underdetermined direction-of-arrival （DOA） estimation, sparse array, reduced-dimensional matrix, real-valued computation

中图分类号:

TN 911.7

李享, 闫锋刚, 孟祥天, 曹丙霞, 沙明辉, 李占国, 金铭. 基于差分共阵的降维高效欠定波达角估计[J]. 系统工程与电子技术, 2026, 48(9): 2949-2957.

Xiang Li, Fenggang Yan, Xiangtian Meng, Bingxia Cao, Minghui Sha, Zhanguo Li, Ming Jin. Efficient reduced-dimensional underdetermined direction-of-arrival estimation based on difference co-array[J]. Systems Engineering and Electronics, 2026, 48(9): 2949-2957.

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算法	计算复杂度
SSMUSIC	$\begin{gathered} 4 \times {O}\left( {{K^2}T} \right) + 4 \times {O}\left( {{L^3}} \right) + 4 \times {O}\left( {J\left( {L + 1} \right)\left( {L - Q} \right)} \right) \end{gathered} $
SSCapon	$\begin{gathered} 4 \times {O}\left( {{K^2}T} \right) + 4 \times {O}\left( {{L^3}} \right) + 4 \times {O}\left( {JL\left( {L + 1} \right)} \right)\end{gathered} $
SSESPRIT	$\begin{gathered} 4 \times {O}\left( {{K^2}T} \right) + 4 \times {O}\left( {{L^3}} \right) + 4 \times {O}\left( {9{Q^3}} \right) \end{gathered} $
RHSD	$\begin{gathered} 4 \times {O}\left( {{K^2}T} \right) + 2 \times {O}\left( {\frac{{{L^3}}}{8}} \right) + {O}\left( {J\left( {L + 1} \right)\left( {L - 2Q} \right)} \right) \end{gathered} $

算法	特征值分解	谱峰搜索	运行时间
SSMUSIC	0.0495	0.0496	0.0991
SSESPRIT	0.0493	—	0.0531
SSCapon	0.0482	0.06	0.1093
RHCSD	0.0085	0.0209	0.0307

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基于差分共阵的降维高效欠定波达角估计

Efficient reduced-dimensional underdetermined direction-of-arrival estimation based on difference co-array

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