针对圆和非圆信号混合入射的多特征融合网络鲁棒测向算法

于淇; 尹洁昕; 刘正武; 王鼎

doi:10.11999/JEIT250884

针对圆和非圆信号混合入射的多特征融合网络鲁棒测向算法

doi: 10.11999/JEIT250884 cstr: 32379.14.JEIT250884

中国人民解放军网络空间部队信息工程大学信息系统工程学院河南郑州 450001

基金项目: 国家自然科学基金(No.61901526, No.62171469, No.62071029)，军事科技领域青年人才托举工程(No.2022-JCJQ-QT-028)，河南省优秀青年科学基金(No. 242300421174)

详细信息

作者简介:
于淇：女，硕士生，研究方向为无线电监测与处理

尹洁昕：女，博士，副教授，硕士生导师，研究方向为无线信号定位、阵列信号处理

刘正武：男，硕士生，研究方向为信号智能分析与处理

王鼎：男，博士，教授，博士生导师，研究方向为无线信号定位、阵列信号处理

通讯作者:
尹洁昕　Cindyin0807@163.com

中图分类号: TN911.7
计量
- 文章访问数: 20
- HTML全文浏览量: 10
- PDF下载量: 1
- 被引次数: 0
出版历程
- 收稿日期: 2025-09-09
- 修回日期: 2025-11-25
- 录用日期: 2025-12-01
- 网络出版日期: 2025-12-09

A Neural Network-Based Robust Direction Finding Algorithm for Mixed Circular and Non-Circular Signals Under Array Imperfections

Institute of Information Engineering, Information Engineering University, Zhengzhou, Henan 450001, China

Funds: The National Natural Science Foundation of China (No.61901526, No.62171469, No.62071029), Youth Talent Recruitment Project in the Military Science and Technology Field (No.2022-JCJQ-QT-028), Outstanding Youth Science Foundation of Henan Province (No. 242300421174)

摘要

摘要: 针对阵列误差影响下圆和非圆信号混合入射的波达方向(DOA)估计问题，提出了一种基于改进视觉转换器(ViT)模型的鲁棒测向算法。该算法通过构建六通道类图像输入架构，融合接收信号的协方差矩阵实部、虚部、相位、幅值及非圆扩展特性，利用梯度掩码机制实现核心特征与辅助特征的自适应融合，充分提取并挖掘了非圆信号伪协方差矩阵中蕴含的额外信息；同时改进传统ViT模型结构，增加特征融合及卷积模块，并设计前后双分类标记注意力机制，增强模型对信号的学习能力和适应性。实验结果表明，该算法在低信噪比、圆与非圆信号混合及多种阵列误差共存等复杂场景下，相比于现有方法展现出了更好的鲁棒性和测向精度。此外，该算法对快拍数变化及未知调制类型的信号亦表现出良好的适应性与稳定性，为复杂环境中的波达方向估计提供了一种新的有效方法。
- 波达方向估计 /
- 多类型圆与非圆混合信号 /
- 多种阵列误差 /
- 多特征融合 /
- Vision Transformer模型
Abstract: Objective Direction of Arrival (DOA) estimation faces significant challenges in practical environments characterized by low signal-to-noise ratios (SNR), the coexistence of circular and non-circular signals, and various array imperfections. Traditional subspace algorithms often suffer from model mismatch and performance degradation under these complex conditions. While deep learning offers promising data-driven solutions, effectively leveraging the unique statistical properties of non-circular signals and ensuring robustness against diverse array errors remain critical yet under-explored areas. This study aims to develop a robust DOA estimation algorithm capable of handling mixed signals and array imperfections, thereby enhancing estimation accuracy and reliability in challenging scenarios. Methods This paper proposes a robust DOA estimation algorithm based on an improved Vision Transformer (ViT) model. First, a novel six-channel, image-like input structure is constructed by fusing multiple features derived from the received signal's covariance matrix and pseudo-covariance matrix, including the real part, imaginary part, magnitude, phase, magnitude ratio (for non-circular characteristic), and phase of the pseudo-covariance matrix. A gradient masking mechanism is introduced to adaptively fuse these core and auxiliary features. Second, the traditional ViT architecture is enhanced: the standard patch embedding is replaced with a convolutional layer for better local feature extraction, and a dual-class token attention mechanism (one at the sequence head and one at the tail) is designed to enrich feature representation. The model utilizes a standard Transformer encoder for deep feature learning and ultimately performs DOA estimation via a multi-label classification head. Results and Discussions Extensive simulations were conducted to evaluate the proposed algorithm (6C-ViT) against several benchmarks, including MUSIC, NC-MUSIC, CNN-based (6C-CNN), ResNet-based (6C-ResNet), and MLP-based (6C-MLP) methods. Performance was assessed using Root Mean Square Error (RMSE) and angular estimation error under various conditions.Under single-source scenarios with low SNR and no array errors, the proposed 6C-ViT achieved near-zero RMSE across most angles, particularly in the central region, and demonstrated minimal edge errors (Fig. 2). It maintained the lowest RMSE across the tested SNR range from –20 dB to 15 dB (Fig. 3), showing good generalization even to untrained SNR levels. In dual-source scenarios involving mixed circular and non-circular signals under array errors, 6C-ViT significantly outperformed all competitors, with estimation errors fluctuating minimally around zero, while other methods exhibited larger errors and instabilities, especially at array edges (Fig. 4). Its RMSE decreased consistently with increasing SNR, dropping below 0.1° at high SNR, whereas traditional methods plateaued around 0.4° (Fig. 5). Further tests confirmed 6C-ViT's strong adaptability and robustness. It exhibited superior performance and stability across varying numbers of signal sources (K=1,2,3) and snapshot numbers (from 100 to 2 000), where other methods showed significant performance degradation or instability, particularly at low snapshots or with multiple sources (Fig. 6). When tested with unknown modulation signals (UQPSK with non-circularity rate 0.6 and 64QAM) under array errors, 6C-ViT maintained the lowest RMSE across most angles (Fig. 7), demonstrating excellent generalization capability. Ablation studies (Fig. 8) verified the individual contributions of the proposed six-channel input, gradient masking, convolutional embedding, and dual-class token mechanism, with the complete model delivering the best overall performance. Conclusions The proposed improved ViT-based DOA estimation algorithm demonstrates superior performance and strong robustness in complex scenarios involving mixed circular and non-circular signals, multiple array imperfections, low SNR, and closely spaced sources. By effectively fusing multi-dimensional signal features and leveraging an enhanced Transformer architecture, the algorithm achieves higher estimation accuracy and better generalization across varying signal types, error conditions, snapshot numbers, and noise environments compared to existing subspace and deep learning methods. This work provides an effective solution for reliable DOA estimation in challenging practical settings.
- Direction of Arrival (DOA) estimation /
- Hybrid circular and non-circular signals /
- Multiple array errors /
- Multi-feature fusion /
- Vision Transformer (ViT)

HTML全文

图 1 改进ViT模型架构

下载: 全尺寸图片幻灯片

图 2 各个角度下单个信源入射时算法RMSE分布对比图

下载: 全尺寸图片幻灯片

图 3 单个信源入射时算法RMSE随着信噪比变化对比曲线

下载: 全尺寸图片幻灯片

图 4 阵列误差影响下圆和非圆混合入射各个算法角度估计误差分布图

下载: 全尺寸图片幻灯片

图 5 阵列误差下圆和非圆混合入射算法均方根误差阵列误差下圆和非圆混合入射算法

下载: 全尺寸图片幻灯片

图 6 不同信源数入射条件下各个算法均方根误差随快拍数变化曲线图

下载: 全尺寸图片幻灯片

图 7 未知调制信号入射条件下各个算法RMSE随真实角度变化曲线图

下载: 全尺寸图片幻灯片

图 8 消融实验各个算法RMSE分布对比图

下载: 全尺寸图片幻灯片

表 1 模型超参数选择

参数名称	参数选取	参数名称	参数选取
图像大小	16×16	学习率衰减因子	0.05
卷积核大小	2×2	权重衰减	0.05
卷积核数量	243	Dropout率	0.2
Transformer层数	6	Attention Dropout率	0.2
注意力头数	9	Drop Path率	0.2
MLP扩展比率	4.0	优化器类型	AdamW
训练轮数	120	Adam Beta1	0.9
批量大小	90	Adam Beta2	0.999
初始学习率	3e-4	分类类别数	121

下载: 导出CSV

表 2 算法复杂度对比表

	FLOPs	Params
6C-CNN	9.64987×10⁷	2.81975×10⁷
6C-MLP	2.00198×10⁶	1.00128×10⁶
6C-ResNet	3.65642×10⁷	1.82041×10⁶
6C-ViT	4.82230×10⁸	4.35152×10⁶

下载: 导出CSV

表 3 消融实验对比模型配置表

对比模型编号	配置
Model-A	标准ViT+三通道输入(实部、虚部、相位)
Model-B	标准ViT+六通道输入
Model-C	标准ViT+六通道输入+梯度掩码
Model-D	传统ViT+三通道输入+卷积(CNN)嵌入层
Model-E	传统ViT +三通道输入+前后双分类标记
Ours	传统ViT +六通道输入+梯度掩码+ CNN嵌入层+前后双分类标记

下载: 导出CSV

参考文献(35)

[1]	张小飞, 李建峰, 徐大专, 等. 阵列信号处理及MATLAB实现[M]. 2版. 北京: 电子工业出版社, 2020: 7–11. ZHANG Xiaofei, LI Jianfeng, XU Dazhuan, et al. Array Signal Processing and MATLAB Implementation[M]. 2nd ed. Beijing: Publishing House of Electronics Industry, 2020: 7–11. (查阅网上资料, 未找到对应的英文翻译, 请确认).
[2]	房云飞. 非理想条件下阵列雷达目标参数估计方法研究[D]. [博士论文], 西安电子科技大学, 2023. doi: 10.27389/d.cnki.gxadu.2023.000046. FANG Yunfei. Research on target parameter estimation approaches for array radar under nonideal conditions[D]. [Ph. D. Dissertation], Xidian University, 2023. doi: 10.27389/d.cnki.gxadu.2023.000046.
[3]	刘其有, 何瑞, 施伟. 基于深度学习的波达方向估计方法综述[J]. 中国电子科学研究院学报, 2025, 20(1): 1–9. doi: 10.3969/j.issn.1673-5692.2025.01.001. LIU Qiyou, HE Rui, and SHI Wei. Survey of DOA estimation methods based on deep learning[J]. Journal of CAEIT, 2025, 20(1): 1–9. doi: 10.3969/j.issn.1673-5692.2025.01.001.
[4]	VALLET P, MESTRE X, and LOUBATON P. Performance analysis of an improved MUSIC DoA estimator[J]. IEEE Transactions on Signal Processing, 2015, 63(23): 6407–6422. doi: 10.1109/TSP.2015.2465302.
[5]	YANG Xuan, ZHENG Guimei, and TANG Jun. ESPRIT algorithm for coexistence of circular and noncircular signals in bistatic MIMO radar[C]. 2016 IEEE Radar Conference, Philadelphia, USA, 2016: 1–4. doi: 10.1109/RADAR.2016.7485149.
[6]	黄心月. 超分辨的子空间测向方法研究与稀疏线阵设计[D]. [硕士论文], 中国科学技术大学, 2024. doi: 10.27517/d.cnki.gzkju.2024.002516. HUANG Xinyue. Super-resolution subspace direction of arrival estimation algorithms and sparse linear array design[D]. [Master dissertation], University of Science and Technology of China, 2024. doi: 10.27517/d.cnki.gzkju.2024.002516.
[7]	吴流丽, 苏怀方, 王平, 等. 基于深度学习的阵列信号测向方法综述[J]. 航天电子对抗, 2022, 38(6): 1–6,20. doi: 10.16328/j.htdz8511.2022.06.001. WU Liuli, SU Huaifang, WANG Ping, et al. A survey of array signal direction finding methods based on deep learning[J]. Aerospace Electronic Warfare, 2022, 38(6): 1–6,20. doi: 10.16328/j.htdz8511.2022.06.001.
[8]	HE Guodong, SONG Maozhong, ZHANG Shanshan, et al. GPS sparse multipath signal estimation based on compressive sensing[J]. Wireless Communications and Mobile Computing, 2021, 2021: 5583429. doi: 10.1155/2021/5583429.
[9]	CHOI Y H. Maximum likelihood based direction estimation for noncircular signals[J]. Signal Processing, 2024, 220: 109434. doi: 10.1016/j.sigpro.2024.109434.
[10]	尹洁昕. 基于非圆信号的阵列误差自校正算法研究[D]. [硕士论文], 解放军信息工程大学, 2014. YIN Jiexin. Research on sensor errors auto-calibration algorithms for non-circular signals[D]. [Master dissertation], PLA Information Engineering University, 2014.
[11]	罗大为. 基于非圆信号的高分辨率波达方向估计算法研究[D]. [硕士论文], 中国科学技术大学, 2017. LUO Dawei. High-resolution DOA estimation algorithms for noncircular signals[D]. [Master dissertation], University of Science and Technology of China, 2017.
[12]	CHARGE P, WANG Yide, and SAILLARD J. A root-MUSIC algorithm for non circular sources[C]. 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing, Salt Lake City, USA, 2001: 2985–2988. doi: 10.1109/ICASSP.2001.940276.
[13]	HUANG Z T, LIU Zhangmeng, LIU Jian, et al. Performance analysis of MUSIC for non-circular signals in the presence of mutual coupling[J]. IET Radar, Sonar & Navigation, 2010, 4(5): 703–711. doi: 10.1049/iet-rsn.2009.0003.
[14]	周俐佟. 脉冲噪声下圆与非圆信号共存的DOA估计[D]. [硕士论文], 大连海事大学, 2024. doi: 10.26989/d.cnki.gdlhu.2024.001080. ZHOU Litong. DOA estimation of coexistence of circular and non-circular signals under pulse noise[D]. [Master dissertation], Dalian Maritime University, 2024. doi: 10.26989/d.cnki.gdlhu.2024.001080.
[15]	GAO Feifei, NALLANATHAN A, and WANG Yide. Improved MUSIC under the coexistence of both circular and noncircular sources[J]. IEEE Transactions on Signal Processing, 2008, 56(7): 3033–3038. doi: 10.1109/TSP.2007.916123.
[16]	LIU Aifei, LIAO Guisheng, XU Qing, et al. A circularity-based DOA estimation method under coexistence of noncircular and circular signals[C]. 2012 IEEE International Conference on Acoustics, Speech and Signal Processing, Kyoto, Japan, 2012: 2561–2564. doi: 10.1109/ICASSP.2012.6288439.
[17]	YUE Yaxing, XU Yougen, and LIU Zhiwen. Closed-form two-dimensional DOA and polarization estimation of coexisted circular and noncircular signals[C]. 2021 CIE International Conference on Radar, Haikou, China, 2021: 1556–1560. doi: 10.1109/Radar53847.2021.10028575.
[18]	陈开源, 李嘉琪, 张小飞. 圆与非圆信号混合入射下的低复杂度分布式信源DOA估计算法[J]. 信号处理, 2025, 41(5): 958–966. doi: 10.12466/xhcl.2025.05.014. CHEN Kaiyuan, LI Jiaqi, and ZHANG Xiaofei. A low-complexity DOA estimation algorithm for distributed sources under the coexistence of circular and non-circular sources[J]. Journal of Signal Processing, 2025, 41(5): 958–966. doi: 10.12466/xhcl.2025.05.014.
[19]	ZHANG Xue, ZHENG Zhi, WANG Wenqin, et al. DOA estimation of mixed circular and noncircular sources using nonuniform linear array[J]. IEEE Transactions on Aerospace and Electronic Systems, 2022, 58(6): 5703–5710. doi: 10.1109/TAES.2022.3176602.
[20]	孙友. 圆和非圆混合信号的DOA估计算法研究[D]. [硕士论文], 南京航空航天大学, 2018. doi: 10.27239/d.cnki.gnhhu.2019.000885. SUN You. Research on DOA estimation algorithm for circular and non-circular mixed signals[D]. [Master dissertation], Nanjing University of Aeronautics and Astronautics, 2018. doi: 10.27239/d.cnki.gnhhu.2019.000885.
[21]	郝崇宇. 阵列DOA估计及通道误差校正研究[D]. [硕士论文], 南京信息工程大学, 2023. doi: 10.27248/d.cnki.gnjqc.2023.001621. HAO Chongyu. Research on array DOA estimation and channel error correction[D]. [Master dissertation], Nanjing University of Information Science & Technology, 2023. doi: 10.27248/d.cnki.gnjqc.2023.001621.(查阅网上资料,未找到对应的英文翻译,请确认).
[22]	韩子文. 基于神经网络的阵列误差校准及DOA估计方法研究[D]. [硕士论文], 北京邮电大学, 2023. doi: 10.26969/d.cnki.gbydu.2023.002620. HAN Ziwen. Research on array error calibration and DOA estimation based on neural network[D]. [Master dissertation], Beijing University of Posts and Telecommunications, 2023. doi: 10.26969/d.cnki.gbydu.2023.002620.
[23]	郭宇. 基于神经网络的DOA估计方法研究[D]. [博士论文], 北京邮电大学, 2024. doi: 10.26969/d.cnki.gbydu.2024.000094. GUO Yu. Research on DOA estimation methods based on neural networks[D]. [Ph. D. dissertation], Beijing University of Posts and Telecommunications, 2024. doi: 10.26969/d.cnki.gbydu.2024.000094.
[24]	CHAKRABARTY S and HABETS E A P. Multi-speaker DOA estimation using deep convolutional networks trained with noise signals[J]. IEEE Journal of Selected Topics in Signal Processing, 2019, 13(1): 8–21. doi: 10.1109/JSTSP.2019.2901664.
[25]	PAPAGEORGIOU G K, SELLATHURAI M, and ELDAR Y C. Deep networks for direction-of-arrival estimation in low SNR[J]. IEEE Transactions on Signal Processing, 2021, 69: 3714–3729. doi: 10.1109/TSP.2021.3089927.
[26]	LIU Zhangmeng, ZHANG Chenwei, and YU P S. Direction-of-arrival estimation based on deep neural networks with robustness to array imperfections[J]. IEEE Transactions on Antennas and Propagation, 2018, 66(12): 7315–7327. doi: 10.1109/TAP.2018.2874430.
[27]	XIANG Houhong, CHEN Baixiao, YANG Minglei, et al. Improved direction-of-arrival estimation method based on LSTM neural networks with robustness to array imperfections[J]. Applied Intelligence, 2021, 51(7): 4420–4433. doi: 10.1007/s10489-020-02124-1.
[28]	ZHENG Shilian, YANG Zhuang, SHEN Weiguo, et al. Deep learning-based DOA estimation[J]. IEEE Transactions on Cognitive Communications and Networking, 2024, 10(3): 819–835. doi: 10.1109/TCCN.2024.3360527.
[29]	ANDO D A, KASE Y, NISHIMURA T, et al. Deep neural networks based end-to-end DOA estimation system[J]. IEICE Transactions on Communications, 2023, E106. B(12): 1350–1362. doi: 10.1587/transcom.2023CEP0006.
[30]	LI Jianxiong, SHAO Xingkai, LI Jie, et al. Direction of arrival estimation of array defects based on deep neural network[J]. Circuits, Systems, and Signal Processing, 2022, 41(9): 4906–4927. doi: 10.1007/s00034-022-02011-9.
[31]	CAI Ruiyan, TIAN Quan, and LUO Yang. DOA estimation based on a deep neural network under impulsive noise[J]. Signal, Image and Video Processing, 2024, 18(1): 785–792. doi: 10.1007/s11760-023-02794-7.
[32]	KASE Y, NISHIMURA T, OHGANE T, et al. Accuracy improvement in DOA estimation with deep learning[J]. IEICE Transactions on Communications, 2022, E105. B(5): 588–599. doi: 10.1587/transcom.2021EBT0001.
[33]	SHEN Lingyu, LI Jianfeng, PAN Jingjing, et al. Domain-adaptive direction of arrival (DOA) estimation in complex indoor environments based on convolutional autoencoder and transfer learning[J]. Sensors, 2025, 25(10): 2959. doi: 10.3390/s25102959.
[34]	QIN Yanhua. Deep networks for direction of arrival estimation with sparse prior in low SNR[J]. IEEE Access, 2023, 11: 44637–44648. doi: 10.1109/ACCESS.2023.3273126.
[35]	李玉洁, 马子航, 王艺甫, 等. 视觉Transformer(ViT)发展综述[J]. 计算机科学, 2025, 52(1): 194–209. doi: 10.11896/jsjkx.240600135. LI Yujie, MA Zihang, WANG Yifu, et al. Survey of vision transformers (ViT)[J]. Computer Science, 2025, 52(1): 194–209. doi: 10.11896/jsjkx.240600135.