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

YU Qi; YIN Jiexin; LIU Zhengwu; WANG Ding

doi:10.11999/JEIT250884

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YU Qi, YIN Jiexin, LIU Zhengwu, WANG Ding. A Neural Network-Based Robust Direction Finding Algorithm for Mixed Circular and Non-Circular Signals Under Array Imperfections[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250884

Citation:

YU Qi, YIN Jiexin, LIU Zhengwu, WANG Ding. A Neural Network-Based Robust Direction Finding Algorithm for Mixed Circular and Non-Circular Signals Under Array Imperfections[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250884

Citation:

YU Qi, YIN Jiexin, LIU Zhengwu, WANG Ding. A Neural Network-Based Robust Direction Finding Algorithm for Mixed Circular and Non-Circular Signals Under Array Imperfections[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250884

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

doi: 10.11999/JEIT250884 cstr: 32379.14.JEIT250884

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)

Received Date: 2025-09-09
Accepted Date: 2025-12-01
Rev Recd Date: 2025-11-25

Available Online: 2025-12-09

Abstract

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)

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References(35)

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