DOA estimation of array signals based on convolutional sparse autoencoder under sparse prior

Abstract

The application of deep learning to direction of arrival (DOA) estimation is of great significance in the field of array signal processing. The use of deep learning for DOA estimation of vector hydrophone array usually directly inputs the covariance matrix of the signal as the signal feature into the network, but this method has limitations such as high data requirements and high computational complexity. This paper proposes a DOA estimation method for vector hydrophone array based on a convolutional sparse autoencoder under sparse prior conditions. This method adds an L1 norm regularization term to the convolutional layer of a convolutional autoencoder to achieve sparsity constraints, and establishes a convolutional sparse autoencoder. At the same time, a residual compensation mechanism is introduced to avoid overfitting and loss of details during the training process. Subsequently, the columns of the signal covariance matrix of the vector hydrophone array are treated as under-sampled noisy linear measurements of the spatial spectrum, and are input into a convolutional sparse autoencoder for feature extraction and reconstruction. Finally, the obtained features are used as inputs for training a convolutional neural network to achieve multi-source DOA estimation. Furthermore, to address the shortcomings of classification methods in off-grid situations, we propose a DOA regression estimation method based on the convolutional sparse autoencoder. The simulation results show that under complex conditions such as low signal-to-noise ratio and a small number of snapshots, the classification method proposed in this paper outperforms various deep learning algorithms and traditional algorithms mentioned in the literature in terms of estimation performance. In addition, the proposed regression method can further improve the DOA estimation performance in off-grid scenarios.

Keywords

vector hydrophone array / direction of arrival estimation / sparse representation / convolutional sparse autoencoder / L1-norm regularization / regression

Acknowledgement

This work was supported by the National Natural Science Foundation of China (No. 61774137) and the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Province (No. 20240011).

Declaration of conflicting interests

The authors have no conflict of interests related to this publication.

References

[1] WEN F Q, SHI J P, GUI G, et al. Joint DOD and DOA estimation for NLOS target using IRS-aided bistatic MIMO radar. IEEE Transactions on Vehicular Technology, 2024, 73(10): 15798-15802.

[2] TIAN Y, FENG Y, LIU W, et al. Reconfigurable intelligent surface aided DOA estimation by a single receiving antenna. IEEE Transactions on Communications, 2025, 73(2): 983-994.

[3] NIU R Z, ZHANG Z Y. Harmonic frequency enhanced direction of arrival estimation using non-uniform linear arrays. IEEE Access, 2024, 12: 36942-36950.

[4] BARTLETT M S. Properties of sufficiency and statistical tests. Proceedings of the Royal Society of London Series A, Mathematical and Physical Sciences, 1937, 160(901): 268-282.

[5] SCHMIDT R. Multiple emitter location and signal parameter estimation. IEEE Transactions on Antennas and Propagation, 1986, 34(3): 276-280.

[6] ROY R, PAULRAJ A, KAILATH T. ESPRIT: a subspace rotation approach to estimation of parameters of cisoids in noise. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1986, 34(5): 1340-1342.

[7] MERKOFER J P, REVACH G, SHLEZINGER N, et al. DA-MUSIC: data-driven DoA estimation via deep augmented MUSIC algorithm. IEEE Transactions on Vehicular Technology, 2024, 73(2): 2771-2785.

[8] LI J Z, YANG G L, REN X Q, et al. Modified ESPRIT and unitary-transformation form for computationally efficient DOA estimation on FPGA. IEEE Transactions on Instrumentation and Measurement, 2025, 74: 2003209.

[9] ZISKIND I, WAX M. Maximum likelihood localization of multiple sources by alternating projection. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1988, 36(10): 1553-1560.

[10] MEI Z Q, LI X, LI H F, et al. Optimization algorithm for DOA estimation accuracy of coherent signal sources based on sparse Bayesian theory. Signal, Image and Video Processing, 2025, 19(3): 249.

[11] LIU Y J, CHEN H X, WANG B. DOA estimation based on CNN for underwater acoustic array. Applied Acoustics, 2021, 172: 107594.

[12] PAPAGEORGIOU G K, SELLATHURAI M, ELDAR Y C. Deep networks for direction-of-arrival estimation in low SNR. IEEE Transactions on Signal Processing, 2021, 69: 3714-3729.

[13] REN J, TAN X H, BAI Y P, et al. Vector hydrophone DOA estimation method based on Complex⁃Valued convolutional denoising autoencoder denoising. Journal of Test and Measurement Technology, 2025, 39(4): 475-482.

[14] QIN Y H. Residual neural network for direction-of-arrival estimation of multiple targets in low SNR. IET Signal Processing, 2024, 2024(1): 4599954.

[15] ZHENG S L, YANG Z, SHEN W G, et al. Deep learning-based DOA estimation. IEEE Transactions on Cognitive Communications and Networking, 2024, 10(3): 819-835.

[16] DAI J S, XU X, ZHAO D A. Direction-of-arrival estimation via real-valued sparse representation. IEEE Antennas and Wireless Propagation Letters, 2013, 12: 376-379.

[17] LIU Z M, HUANG Z T, ZHOU Y Y. Sparsity-inducing direction finding for narrowband and wideband signals based on array covariance vectors. IEEE Transactions on Wireless Communications, 2013, 12(8): 1-12.

[18] BECK A, TEBOULLE M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences, 2009, 2(1): 183-202.

[19] WU L L, LIU Z M, HUANG Z T. Deep convolution network for direction of arrival estimation with sparse prior. IEEE Signal Processing Letters, 2019, 26(11): 1688-1692.

[20] QIN Y H. Deep networks for direction of arrival estimation with sparse prior in low SNR. IEEE Access, 2023, 11: 44637-44648.

[21] RUMELHART D E, HINTON G E, WILLIAMS R J. Learning representations by back-propagating errors. Nature, 1986, 323(6088): 533-536.

[22] LI J M, ZHANG J, BAH M J, et al. An auto-encoder with genetic algorithm for high dimensional data: towards accurate and interpretable outlier detection. Algorithms, 2022, 15(11): 429.

[23] MASCI J, MEIER U, CIREŞAN D, et al. Stacked convolutional auto-encoders for hierarchical feature extraction//Artificial Neural Networks and Machine Learning-ICANN 2011. Berlin, Heidelberg: Springer, 2011: 52-59.

[24] EFRON B, HASTIE T, JOHNSTONE I, et al. Least angle regression. The Annals of Statistics, 2004, 32(2): 407-451.

[25] HE K M, ZHANG X Y, REN S Q, et al. Deep residual learning for image recognition//2016 IEEE Conference on Computer Vision and Pattern Recognition, June 27-30, 2016, Las Vegas, NV, USA. New York: IEEE, 2016: 770-778.

[26] AICH A, PALANISAMY P. On-grid DOA estimation method using orthogonal matching pursuit//2017 International Conference on Signal Processing and Communication, July 28-29, 2017, Coimbatore, India. New York: IEEE, 2018: 483-487.