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Direction of Arrival Estimation of Array Defects Based on Deep Neural Network

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Abstract

For the case where the antenna array has defects, most traditional direction of arrival (DOA) estimation methods are poorly adapted. In this paper, a DOA estimation method based on residual neural networks (ResNets) is introduced to obtain better adaptability to the defects of the antenna array and improve the generalization ability to unknown scenes. The framework of deep neural network mainly includes two parts: spatial classification networks (SCN) and ResNets. Firstly, the received signals are divided into corresponding signal space subregions, this operation can relieve the generalization burden of the ResNet that follows. Then, the output of the SCN is used as the input of several parallel ResNets, and each of ResNet judges whether there are signal components in the preset grid of the corresponding subspace regions. Finally, the results of all ResNets are combined into a spatial spectrum, and a spectrum peak search is performed to obtain the estimated direction of the signal. A large number of simulation results are available to confirm that the proposed method not only has excellent generalization ability, but also has high estimation accuracy under different array defects.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. Abadi et al., "Tensorflow: Large-scale machine learning on heterogeneous distributed systems," [Online]. Available: https://arxiv.org/abs/1603.04467

  2. B. Allen, M. Ghavami, Adaptive array systems: fundamentals and applications (Wiley, Hoboken, NJ, USA, 2005)

    Google Scholar 

  3. S. Chakrabarty, E.A.P. Habets, Multi-speaker DOA estimation using deep convolutional networks trained with noise signals. IEEE J. Selected Top. Signal Process. 13(1), 8–21 (2019)

    Article  Google Scholar 

  4. H. Chen, Y. Bao, W. Ser, Effects of sensor position errors on farfield/nearfield wideband beamformers for microphone arrays. IEEE Sens. J. 15(9), 4812–4825 (2015)

    Article  Google Scholar 

  5. Chen Y, Chang A, Lee HT (2015) Array calibration methods for sensor position and pointing errors. Microwave Opt. Technol. Lett. 26(2), 132–137

  6. A.M. Elbir, Deepmusic: multiple signal classification via deep learning. IEEE Sensors Lett. 4(4), 1–4 (2020)

    Article  Google Scholar 

  7. Y. Gao, D. Hu, Y. Chen, Y. Ma, Gridless 1-b DOA Estimation Exploiting SVM Approach. IEEE Commun. Lett. 21(10), 2210–2213 (2017)

    Article  Google Scholar 

  8. X. Glorot, A. Bordes, Y. Bengio, Deep Sparse Rectifier Neural Networks, in Proceedings of the 14th International Conference on Artificial Intelligence and Statistics (2011), pp. 315–323

  9. K. He, X. Zhang, S. Ren, J. Sun, Deep Residual Learning for Image Recognition. presented at the 2016 IEEE Conference on Computer Vision and Pattern Recognition (2016), pp. 770–778

  10. G. Hinton, R. Salakhutdinov, Reducing the dimensionality of data with neural networks. Science 313(5786), 504–507 (2006)

    Article  MathSciNet  Google Scholar 

  11. B. Hu, M. Liu, F. Yi, H. Song, N. Zhao, DOA robust estimation of echo signals based on deep learning networks with multiple type illuminators of opportunity. IEEE Access. 8(1), 14809–14819 (2020)

    Article  Google Scholar 

  12. H. Huang, Y. Jie, Y. Song, H. Hao, G. Guan, deep learning for super-resolution channel estimation and DOA estimation based massive MIMO system. IEEE Trans. Veh. Technol. 67(9), 8549–8560 (2018)

    Article  Google Scholar 

  13. S. Ioffe, C. Szegedy, Batch normalization: accelerating deep network training by reducing internal covariate shift, in International conference on machine learning, (2015), pp. 448–456

  14. Y. Kase, T. Nishimura, T. Ohgane, Y. Ogawa, Y. Kishiyama, Performance analysis of DOA estimation of two targets using deep learning, in 2019 22nd International Symposium on Wireless Personal Multimedia Communications (2019): IEEE, pp. 1–6

  15. H. Krim, M. Viberg, Two decades of array signal processing research: the parametric approach. IEEE Sig Proc Magazine. 13(4), 67–94 (1996)

    Article  Google Scholar 

  16. R. Levanda, A. Leshem, Adaptive selective sidelobe canceller beamformer with applications to interference mitigation in radio astronomy. IEEE Trans. Signal Process. 61(20), 5063–5074 (2013)

    Article  MathSciNet  Google Scholar 

  17. J. Li, M. Jin, Y. Zheng, G. Liao, L. Lv, Transmit and receive array gain-phase error estimation in bistatic MIMO radar. IEEE Antennas Wirel. Propag. Lett. 14(1), 32–35 (2014)

    Google Scholar 

  18. L. Liu, Y. Wu, Direction of arrival estimation by convex optimization methods with unknown sensor gain and phase. IEEE Access 6(1), 65367–65375 (2018)

    Article  Google Scholar 

  19. Z.M. Liu, F.C. Guo, Azimuth and elevation estimation with rotating long-baseline interferometers. IEEE Trans. Signal Process. 63(9), 2405–2419 (2015)

    Article  MathSciNet  Google Scholar 

  20. Z.M. Liu, C. Zhang, P.S. Yu, Direction-of-arrival estimation based on deep neural networks with robustness to array imperfections. IEEE Trans. Antennas Propag. 66(12), 7315–7327 (2018)

    Article  Google Scholar 

  21. W. Mao, G. Li, X. Xie, Q. Yu, DOA estimation of coherent signals based on direct data domain under unknown mutual coupling. IEEE Antennas Wirel. Propag. Lett. 13(1), 1525–1528 (2014)

    Article  Google Scholar 

  22. U. Nielsen, J. Dall, Direction-of-arrival estimation for radar ice sounding surface clutter suppression. IEEE Trans. Geosci. Remote Sens. 53(9), 5170–5179 (2015)

    Article  Google Scholar 

  23. M. Pastorino, A. Randazzo, A smart antenna system for direction of arrival estimation based on a support vector regression. IEEE Trans. Antennas Propag. 53(7), 2161–2168 (2005)

    Article  Google Scholar 

  24. C. Peng, Y. Yang, W. Yong, Y. Ma, Adaptive beamforming with sensor position errors using covariance matrix construction based on subspace bases transition. IEEE Signal Process. Lett. 26(1), 19–23 (2019)

    Article  Google Scholar 

  25. H. Qiao, P. Pal, On maximum-likelihood methods for localizing more sources than sensors. IEEE Signal Process. Lett. 24(5), 703–706 (2017)

    Article  Google Scholar 

  26. R. Roy, T. Kailath, ESPRIT - Estimation of Signal Parameters via Rotational Invariance Techniques. IEEE Trans. Acoust. Speech Signal Process. 37(7), 984–995 (1989)

    Article  Google Scholar 

  27. R. Schmidt, R.O. Schmidt, Multiple emitter location and signal parameter estimation. IEEE Trans. Antennas Propag. 34(3), 276–280 (1986)

    Article  Google Scholar 

  28. M. Viberg, A.L. Swindlehurst, Analysis of the combined effects of finite samples and model errors on array processing performance. IEEE Trans. Signal Process. 42(11), 3073–3083 (1994)

    Article  Google Scholar 

  29. P. Wang, Y. Kong, X. He, M. Zhang, X. Tan, An improved squirrel search algorithm for maximum likelihood DOA estimation and application for MEMS vector hydrophone array. IEEE Access 7(99), 118343–118358 (2019)

    Article  Google Scholar 

  30. J. Xie, L. Wang, Y. Wang, Efficient real-valued rank reduction algorithm for DOA estimation of noncircular sources under mutual coupling. IEEE Access. 6(1), 64450–64460 (2018)

    Article  Google Scholar 

  31. Z. Yang, D. Wang, B. Yang, F. Wei, Robust Direct position determination against sensor gain and phase errors with the use of calibration sources. Multidimens. Syst. Signal Process. 31(4), 1435–1468 (2020)

    Article  MathSciNet  Google Scholar 

  32. Z. Yang, L. Xie, C. Zhang, Off-grid direction of arrival estimation using sparse Bayesian inference. IEEE Trans. Signal Process. 61(1), 38–43 (2012)

    Article  MathSciNet  Google Scholar 

  33. Y. Zhang, H. Zhao, Failure diagnosis of a uniform linear array in the presence of mutual coupling. IEEE Antennas Wirel. Propag. Lett. 14(1), 1010–1013 (2015)

    Article  Google Scholar 

  34. W. Zhu, M. Zhang, P. Li, C. Wu, Two-dimensional DOA estimation via deep ensemble learning. IEEE Access. 8(1), 124544–124552 (2020)

    Article  Google Scholar 

  35. A.H.E. Zooghby, C.G. Christodoulou, M. Georgiopoulos, A neural network-based smart antenna for multiple source tracking. IEEE Trans. Antennas Propag. 48(5), 768–776 (2000)

    Article  Google Scholar 

  36. Y. Zou, H. Xie, L. Wan, G. Han, A. Li, 2D-DOA and Mutual Coupling Estimation in Vehicle Communication System via Conformal Array. Mobile Information Systems (2015), pp. 1–10

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 51877151, Tianjin Municipal Natural Science Foundation under Grant 18JCZDJC99900 and the Program for Innovative Research Team in University of Tianjin under Grant TD13-5040.

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Correspondence to Jie Li.

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Li, J., Shao, X., Li, J. et al. Direction of Arrival Estimation of Array Defects Based on Deep Neural Network. Circuits Syst Signal Process 41, 4906–4927 (2022). https://doi.org/10.1007/s00034-022-02011-9

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