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\(l_0\) Norm Constraint Bayesian Strategy for Direction-of-Arrival Estimation

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Abstract

Recent research on sparse signal reconstruction (SSR) shows that the sparse Bayesian learning (SBL) method is one of the most popular methods for direction-of-arrival (DOA) estimation. However, the high computational complexity and the time-consuming iterations in the Bayesian learning make the SBL-based methods difficult in practical applications. To address this problem, the iterative process in the SBL method is improved in this paper. Inspired by the spatial sparsity of the signal variance, an \(l_0\) norm constraint Bayesian strategy for DOA estimation is proposed. An additional \(l_0\) norm penalty is integrated into the objective function of the signal variance vector to achieve zero attraction. With a few user-adjusted parameters, the proposed strategy achieves a faster implementation while inheriting the superior performance of the SBL method for DOA estimation. Numerical simulations demonstrate that the proposed strategy can significantly improve the convergence rate and accelerate the iterative process. The innovative work increases the possibility of real-time implementation.

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Data Availability Statement

All data included in this study are available upon request by contact with the corresponding author.

References

  1. H. Bai, M.F. Duarte, R. Janaswamy, Direction of arrival estimation for complex sources through L1 norm sparse Bayesian learning. IEEE Signal Process. Lett. 26(5), 765–769 (2019)

    Article  Google Scholar 

  2. M. Chen, X. Mao, C. Zhao, Direct localization of emitters based on sparse Bayesian learning. IEEE Trans. Veh. Technol. 68(6), 5769–5781 (2019)

    Article  Google Scholar 

  3. P. Chen, Z. Cao, Z. Chen et al., Off-grid DOA estimation using sparse Bayesian learning in MIMO radar with unknown mutual coupling. IEEE Trans. Signal Process. 67(1), 208–220 (2019)

    Article  MathSciNet  Google Scholar 

  4. J. Dai, X. Bao, W. Xu et al., Root sparse Bayesian learning for off-grid DOA estimation. IEEE Signal Process. Lett. 24(1), 46–50 (2017)

    Article  Google Scholar 

  5. A. Das, Real-valued sparse Bayesian learning for off-grid direction-of-arrival (DOA) estimation in ocean acoustics. IEEE J. Ocean. Eng. 46(1), 172–182 (2021)

    Article  Google Scholar 

  6. H. Ge, L. Wang, J. Wen et al., An RIP condition for exact support recovery with covariance-assisted matching pursuit. IEEE Signal Process. Lett. 26(3), 520–524 (2019)

    Article  Google Scholar 

  7. Y. Gu, J. Jin, S. Mei, \(l_0\) Norm constraint LMS algorithm for sparse system identification. IEEE Signal Process. Lett. 16(9), 774–777 (2009)

    Article  Google Scholar 

  8. D.A. Harville, Maximum likelihood approaches to variance component estimation and to related problems. J. Am. Stat. Assoc. 72(358), 320–338 (1977)

    Article  MathSciNet  Google Scholar 

  9. Z. He, X. Yuan, L. Chen, Super-resolution channel estimation for massive MIMO via clustered sparse Bayesian learning. IEEE Trans. Veh. Technol. 68(6), 6156–6160 (2019)

    Article  Google Scholar 

  10. K. Huang, Z. Yang, Robust sparse Bayesian learning for sparse signal recovery under unknown noise distributions. Circuits Syst. Signal Process. 40, 1365–1382 (2021)

    Article  Google Scholar 

  11. Y. Huang, Z. Zheng, Difference coarray-based direction finding via covariance fitting. IEEE Commun. Lett. 25(8), 2569–2573 (2021)

    Article  Google Scholar 

  12. J. Kim, J. Wang, B. Shim, Nearly optimal restricted isometry condition for rank aware order recursive matching pursuit. IEEE Trans. Signal Process. 67(17), 4449–4463 (2019)

    Article  MathSciNet  Google Scholar 

  13. P. Li, J. Li, Q. Zhang et al., A DOA estimation method for UCA based on orthogonal subspace compensation. IEEE Commun. Lett. 14(8), 3267–3271 (2021)

    Google Scholar 

  14. T. Long, J. Chen, G. Huang et al., Acoustic source localization based on geometric projection in reverberant and noisy environments. IEEE J. Sel. Top. Signal Process. 13(1), 143–155 (2019)

    Article  Google Scholar 

  15. D. Malioutov, M. Cetin, A.S. Willsky, A sparse signal reconstruction perspective for source localization with sensor arrays. IEEE Trans. Signal Process. 53(8), 3010–3022 (2005)

    Article  MathSciNet  Google Scholar 

  16. E. Michael, Tipping, sparse Bayesian learning and the relevance vector machine. J. Mach. Learn. Res. 1(3), 211–244 (2001)

    MathSciNet  MATH  Google Scholar 

  17. D.P. Wipf, B.D. Rao, An empirical Bayesian strategy for solving the simultaneous sparse approximation problem. IEEE Trans. Signal Process. 55(7), 3704–3716 (2007)

    Article  MathSciNet  Google Scholar 

  18. D.P. Wipf, B.D. Rao, Sparse Bayesian learning for basis selection. IEEE Trans. Signal Process. 52(8), 2153–2164 (2004)

    Article  MathSciNet  Google Scholar 

  19. H. Yang, P. Wang, Z. Ye, Robust adaptive beamforming via covariance matrix reconstruction under colored noise. IEEE Signal Process. Lett. 28, 1759–1763 (2021)

    Article  Google Scholar 

  20. J. Yang, Y. Yang, Sparse bayesian DOA estimation using hierarchical synthesis lasso priors for off-grid signals. IEEE Trans. Signal Process. 68, 872–884 (2020)

    Article  MathSciNet  Google Scholar 

  21. J. Yang, Y. Yang, J. Lu, A variational Bayesian strategy for solving the DOA estimation problem in sparse array. Digit. Signal Prog. 90, 28–35 (2019)

    Article  MathSciNet  Google Scholar 

  22. Z. Yang, L. Xie, C. Zhang, Off-grid direction of arrival estimation using sparse Bayesian inference. IEEE Trans. Signal Process. 61(1), 38–43 (2013)

    Article  MathSciNet  Google Scholar 

  23. R. Zdunek, A. Cichocki, Improved M-FOCUSS algorithm with overlapping blocks for locally smooth sparse signals. IEEE Trans. Signal Process. 56(10), 4752–4761 (2008)

    Article  MathSciNet  Google Scholar 

  24. Z. Zhang, B.D. Rao, Sparse signal recovery with temporally correlated source vectors using sparse Bayesian learning. IEEE J. Sel. Top. Signal Process. 5(5), 912–926 (2011)

    Article  Google Scholar 

  25. J. Zhao, R. Gui, X. Dong, PHD filtering for multi-source DOA tracking with extended co-prime array: an improved MUSIC pseudo-likelihood. IEEE Commun. Lett. 25(10), 3267–3271 (2021)

    Article  Google Scholar 

  26. Z. Zheng, Y. Huang, W.-Q. Wang et al., Augmented covariance matrix reconstruction for DOA estimation using difference coarray. IEEE Trans. Signal Process. 69, 5345–5358 (2021)

    Article  MathSciNet  Google Scholar 

  27. Z. Zheng, Y. Huang, W.-Q. Wang et al., Direction-of-arrival estimation of coherent signals via coprime array interpolation. IEEE Signal Process. Lett. 27(1), 585–589 (2020)

    Article  Google Scholar 

  28. T. Zhou, J. Huang, W. Du et al., 2-D Deconvolved conventional beamforming for a planar array. Circuits Syst. Signal Process. 40, 5572–5593 (2021)

    Article  Google Scholar 

  29. H. Zhu, G. Leus, G.B. Giannakis, Sparsity-cognizant total least-squares for perturbed compressive sampling. IEEE Trans. Signal Process. 59(5), 2002–2016 (2011)

    Article  MathSciNet  Google Scholar 

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Funding

The research of this project was supported by the National Key R & D Program of China (2016YFC1400101) and National Defense Basic Scientific Research Project (JCKY2019604B001)

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Authors and Affiliations

  1. Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin, 150001, China

    Guolong Liang, Chenmu Li, Longhao Qiu, Nan Zou & Jin Fu

  2. Academy of Military Science of the People’s Liberation Army National Innovation Institute of Defence, Beijing, 100091, China

    Chenmu Li, Nan Zou, Tongsheng Shen & Jin Fu

  3. Ministry of Industry and Information Technology, Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Harbin, 150001, China

    Guolong Liang, Chenmu Li, Longhao Qiu & Nan Zou

  4. College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin, 150001, China

    Guolong Liang, Chenmu Li, Longhao Qiu, Nan Zou & Jin Fu

  5. Qingdao Haina Underwater Information Technology Co., Ltd., Qingdao, 266400, China

    Guolong Liang, Longhao Qiu, Nan Zou & Jin Fu

Authors
  1. Guolong Liang
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  2. Chenmu Li
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  3. Longhao Qiu
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  4. Nan Zou
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  5. Tongsheng Shen
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  6. Jin Fu
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Correspondence to Longhao Qiu.

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The research of this project was supported by the National Key R & D Program of China (2016YFC1400101) and National Defense Basic Scientific Research Project (JCKY2019604B001).

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Liang, G., Li, C., Qiu, L. et al. \(l_0\) Norm Constraint Bayesian Strategy for Direction-of-Arrival Estimation. Circuits Syst Signal Process 41, 4028–4040 (2022). https://doi.org/10.1007/s00034-022-01972-1

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  • DOI: https://doi.org/10.1007/s00034-022-01972-1

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