Skip to main content
SpringerLink
Log in

Autoregressive Power Spectrum-Based Covariance Matrix Reconstruction for Robust Adaptive Beamforming

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

In this paper, a new robust adaptive beamforming method based on the autoregressive (AR) power spectrum is proposed. To improve the robustness of the Capon spectrum, the AR model is applied to realize the desired signal power and interference power estimations, which are used to reconstruct the covariance matrix. Besides, the eigenvalue decomposition is used to remove the redundancy of the reconstructed interference-plus-noise covariance matrix, where the number of interferences is confirmed by the maximum ratio index of the adjacent eigenvalues. Numerical simulations highlight that the proposed method is more robust against some common errors compared with several beamformers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Data Availability

Not applicable.

References

  1. J. Capon, High-resolution frequency-wavenumber spectrum analysis. Proc. IEEE 57(8), 1408–1418 (1969)

    Article  Google Scholar 

  2. F. Dowla, J. Lim, Relationship between likelihood method and autoregressive modeling in multidimensional power spectrum estimation. IEEE Trans. Acoust. Speech Signal Process. 32(5), 1083–1087 (1984)

    Article  Google Scholar 

  3. L. Du, J. Li, P. Stoica, Fully automatic computation of diagonal loading levels for robust adaptive beamforming. IEEE Trans. Aerosp. Electron. Syst. 46(1), 449–458 (2010)

    Article  Google Scholar 

  4. A. Elnashar, S.M. Elnoubi, H.A. El-Mikati, Further study on robust adaptive beamforming with optimum diagonal loading. IEEE Trans. Antennas Propag. 54(12), 3647–3658 (2006)

    Article  Google Scholar 

  5. D.D. Feldman, An analysis of the projection method for robust adaptive beamforming. IEEE Trans. Antennas Propag. 44(7), 1023–1030 (1996)

    Article  Google Scholar 

  6. D.D. Feldman, L.J. Griffiths, A projection approach for robust adaptive beamforming. IEEE Trans. Signal Process. 42(4), 867–876 (1994)

    Article  Google Scholar 

  7. S. Ge, C. Fan, J. Wang, X. Huang, Robust adaptive beamforming based on sparse bayesian learning and covariance matrix reconstruction. IEEE Commun. Lett. 26(8), 1893–1897 (2022)

    Article  Google Scholar 

  8. Grant, M., Boyd, S.: CVX: Matlab Software for Disciplined Convex Programming, version 2.2 (2020)

  9. Y. Gu, N.A. Goodman, S. Hong, Y. Li, Robust adaptive beamforming based on interference covariance matrix sparse reconstruction. Signal Process. 96, 375–381 (2014)

    Article  Google Scholar 

  10. Y. Gu, A. Leshem, Robust adaptive beamforming based on interference covariance matrix reconstruction and steering vector estimation. IEEE Trans. Signal Process. 60(7), 3881–3885 (2012)

    Article  MathSciNet  Google Scholar 

  11. J. Guo, H. Yang, Z. Ye, A novel robust adaptive beamforming algorithm based on subspace orthogonality and projection. IEEE Sens. J. 23, 1–8 (2023)

    Google Scholar 

  12. L. Huang, J. Zhang, X. Xu, Z. Ye, Robust adaptive beamforming with a novel interference-plus-noise covariance matrix reconstruction method. IEEE Trans. Signal Process. 63(7), 1643–1650 (2015)

    Article  MathSciNet  Google Scholar 

  13. W. Jia, W. Jin, S. Zhou, M. Yao, Robust adaptive beamforming based on a new steering vector estimation algorithm. Signal Process. 93(9), 2539–2542 (2013)

    Article  Google Scholar 

  14. A. Khabbazibasmenj, S.A. Vorobyov, A. Hassanien, Robust adaptive beamforming based on steering vector estimation with as little as possible prior information. IEEE Trans. Signal Process. 60(6), 2974–2987 (2012)

    Article  MathSciNet  Google Scholar 

  15. H. Li, J. Geng, J. Xie, Robust adaptive beamforming based on covariance matrix reconstruction with rcb principle. Digit. Signal Process. 127, 103565 (2022)

    Article  Google Scholar 

  16. J. Li, P. Stoica, Z. Wang, On robust capon beamforming and diagonal loading. IEEE Trans. Signal Process. 51(7), 1702–1715 (2003)

    Article  Google Scholar 

  17. J.P. Lie, W. Ser, C.M.S. See, Adaptive uncertainty based iterative robust capon beamformer using steering vector mismatch estimation. IEEE Trans. Signal Process. 59(9), 4483–4488 (2011)

    Article  MathSciNet  Google Scholar 

  18. T. Luo, P. Chen, Z. Cao, L. Zheng, Z. Wang, URGLQ: an efficient covariance matrix reconstruction method for robust adaptive beamforming. IEEE Trans. Aerosp. Electron Syst. (2023). https://doi.org/10.1109/TAES.2023.3263386

  19. L. Marple. High resolution autoregressive spectrum analysis using noise power cancellation, in ICASSP’78. IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 3, pp. 345–348 (1978)

  20. S. Mohammadzadeh, V.H. Nascimento, R.C. de Lamare, O. Kukrer, Maximum entropy-based interference-plus-noise covariance matrix reconstruction for robust adaptive beamforming. IEEE Signal Process. Lett. 27, 845–849 (2020)

    Article  Google Scholar 

  21. F. Shen, F. Chen, J. Song, Robust adaptive beamforming based on steering vector estimation and covariance matrix reconstruction. IEEE Commun. Lett. 19(9), 1636–1639 (2015)

    Article  Google Scholar 

  22. P. Stoica, R.L. Moses et al., Spectral Analysis of Signals (Pearson Prentice Hall, Upper Saddle River, 2005)

    Google Scholar 

  23. S.A. Vorobyov, A.B. Gershman, Z.-Q. Luo, Robust adaptive beamforming using worst-case performance optimization: a solution to the signal mismatch problem. IEEE Trans. Signal Process. 51(2), 313–324 (2003)

    Article  Google Scholar 

  24. H. Yang, L. Dong, Robust adaptive beamforming based on steering vector estimation and interference power correction via subspace orthogonality. Circuits Syst. Signal Process. (2023). https://doi.org/10.1007/s00034-023-02444-w

  25. H. Yang, L. Dong, Robust widely linear beamforming via noncircularity coefficient integration and extended covariance matrix reconstruction. IEEE Sens. J. (2023). https://doi.org/10.1109/JSEN.2023.3307893

  26. H. Yang, P. Wang, Z. Ye, Robust adaptive beamforming via covariance matrix reconstruction and interference power estimation. IEEE Commun. Lett. 25(10), 3394–3397 (2021)

    Article  Google Scholar 

  27. 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 

  28. H. Yang, Z. Ye, Robust adaptive beamforming based on covariance matrix reconstruction via steering vector estimation. IEEE Sens. J. 23(3), 2932–2939 (2023)

    Article  Google Scholar 

  29. Y. Yang, X. Xu, H. Yang, W. Li, Robust adaptive beamforming via covariance matrix reconstruction with diagonal loading on interference sources covariance matrix. Digit. Signal Process. 136, 103977 (2023)

    Article  Google Scholar 

  30. X.-J. Zhang, D.-Z. Feng, W.-K. Nie, S.-Y. Lin, H.-S. Hu, Robust adaptive beamforming algorithm based on damped singular value decomposition regularization. Digit. Signal Process. 122, 103356 (2022)

    Article  Google Scholar 

  31. Z. Zhang, W. Liu, W. Leng, A. Wang, H. Shi, Interference-plus-noise covariance matrix reconstruction via spatial power spectrum sampling for robust adaptive beamforming. IEEE Signal Process. Lett. 23(1), 121–125 (2016)

    Article  Google Scholar 

  32. H. Zheng, C. Zhou, Z. Shi, C. Yan, Joint coprime weights optimization for sub-nyquist tensor beamforming, in 2022 IEEE Radar Conference (RadarConf22), pp. 1–6 (2022)

  33. Z. Zheng, T. Yang, W.Q. Wang, H.C. So, Robust adaptive beamforming via simplified interference power estimation. IEEE Trans. Aerosp. Electron. Syst. 55(6), 3139–3152 (2019)

    Article  Google Scholar 

  34. C. Zhou, Y. Gu, S. He, Z. Shi, A robust and efficient algorithm for coprime array adaptive beamforming. IEEE Trans. Veh. Technol. 67(2), 1099–1112 (2018)

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful to the Associate Editor Jin He and the anonymous reviewers for their useful comments.

Author information

Authors and Affiliations

  1. Department of Electronic Engineering and Information Science, University of Science and Technology of China, Hefei, 230027, Anhui, China

    Huichao Yang

  2. National Engineering Research Center of Speech and Language Information Processing, University of Science and Technology of China, Hefei, 230027, Anhui, China

    Huichao Yang

  3. School of Mechanical Engineering, Southeast University, Nanjing, 210096, Jiangsu, China

    Linjie Dong

Authors
  1. Huichao Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Linjie Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

HY contributed to formal analysis; investigation; methodology; validation; visualization; and writing-original draft. LD contributed to formal analysis; investigation; and writing-original draft.

Corresponding author

Correspondence to Huichao Yang.

Ethics declarations

Conflict of interest

The authors declare no conflicts of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, H., Dong, L. Autoregressive Power Spectrum-Based Covariance Matrix Reconstruction for Robust Adaptive Beamforming. Circuits Syst Signal Process 43, 1157–1174 (2024). https://doi.org/10.1007/s00034-023-02508-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-023-02508-x

Keywords

Search

Navigation