Skip to main content
Log in

Robust Adaptive Beamforming Based on Steering Vector Estimation and Interference Power Correction via Subspace Orthogonality

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

Abstract

To address the issue of performance degradation in the Capon beamformer when the desired signal appears in the training data, the integration operation is introduced for the interference-plus-noise covariance matrix reconstruction, and the steering vector (SV) is estimated by solving a convex optimization problem in some robust adaptive beamforming papers. However, this approach suffers from high computational complexity and is limited by the resolution of the Capon spectrum. In light of this, our paper proposes a novel robust adaptive beamforming method. To overcome the limited resolution of the Capon spectrum, we introduce the multiple signal classification method to acquire the nominal SVs. Subsequently, the SVs are updated based on subspace orthogonality. The proposed method constructs orthogonal components from the nominal SVs to circumvent the convex problem and reduce computational complexity. Additionally, the interference powers are obtained using the Capon spectrum without the noise component via eigenvalue decomposition. This refinement improves the accuracy of the estimated interference powers. Simulation results demonstrate that the proposed method is effective and robust against common mismatch errors.

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

Access this article

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

Instant access to the full article PDF.

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. H. Akaike, A new look at the statistical model identification. IEEE Trans. Autom. Control 19(6), 716–723 (1974)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  3. B.D. Carlson, Covariance matrix estimation errors and diagonal loading in adaptive arrays. IEEE Trans. Aerosp. Electron. Syst. 24(4), 397–401 (1988)

    Article  Google Scholar 

  4. 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 

  5. 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 

  6. 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 

  7. 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 

  8. M. Grant and S. Boyd. CVX: Matlab software for disciplined convex programming, version 2.2. http://cvxr.com/cvx, Jan. 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  MATH  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(11), 12076–12083 (2023)

    Article  Google Scholar 

  12. A. Hassanien, S. Vorobyov, K. Wong, Robust adaptive beamforming using sequential quadratic programming: an iterative solution to the mismatch problem. IEEE Trans. Signal Process. 15, 733–736 (2008)

    Article  Google Scholar 

  13. O. Hu, F. Zheng, and M. Faulkner. Detecting the number of signals using antenna array: a single threshold solution. In ISSPA ’99. Proceedings of the Fifth International Symposium on Signal Processing and its Applications, volume 2, pages 905–908 vol.2, 1999

  14. F. Huang, W. Sheng, X. Ma, Modified projection approach for robust adaptive array beamforming. Signal Process. 92(7), 1758–1763 (2012)

    Article  Google Scholar 

  15. 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  MATH  Google Scholar 

  16. 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 

  17. Y. Li, H. Ma, D. Yu, L. Cheng, Iterative robust capon beamforming. Signal Process. 118, 211–220 (2016)

    Article  Google Scholar 

  18. R.G. Lorenz, S.P. Boyd, Robust minimum variance beamforming. IEEE Trans. Signal Process. 53(5), 1684–1696 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  19. S. Mohammadzadeh, O. Kukrer, Robust adaptive beamforming with improved interferences suppression and a new steering vector estimation based on spatial power spectrum. Circuits Syst. Signal Process. 38, 4162–4179 (2019)

    Article  Google Scholar 

  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. S.E. Nai, W. Ser, Z. Yu, H. Chen, Iterative robust minimum variance beamforming. IEEE Trans. Signal Process. 59(4), 1601–1611 (2011)

    Article  Google Scholar 

  22. J. Qian, Z. He, T. Liu, N. Huang, Robust beamforming based on steering vector and covariance matrix estimation. Circuits Syst. Signal Process. 20, 401–407 (2020)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  24. H. Trees, Optimum Array Processing - Part IV of Detection, Estimation, and Modulation Theory (John Wiley and Sons Inc., New York, 2002)

    Book  Google Scholar 

  25. S.A. Vorobyov, A.B. Gershman, Z. 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 

  26. M. Wax, T. Kailath, Detection of signals by information theoretic criteria. IEEE Trans. Acoust. Speech Signal Process. 33(2), 387–392 (1985)

    Article  MathSciNet  Google Scholar 

  27. 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 

  28. 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 

  29. 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 

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

    Article  Google Scholar 

  31. X. Yuan, L. Gan, Robust adaptive beamforming via a novel subspace method for interference covariance matrix reconstruction. Signal Process. 130, 233–242 (2017)

    Article  Google Scholar 

  32. P. Zhang, Z. Yang, G. Jing, T. Ma, Adaptive beamforming via desired signal robust removal for interference-plus-noise covariance matrix reconstruction. Circuits Syst. Signal Process. 20, 401–407 (2020)

    Google Scholar 

  33. 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 

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

    Article  Google Scholar 

  35. X. Zhu, X. Xu, Z. Ye, Robust adaptive beamforming via subspace for interference covariance matrix reconstruction. Signal Process. 167, 107289.1-107289.10 (2020)

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful to the Associate Editor Prof. Gongping Huang and the anonymous reviewers for their useful comments.

Author information

Authors and Affiliations

Authors

Contributions

HY involved in formal analysis; investigation; methodology; validation; visualization; and writing—original draft. LD involved in formal analysis; investigation; visualization; 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. Robust Adaptive Beamforming Based on Steering Vector Estimation and Interference Power Correction via Subspace Orthogonality. Circuits Syst Signal Process 42, 7315–7334 (2023). https://doi.org/10.1007/s00034-023-02444-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-023-02444-w

Keywords

Navigation