Adaptive Beamforming via Desired Signal Robust Removal for Interference-Plus-Noise Covariance Matrix Reconstruction

Abstract

To tackle the problem of the desired signal (DS) steering vector mismatch, especially in the situation of direction-of-arrival error and array perturbations, a robust interference-plus-noise covariance matrix (INCM) reconstruction method based upon DS removal is presented. Unlike previous studies, this paper proposes to remove the DS component from the training data by building a blocking matrix, which is computed as the inverse of the DS-plus-noise covariance matrix (DSNCM). More specifically, to increase the robustness against arbitrary mismatches, the DS steering vector estimated as the prime eigenvector of the DS matrix, which is attained through integrating the Capon spectrum estimator over the annulus uncertainty sets of the mainlobe region in advance, is adopted to give a faithful blocking matrix. After that, utilizing the obtained blocking matrix to process the training data, the quasi INCM is computed indeed. Finally, a precise INCM is reconstructed by projecting the principal components of the quasi INCM onto the aforesaid DSNCM. Numerical simulations have illustrated that the proposed adaptive beamformer can outperform the existing ones and gain almost optimal performance under different scenarios.

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References

  1. 1.

    K.M. Buckley, L.J. Griffths, An adaptive generalized sidelobe canceller with derivative constraints. IEEE Trans. Antennas Propag. 34(3), 311–319 (1986)

    Article  Google Scholar 

  2. 2.

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

    Article  Google Scholar 

  3. 3.

    L. Chang, C.C. Yeh, Performance of DMI and eigenspace-based beamformers. IEEE Trans. Antennas Propag. 40(11), 1336–1347 (1992)

    Article  Google Scholar 

  4. 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. 5.

    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 

  6. 6.

    Y.J. 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)

    MathSciNet  Article  Google Scholar 

  7. 7.

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

    Article  Google Scholar 

  8. 8.

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

    MathSciNet  Article  Google Scholar 

  9. 9.

    N.K. Jablon, Adaptive beamforming with the generalized sidelobe canceller in the presence of array imperfections. IEEE Trans. Antennas Propag. 34(8), 996–1012 (1986)

    Article  Google Scholar 

  10. 10.

    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 

  11. 11.

    Z.H. Li, Y.S. Zhang, Q.C. Ge, Y.D. Guo, Middle subarray interference covariance matrix reconstruction approach for robust adaptive beamforming with mutual coupling. IEEE Commun. Lett. 23(4), 664–667 (2019)

    Article  Google Scholar 

  12. 12.

    B. Liao, S.C. Chan, K.M. Tsui, Recursive steering vector estimation and adaptive beamforming under uncertainties. IEEE Trans. Aerosp. Electron. Syst. 49(1), 489–501 (2013)

    Article  Google Scholar 

  13. 13.

    B. Liao, C.T. Guo, L. Huang, Q. Li, H.S. So, Robust adaptive beamforming with precise main beam control. IEEE Trans. Aerosp. Electron. Syst. 53(1), 345–356 (2017)

    Article  Google Scholar 

  14. 14.

    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)

    MathSciNet  Article  Google Scholar 

  15. 15.

    F.L. Liu, R.Y. Du, J. Wu, Q.P. Zhou, Z.X. Zhang, Y.J. Cheng, Multiple constrained l2-norm minimization algorithm for adaptive beamforming. IEEE Sens. J. 18(15), 6311–6318 (2018)

    Article  Google Scholar 

  16. 16.

    K.W. Lo, Improving performance of real-symmetric adaptive array by signal blocking. IEEE Trans. Aerosp. Electron. Syst. 31(2), 821–830 (1995)

    Article  Google Scholar 

  17. 17.

    S. Mohammadzadeh, S. 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 

  18. 18.

    J.H. Qian, Z.S. He, T. Liu, N. Huang, Robust beamforming based on steering vector and covariance matrix estimation. Circuits Syst. Signal Process. 37, 4665–4682 (2018)

    MathSciNet  Article  Google Scholar 

  19. 19.

    M. Rahmani, M.H. Bastani, S. Shahraini, Two layers beamforming robust against direction-of-arrival mismatch. IET Signal Process. 8(1), 49–58 (2014)

    Article  Google Scholar 

  20. 20.

    I.S. Reed, J.D. Mallett, L.E. Brennan, Rapid convergence rate in adaptive arrays. IEEE Trans. Aerosp. Electron. Syst. 10(6), 853–863 (1974)

    Article  Google Scholar 

  21. 21.

    H. Ruan, R.C. de Lamare, Robust adaptive beamforming based on low-rank and cross-correlation techniques. IEEE Trans. Signal Process. 64(15), 3919–3932 (2016)

    MathSciNet  Article  Google Scholar 

  22. 22.

    P. Stoica, Z. Wang, J. Li, Robust Capon beamforming. IEEE Signal Process. Lett. 10(6), 172–175 (2003)

    Article  Google Scholar 

  23. 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. 24.

    X.P. Yang, Z.A. Zhang, T. Zeng, T. Long, T.K. Sarkar, Mainlobe interference suppression based on eigen-projection processing and covariance matrix reconstruction. IEEE Antennas Wirel. Propag. Lett. 13, 1369–1372 (2014)

    Article  Google Scholar 

  25. 25.

    X.L. 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 

  26. 26.

    X.L. Yuan, L. Gan, Robust algorithm against large look direction error for interference-plus-noise covariance matrix reconstruction. Eletron. Lett. 52(6), 448–450 (2016)

    Article  Google Scholar 

  27. 27.

    M. Zhang, A. Zhang, Q. Yang, Robust adaptive beamforming based on conjugate gradient algorithms. IEEE Trans. Signal Process. 64(22), 6046–6057 (2016)

    MathSciNet  Article  Google Scholar 

  28. 28.

    Y.P. Zhang, Y.J. Lin, M.G. Gao, Robust adaptive beamforming based on the effectiveness of reconstruction. Signal Process. 120, 572–579 (2016)

    Article  Google Scholar 

  29. 29.

    X.J. Zhang, Z.S. He, B. Liao, X.P. Zhang, Z.Y. Cheng, Y.X. Li, A2RC: an accurate array response control algorithm for pattern synthesis. IEEE Trans. Signal Process. 65(7), 1810–1824 (2017)

    MathSciNet  Article  Google Scholar 

  30. 30.

    X.J. Zhang, Z.S. He, B. Liao, X.P. Zhang, W.L. Peng, Robust quasi-adaptive beamforming against direction-of-arrival mismatch. IEEE Trans. Aerosp. Electron. Syst. 54(3), 1197–1207 (2018)

    Article  Google Scholar 

  31. 31.

    Z.Y. Zhang, W. Liu, W. Leng, A.G. Wang, H.P. 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. 32.

    Z. Zheng, W.Q. Wang, H.C. So, Y. Liao, Robust adaptive beamforming using a novel signal power estimation algorithm. Digital Signal Process. 95, 102574 (2019)

    Article  Google Scholar 

  33. 33.

    X.Y. Zhu, X. Xu, Z.F. Ye, Robust adaptive beamforming via subspace for interference covariance matrix reconstruction. Signal Process. 167, 233–242 (2020)

    Article  Google Scholar 

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Correspondence to Pan Zhang.

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Zhang, P., Yang, Z., Jing, G. et al. Adaptive Beamforming via Desired Signal Robust Removal for Interference-Plus-Noise Covariance Matrix Reconstruction. Circuits Syst Signal Process (2020). https://doi.org/10.1007/s00034-020-01481-z

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Keywords

  • Array signal processing
  • Adaptive beamforming
  • INCM reconstruction
  • DS removal
  • Annulus uncertainty set