Robust Adaptive Beamforming with Improved Interferences Suppression and a New Steering Vector Estimation Based on Spatial Power Spectrum

  • Saeed MohammadzadehEmail author
  • Osman Kukrer


In this paper, a new robust adaptive beamforming algorithm is proposed with increased attenuation of interference signals. This is achieved by reconstructing the interference-plus-noise covariance matrix using the Capon spatial power estimator. In the latter the total sample covariance matrix is replaced by its square, which is shown to enhance the interference rejection capability of the minimum variance distortionless response beamformer. Also, a new method for estimating the desired signal’s steering vector is introduced based on reconstructing the desired signal’s covariance matrix and employing the discrete Fourier transform of the correlation sequence. The effectiveness of the proposed method is demonstrated by numerical results.


Discrete Fourier transform Robust adaptive beamforming Signal covariance matrix Spatial power spectrum 



  1. 1.
    O. Besson, F. Vincent, P. Stoica, A.B. Gershman, Approximate maximum likelihood estimators for array processing in multiplicative noise environments. IEEE Trans. Signal Process. 48(9), 2506–2518 (2000)zbMATHGoogle Scholar
  2. 2.
    J. Capon, High resolution frequency wavenumber spectrum analysis. Proc. IEEE 57(8), 1408–1418 (1969)Google Scholar
  3. 3.
    F. Chen, F. Shen, J. Song, Robust adaptive beamforming using low-complexity correlation coefficient calculation algorithms. IET Electron. Lett. 51(6), 443–445 (2015)Google Scholar
  4. 4.
    H. Cox, R. Zeskind, M. Owen, Robust adaptive beamforming. IEEE Trans. Acoust. Speech Signal Process. 35(10), 1365–1376 (1987)Google Scholar
  5. 5.
    L. Du, J. Li, P. Stoica, Fully automatic computation of diagonal loading levels for robust adaptive beamforming. IEEE Trans. Signal Process. 46(1), 449–458 (2010)Google Scholar
  6. 6.
    A. Elnashar, S.M. Elnoubi, H.A. ElMikati, Further study on robust adaptive beamforming with optimum diagonal loading. IEEE Trans. Signal Process. 54(12), 3647–3658 (2006)Google Scholar
  7. 7.
    M.H. Er, B. Ng, A new approach to robust beamforming in the presence of steering vector errors. IEEE Trans. Signal Process. 42(7), 1826–1829 (1994)Google Scholar
  8. 8.
    D.D. Feldman, L.J. Griffiths, A projection approach for robust adaptive beamforming. IEEE Trans. Signal Process. 42(4), 867–876 (1994)Google Scholar
  9. 9.
    A.B. Gershman, E. Nemeth, J.F. Bohme, Experimental performance of adaptive beamforming in a sonar environment with a towed array and moving interfering sources. IEEE Trans. Signal Process. 48(1), 246–250 (2000)Google Scholar
  10. 10.
    J. Goldberg, H. Messer, Inherent limitations in the localization of a coherently scattered source. IEEE Trans. Signal Process. 46(12), 3441–3444 (1998)Google Scholar
  11. 11.
    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)MathSciNetzbMATHGoogle Scholar
  12. 12.
    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)Google Scholar
  13. 13.
    Y. Hua, A.B. Gershman, Q. Cheng, High-Resolution and Robust Signal Processing (Marcel Dekker, New York, 2003)Google Scholar
  14. 14.
    F. Huang, W. Sheng, X. Ma, Modified projection approach for robust adaptive array beamforming. Signal Process. 92(7), 1758–1763 (2012)Google Scholar
  15. 15.
    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)Google Scholar
  16. 16.
    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)MathSciNetzbMATHGoogle Scholar
  17. 17.
    O. Kukrer, S. Mohammadzadeh, Generalised loading algorithm for adaptive beamforming in ULAs. IET Electron. Lett. 50(13), 910–912 (2014)Google Scholar
  18. 18.
    C.C. Lee, J.H. Lee, Eigenspace-based adaptive array beamforming with robust capabilities. IEEE Trans. Signal Process. 45(12), 1711–1716 (1997)Google Scholar
  19. 19.
    X. Mestre, M.A. Lagunas, Finite sample size effect on minimum variance beamformers: optimum diagonal loading factor for large arrays. IEEE Trans. Signal Process. 54(1), 69–82 (2006)zbMATHGoogle Scholar
  20. 20.
    S. Mohammadzadeh, O. Kukrer, Adaptive beamforming based on theoretical interference-plus-noise covariance and direction-of-arrival estimation. IET Signal Process. 12(7), 819–823 (2018)Google Scholar
  21. 21.
    S. Mohammadzadeh, O. Kukrer, Modified robust capon beamforming with approximate orthogonal projection onto the signal-plus-interference subspace. Circuits Syst. Signal Process. 37(12), 5351–5368 (2018)MathSciNetGoogle Scholar
  22. 22.
    V. Pisarenko, On the estimation of spectra by means of non-linear functions of the covariance matrix. Geophys. J. Int. 28(5), 11–531 (1972)zbMATHGoogle Scholar
  23. 23.
    P. Stoica, O. Besson, A.B. Gershman, Direction-of-arrival estimation of an amplitude-distorted wavefront. IEEE Trans. Signal Process. 49(2), 269–276 (2001)Google Scholar
  24. 24.
    P. Stoica, R.L. Moses, Spectral analysis of signals, in Parametric Methods for Line Spectra, ed. by T. Robbins (Prentice Hall, New Jersey, 2005), pp. 159–163Google Scholar
  25. 25.
    H. Van Trees, Detection, Estimation, and Modulation Theory-Part IV Optimum Array Processing (Wiley, New York, 2002)Google Scholar
  26. 26.
    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)Google Scholar
  27. 27.
    S.A. Vorobyov, A.B. Gershman, K.M. Wong, Maximum likelihood direction-of-arrival estimation in unknown noise fields using sparse sensor arrays. IEEE Trans. Signal Process. 53(1), 34–43 (2005)MathSciNetzbMATHGoogle Scholar
  28. 28.
    J. Xie, H. Li, Z. He, C. Li, A robust adaptive beamforming method based on the matrix reconstruction against a large DOA mismatch. EURASIP J. Adv. Signal Process. (2014). Google Scholar
  29. 29.
    X. Yuan, L. Gan, Robust adaptive beamforming via a novel subspace method for interference covariance matrix reconstruction. Signal Process. 130, 233–242 (2017)Google Scholar
  30. 30.
    Y. Zhang, Y. Li, M. Gao, Robust adaptive beamforming based on the effectiveness of reconstruction. Signal Process. 120, 572–579 (2016)Google Scholar
  31. 31.
    C. Zhou, Z. Shi, Y. Gu, Coprime array adaptive beamforming with enhanced degrees-of-freedom capability, in IEEE Conference (Radar, Seattle, 2017), pp. 1357–1361Google Scholar
  32. 32.
    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)Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Electrical and Electronics DepartmentEastern Mediterranean Universityvia mersin 10Turkey

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