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.
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References
H. Akaike, A new look at the statistical model identification. IEEE Trans. Autom. Control 19(6), 716–723 (1974)
J. Capon, High-resolution frequency-wavenumber spectrum analysis. Proc. IEEE 57(8), 1408–1418 (1969)
B.D. Carlson, Covariance matrix estimation errors and diagonal loading in adaptive arrays. IEEE Trans. Aerosp. Electron. Syst. 24(4), 397–401 (1988)
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)
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)
D.D. Feldman, An analysis of the projection method for robust adaptive beamforming. IEEE Trans. Antennas Propag. 44(7), 1023–1030 (1996)
D.D. Feldman, L.J. Griffiths, A projection approach for robust adaptive beamforming. IEEE Trans. Signal Process. 42(4), 867–876 (1994)
M. Grant and S. Boyd. CVX: Matlab software for disciplined convex programming, version 2.2. http://cvxr.com/cvx, Jan. 2020
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)
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)
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)
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)
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
F. Huang, W. Sheng, X. Ma, Modified projection approach for robust adaptive array beamforming. Signal Process. 92(7), 1758–1763 (2012)
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)
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)
Y. Li, H. Ma, D. Yu, L. Cheng, Iterative robust capon beamforming. Signal Process. 118, 211–220 (2016)
R.G. Lorenz, S.P. Boyd, Robust minimum variance beamforming. IEEE Trans. Signal Process. 53(5), 1684–1696 (2005)
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)
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)
S.E. Nai, W. Ser, Z. Yu, H. Chen, Iterative robust minimum variance beamforming. IEEE Trans. Signal Process. 59(4), 1601–1611 (2011)
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)
R. Schmidt, Multiple emitter location and signal parameter estimation. IEEE Trans. Antennas Propag. 34(3), 276–280 (1986)
H. Trees, Optimum Array Processing - Part IV of Detection, Estimation, and Modulation Theory (John Wiley and Sons Inc., New York, 2002)
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)
M. Wax, T. Kailath, Detection of signals by information theoretic criteria. IEEE Trans. Acoust. Speech Signal Process. 33(2), 387–392 (1985)
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)
H. Yang, P. Wang, Z. Ye, Robust adaptive beamforming via covariance matrix reconstruction under colored noise. IEEE Signal Process. Lett. 28, 1759–1763 (2021)
H. Yang, Z. Ye, Robust adaptive beamforming based on covariance matrix reconstruction via steering vector estimation. IEEE Sens. J. 23(3), 2932–2939 (2023)
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)
X. Yuan, L. Gan, Robust adaptive beamforming via a novel subspace method for interference covariance matrix reconstruction. Signal Process. 130, 233–242 (2017)
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)
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)
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)
X. Zhu, X. Xu, Z. Ye, Robust adaptive beamforming via subspace for interference covariance matrix reconstruction. Signal Process. 167, 107289.1-107289.10 (2020)
Acknowledgements
The authors are grateful to the Associate Editor Prof. Gongping Huang and the anonymous reviewers for their useful comments.
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HY involved in formal analysis; investigation; methodology; validation; visualization; and writing—original draft. LD involved in formal analysis; investigation; visualization; and writing—original draft.
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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
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DOI: https://doi.org/10.1007/s00034-023-02444-w