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An uncertainty-set-shrinkage-based covariance matrix reconstruction algorithm for robust adaptive beamforming

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Abstract

This paper presents an uncertainty-set-shrinkage (USS) algorithm that aims to reconstruct a precise interference-plus-noise covariance matrix (INCM) and improve the performance of adaptive beamformers when steering vector (SV) mismatch exists. Both of the interference covariance matrix (ICM) and the desired signal covariance matrix (DSCM) can be divided into two parts, namely the nominal matrix reconstructed using the nominal SVs and the error matrix consisting of the residual component of the covariance matrix. By using a two-step uncertainty set shrinkage method, the proposed beamformer constructs the error matrices by integrating the estimated spatial spectrum over the shrinked uncertainty set at a cost of low computational complexity. After extracting the principal component of the reconstructed ICM and DSCM, the INCM and the SV of the source of interest (SOI) can be estimated without solving any optimization problem. Both of numerical simulations and experimental results demonstrate that the performance of the proposed algorithm is robust with several categories of SV mismatches.

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References

  • Besson, O., & Stoica, P. (2000). Decoupled estimation of DOA and angular spread for a spatially distributed source. IEEE Transactions on Signal Processing, 48(7), 1872.

    Article  Google Scholar 

  • Capon, J. (1969). High-resolution frequency-wavenumber spectrum analysis. Proceedings of the IEEE, 57(8), 1408.

    Article  Google Scholar 

  • Chen, P., Yang, Y., Wang, Y., & Ma, Y. (2018). Robust adaptive beamforming with sensor position errors using weighted subspace fitting-based covariance matrix reconstruction. Sensors (Basel), 18(5), 1476.

    Article  Google Scholar 

  • Chen, P., Yang, Y., Wang, Y., & Ma, Y. (2019). Adaptive beamforming with sensor position errors using covariance matrix construction based on subspace Bases Transition. IEEE Signal Processing Letters, 26(1), 19.

    Article  Google Scholar 

  • Cox, H., Zeskind, R. M., & Owen, M. M. (1987). Robust adaptive beamforming. IEEE Transactions on Acoustics Speech and Signal Processing, 35(10), 1365.

    Article  Google Scholar 

  • Gershman, A., Sidiropoulos, N., Shahbazpanahi, S., Bengtsson, M., & Ottersten, B. (2010). Convex optimization-based beamforming. IEEE Signal Processing Magazine, 27(3), 62.

    Article  Google Scholar 

  • Gu, Y. J., Goodman, N. A., Hong, S. H., & Li, Y. (2014). Robust adaptive beamforming based on interference covariance matrix sparse reconstruction. Signal Processing, 96, 375.

    Article  Google Scholar 

  • Gu, Y. J., & Leshem, A. (2012). Robust adaptive beamforming based on interference covariance matrix reconstruction and steering vector estimation. IEEE Transactions on Signal Processing, 60(7), 3881.

    Article  MathSciNet  Google Scholar 

  • Huang, L., Zhang, J., Xu, X., & Ye, Z. F. (2015). Robust adaptive beamforming with a novel interference-plus-noise covariance matrix reconstruction method. IEEE Transactions on Signal Processing, 63(7), 1643.

    Article  MathSciNet  Google Scholar 

  • Jian, L., Stoica, P., & Zhisong, W. (2003). On robust Capon beamforming and diagonal loading. IEEE Transactions on Signal Processing, 51(7), 1702.

    Article  Google Scholar 

  • Mallipeddi, R., Lie, J. P., Razul, S. G., Suganthan, P., & See, C. M. (2011). Robust adaptive beamforming based on covariance matrix reconstruction for look direction mismatch. Progress In Electromagnetics Research Letters, 25, 37.

    Article  Google Scholar 

  • Mohammadzadeh, S., & Kukrer, O. (2019). Robust adaptive beamforming with improved interferences suppression and a new steering vector estimation Based on Spatial Power Spectrum. Circuits Systems and Signal Processing, 38(9), 4162.

    Article  Google Scholar 

  • Nai, S. E., Ser, W., Yu, Z. L., & Chen, H. W. (2011). Iterative robust minimum variance beamforming. IEEE Transactions on Signal Processing, 59(4), 1601.

    Article  Google Scholar 

  • Ruan, H., & de Lamare, R. C. (2014). Robust adaptive beamforming using a low-complexity shrinkage-based mismatch estimation algorithm. IEEE Signal Processing Letters, 21(1), 60.

    Article  Google Scholar 

  • Ruan, H., & de Lamare, R. C. (2016). Robust adaptive beamforming based on low-rank and cross-correlation techniques. IEEE Transactions on Signal Processing, 64(15), 3919.

    Article  MathSciNet  Google Scholar 

  • Somasundaram, S. D. (2012). Linearly constrained robust capon beamforming. IEEE Transactions on Signal Processing, 60(11), 5845.

    Article  MathSciNet  Google Scholar 

  • Stoica, P., Zhisong, W., & Jian, L. (2003). Robust Capon beamforming. IEEE Signal Processing Letters, 10(6), 172.

    Article  Google Scholar 

  • Vorobyov, S. A., Chen, H. H., & Gershman, A. B. (2008). On the relationship between robust minimum variance beamformers with probabilistic and worst-case distortionless response constraints. IEEE Transactions on Signal Processing, 56(11), 5719.

    Article  MathSciNet  Google Scholar 

  • Vorobyov, S. A., Gershman, A. B., & Luo, Z. Q. (2003). Robust adaptive beamforming using worst-case performance optimization: A solution to the signal mismatch problem. IEEE Transactions on Signal Processing, 51(2), 313.

    Article  Google Scholar 

  • Wang, Y. S., Bao, Q. L., & Chen, Z. P. (2016). Robust adaptive beamforming using IAA-based interference-plus-noise covariance matrix reconstruction. Electronics Letters, 52(13), 1185.

    Article  Google Scholar 

  • Yan, S., & Hovem, J. M. (2008). Array pattern synthesis with robustness against manifold vectors uncertainty. IEEE Journal of Oceanic Engineering, 33(4), 405.

    Article  Google Scholar 

  • Yuan, X., & Gan, L. (2017). Robust adaptive beamforming via a novel subspace method for interference covariance matrix reconstruction. Signal Processing, 130, 233.

    Article  Google Scholar 

  • Zhang, Z. Y., Liu, W., Leng, W., Wang, A. G., & Shi, H. P. (2016). Interference-plus-noise covariance matrix reconstruction via spatial power spectrum sampling for robust Adaptive Beamforming. IEEE Signal Processing Letters, 23(1), 121.

    Article  Google Scholar 

  • Zheng, Z., Zheng, Y., Wang, W. Q., & Zhang, H. (2018). Covariance matrix reconstruction with interference steering vector and power estimation for robust adaptive Beamforming. IEEE Transactions on Vehicular Technology, 67(9), 8495.

    Article  Google Scholar 

  • Zhou, C., Gu, Y., He, S., & Shi, Z. (2018). A robust and efficient algorithm for coprime array adaptive beamforming. IEEE Transactions on Vehicular Technology, 67(2), 1099.

    Article  Google Scholar 

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Acknowledgements

This work is supported by the China Postdoctoral Science Foundation under Grant 2019M660049XB, and by the Fundamental Research Funds for the Central Universities, CHD under Grant 300102240302.

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Authors and Affiliations

  1. School of Information Engineering, Chang’an University, Xi’an, China

    Peng Chen

  2. School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an, China

    Yixin Yang

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  1. Peng Chen
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  2. Yixin Yang
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Correspondence to Peng Chen.

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Chen, P., Yang, Y. An uncertainty-set-shrinkage-based covariance matrix reconstruction algorithm for robust adaptive beamforming. Multidim Syst Sign Process 32, 263–279 (2021). https://doi.org/10.1007/s11045-020-00737-w

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  • DOI: https://doi.org/10.1007/s11045-020-00737-w

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