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Robust Beamforming Based on Steering Vector and Covariance Matrix Estimation

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Abstract

In this paper, a novel robust design algorithm based on estimation of signal steering vector and covariance matrix is developed. The theoretical covariance matrix is first estimated via the shrinkage method. Subsequently, the desired signal steering vector is estimated based on maximizing array output power under the correlation coefficient constraint and norm constraint. The original nonconvex quadratic programming problem, whose relaxation is tight through analyzing the hidden convexity properties, can be solved by the relaxed semidefinite programming method. Moreover, the interference-plus-noise covariance matrix is estimated with the corrected steering vector and the subspace theorem, whose efficiency is analytically proven. Numerical experiments show that the proposed algorithm has the advantages of high efficiency and accuracy.

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Notes

  1. In this work, we assume that the interference is neither close to nor in the mainlobe beam region of the array [19].

  2. Here, we consider a general homogenized form for the optimization problem \({\mathcal {P}1}\) with an extra variable s. A similar procedure was employed in [1, 13].

  3. Functions \({\mathcal{D}_1}\) and \({\mathcal{D}_2}\) are used to schematize the mapping (formally defined and proved in [1, Theorem 2.3]) between \({\mathbf{A}}^\# \) and a rank-one matrix \({{{\tilde{\mathbf{a}}}}^{\# }} \left( {{{\tilde{\mathbf{a}}}}^{\# }} \right) ^{H}\) for cases where \({\mathrm{rank}}\left( {\mathbf{A}}^\# \right) \ge 3\) and \({\mathrm{rank}}\left( {\mathbf{A}}^\# \right) = 2\), respectively. The MATLAB implementation is provided in http://www1.se.cuhk.edu.hk/~ywhuang/dcmp/paper.html.

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Authors and Affiliations

  1. Electrical Engineering Department, University of Electronic Science and Technology of China, Chengdu, 611731, People’s Republic of China

    Junhui Qian & Zishu He

  2. National Mobile Communications Research Laboratory, Southeast University, Nanjing, 210096, People’s Republic of China

    Ting Liu & Nuo Huang

Authors
  1. Junhui Qian
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  2. Zishu He
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  3. Ting Liu
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  4. Nuo Huang
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Corresponding author

Correspondence to Junhui Qian.

Additional information

This work was supported by the National Natural Science Foundation of China under Grants 61671139 and 61671137, and in part by China Scholarship Council (CSC) under Grant 201606070009.

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Qian, J., He, Z., Liu, T. et al. Robust Beamforming Based on Steering Vector and Covariance Matrix Estimation. Circuits Syst Signal Process 37, 4665–4682 (2018). https://doi.org/10.1007/s00034-018-0766-z

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  • DOI: https://doi.org/10.1007/s00034-018-0766-z

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