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Joint Probabilistic Constrained Robust Beamforming and Antenna Selection

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Abstract

A novel method is proposed for joint probabilistic constrained robust beamforming and antenna selection used in cognitive radio networks. Assuming complex Gaussian distributed channel state information errors, the Bernstein-type inequalities are introduced to transform no closed-form probabilistic constrained forms into the deterministic forms. Moreover, the ℓ1-norm is used as the closest convex approximation of ℓ0-norm. Thus the original NP-hard optimal problem can be relaxed as a tractable convex optimization problem. A computationally efficient and near-optimal solution is obtained by an iteratively re-weighted algorithm. Simulations show that the proposed algorithm satisfies the predetermined service levels at relatively small excess transmission power in a number of transmitter reduction scenarios.

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Acknowledgments

This work is supported by the National Nature Science Foundation of China (Nos. U1204611, 61300214 and 61374134), Nature Science Foundation of Henan Province of China (132300410148) and Science and Technology Innovation Team Support Program of Henan Province, China (13IRTSTHN021).

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Authors and Affiliations

  1. Institute of Image Processing and Pattern Recognition, Henan University, Kaifeng, 475001, China

    Yong Jin, Zhentao Hu, Jinwang Yue & Xianxing Liu

Authors
  1. Yong Jin
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  2. Zhentao Hu
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  3. Jinwang Yue
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  4. Xianxing Liu
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Corresponding author

Correspondence to Yong Jin.

Appendix

Appendix

Using Table 3, subject to the each of SU receive-SINR and co-existing PU IT probabilistic constraints, we propose a minimizing transmit-power beamforming algorithm which uses \( L \le N \) antennas. Our algorithm is summarized Table 4.

Table 3 Iteratively re-weighted ℓ1-norm penalty algorithm
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Table 4 Algorithm of joint probabilistic constrains beamforming and antenna selection
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Jin, Y., Hu, Z., Yue, J. et al. Joint Probabilistic Constrained Robust Beamforming and Antenna Selection. Wireless Pers Commun 84, 2385–2396 (2015). https://doi.org/10.1007/s11277-015-2710-x

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  • DOI: https://doi.org/10.1007/s11277-015-2710-x

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