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Joint Beamforming and Power Allocation for Cognitive MIMO Systems Under Imperfect CSI Based on Game Theory

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An Erratum to this article was published on 15 November 2013

Abstract

The problem of joint beamforming and power allocation for cognitive multi-input multi-output systems is studied via game theory. The objective is to maximize the sum utility of secondary users (SUs) subject to the primary user (PU) interference constraint, the transmission power constraint of SUs, and the signal-to-interference-plus-noise ratio (SINR) constraint of each SU. In our earlier work, the problem was formulated as a non-cooperative game under the assumption of perfect channel state information (CSI). Nash equilibrium (NE) is considered as the solution of this game. A distributed algorithm is proposed which can converge to the NE. Due to the limited cooperation between the secondary base station (SBS) and the PU, imperfect CSI between the SBS and the PU is further considered in this work. The problem is formulated as a robust game. As it is difficult to solve the optimization problem in this case, existence of the NE cannot be analyzed. Therefore, convergence property of the sum utility of SUs will be illustrated numerically. Simulation results show that under perfect CSI the proposed algorithm can converge to a locally optimal pair of transmission power vector and beamforming vector, while under imperfect CSI the sum utility of SUs converges with the increase of the transmission power constraint of SUs.

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References

  1. Scutari, G., Palomar, D. P., & Barbarossa, S. (2008). Cognitive MIMO radio. IEEE Signal Processing Magazine, 25(6), 546–592.

    Article  Google Scholar 

  2. Islam, H., Liang, Y., & Hoang, A. T. (2008). Joint power control and beamforming for cognitive radio networks. IEEE Transactions on Wireless Communications, 7(7), 2415–2419.

    Article  Google Scholar 

  3. Zhang, L., Liang, Y., & Xin, Y. (2008). Joint beamforming and power control allocation for multiple access channels in cognitive radio networks. IEEE Journal on Selected Areas in Communications, 26(1), 38–51.

    Article  MATH  Google Scholar 

  4. Wang, F. G., & Wang, W. B. (2010). Sum rate optimization in interference channel of cognitive radio network. IEEE International Conference on Communications.

  5. Jiang, D., Zhang, H., & Yuan, D. (2010). Linear precoding and power allocation in the downlink of cognitive radio networks. IEEE International Conference on Communications, Circuits and Systems.

  6. Li, H., Gai, Y., He, Z., Niu, K., & Wu, W. (2008). Optimal power control game algorithm for cognitive radio networks with multiple interference temperature limits. IEEE Vehicular Technology Conference.

  7. Zhou, P., Yuan, W., Liu, W., & Cheng, W. G. (2008). Joint power and rate control in cognitive radio networks: A game-theoretical approach. IEEE International Conference on Communications.

  8. Scutari, G., & Palomar, D. P. (2010). MIMO cognitive radio: A game theoretical approach. IEEE Transactions on Signal Processing, 58(2), 761–780.

    Article  MathSciNet  Google Scholar 

  9. Zhong, W., Xu, Y. Y., & Tianfield, H. (2011). Game-theoretic opportunistic spectrum sharing strategy selection for cognitive MIMO multiple access channels. IEEE Transactions on Signal Processing, 59(6), 2745–2759.

    Article  MathSciNet  Google Scholar 

  10. Zhang, L., Liang, Y., Xin, Y., & Poor, H. V. (2009). Robust cognitive beamforming with partial channel state information. IEEE Transactions on Wireless Communications, 8(8), 4143–4153.

    Article  Google Scholar 

  11. Zheng, G., Wong, K., & Ottersten, B. (2009). Robust cognitive beamforming with bounded channel uncertainties. IEEE Transactions on Signal Processing, 57(12), 4871–4881.

    Article  MathSciNet  Google Scholar 

  12. Wang, F., & Wang, W. (2010). Robust beamforming and power control for multiuser cognitive radio network. IEEE GLOBECOM.

  13. Shenouda, T. N., & Davidson, M. (2008). On the design of linear transceivers for multiuser systems with channel uncertainty. IEEE Journal on Selected Areas in Communications, 26(6), 1015–1024.

    Article  Google Scholar 

  14. Parsaeefard, S., & Sharafat, A. R. Robust distributed power control in cognitive radio networks. IEEE Transactions on Mobile Computing, published online.

  15. Wang, J., Scutari, G., & Palomar, D. P. (2011). Robust MIMO cognitive radio via game theory. IEEE Transactions on Signal Processing, 59(3), 1183–1201.

    Article  MathSciNet  Google Scholar 

  16. Anandkumar, A. J. G., Anandkumar, A., Lambotharan, S., & Chambers, J. A. (2011). Robust rate-maximization game under bounded channel uncertainty. IEEE Transactions on Vehicular Technology, 60(9), 4471–4486.

    Article  Google Scholar 

  17. Parsaeefard, S., Sharafat, A. R., & van der Schaar, M. (2011). Robust equilibria in additively coupled games in communications networks. IEEE GLOBECOM.

  18. Zhao, F., Li, B., & Chen, H. B. (2012). Joint beamforming and power allocation algorithm for cognitive MIMO systems via game theory. 7th International Conference on Wireless Algorithms, Systems, and Applications (WASA’12).

  19. Hamdi, K., Zhang, W., & Letaief, K. B. (2009). Opportunistic spectrum sharing in cognitive MIMO wireless networks. IEEE Transactions on Wireless Communications, 8(8), 4098–4109.

    Article  Google Scholar 

  20. Niyato, D., & Hossain, E. (2008). Competitive spectrum sharing in cognitive radio networks: A dynamic game approach. IEEE Transactions on Wireless Communications, 7(7), 2651–2660.

    Article  Google Scholar 

  21. Kang, G. H., Fan, X. N., & Zhu, C. P. (2011). Distributed beam-forming and power control in multi-relay underlay cognitive radio networks: A game-theoretical approach. 6th International ICST Conference on CROWNCOM.

  22. Chrisanthopoulou, M., & Tsoukatos, K. P. (2007). Joint beamforming and power control for CDMA uplink throughput maximization. IEEE 18th International Symposium on Personal, Indoor and Mobile Radio, Communications.

  23. Boyd, S., & Vandenberghe, L. (2004). Convex Optimization. Cambridge: Cambridge University Press.

    Book  MATH  Google Scholar 

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Acknowledgments

This research was supported by the National Natural Science Foundation of China (61172055, 61162008), the Guangxi Natural Science Foundation (2013GXNSFGA019004), the Key Project of Chinese Ministry of Education (212131), the Foundation of Department of Education of Guangxi Province (201202ZD045, 201202ZD046), and the Open Research Fund of Guangxi Key Lab of Wireless Wideband Communication & Signal Processing (12103, 12106).

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Authors and Affiliations

  1. Key Laboratory of Cognitive Radio and Information Processing, Ministry of Education, Guilin University of Electronic Technology, Guilin, 541004, China

    Feng Zhao, Bin Li, Hongbin Chen & Xuezhi Lv

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  1. Feng Zhao
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  2. Bin Li
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  3. Hongbin Chen
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  4. Xuezhi Lv
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Correspondence to Hongbin Chen.

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Zhao, F., Li, B., Chen, H. et al. Joint Beamforming and Power Allocation for Cognitive MIMO Systems Under Imperfect CSI Based on Game Theory. Wireless Pers Commun 73, 679–694 (2013). https://doi.org/10.1007/s11277-013-1210-0

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