Aprojected gradient based game theoretic approach for multi-user power control in cognitive radio network

  • Yun-zheng Tao
  • Chun-yan Wu
  • Yu-zhen Huang
  • Ping Zhang


The fifth generation (5G) networks have been envisioned to support the explosive growth of data demand caused by the increasing traditional high-rate mobile users and the expected rise of interconnections between human and things. To accommodate the ever-growing data traffic with scarce spectrum resources, cognitive radio (CR) is considered a promising technology to improve spectrum utilization. We study the power control problem for secondary users in an underlay CR network. Unlike most existing studies which simplify the problem by considering only a single primary user or channel, we investigate a more realistic scenario where multiple primary users share multiple channels with secondary users. We formulate the power control problem as a non-cooperative game with coupled constraints, where the Pareto optimality and achievable total throughput can be obtained by a Nash equilibrium (NE) solution. To achieve NE of the game, we first propose a projected gradient based dynamic model whose equilibrium points are equivalent to the NE of the original game, and then derive a centralized algorithm to solve the problem. Simulation results show that the convergence and effectiveness of our proposed solution, emphasizing the proposed algorithm, are competitive. Moreover, we demonstrate the robustness of our proposed solution as the network size increases.

Key words

Cognitive radio networks Multi-user power control Non-cooperative game Nash equilibrium Projected gradient 

CLC number



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  1. Arrow K, Hurwicz L, Uzawa H, 1961. Constraint qualifications in maximization problems. Nav Res Log Q, 8(2):175–191. MathSciNetCrossRefzbMATHGoogle Scholar
  2. Bedeer E, Dobre O, Ahmed M, et al., 2014. A multiobjective optimization approach for optimal link adaptation of OFDM-based cognitive radio systems with imperfect spectrum sensing. IEEE Trans Wirel Commun, 13(4):2339–2351. CrossRefGoogle Scholar
  3. Goldsmith A, 2005. Wireless Communications. Cambridge University Press, Cambridge, UK.CrossRefGoogle Scholar
  4. Han Z, Niyato D, Basar T, et al., 2012. Game Theory in Wireless and Communication Networks. Cambridge University Press, Cambridge, UK.zbMATHGoogle Scholar
  5. Kolodzy P, 2006. Interference temperature: a metric for dynamic spectrum utilization. Int J Netw Manag, 16(2):103–113. CrossRefGoogle Scholar
  6. Le LB, Hossain E, 2008. Resource allocation for spectrum underlay in cognitive radio networks. IEEE Trans Wirel Commun, 7(12):5306–5315. CrossRefGoogle Scholar
  7. Lin Y, Liu K, Hsieh H, 2010. Design of power control protocols for spectrum sharing in cognitive radio networks: a game-theoretic perspective. IEEE Int Conf on Communications, p.1–6. Google Scholar
  8. Mercier B, Fodor V, Thobaben R, et al., 2008. Sensor networks for cognitive radio: theory and system design. Proc ICT Mobile and Wireless Communications Summit, p.10–17. Google Scholar
  9. Neel J, Reed J, Gilles R, 2004. Convergence of cognitive radio networks. IEEE Wirel Communication and Networking Conf, p.2250–2255. Google Scholar
  10. Rosen J, 1960. The gradient projection method for nonlinear programming. Part I. Linear constraints. J Soc Ind Appl Math, 8(1):181–217. MathSciNetCrossRefzbMATHGoogle Scholar
  11. Rosen J, 1965. Existence and uniqueness of equilibrium points for concave n-person games. Econometrica, 33(3):520–534. MathSciNetCrossRefzbMATHGoogle Scholar
  12. Wang Z, Jiang L, He C, 2013. A novel price-based power control algorithm in cognitive radio networks. IEEE Commun Lett, 17(1):43–46. CrossRefGoogle Scholar
  13. Wild B, Ramchandran K, 2005. Detecting primary receivers for cognitive radio applications. 1st IEEE Int Symp on New Frontiers in Dynamic Spectrum Access Networks, p.124–130. Google Scholar
  14. Wu Y, Tsang D, 2008. Distributed multichannel power allocation algorithm for spectrum sharing cognitive radio networks. IEEE Wireless Communications and Networking Conf, p.1436–1441. Google Scholar
  15. Yang G, Li B, Tan X, et al., 2015. Adaptive power control algorithm in cognitive radio based on game theory. IET Commun, 9(15):1807–1811. CrossRefGoogle Scholar
  16. Zhou P, Chang Y, Copeland J, 2012. Reinforcement learning for repeated power control game in cognitive radio networks. IEEE J Sel Areas Commun, 30(1):54–69. CrossRefGoogle Scholar

Copyright information

© Zhejiang University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Networking and Switching TechnologyBeijing University of Posts and TelecommunicationsBeijingChina
  2. 2.College of Communications EngineeringPLA University of Science and TechnologyNanjingChina

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