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Wireless Personal Communications

, Volume 109, Issue 4, pp 2289–2303 | Cite as

Differential Game for Distributed Power Control in Device-to-Device Communications Underlaying Cellular Networks

  • Minh-Thuyen Thi
  • Amr Radwan
  • Thong Huynh
  • Won-Joo HwangEmail author
Article
  • 44 Downloads

Abstract

In the formulating of power control for wireless networks, the radio channel is commonly formulated using static models of optimization or game theory. In these models, the optimization programming or static game is played from time point to time point. Therefore, this approach neglects the dynamics of the time-varying channels and assumes the statistical independence between the successive time points. In this paper, we utilize differential equations to model the wireless links, then formulate a differential game for the power control problem in device-to-device (D2D) communications underlaying cellular networks. The game players are the D2D pairs, which manage their transmit power by solving the continuous-time optimal control problems. The time-dependant cost function allows us to optimize the long-term expected cost, instead of point-wise instantaneous cost. We formulate the problem in an affine quadratic form that admits analytical solutions. The unique feedback Nash equilibrium of the game is shown to exist. From a stochastic optimal control algorithm, we design a distributed power control mechanism that converges to the game’s equilibrium. The simulation results show that the proposed approach achieves significant performance improvement compared to the point-wise based approaches.

Keywords

Device-to-device Power control Differential game Optimal control 

Notes

Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MEST) (No. NRF-2016R1A2B1013733).

References

  1. 1.
    Huang, M., Caines, P. E., & Malhamé, R. P. (2004). Uplink power adjustment in wireless communication systems: A stochastic control analysis. IEEE Transactions on Automatic Control, 49(10), 1693–1708.MathSciNetCrossRefGoogle Scholar
  2. 2.
    Charalambous, C. D., Djouadi, S. M., & Denic, S. Z. (2005). Stochastic power control for wireless networks via sdes: Probabilistic QoS measures. IEEE Transactions on Information Theory, 51(12), 4396–4401.MathSciNetCrossRefGoogle Scholar
  3. 3.
    Holliday, T., Goldsmith, A., Glynn, P., & Bambos, N. (2004). Distributed power and admission control for time varying wireless networks. In IEEE global telecommunications conference, 2004 (GLOBECOM’04) (Vol. 2, pp. 768–774).Google Scholar
  4. 4.
    Chamberland, J. F., & Veeravalli, V. V. (2003). Decentralized dynamic power control for cellular CDMA systems. IEEE Transactions on Wireless Communications, 2(3), 549–559.CrossRefGoogle Scholar
  5. 5.
    Mériaux, F., Lasaulce, S., & Tembine, H. (2013). Stochastic differential games and energy-efficient power control. Dynamic Games and Applications, 3(1), 3–23.MathSciNetCrossRefGoogle Scholar
  6. 6.
    Lee, N., Lin, X., Andrews, J. G., & Heath, R. W. (2015). Power control for D2D underlaid cellular networks: Modeling, algorithms, and analysis. IEEE Journal on Selected Areas in Communications, 33(1), 1–13.CrossRefGoogle Scholar
  7. 7.
    Ren, Y., Liu, F., Liu, Z., Wang, C., & Ji, Y. (2015). Power control in D2D-based vehicular communication networks. IEEE Transactions on Vehicular Technology, 64(12), 5547–5562.CrossRefGoogle Scholar
  8. 8.
    Yanfang, X., Yin, R., Han, T., & Guanding, Y. (2014). Dynamic resource allocation for device-to-device communication underlaying cellular networks. International Journal of Communication Systems, 27(10), 2408–2425.CrossRefGoogle Scholar
  9. 9.
    Meshkati, F., Chiang, M., Poor, H. V., & Schwartz, S. C. (2006). A game-theoretic approach to energy-efficient power control in multicarrier CDMA systems. IEEE Journal on Selected Areas in Communications, 24(6), 1115–1129.CrossRefGoogle Scholar
  10. 10.
    Wang, X., Zheng, W., Zhaoming, L., Wen, X., & Li, W. (2016). Dense femtocell networks power self-optimization: An exact potential game approach. International Journal of Communication Systems, 29(1), 16–32. IJCS-13-0930.R1.CrossRefGoogle Scholar
  11. 11.
    Buzzi, S., & Saturnino, D. (2011). A game-theoretic approach to energy-efficient power control and receiver design in cognitive CDMA wireless networks. IEEE Journal of Selected Topics in Signal Processing, 5(1), 137–150.CrossRefGoogle Scholar
  12. 12.
    Chen, X., Hu, R. Q., & Qian, Y. (2014). Distributed resource and power allocation for device-to-device communications underlaying cellular network. In 2014 IEEE global communications conference (pp. 4947–4952).Google Scholar
  13. 13.
    Le Treust, M., & Lasaulce, S. (2010). A repeated game formulation of energy-efficient decentralized power control. IEEE Transactions on Wireless Communications, 9(9), 2860–2869.CrossRefGoogle Scholar
  14. 14.
    Thuc, T. K., Hossain, E., & Tabassum, H. (2015). Downlink power control in two-tier cellular networks with energy-harvesting small cells as stochastic games. IEEE Transactions on Communications, 63(12), 5267–5282.CrossRefGoogle Scholar
  15. 15.
    Semasinghe, P., & Hossain, E. (2015). Downlink power control in self-organizing dense small cells underlaying macrocells: A mean field game. IEEE Transactions on Mobile Computing, 15(2), 350–363.CrossRefGoogle Scholar
  16. 16.
    Huang, M., Caines, P. E., & Malhamé, R. P. (2007). Large-population cost-coupled LQG problems with nonuniform agents: Individual-mass behavior and decentralized \(\varepsilon\)-Nash equilibria. IEEE Transactions on Automatic Control, 52(9), 1560–1571.MathSciNetCrossRefGoogle Scholar
  17. 17.
    Charalambous, C. D., & Menemenlis, N. (1999). Stochastic models for long-term multipath fading channels and their statistical properties. In Proceedings of the 38th IEEE conference on decision and control, 1999 (Vol.  5, pp. 4947–4952). IEEE.Google Scholar
  18. 18.
    Nocedal, J., & Wright, S. (2006). Numerical optimization. Berlin: Springer.zbMATHGoogle Scholar
  19. 19.
    Song, L., Niyato, D., Han, Z., & Hossain, E. (2015). Wireless device-to-device communications and networks. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  20. 20.
    Basar, T., & Olsder, G. J. (1999). Dynamic noncooperative game theory (2nd edn.). Classics in applied mathematics. Society for Industrial and Applied Mathematics.Google Scholar
  21. 21.
    Han, Z. (2012). Game theory in wireless and communication networks: Theory, models, and applications. Cambridge: Cambridge University Press.zbMATHGoogle Scholar
  22. 22.
    Song, H., Jong Yeol, R., Choi, W., & Schober, R. (2015). Joint power and rate control for device-to-device communications in cellular systems. IEEE Transactions on Wireless Communications, 14(10), 5750–5762.CrossRefGoogle Scholar
  23. 23.
    Chiang, M., Hande, P., Lan, T., & Tan, C. W. (2008). Power control in wireless cellular networks. Foundations and Trends® in Networking, 2(4), 381–533.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Information and Communications SystemInje UniversityGimhaeKorea
  2. 2.Department of Electrical EngineeringTokyo University of ScienceKatsushika-kuJapan
  3. 3.Department of Electronic, Telecommunications, Mechanical and Automotive Engineering, HSV-TRCInje UniversityGimhaeKorea

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