Open Access

Stochastic Power Control for Time-Varying Long-Term Fading Wireless Networks

  • Mohammed M. Olama1Email author,
  • Seddik M. Djouadi1 and
  • Charalambos D. Charalambous2
EURASIP Journal on Advances in Signal Processing20062006:089864

https://doi.org/10.1155/ASP/2006/89864

Received: 1 June 2005

Accepted: 7 April 2006

Published: 29 June 2006

Abstract

A new time-varying (TV) long-term fading (LTF) channel model which captures both the space and time variations of wireless systems is developed. The proposed TV LTF model is based on a stochastic differential equation driven by Brownian motion. This model is more realistic than the static models usually encountered in the literature. It allows viewing the wireless channel as a dynamical system, thus enabling well-developed tools of adaptive and nonadaptive estimation and identification techniques to be applied to this class of problems. In contrast with the traditional models, the statistics of the proposed model are shown to be TV, but converge in steady state to their static counterparts. Moreover, optimal power control algorithms (PCAs) based on the new model are proposed. A centralized PCA is shown to reduce to a simple linear programming problem if predictable power control strategies (PPCS) are used. In addition, an iterative distributed stochastic PCA is used to solve for the optimization problem using stochastic approximations. The latter solely requires each mobile to know its received signal-to-interference ratio. Generalizations of the power control problem based on convex optimization techniques are provided if PPCS are not assumed. Numerical results show that there are potentially large gains to be achieved by using TV stochastic models, and the distributed stochastic PCA provides better power stability and consumption than the distributed deterministic PCA.

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Authors’ Affiliations

(1)
Department of Electrical and Computer Engineering, University of Tennessee
(2)
Department of Electrical and Computer Engineering, University of Cyprus

References

  1. Huang M, Caines PE, Charalambous CD, Malhamé RP: Power control in wireless systems: a stochastic control formulation. Proceedings of the American Control Conference, June 2001, Arlington, Va, USA 2: 750-755.View ArticleGoogle Scholar
  2. Charalambous CD, Djouadi SM, Denic SZ: Stochastic power control for wireless networks via SDEs: probabilistic QoS measures. IEEE Transactions on Information Theory 2005, 51(12):4396-4401. 10.1109/TIT.2005.858984MathSciNetView ArticleMATHGoogle Scholar
  3. Charalambous CD, Menemenlis N: Stochastic models for long-term multipath fading channels and their statistical properties. Proceedings of the 38th IEEE Conference on Decision and Control (CDC '99), December 1999, Phoenix, Ariz, USA 5: 4947-4952.Google Scholar
  4. Charalambous CD, Menemenlis N: General non-stationary models for short-term and long-term fading channels. Proceedings of IEEE/AFCEA Conference on Information Systems for Enhanced Public Safety and Security (EUROCOMM '00), May 2000, Munich, Germany 142-149.Google Scholar
  5. Olama MM, Shajaat SM, Djouadi SM, Charalambous CD: Stochastic power control for time-varying short-term flat fading wireless channels. Proceedings of the 16th IFAC World Congress, July 2005, Prague, Czech RepublicGoogle Scholar
  6. Olama MM, Shajaat SM, Djouadi SM, Charalambous CD: Stochastic power control for time-varying long-term fading wireless channels. Proceedings of the American Control Conference, June 2005, Portland, Ore, USA 1817-1822.Google Scholar
  7. Rappaport TS: Wireless Communications: Principles and Practice. Prentice-Hall, Upper Saddle River, NJ, USA; 1996.MATHGoogle Scholar
  8. Zhang J, Chong EKP, Kontoyiannis I: Unified spatial diversity combining and power allocation for CDMA systems in multiple time-scale fading channels. IEEE Journal on Selected Areas in Communications 2001, 19(7):1276-1288. 10.1109/49.932696View ArticleGoogle Scholar
  9. Ljung L, Sodestrom T: Theory and Practice of Recursive Estimation. MIT Press, Cambridge, Mass, USA; 1983.Google Scholar
  10. Benveniste A, Metivier M, Priouet P: Adaptive Algorithms and Stochastic Approximations. Springer, New York, NY, USA; 1990.View ArticleGoogle Scholar
  11. Kouritzin MA:Inductive methods and rates of th-mean convergence in adaptive filtering. Stochastic and Stochastic Reports 1994, 51: 241-266.MathSciNetView ArticleMATHGoogle Scholar
  12. Zander J: Performance of optimum transmitter power control in cellular radio systems. IEEE Transactions on Vehicular Technology 1992, 41(1):57-62. 10.1109/25.120145View ArticleGoogle Scholar
  13. Aein JM: Power balancing in systems employing frequency reuse. COMSAT Technical Review 1973, 3(2):277-299.Google Scholar
  14. Grandhi SA, Zander J, Yates R: Constrained power control. Wireless Personal Communications 1995, 1(4):257-270.View ArticleGoogle Scholar
  15. Bambos N, Kandukuri S: Power-controlled multiple access schemes for next-generation wireless packet networks. IEEE Wireless Communications 2002, 9(3):58-64. 10.1109/MWC.2002.1016712View ArticleGoogle Scholar
  16. Li X, Gajic Z: An improved SIR-based power control for CDMA systems using Steffensen iterations. Proceedings of the Conference on Information Science and Systems, March 2002, Princeton, NJ, USA 287-290.Google Scholar
  17. Foschini GJ, Miljanic Z: Simple distributed autonomous power control algorithm and its convergence. IEEE Transactions on Vehicular Technology 1993, 42(4):641-646. 10.1109/25.260747View ArticleGoogle Scholar
  18. Kandukuri S, Boyd S: Optimal power control in interference-limited fading wireless channels with outage-probability specifications. IEEE Transactions on Wireless Communications 2002, 1(1):46-55. 10.1109/7693.975444View ArticleGoogle Scholar
  19. Viterbi AM, Viterbi AJ: Erlang capacity of a power controlled CDMA system. IEEE Journal on Selected Areas in Communications 1993, 11(6):892-900. 10.1109/49.232298View ArticleGoogle Scholar
  20. Ulukus S, Yates RD: Stochastic power control for cellular radio systems. IEEE Transactions on Communications 1998, 46(6):784-798. 10.1109/26.681417View ArticleGoogle Scholar
  21. Varanasi MK, Das D: Fast stochastic power control algorithms for nonlinear multiuser receivers. IEEE Transactions on Communications 2002, 50(11):1817-1827. 10.1109/TCOMM.2002.805274View ArticleGoogle Scholar
  22. Holliday T, Goldsmith AJ, Glynn P: Distributed power control for time-varying wireless networks: optimality and convergence. Proceedings of 41st Annual Allerton Conference on Communications, Control, and Computing, October 2003, Monticello, Ill, USAGoogle Scholar
  23. Mandayam NB, Chen P-C, Holtzman JM: Minimum duration outage for cellular systems: a level crossing analysis. Proceedings of 46th IEEE Vehicular Technology Conference, April 1996, Atlanta, Ga, USA 2: 879-883.Google Scholar
  24. Buche R, Kushner HJ: Control of mobile communications with time-varying channels in heavy traffic. IEEE Transactions on Automatic Control 2002, 47(6):992-1003. 10.1109/TAC.2002.1008363MathSciNetView ArticleGoogle Scholar
  25. Huang M, Caines PE, Malhamé RP: Uplink power adjustment in wireless communication systems: a stochastic control analysis. IEEE Transactions on Automatic Control 2004, 49(10):1693-1708. 10.1109/TAC.2004.835388View ArticleMathSciNetGoogle Scholar
  26. Chamberland J-F, Veeravalli VV: Decentralized dynamic power control for cellular CDMA systems. IEEE Transactions on Wireless Communications 2003, 2(3):549-559. 10.1109/TWC.2003.811186View ArticleGoogle Scholar
  27. Song L, Mandayam NB, Gajic Z: Analysis of an up/down power control algorithm for the CDMA reverse link under fading. IEEE Journal on Selected Areas in Communications 2001, 19(2):277-286. 10.1109/49.914505View ArticleGoogle Scholar
  28. Sung CW, Wong WS: Performance of a cooperative algorithm for power control in cellular systems with a time-varying link gain matrix. Wireless Networks 2000, 6(6):429-439. 10.1023/A:1019128224779View ArticleMATHGoogle Scholar
  29. Graziosi F, Pratesi M, Ruggieri M, Santucci F: Multicell model of handover initiation in mobile cellular networks. IEEE Transactions on Vehicular Technology 1999, 48(3):802-814. 10.1109/25.764997View ArticleGoogle Scholar
  30. Graziosi F, Santucci F: A general correlation model for shadow fading in mobile radio systems. IEEE Communications Letters 2002, 6(3):102-104. 10.1109/4234.991146View ArticleGoogle Scholar
  31. Taaghol P, Tafazolli R: Correlation model for shadow fading in landmobile satellite systems. Electronics Letters 1997, 33(15):1287-1289. 10.1049/el:19970905View ArticleGoogle Scholar
  32. Mees AI: Nonlinear Dynamics and Statistics. Birkhäuser, Boston, Mass, USA; 2001.View ArticleMATHGoogle Scholar
  33. Yates RD: A framework for uplink power control in cellular radio systems. IEEE Journal on Selected Areas in Communications 1995, 13(7):1341-1347. 10.1109/49.414651MathSciNetView ArticleGoogle Scholar
  34. Luo J, Ulukus S, Ephremides A: Standard and quasi-standard stochastic power control algorithms. IEEE Transactions on Information Theory 2005, 51(7):2612-2624. 10.1109/TIT.2005.850105MathSciNetView ArticleMATHGoogle Scholar
  35. Oksendal B: Stochastic Differential Equations: An Introduction with Applications. Springer, Berlin, Germany; 1998.View ArticleMATHGoogle Scholar
  36. Nelson R: Probability, Stochastic Processes, and Queuing Theory: The Mathematics of Computer Performance Modeling. 3rd edition. Springer, New York, NY, USA; 2000.Google Scholar

Copyright

© Olama et al. 2006