Skip to main content

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

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.

References

  1. 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.

    Article  Google Scholar 

  2. 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.2005.858984

    MathSciNet  Article  Google Scholar 

  3. 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. 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. 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 Republic

    Google Scholar 

  6. 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. 7.

    Rappaport TS: Wireless Communications: Principles and Practice. Prentice-Hall, Upper Saddle River, NJ, USA; 1996.

    Google Scholar 

  8. 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. 10.1109/49.932696

    Article  Google Scholar 

  9. 9.

    Ljung L, Sodestrom T: Theory and Practice of Recursive Estimation. MIT Press, Cambridge, Mass, USA; 1983.

    Google Scholar 

  10. 10.

    Benveniste A, Metivier M, Priouet P: Adaptive Algorithms and Stochastic Approximations. Springer, New York, NY, USA; 1990.

    Google Scholar 

  11. 11.

    Kouritzin MA:Inductive methods and rates ofth-mean convergence in adaptive filtering. Stochastic and Stochastic Reports 1994, 51: 241–266.

    MathSciNet  Article  Google Scholar 

  12. 12.

    Zander J: Performance of optimum transmitter power control in cellular radio systems. IEEE Transactions on Vehicular Technology 1992, 41(1):57–62. 10.1109/25.120145

    Article  Google Scholar 

  13. 13.

    Aein JM: Power balancing in systems employing frequency reuse. COMSAT Technical Review 1973, 3(2):277–299.

    Google Scholar 

  14. 14.

    Grandhi SA, Zander J, Yates R: Constrained power control. Wireless Personal Communications 1995, 1(4):257–270.

    Article  Google Scholar 

  15. 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.2002.1016712

    Article  Google Scholar 

  16. 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. 17.

    Foschini GJ, Miljanic Z: Simple distributed autonomous power control algorithm and its convergence. IEEE Transactions on Vehicular Technology 1993, 42(4):641–646. 10.1109/25.260747

    Article  Google Scholar 

  18. 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. 10.1109/7693.975444

    Article  Google Scholar 

  19. 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. 10.1109/49.232298

    Article  Google Scholar 

  20. 20.

    Ulukus S, Yates RD: Stochastic power control for cellular radio systems. IEEE Transactions on Communications 1998, 46(6):784–798. 10.1109/26.681417

    Article  Google Scholar 

  21. 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.2002.805274

    Article  Google Scholar 

  22. 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, USA

    Google Scholar 

  23. 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. 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.2002.1008363

    MathSciNet  Article  Google Scholar 

  25. 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.2004.835388

    MathSciNet  Article  Google Scholar 

  26. 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.2003.811186

    Article  Google Scholar 

  27. 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. 10.1109/49.914505

    Article  Google Scholar 

  28. 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:1019128224779

    Article  Google Scholar 

  29. 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. 10.1109/25.764997

    Article  Google Scholar 

  30. 30.

    Graziosi F, Santucci F: A general correlation model for shadow fading in mobile radio systems. IEEE Communications Letters 2002, 6(3):102–104. 10.1109/4234.991146

    Article  Google Scholar 

  31. 31.

    Taaghol P, Tafazolli R: Correlation model for shadow fading in landmobile satellite systems. Electronics Letters 1997, 33(15):1287–1289. 10.1049/el:19970905

    Article  Google Scholar 

  32. 32.

    Mees AI: Nonlinear Dynamics and Statistics. Birkhäuser, Boston, Mass, USA; 2001.

    Google Scholar 

  33. 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. 10.1109/49.414651

    Article  Google Scholar 

  34. 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.2005.850105

    MathSciNet  Article  Google Scholar 

  35. 35.

    Oksendal B: Stochastic Differential Equations: An Introduction with Applications. Springer, Berlin, Germany; 1998.

    Google Scholar 

  36. 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 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Mohammed M. Olama.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Olama, M.M., Djouadi, S.M. & Charalambous, C.D. Stochastic Power Control for Time-Varying Long-Term Fading Wireless Networks. EURASIP J. Adv. Signal Process. 2006, 089864 (2006). https://doi.org/10.1155/ASP/2006/89864

Download citation

Keywords

  • Stochastic Model
  • Power Control
  • Stochastic Differential Equation
  • Linear Programming Problem
  • Optimal Power