1. Stochastic Power Control for Short-Term Flat Fading Wireless Networks: Almost Sure QoS Measures C. D. Charalambous 1, S. Z. Denic 2, S. M. Djouadi 3, N. Menemenlis 4 University of Ottawa 1,2, University of Arkansas 3, McGill University 4 2001 CDC, Dec. 4-7, Orlando, FL

2. 2 Outline u Review of the Power Control Problem u Probabilistic QoS Measures u Modeling of Log-Normal Shadowing Log-Normal SDE’s u Stochastic Optimal Control Predictable Strategies Linear Programming

3. 3 QoS Measures u Review of the Power Control Problem

4. 4 QoS Measures u Vector Form [Yates 1981] Then

5. 5 QoS Measures u Probabilistic QoS Measures Define The Constraints are equivalent to

6. 6 QoS Measures u Decentralized Probabilistic QoS

7. 7 QoS Measures

8. 8 u Centralized Probabilistic QoS

9. 9 Log-Normal Shadowing u Received Power u Power Path Loss

10. 10 Large-Scale Shadowing u Attenuation Coefficient

11. 11 Large-Scale Shadowing u Log-Normal Attenuation Coefficient u Log-Normal power Path Loss

12. 12 Stochastic Models u Attenuation Coefficient u Power Path Loss

13. 13 Temporal Power-Loss/ Attenuation u Mean-Reverting Power-Loss

14. 14 Space-Time Mean-Reverting Power-Loss

15. 15 Space-Time Mean-Reverting Power-Loss

16. 16 QoS Measures u Stochastic Optimal Control Received Signal State Space Representation

17. 17 QoS Measures Pathwise QoS and Predictable Strategies Define Then where

18. 18 QoS Measures Define

19. 19 QoS Measures Predictable Strategies over the interval Predictable Strategies Linear Programming

20. 20 QoS Measures

21. 21 QoS Measures

22. 22 QoS Measures u Generalizations Linear Programming Stochastic Optimal Control with Integral/Exponential-of-Integral Constraints

23. 23 Conclusions u Predictable Strategies and Dynamic Models Linear Programming u Probabilistic QoS Measures u Stochastic Optimal Control Linear Programming