Efficient Power Control Via Pricing in Wireless Data Networks

1. Efficient Power Control Via Pricing in Wireless Data Networks Cem U. Saraydar, Narayan B. Mandayam and David J. Goodman Presented by Ramesh Mishra

2. The Incentive for Power Control Need for QoS for a wireless terminal. Need for Efficient use of radio resources. Need for a mechanism that maximizes the overall utility of the system.

3. Some Basic Concepts Utility Function It refers to the level of satisfaction the decision taker gets as a result of its actions.

4. System Model Single Cell System. Each user transmits �L� information bits in packets of size �M� > �L�. The Rate of Transmission is �R� and power used is �p�. The probability of correct reception of a frame is Pc (FSR) which is a function of SIR.

5. Continued� FSR( Frame Success Rate) is defined as Pc = ( 1 - Pe )M. where Pe is the bit error rate. Under these definitions the utility function is defined as u = (L* R* Pc/M*p) bits/joule

6. Degenerate Solution and Efficiency Function We have a degenerate solution when p = 0. Efficiency function that closely follows the behavior of the original function is introduced f(y) = (1-2*Pe)M.

8. Non-Cooperative Power Control Game Let G = [N, {Pj}, {uj(.)}] denote a non-cooperative power control game(NPG). The utility of user j obtained by expending power pj can be expressed as

9. NPG �A Formal Look Formally the Power Control Game can be expressed as

10. Nash Equilibrium in NPG At Nash Equilibrium, no user can improve its utility, given the power level of other users. The power level chosen by a rational user constitutes its best response.

12. Some Results The Nash Equilibrium exists in NPG, G = [N, {Pj}, {uj(.)}]. The NPG has a unique Equilibrium.

13. Inefficiency of NPG and Pareto Dominance. The power allocation can be made more efficient (Pareto dominant) if we can increase the utility of some of the terminals without hurting others. The NPG equilibrium is inefficient.

14. Pareto Dominance

15. Non-Cooperative Power Control with Pricing. Pricing is motivated by two objectives. Generates revenues for the system. Encourages players to use system resources more efficiently. Many possible pricing schemes eg (flat rate, access based, usage based, priority based etc). Efficiency in power control can be promoted by a usage-based pricing scheme strategy where the penalty is proportional to its transmit power.

16. NPGP- A Formal Look Let Gc = [N, {Pj}, {ucj (.)}] denote an N � player non-cooperative Game with pricing. Utility is defined as:

18. Supermodularity and NPGP A Theorem: The set of Nash Equilibrium of a super modular game is nonempty. Furthermore, the Nash set has a largest and smallest element. A Definition: A Game Ge with exogenous parameter e is said to be supermodular, or it is a parameterized game with complementarities if

20. Algorithm for generating a sequence of powers.

21. Algorithm(Network)

22. Numerical Results: