Impact of fading wireless channel on the performance of game theoretic power control algorithms for CDMA wireless data

Our goal in this paper is to study the performance of the game-theoretic power control algorithms for wireless data introduced by Saraydar et al [1] in two realistic channels: (a1) fast flat fading channel and (a2) Slow flat fading channel. The fading coefficients under both (a1) and (a2) are studied under an appropriate small scale channel model that is used in the CDMA cellular systems, namely Nakagami channel model. To do so, we derive a closed- form expression of the average utility function which represents the number of bits received correctly at the receiver per one Joule expended. Then, using this expression we study the existence, uniqueness of Nash equilibrium (NE), and the social desirability of NE in the Pareto sense.