Game theoretic distributed power control algorithms for uplink wireless data in flat fading channels

In this paper we present a game-theoretic power control algorithms for wireless data in CDMA cellular systems under two realistic channels: (a1) Fast flat fading channel and (a2) Slow flat fading channel. The fading coefficients under both (a1) and (a2) are studied for three appropriate small scale channel models that are used in the CDMA cellular systems: Rayleigh channel, Rician channel and Nakagami channel. This work is inspired by the results presented by [1] under nonfading channels. In other words, we study the impact of the realistic channel models on the findings in [1] through the followings: we evaluate the average utility function, the average number of bits received correctly at the receiver per one Joule expended, for each channel model. Then, using the average utility function we study the existence, uniqueness of Nash equilibrium (NE) if it exists, and the social desirability of NE in the Pareto sense. Results show that in a non-cooperative game (NPG) the best policy for all users in the cell is to target a fixed signal-to-interference and noise ratio (SINR) similar to what was shown in [1] for non-fading channel. The difference however is that the target SINR in fading channels is much higher than that in a non-fading channel. Also, for spreading gain less than or equal to 100, both NPG and non-cooperative power control game with pricing (NPGP) perform poorly, where all the terminals except the nearest one were not able to attain their corresponding minimum SINR even if sending at the maximum powers in their strategy spaces.