A power control game based on outage probabilities for multicell wireless data networks

We present a game-theoretic treatment of distributed power control in CDMA wireless systems using outage probabilities. We first prove that the noncooperative power control game considered admits a unique Nash equilibrium (NE) for uniformly strictly convex pricing functions and under some technical assumptions on the SIR threshold levels. We then analyze global convergence of continuous-time as well as discrete-time synchronous and asynchronous iterative power update algorithms to the unique NE of the game. Furthermore, we show that a stochastic version of the discrete-time update scheme, which models the uncertainty due to quantization and estimation errors, converges almost surely to the unique NE point. We finally investigate and demonstrate the convergence and robustness properties of these update schemes through simulation studies.