Learning Equilibrium Play for Stochastic Parallel Gaussian Interference Channels

Distributed power control for parallel Gaussian interference channels recently draws great interests. However, all existing works only studied this problem under deterministic communication channels and required certain perfect information to carry out their proposed algorithms. In this paper, we study this problem for stochastic parallel Gaussian interference channels. In particular, we take into account the randomness of the communication environment and the estimation errors of the desired information, and thus formulate a stochastic noncooperative power control game. We then propose a stochastic distributed learning algorithm SDLA-I to help communication pairs learn the Nash equilibrium. A careful convergence analysis on SDLA-I is provided based on stochastic approximation theory and projected dynamic systems approach. We further propose another learning algorithm SDLA-II by including a simple iterate averaging idea into SDLA-I to improve algorithmic convergence performance. Numerical results are also presented to demonstrate the performance of our algorithms and theoretical results.