  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.
