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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, the authors study this problem for stochastic parallel Gaussian interference channels. In particular, they take into account the randomness of the communication environment and the estimation errors of the desired information, and thus formulate a stochastic non-cooperative power control game. They 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.
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