Power allocation games on interference channels with complete and partial information

We consider a Gaussian interference channel with independent direct and cross link channel gains, each of which is independent and identically distributed across time. Each transmitter-receiver user pair aims to maximize its long-term average transmission rate subject to an average power constraint. We formulate a stochastic game for this system in three different scenarios. First, we assume that each user knows all direct and cross link channel gains. Later, we assume that each user knows channel gains of only the links that are incident on its receiver. Lastly, we assume that each user knows only its own direct link channel gain. In all cases, we formulate the problem of finding the Nash equilibrium as a variational inequality (VI) problem and present a novel heuristic for solving the VI. We also present a lower bound on the utility for each user at any Nash equilibrium in the case of the games with partial information. We obtain this lower bound using a water-filling like power allocation that requires only knowledge of the distribution of a user´s own channel gains and average power constraints of all users.