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In this paper, recent results in game theory and stochastic approximation are brought together to mitigate the problem of femto-to-macrocell cross-tier interference. The main result of this paper is an algorithm which reduces the impact of interference of femtocells over the existing macrocells. Such algorithm relies on the observations of the signal to interference plus noise ratio (SINR) of all active communications in both macro and femtocells when they are fed back to the corresponding base stations. Based on such observations, femto base stations learn the probability distributions over the feasible transmit configurations (frequency band and power levels) such that a minimum time-average SINR can be guaranteed in the macrocells, at the equilibrium. In this paper, we introduce the concept of logit equilibrium (LE) and present its interpretation in terms of the trade-off faced by femtocells when experimenting several actions to discover the network, and taking the action to maximize their instantaneous performance. Finally, numerical results are given to validate our theoretical findings.
Bennis et al. (Wed,) studied this question.