Learning to Use the Spectrum in Self-Configuring Heterogenous Networks: A Logit Equilibrium Approach

In this paper, we study the particular scenario where several transmitter-receiver pairs communicate subject to mutual interference due to the usage of the same frequency bands. In particular, we focus on the case of heterogeneous networks, where radio devices have dierent interests (utility functions), transmit congurations (sets of actions), as well as dierent signal processing and calculation capabilities. The underlying assumptions of this work are the followings: (i) the network is described by a set of states, for instance, the channel realization vector; (ii) radio devices are interested in their long-term average performance rather than instantaneous performance; (iii) each radio device is able to obtain a measure of its achieved performance at least once after updating its transmission conguration. Considering these conditions, we model the heterogenous network by a stochastic game. Our main contribution consists of a family of behavioral rules that allow radio devices to achieve an epsilon-Nash equilibrium of the corresponding stochastic game, namely a logit equilibrium. A thorough analysis of the convergence properties of these behavioral rules is presented. Finally, our approach is used in the context of a classical parallel interference channel in order to compare with existing results.