Learning coarse correlated equilibria in two-tier wireless networks

In this paper, we study the strategic coexistence between macro and femto cell tiers from a game theoretic learning perspective. A novel regret-based learning algorithm is proposed whereby cognitive femtocells mitigate their interference toward the macrocell tier, on the downlink. The proposed algorithm is fully decentralized relying only on the signal-to-interference-plus-noise ratio (SINR) feedback to the corresponding femtocell base stations. Based on these local observations, femto base stations learn the probability distribution of their transmission strategies (power levels and frequency band) by minimizing their regrets for using certain strategies, while adhering to the cross-tier interference constraint. The decentralized regret based learning algorithm is shown to converge to an ϵ-coarse correlated equilibrium (ϵ-CCE) which is a generalization of the classical Nash Equilibrium (NE). Finally, numerical results are shown to corroborate our findings where, quite remarkably, our learning algorithm achieves the same performance as the classical regret matching, but with substantially much less overhead.