Distributed stochastic pricing for sum-rate maximization in femtocell networks with random graph and quantized communications

In this paper, we consider a pricing mechanism aimed at maximizing the sum-rate of a femtocell network in a distributed manner, thanks to a limited exchange of information among neighbor femto access points (FAPs). In a femtocell network, coordination among FAPs is possible exploiting the IP-based backhaul link. In particular, we consider the case where the exchange of information among FAPs is quantized and happens through a network graph (typically a sparse graph), whose links fail randomly across iterations. Using results from stochastic approximation theory, we propose a distributed projection based Robbins-Monro (RM) scheme that converges almost surely (a. s.) on a final allocation equilibrium dependent on the mean graph of the network, even in the presence of such imperfect communication scenario. Numerical results show how the system performance reduces due to the effect of link failures, which cause a lower coordination among FAPs to mitigate interference. Nevertheless, supposing to know the probability with which each link fails, we show how to counteract the effect of failures through a proper weighting of the price coefficients received by the neighbor FAPs. The distributed allocation algorithm is then robust to channel imperfections, whose effect is only to slow down the convergence process.