Load balancing in heterogeneous networks based on distributed learning in potential games

We present a novel approach for distributive load balancing in heterogeneous networks that use cell range expansion (CRE) for user association. First, we formulate the problem as a minimisation of an α-fairness objective function. Depending on α, different objectives in terms of network performance or fairness can be achieved. Next, we model the interactions among the base stations for load balancing as a potential game, in which the potential function is the α-fairness function. The optimal Nash equilibrium of the game is found by using distributed learning algorithms. We use log-linear and binary log-linear learning algorithms for complete and partial information settings, respectively. By running extensive simulations, we show that the proposed algorithms converge within a few tens of iterations. The convergence speed in the case of partial information setting is comparable to that of the complete information setting. We also show that the best response algorithm does not necessarily converge to the optimal Nash equilibrium.