Hierarchical Competition for Downlink Power Allocation in OFDMA Femtocell Networks

This paper considers the problem of downlink power allocation in an orthogonal frequency-division multiple access (OFDMA) cellular network with macrocells underlaid with femtocells. The femto-access points (FAPs) and the macro-base stations (MBSs) in the network are assumed to compete with each other to maximize their capacity under power constraints. This competition is captured in the framework of a Stackelberg game with the MBSs as the leaders and the FAPs as the followers. The leaders are assumed to have foresight enough to consider the responses of the followers while formulating their own strategies. The Stackelberg equilibrium is introduced as the solution of the Stackelberg game, and it is shown to exist under some mild assumptions. The game is expressed as a mathematical program with equilibrium constraints (MPEC), and the best response for a one leader-multiple follower game is derived. The best response is also obtained when a quality-of-service constraint is placed on the leader. Orthogonal power allocation between leader and followers is obtained as a special case of this solution under high interference. These results are used to build algorithms to iteratively calculate the Stackelberg equilibrium, and a sufficient condition is given for its convergence. The performance of the system at a Stackelberg equilibrium is found to be much better than that at a Nash equilibrium.