Distributed Power Control in a Two-Tier Heterogeneous Network

This paper investigates downlink distributed power control for femtocell networks with QoS provisioning for macro-cell user equipments (MUE). Specifically, we propose two non-cooperative game formulations: the Rate Maximization Game (RMG) and the Gradient-norm Minimization Game (GMG). We treat both the macro base-station (MBS) and femto base-stations (FBS) as active players capable of adjusting their respective transmission power in response to changing environments. With the same MBS pay-off function for both games, RMG lets each femtocell maximize its rate penalized by the price paid for its transmission, whereas GMG lets each femtocell minimize a weighted norm of the “local gradient” of the Lagrangian. We propose two different categories of algorithms, the iterative-waterfilling-based algorithms and the stochastic-approximation-based algorithms, to find the corresponding Nash equilibria (NE) of both games. We also characterize sufficient conditions for the convergence of both classes of algorithms under fixed price. With proper price choice, the NEs of both RMG and GMG are related to locally optimal solutions to the system rate maximization problem with the MUE QoS constraints. To further improve system performance for FBS´s, we propose two price update methods with QoS provisioning of MUEs.