Energy-Efficient Noncooperative Power Control in Small-Cell Networks

In this paper, energy-efficient power control for small cells underlaying a macrocellular network is investigated. We formulate the power control problem in self-organizing small-cell networks as a noncooperative game and propose a distributed energy-efficient power control scheme, which allows the small base stations (SBSs) to take individual decisions for attaining the Nash equilibrium (NE) with minimum information exchange. In particular, in the noncooperative power control game, a nonconvex optimization problem is formulated for each SBS to maximize their energy efficiency (EE). By exploiting the properties of parameter-free fractional programming and the concept of perspective function, the nonconvex optimization problem for each SBS is transformed into an equivalent constrained convex optimization problem. Then, the constrained convex optimization problem is converted into an unconstrained convex optimization problem by exploiting the mixed penalty function method. The inequality constraints are eliminated by introducing the logarithmic barrier functions, and the equality constraint is eliminated by introducing the quadratic penalty function. We also theoretically show the existence and the uniqueness of the NE in the noncooperative power control game. Simulation results show remarkable improvements in terms of EE by using the proposed scheme.