Distributed Pareto-Optimal Power Control in Femtocell Networks

This paper aims to devise a power control solution for femtocell networks that can be implemented distributively and, more importantly, is optimal in Pareto sense. For this, a complete characterization of the Pareto-optimal boundary of the signal-to-interference-plus-noise ratio (SINR) feasible region is first derived. The complicated interdependency between the macrocell and femtocell networks, whose access priorities and design objectives are inherently distinct, is also revealed. Our result confirms that the Pareto-optimal SINRs of the femtocell network can only be achieved conditionally upon the guaranteed performance of macrocell users. Through a suitable parametrization, we show that all SINR points on the aforementioned boundary can be realized. A unique operating SINR point is chosen among those infinite possible solutions, based upon the specific utility of femtocell users as well as the minimum SINR requirements of the macrocell network. Distributed transmit power adaptation is then performed to attain such optimal design target. We prove that the developed algorithm converges to the global optimum, wherein the performance of femtocell users is optimized while macrocell users being robustly protected with their minimum required SINRs maintained at all times. The merits of our approach are illustrated by numerical results.