Distributed power control in femto cells using Bayesian density tracking

In this paper we develop a framework for distributed power control in a wireless network where femto and macro cells co-exist and interfere with each other. In order to ensure a minimum QoS, femto and macro access points have the challenging and realistic objective of minimizing their users´ SINR (Signal to Interference and Noise Ratio) outage. Furthermore, due to mobility and interference, an accurate closed form expression of the SINR density function is hard to obtain in a realistic scenario which makes the problem more challenging. In this paper, our contribution is twofold. We propose a Nash seeking based power control algorithm that utilizes the numerical value to maximize the reward. We then propose a Bayesian based technique that tracks the density of the SINR of macro and femto users to estimate the reward and achieve our aforementioned goals. It is worth noting that our power control strategy requires that each Access Point (AP) knows only a numerical value (and not closed form expression) of the reward of its own users which is quite realistic in a dynamic environment (mobility, interference, etc.) where a closed form expression of the reward is hard/impossible to obtain. Numerical results at the end of the paper show that our framework outperforms existing works.