The requirements of the International Telecommunication Union (ITU) for the 4th generation of mobile devices raised up to 100 Mbps for high and 1Gbps for low mobility conditions. Reaching such challenging targets requires the deployment of picocells and femtocells. These techniques permit to achieve large cell capacity but also lead to diculties in terms of interference. The GRACE algorithm, based on Cognitive Radio and Game Theory, has shown a fair balance between cell capacity and outage as well as short convergence time, low complexity and easy scalability. The aim of this work is to find an ecient power control algorithm that fits GRACE these goals. Therefore, a study of Cognitive Radio, Game Theory and Power Control algorithms is developed and a new power control algorithm is proposed. The simulation results show that the Fractional Power Control can increase notably the outage performance and the energy saving to the mobile devices.