Power control in a cognitive radio system using bargaining theory

In this paper, we study the problem of power control according to a cognitive radio system composed of two users. Since the users are interactive, a static game can be defined: both users identify the players of the game, powers are the strategies while energy efficiency is considered to be the utility function. Power control, the major issue of this work, can be explored using a non cooperative game through the Nash equilibrium (NE). It is proven that such a solution is Pareto inefficient. To deal with this inefficiency, investigating the cooperative games is the solution. Thus, we are interested in studying the bargaining theory and in particular the Nash bargaining solution (NBS) which is unique and Pareto efficient. Numerical results show that utilities and powers can be improved efficiently through cooperation. Moreover, we showed how the utility function (regardless of the equilibrium) is a decreasing function of the noise power while it is an increasing function of the spreading factor. We showed also how the NE converges to the NBS for high values of the spreading factor.