Optimal power control game for primary-secondary user in cognitive radio network

In cognitive radio network (CRN), the utilities results in Nash equilibrium of power control game without using pricing are inefficient. In this paper, a distributed power control algorithm is proposed to improve the utilities of both primary user (PU) and secondary users (SUs) in the CRN based on game theoretic framework. A distributed power control is a non-cooperative power control game, and the quality of service (QoS) received by PU and SUs terminals are referred to as the utility function. PU and SUs act as decision makers in the game and they maximize their utilities in a distributed fashion. We introduce a new pricing function for SUs as a function of transmit power and square amount of interference in order to guide SUs to an efficient Nash equilibrium point. Analysis of the existence and uniqueness of Nash equilibrium for the proposed power control game with pricing is presented. Simulation results show that the proposed power control algorithm via a new pricing function maximizes the number of SUs access the unused spectrum, and improves the utilities of PU and SUs.