A Nash game algorithm for power allocation jointing sensing time for cognitive networks

We study the problem of power allocation in cognitive radio networks. A distributed power allocation Joint sensing time Nash game (PASTG) in two Dimension field is proposed. Based on this model, a Utility function is defined for SUs, considering the fairness of the sensing time cost with the power allocation. We prove that the game with this utility function converges to its unique Nash equilibrium. Also we point out the system parameter of time slot T should be jointly designed with the power allocation under the cooperative sensing time constraint. Numerical results are provided to show the performance of PASTG. It is show that the sensing time is influenced by the power allocation. More transmitting power used should contribute more sensing cost in overall system. Along with the number of secondary user increasing, the achievable power balancing SINR are decreased significantly and the cost of the power is increasing sharply.