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To resolve the problem that the cognitive radio needs to realize the fairness of spectrum of spectrum allocation in the cognitive radio and satisfy the demand of modern green communication,a new utility function considering channel status ,non-cooperative game theory and interference temperature is proposed,meanwhile,the convergence and the existent and unique of the Nash equilibrium is proved in this paper. The advantage of the proposed algorithm is not only meet to the real-time communication with rapid convergence but also can be implemented distributively with simple. Compared with the referenced algorithm,simulation show that this algorithm not only can save energy consumption and achieve better anti-noise effect but also can improve the overall effectiveness of the network with low power and low interference and satisfy the demand of modern green communication .