In cognitive radio networks, the unlicensed users can utilize the unoccupied licensed spectrum opportunistically. In this paper, we propose a joint power and end-to-end rate control algorithm considering restricting the interference to licensed users. By duality theory, the optimal resource allocation solution is given for the unlicensed users while satisfying the interference temperature limits. An asynchronous algorithm is proposed to be implemented in practical networks. Finally, we give a discussion to the proposed algorithm's performance on fairness. Numerical results show that the proposed algorithm can limit the interference to licensed user under a predefined threshold while maintaining a satisfied data rate fairly.