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In this paper, a distributed power and end-to-end rate control algorithm is proposed in the presence of licensed users. By Lagrangian duality theory, the optimal power and rate control solution is given for the unlicensed users while satisfying the interference temperature limits to licensed users. It is obtained that transmitting with either 0 or the maximum node power is the optimal scheme. The synchronous and asynchronous distributed algorithms are proposed to be implemented at the nodes and links. The convergence of the proposed algorithms are proved. Finally, further discussion on the utility-based fairness is provided for the proposed algorithms. Numerical results show that the proposed algorithm can limit the interference to licensed user under a predefined threshold.