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In the cognitive networks, one of the major concerns is the fact that cognitive users may cause harmful interference to licensed users. And the fairness of resource allocation is another important problem in this network. This paper focuses on a joint channel and power allocation algorithm that can both protect licensed users and guarantee the fairness of spectrum sharing among cognitive users. This resource assigning problem can be formulated as a nonlinear programming. In this paper, an extended version of joint channel and power allocation algorithm is proposed. We consider the signal-to-interference ratio (SIR) constraint at the cognitive users who share the same channel, and introduce the fairness utility based on the definition of poverty line (PL), which is the minimum number of available channels for each user. Simulation results show that the proposed algorithm makes good performances in both fairness utility and network capacity.