In this paper, we study the problem of joint admission control and power allocation for cognitive radio networks. In such a scenario, the quality of service for primary and secondary users is needed to be guaranteed, which can be translated into the following two constraints: the inference temperature constraint for primary users and the minimum signal-to-interference-plus-noise ratio (SINR) constraint for secondary users. Due to the high density or the mobility of the secondary users, not all the secondary users are supportable. The problem of our interest is to select the maximum subset of secondary users given that the above constraints are satisfied. Moreover, because different secondary users have different revenue outputs, the problem becomes how we can find a subset of the secondary users such that the total revenue output of the networks is maximized. It can be shown that finding the optimal removal set is a NP hard problem. Therefore, we transform the original problem into a smooth optimization problem, and solve it by using a gradient descent based algorithm. This algorithm solves the power allocation and admission control jointly, and its superior performance over the existing algorithms is demonstrated through simulations.
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