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This paper considers a cognitive radio model where the secondary users (SUs) apply cooperative relay to fulfill the communication demand. Specially, under the constraint that the interference power introduced to primary users (PUs) is kept under a tolerable threshold, we investigate the system throughput maximization problem during the cognitive relay transmission. In order to make the formulated problem feasible to solve, Maclaurin expansions are employed as substitutions. Moreover, based on convex optimization theory, an iterative power allocation algorithm repeated between the powers of secondary source node and relay node is developed to obtain the optimal solution. Corroborant numerical examples are provided to illustrate the quick convergence behavior of the proposed algorithm and the superiority of applying cooperative relay in cognitive radio networks is also presented.