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In this letter, we investigate the joint optimization of sensing time and power allocation for amplify-and-forward cognitive relay networks. By jointly considering the sensing slot and the data transmission slot, the optimization problems are respectively formulated to maximize the average network throughput and minimize the approximate outage probability of secondary transmission under the average transmit power constraint of secondary users and the average interference power constraint of primary user. The optimal algorithms are developed to acquire the optimal sensing time and power allocation. Simulation results demonstrate that significant improvements in the average throughput and outage behavior are achieved through the joint optimization.