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In this paper, we consider a cognitive radio system in fading wireless channels and propose an opportunistic power control strategy for the cognitive users, which serves as an alternative way to protect the primary user's transmission and to realize spectrum sharing between the primary user and the cognitive users. The key feature of the proposed strategy is that, via opportunistically adapting its transmit power, the cognitive user can maximize its achievable transmission rate without degrading the outage probability of the primary user. If compared with the existing cognitive protocols, which usually try to keep the instantaneous rate of the primary user unchanged, our strategy relieves the cognitive users from the burden of detecting and relaying the message of the primary user and relaxes the system synchronization requirements. The achievable rate of a cognitive user under the proposed power control strategy is analyzed and simulated, taking into account the impact of imperfect channel estimation. A modified power control strategy is also proposed to reduce the sensitivity of our strategy to the estimation errors. Its effectiveness is verified by the simulations.