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In this article, we develop a novel adaptive spectrum sensing scheme to improve the throughput of cognitive radio (CR) users. The new scheme takes the variation of wireless channels into consideration and requires no priori knowledge of primary user activity statistics. At the beginning of each time frame, this adaptive sensing scheme adjusts the spectrum sensing parameters according to the latest sensing results and channel state information (CSI) of the time-varying channels. Numerical results show that the proposed adaptive spectrum sensing scheme can significantly outperform the traditional spectrum sensing scheme.