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In this article, we investigate joint sensing block length and detection threshold optimization to maximize the throughput of a cognitive radio (CR) network with limited interference to the primary user (PU). The CR network operates on a frame-by-frame basis, where the status of the PU can change at any time within one frame. Through theoretical analysis, optimal solution is derived, which is helpful to system design. Numerical results show that higher throughput can be obtained by considering the PU status change than the case without considering it.