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Cognitive radio offers a promising technology to mitigate spectrum shortage in wireless communications. It enables secondary users (SUs) to opportunistically access low-occupancy primary spectral bands as long as their negative effect on the primary user (PU) access is constrained. This PU protection requirement is particularly challenging for multiple SUs over a wide geographical area. In this paper, we study the fundamental performance limit on the throughput of cognitive radio networks under the PU packet collision constraint. With perfect sensing, we develop an optimum spectrum access strategy under generic PU traffic patterns. Without perfect sensing, we quantify the impact of missed detection and false alarm, and propose a modified threshold-based spectrum access strategy that achieves close-to-optimal performance. Moreover, we develop and evaluate a distributed access scheme that enables multiple SUs to collectively protect the PU while adapting to behavioral changes in PU usage patterns. Our results provide useful insight on the trade-off between the protection of the primary user and the throughput performance of cognitive radios.