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Dynamic spectrum access in cognitive radio networks can greatly improve the spectrum utilization efficiency. Nevertheless, interference may be introduced to the Primary User (PU) when the Secondary Users (SUs) dynamically utilize the PU's licensed channels. If the SUs can be synchronous with the PU's time slots, the interference is mainly due to their imperfect spectrum sensing of the primary channel. However, if the SUs have no knowledge about the PU's exact communication mechanism, additional interference may occur. In this paper, we propose a dynamic spectrum access protocol for the SUs confronting with unknown primary behavior and study the interference caused by their dynamic access. Through analyzing the SUs' dynamic behavior in the primary channel which is modeled as an ON-OFF process, we prove that the SUs' communication behavior is a renewal process. Based on the Renewal Theory, we quantify the interference caused by the SUs and derive the corresponding closed-form expressions. With the interference analysis, we study how to optimize the SUs' performance under the constraints of the PU's communication quality of service (QoS) and the secondary network's stability. Finally, simulation results are shown to verify the effectiveness of our analysis.