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The MAC protocol of a cognitive radio (CR) device should allow it to access unused or under-utilized spectrum without (or with minimal) interference to primary users dynamically. To fulfill such a goal, we propose a cognitive MAC protocol using statistical channel allocation and call it SCA-MAC in this work. SCA-MAC is a CSMA/CA-based protocol, which exploits statistics of spectrum usage for decision making on channel access. For each transmission, the sender negotiates with the receiver on transmission parameters through the control channel. A model is developed for CR devices to evaluate the successful rate of transmission. A CR device should pass the threshold of the successful transmission rate via negotiation before it can begin a valid transmission on data channels. The operating range and channel aggregation are two control parameters introduced to maintain the MAC performance. To validate our ideas, we conducted theoretical analysis and simulations to show that SCA-MAC does improve the throughput performance and guarantee the interference to incumbents to be bounded by a predetermined acceptable rate. The proposed MAC protocol does not need a centralized controller, as the negotiation between the sender and the receiver is performed using the CSMA/CA-based algorithm.