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A new medium access control (MAC) scheme embedding physical channels into multiband carrier sense multiple access/collision avoidance (CSMA/CA) networks is proposed to provide strict quality of service (QoS) guarantee to high priority users. In the proposed scheme, two priority classes of users, primary and secondary users, are supported. For primary users physical channels are provided to ensure strict QoS, whereas secondary users are provided with best-effort service using CSMA/CA modified for multiband operation. The performance of the proposed MAC scheme is investigated using a new multiband CSMA/CA Markov chain model capturing the primary user activity and the operation of secondary users in multiple bands. The throughput of secondary users is obtained as a function of the primary user activity and other CSMA/CA parameters. It is shown that the new MAC scheme yields larger throughput than the conventional single-band CSMA/CA when both schemes use the same bandwidth.