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In Cognitive Radio (CR) networks, spectrum sensing is a crucial technique to discover spectrum opportunities for the Secondary Users (SUs). The Quality-of-Service (QoS) of spectrum sensing is characterized by both sensing accuracy and sensing efficiency. Here, sensing accuracy is represented by the false alarm probability and the detection probability while sensing efficiency is represented by the metrics sensing overhead and throughput. The literature has mainly focused on improving sensing accuracy while sensing efficiency has been largely ignored. In this paper, we propose a group-based cooperative Medium Access Control (MAC) protocol, which concentrates on improving sensing efficiency without degrading spectrum sensing accuracy. The MAC protocol is specified and implemented in three phases: reservation, sensing and transmission. The protocol incorporates a group-based cooperative spectrum sensing scheme. In particular, the cooperative SUs are grouped into several teams. During a sensing period, each team senses a different channel. As a consequence, multiple distinct channels can be simultaneously detected within one sensing period. Then, we formulate throughput maximization problems in both time-invariant and time-varying channel scenarios to determine the key design parameters. In addition, an SU-selecting algorithm is presented to selectively choose the cooperative SUs based on the channel dynamics and usage patterns in order to substantially reduce sensing overhead. Numerical results indicate that the proposed strategy is able to significantly decrease sensing overhead and increase throughput with guaranteed sensing accuracy.