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For high-data-rate wireless communication systems, two major issues are the underutilization of limited available radio spectrum and the effect of channel fading. Using dynamic spectrum access, cognitive radio can improve spectrum utilization. Almost all proposed CR systems are based on multicarrier modulation since multiple users can access the MCM systems by allocating subcarriers. Generally, MCM mainly includes two different schemes, orthogonal frequency-division multiplexing and filtered multitone modulation. Considering mutual interference elimination, synchronization, and transmission efficiency, we conclude that FMT is better than OFDM in MCM-based CR systems. Additionally, cooperative diversity can reduce the fading effect since the space diversity gain can be obtained through the distributed antennas of each user. Hence, in this article, we combine CR with the cooperative diversity technique, and then construct three cooperative diversity cognitive models: the collaborative spectrum sensing model, the cooperative communication cognitive model, and the hybrid model. Additionally, radio resources can be extended from time-frequency dimensions to space-time-frequency dimensions in the proposed models, which effectively improves both spectrum utilization and MCM-CR system performance. Finally, extensive simulations are conducted to show the validity and effectiveness of the proposed models.