In cognitive radio (CR) systems, it is crucial for secondary users to reliably detect spectral opportunities across a wide frequency range. This paper studies a novel multirate sub-Nyquist spectrum sensing (MS 3 ) system capable of performing wideband spectrum sensing in a cooperative CR network over fading channels. The aliasing effects of sub-Nyquist sampling are modeled. To mitigate such effects, different sub-Nyquist sampling rates are applied such that the numbers of samples at different CRs are consecutive prime numbers. Moreover, the performance of MS 3 over fading channels (Rayleigh fading and lognormal fading) is analyzed in the form of bounds on the probabilities of detection and false alarm. The key finding is that the wideband spectrum can be sensed using sub-Nyquist sampling rates in MS 3 over fading channels, without the need for spectral recovery. In addition, the aliasing effects can be mitigated by the use of different sub-Nyquist sampling rates in a multirate sub-Nyquist sampling system.