A significant challenge of cognitive radio (CR) is to perform wideband spectrum sensing in a fading environment. In this paper, a novel multi-rate sub-Nyquist spectrum detection(MSSD) system is introduced for cooperative wideband spectrum sensing in a distributed CR network. Using only a few sub- Nyquist samples, MSSD is able to sense the wideband spectrum without full spectrum recovery. Specifically, given the low spectral occupancy, sub-Nyquist sampling is performed in each sampling channel and a test statistic is formed by using sub-Nyquist samples from multiple sampling channels. Furthermore, the use of different sub-Nyquist sampling rates is proposed to improve the system detection performance, and the performance of MSSD over both non-fading and Rayleigh fading channels is analyzed. Numerical results show that MSSD can considerably improve the wideband spectrum sensing performance in a fading scenario, with a relatively low implementation complexity and a low computational complexity.