  Wideband spectrum sensing is becoming increasingly important to cognitive
radio (CR) systems for exploiting spectral opportunities. This paper introduces
a novel multi-rate sub-Nyquist spectrum sensing (MS3) system that implements
cooperative wideband spectrum sensing in a CR network. MS3 can detect the
wideband spectrum using partial measurements without reconstructing the full
frequency spectrum. Sub-Nyquist sampling rates are adopted in sampling channels
for wrapping the frequency spectrum onto itself. This significantly reduces
sensing requirements of CR. The effects of sub-Nyquist sampling are considered,
and the performance of multi-channel sub-Nyquist samplings is analyzed. To
improve its detection performance, sub-Nyquist sampling rates are chosen to be
different such that the numbers of samples are consecutive prime numbers.
Furthermore, when the received signals at CRs are faded or shadowed, the
performance of MS3 is analytically evaluated. Numerical results show that the
proposed system can significantly enhance the wideband spectrum sensing
performance while requiring low computational and implementation complexities.
