  Spectrum sensing in cognitive radio necessitates effective monitoring of wide
bandwidths, which requires high-rate sampling. Traditional spectrum sensing
methods employing high-precision analog-to-digital converters (ADCs) result in
increased power consumption and expensive hardware costs. In this paper, we
explore blind spectrum sensing utilizing one-bit ADCs. We derive a closed-form
detector based on Rao's test and demonstrate its equivalence with the
second-order eigenvalue-moment-ratio test. Furthermore, a near-exact
distribution based on the moment-based method, and an approximate distribution
in the low signal-to-noise ratio (SNR) regime with the use of the central limit
theorem, are obtained. Theoretical analysis is then performed and our results
show that the performance loss of the proposed detector is approximately $2$ dB
($\pi/2$) compared to detectors employing $\infty$-bit ADCs when SNR is low.
This loss can be compensated for by using approximately $2.47$ ($\pi^2/4$)
times more samples. In addition, we unveil that the efficiency of incoherent
accumulation in one-bit detection is the square root of that of coherent
accumulation. Simulation results corroborate the correctness of our theoretical
calculations.
