The frequency diversity exhibited by cyclostationary signals is exploited in this paper. A novel rank-1 frequency-domain representation of a digital waveform is proposed to address the generalized likelihood ratio (GLR) detection of a cyclo-stationary signal with unknown white noise. With the aim of avoiding the well-known sensitivity of cyclostationary-based detectors to frequency-selective fading channels, a parametric channel model based on the coherence bandwidth is adopted and incorporated in the GLR test. The proposed detector outperforms the classical spectral correlation magnitude detectors by exploiting the rank-1 structure of small spectral co-variance matrices