Compressed sensing (CS) is often utilized to lower the complexity of cyclostationary detector (CD) in wideband sensing. In this paper, a methodology is proposed to further simplify the complexity for the combination of CS and CD. Firstly, the relationship between spectral coherence function (SCF) and the compressed samples is deduced in matrix form, thus the reconstruction of original signal can be skipped. Secondly, we notice complexity is highly dependent on compression ratio, which is determined by signal sparsity. Through careful analysis, a strong dependence of sparsity on modulation mode and symbol rate is discovered. Therefore we propose to adjust compression ratio according to the modulation mode and symbol rate of the target signal. To facilitate the adjustment, a modulation classification algorithm based on correlation of SCF is formulated. Moreover, the relationship between compression ratio and performance loss is also explored. Simulation proves our method can reduce complexity significantly with marginal loss in accuracy.