Detection of cyclostationary primary user (PU) signals in colored Gaussian noise for cognitive radio systems is considered based on looking for a cycle frequency at a particular time lag in the cyclic autocorrelation function (CAF) of the noisy PU signal. We explicitly exploit the knowledge that under the null hypothesis of PU signal absent, the measurements originate from colored Gaussian noise with possibly unknown correlation function. We consider both single and multiple antenna receivers. A performance analysis of the proposed detector is carried out. Supporting simulation examples are provided using an OFDM PU signal and they show that our proposed approaches are computationally much cheaper than the Dandawate-Giannakis and related approaches while having quite similar detection performance for a given false alarm rate.