Detection of cyclostationary primary user (PU) signals in colored Gaussian noise for cognitive radio systems is considered based on looking for single or multiple cycle frequencies at single or multiple time lags 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 possible colored Gaussian noise with unknown correlation function. Our formulation allows us to simplify the spectrum sensing detector and obviates the need for estimating an unwieldy covariance matrix needed in some prior works. We consider both single and multiple antenna receivers, and both nonconjugate and conjugate CAFs. A performance analysis of the proposed detector is carried out. Supporting simulation examples are provided to demonstrate the efficacy of the proposed approaches and to compare them with some existing approaches. Our proposed approaches are computationally cheaper than the Dandawate-Giannakis and related approaches while having quite similar detection performance for a given false alarm rate.