The sensing scheme based on the generalized likelihood ratio test (GLRT) technique has attracted a lot of research interest in the field of cognitive radios (CR). Although its potential advantages in detecting correlated primary signal have been illustrated in prior work, no theoretical analysis of the positive effects of the correlation has appeared in the literature. In this letter, we derive the theoretical false-alarm and detection probabilities of GLRT detector. The theoretical analysis shows that, in the low signal-to-noise ratio (SNR) region, the detector's performance can be improved by exploiting the high correlations between the primary signal samples. The conclusions of the analysis are verified by numerical simulation results.