Automatic modulation classification is one of the most challenging problems of cognitive radio and has significant commercial and military application. This letter focuses on blind modulation classification of first-order cyclostationary signals under a Gaussian channel. A detailed theoretical analysis of the first-order cyclostationarity test has been performed. We present the theoretical expressions of the probability of false alarm P-fa and the probability of detection P-d as a function of the selected threshold for the first-order cyclostationarity test based constant false alarm rate detector. The P-d is presented for only AM and M-FSK signals, which are the only signals that possess first-order cyclostationary features. Theoretical formulations presented in this letter are validated by extensive simulation results.