Probabilities of False Alarm and Detection for the First-Order Cyclostationarity Test: Application to Modulation Classification

Abstract

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.