Performance analysis of a statistical test for presence of cyclostationarity in a noisy observation

The purpose of this paper is to evaluate theoretically in terms of receiver operating characteristics (ROC) the performance of a statistical test (based on the second order statistic) for the presence of cyclostationarity in a noisy observation. In order to obtain false alarm and detection probabilities, we consider the following specific situation: we choose a cycle frequency contained in a binary-phase-shift-keyed (BPSK) signal of interest (SOI) (BPSK signal is considered for its increasing attention in digital communications) and we test the presence of cyclostationarity of the SOI in a noisy observation. Two examples are considered, the SOI is buried either in a stationary Gaussian noise or in an another BPSK signal