Detection and classification of spectrally equivalent processes using higher order statistics

This paper addresses the problem of detecting two spectrally equivalent processes, which are modeled by a noisy AR process and an ARMA process. Higher order statistics (HOS) are shown to be efficient tools for detection. Two HOS-based detectors are derived for the binary hypothesis testing problem (i.e., known signal spectrum): The first detector exploits the asymptotic Gaussianity of the sample estimates of the cumulants. The second detector exploits the singularity of a certain matrix based on HOS. The more general composite hypothesis testing problem (i.e., with unknown signal spectrum) is then considered and a detector proposed. The performances of the different detectors are compared in terms of receiver operating characteristic (ROC) curves. Approximate closed-form expressions are derived for the threshold and the ROCs of the three detectors