Quickness of the instantaneous frequency based classifier distinguishing BFSK from QAM and PSK modulations

In this paper we study the quickness of a classifier based on simple feature that we have previously proposed to distinguish frequency from amplitude-phase digital modulations. The feature is based on the product of two consecutive signal values and on time averaging of the imaginary part of the product. First, the conditional probability density functions of the feature given the present modulation are determined. The central limit theorem for strictly stationary m-dependent sequences is used to obtain Gaussian approximations. Then thresholds are determined based on the minimization of the total probability of misclassification. Following that effects of carrier offsets, of fast fading, and of the symbol period and time delay being non-integer multiples of sampling period on the performance are studied. In the course of doing that, the proposed classifier is compared to the maximum likelihood classifier and the wavelet based classifier using support vector machine.