Performance of the instantaneous frequency based classifier distinguishing BFSK from QAM and PSK modulations for asynchronous sampling and slow and fast fading

In this paper we propose a feature to distinguish frequency from amplitude-phase digital modulations. We compare the performance of the feature where every symbol is sampled more than once to that where every symbol is sampled only once. The feature is based on the product of two consecutive signal values and on time averaging of the imaginary part of the product if a symbol is sampled more than once. 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 fast and slow fading, and of the symbol period and 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.