Classification of multiple M-ary frequency-shift keying signals over a Rayleigh fading channel

We develop and analyze classifiers for multiple M-ary frequency-shift keying (MFSK) signals traveled over a static frequency nonselective Rayleigh fading channel. The classifier is based on approximating the likelihood function (LF) of the frequency modulated digital signals and is derived for both synchronous and asynchronous waveforms. Two cases are considered; the first one is concerned with the signals that have identical modulation type [for example, binary FSK (BFSK) or quaternary FSK (QFSK)]. The second case deals with the signals with different modulation type. We use complex envelope representation of the signals and noise to derive the LF. Simulation experiments are illustrated to validate the theoretical developments