The first Nyquist criterion applied to coherent receiver design for generalised MSK signals

A simple procedure for designing the post-detection filter of an MSK-type receiver for continuous phase modulation with modulation index h=0.5 (generalized MSK signals) is proposed: the criterion descends from a useful, general representation of this class of signals. The frequency response of the baseband receiver filter is analytically optimized in closed form whatever the modulation pulse shaping of the transmitted signal, and signal-to-noise ratio at the receiver. The criterion is pointed out through a significant, exact representation of generalized MSK signals, whatever the modulation pulse-shaping waveform, which is assumed to be included in a time range equal to LT, T=symbol time. The main part of intersymbol interference, as appears from the representation of the CPM signal, is cancelled by applying the Nyquist criterion to the most significant function among those describing the signal structure. The numerical results obtained show a performance improvement with respect to the averaged matched filter (AMF) criterion and are very close to the results reported in the literature, deriving from more complex design criteria. The suitability of the design criterion is also tested in the presence of interferers, showing a significant advantage of the proposed filter when considering adjacent channel interference