Analytical representation of generalized MSK signals and coherent receiver design criterion

A significant, exact representation of generalized MSK signals is proposed, whatever the modulation pulse-shaping waveform, which is assumed to be included in a time range equal to LT, T=symbol time. This representation shows that the complex envelope of the generalized MSK signal is a combination of various functions, dependent on the modulation pulse shaping which are suitably weighted by the input bits. The present representation suggests a very simple way of designing the postdetection filter by means of a criterion leading to cancellation of the intersymbol interference due to the most significant function characterizing the structure of the CPM (continuous phase modulation) signal. In this way a closed form for the receiver filter is easily obtainable whatever the modulation pulse shaping of the transmitted signal or the signal-to-noise ratio at the receiver. The numerical results obtained show a significant improvement, in all the cases analyzed, with respect to the choice referred to the average matched filter, and are very close to various results reported in the literature deriving from complex design criteria