Optimum MSK-type receivers for CPM on Gaussian and Rayleigh fading channels

The utilization of continuous phase modulation (CPM) schemes makes it possible to construct power efficient modulation with very attractive power spectra. However, problems arise with these schemes as a consequence of receiver complexity. A maximum-likelihood sequence detector implemented by means of a Viterbi detector is needed for an optimum coherent detection of CPM schemes. There exist cases of CPM, however, for which the use of the Viterbi detector is unnecessary. The present investigation is concerned with an analysis of a parallel MSK (minimum frequency shift keying) type of receiver, taking ito account a general CPM signal. A distance measure providing asymptotic performance on the Gaussian channel is introduced, and error probability formulas are given both for the Gaussian and the Rayleigh fading additive channels. Optimum filters are presented for several smooth CPM schemes with low spectral sidelobes.