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

Power efficient schemes with excellent power spectra are contained among the continuous phase modulation (CPM) schemes. This is a constant envelope digital modulation technique, which in general requires a maximum-likelihood sequence detector (Viterbi detector) for efficient detection. This optimum receiver is sometimes complex. In this paper a parallel MSK-type receiver is studied. It is useful for binary schemes with modulation index h = 1/2. We consider coherent detection of signals transmitted over an additive white Gaussian noise channel and also over a Rayleigh fading channel. The MSK-type receiver can be implemented with only two filters and simple decision logic. Error probability formulas are given both for the nonfading and the fading channel. A simple algorithm giving the optimum filter for the Gaussian channel for high signal/noise ratios is presented. The optimum filter for low signal/noise ratios is also derived. For intermediate signal/noise ratios numerical optimisations are presented, both for the Gaussian and the Rayleigh fading channels. We have also considered diversity schems with ideal two-branch maximal ratio combining and selection combining. The optimum receiver filters are given for some selected schemes. It is shown that also, for the more complex CPM schemes, the loss compared to the optimum receiver is moderate.