Cutoff rate for channel having precoding, continuous-phase modulation, and differential detection

The authors consider encoded M-ary continuous-phase-modulated signaling with suboptimal demodulation-decoding, a transmission scheme useful when bandwidth and power are limited. Demodulation is via differential detection, and decoding is optimal. It is assumed that additive white Gaussian noise is the only disturbance. A form of precoding that undoes, before it is done, the correlation among symbols introduced by the modulation and differential detection is developed. The duration of the frequency pulse may be one symbol time or more, and the other channel parameters are not much constrained by the analysis assumptions. The authors compute the cutoff rate R₀ for the channel, since R₀ is generally regarded as the quality measure of a channel over which coded data are to be sent. It is shown that a memoryless channel can be constructed from the original one and that R₀ is the same for both. Besides signal-to-noise ratio, R₀ is a function of only M and one other parameter and not directly of pulse type, duration, or modulation index. Examples are given of how to pick good channel parameters, good for both channel quality and narrowness of signal spectrum, for four families of frequency pulse. Finally, R₀ for the studied channel is compared with R₀ for the coherent channel with optimal demodulation-decoding