Error probability of a binary differentially coherent phase-shift-keyed system having a realisable receiver filter

The effect of using bandpass filters derived from lowpass filters by means of a standard lowpass-bandpass transformation as receiver filters in a binary differentially coherent phase-shift-keyed system is examined. The results presented show how the system-error performance depends on the ratios between the intermediate frequency (i.f.), bit rate and bandwidth. In particular, if the optimum value of the bandwidth/bit-rate ratio is chosen, for i.f./bit-rate ratios as low as 4, there is only a very small degradation in system performance relative to that obtained with the corresponding arithmetically symmetric receiver filter, which is more difficult to design.