DPSK Versus FSK with Frequency Uncertainty

Expressions and curves of error probabilities of differential phase shift keying (DPSK) and noncoherent frequency shift keying (FSK) are obtained as a function of the pulse carrier frequency offset. These indicate that the frequency offset which causes the DPSK error probability to be larger than the FSK error probability is approximately
\Delta\omegaT
= 0.74. This crossover frequency appears to be a linear function of the signal-to-noise ratio over the range-4 dB to 14 dB. The crossover point is extended by sub-bit processing and the previous curves are modified for this case.