Fast digital algorithms for the coherent demodulation of the phase-shift keyed signals

We introduce the fast digital algorithms for the coherent demodulation of binary and four position differential phase-shift keyed signals. These algorithms can be practically implemented with the minimum number of simple arithmetic operations over the input signal period and they are is fully compatible with the modern hardware components available. We obtain the timing diagrams of the demodulators responses and we also determine the probabilities of error demodulation. It is shown that the considered algorithms provide a potential interference immunity when receiving the signal against Gaussian white noise.