The possible options in designing digital coherent demodulators of multi-level phase-shift keyed (MPSK) and multi-level differential phase-shift keyed (MDPSK) signals based on a digital phase detector are studied. The demodulation algorithms are introduced that provide optimal digital coherent signal processing. Digital MPSK signal processing requires phase synchronization of the samples produced by the analog-to-digital converter, while the demodulator of MDPSK signals can be implemented without phase synchronization of the reference clock. The analysis of the signal processing procedures is carried out and the time realizations of the responses of the processing algorithms are demonstrated. The estimates of the interference immunity of the proposed demodulation algorithms and the results of statistical simulation of their operation are obtained. The software or hardware implementation of the considered algorithms is discussed.

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