Noise immunity of autocorrelation demodulator of signals with differential phase shift keying in the presence of rayleigh fading and harmonic interference

The wide spread of various radio systems with phase shift keying, including multi-position (MPSK), is due to their high noise immunity and ease of construction of the transmitting and receiving parts of the equipment. In real equipment, additional differential (relative) encoding is used when implementing transmitter and receiver circuits and, accordingly, DMPSK signals are used. One of the ways to receive such signals is to use an autocorrelation demodulator built on a quadrature scheme. The paper studies the noise immunity of an autocorrelation demodulator of signals with differential phase shift keying in the presence of Gaussian noise, Rayleigh fades and harmonic interference in the radio channel. The statistical parameters of signals and interference in the inphase and quadrature channels of the autocorrelation demodulator are determined. For M = 2 and 4, analytical formulas are obtained for the probability of a symbolic error, conditional on the random phase of harmonic. It is verified that the formula at M = 2 without harmonic interference reduces to an expression known from the literature. The values of the unconditional probabilities of symbolic errors are obtained by numerical averaging. It is shown that at a low level of harmonic interference, Rayleigh fading has a dominant effect. With a large level of interference, the additional energy loss can be several decibels, and at M = 4 these losses are significantly greater than at M = 2