The model for evaluating the influence of the phase error of the coherent demodulator synchronization system on the bit error probability of multi­position phase manipulation signals

Abstract

In the article, a new topical scientific task is solved regarding the assessment of the impact of the error of the synchronization system of the coherent demodulator on the immunity of signals with multi-position phase manipulation. The probability of a bit error is proposed in the article as a criterion for evaluating the immunity of coherent reception of signals with multi-position phase modulation in the presence of a phase error. A model for evaluating the effect of the error of the coherent demodulator synchronization system on the bit error probabilities of signals with multi-position phase manipulation is developed and presented. The presented model is based on the probabilistic characteristics of the appearance of a bit error of a signal with multi-positional phase modulation relative to the accepted level of the phase error of the coherent demodulator at different values of the signal-to-noise ratio at the input of the coherent receiver for signals with different positions. The results of the evaluation of the probability characteristics of the appearance of a bit error in a signal with multi-positional phase modulation in the presence of a phase error of a coherent demodulator showed that with an increase in the positionality of the BFM signal, the influence of static and random errors of the synchronization system on the probability of bit errors increases. At large signal-to-noise ratios, a small phase estimation error, from π/180 to π/90, leads to a significant increase in the probability of bit errors. With random phase fluctuations for signals with M ≥ 4, when the variance Dϕ changes from 0 to 0.01, the error probability can be changed by one or two orders of magnitude. The obtained results allow us to come to the conclusion that during the reception of BFM signals, the permissible value of the carrier phase estimation error depends on the positionality of M and varies from π/36 – π/72 for 2-FM to π/180 for 32-FM.