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The mathematical analysis of the probabilistic characteristics of signals transmitted through compressed communication channels with orthogonal frequency separation in the presence of fading in the communication channel obeying the Nakagami-m distribution law is carried out in the paper. In contrast to previous studies, the effect of a non-uniform distribution of the fading phase in a communication channel on the probability of signal reception errors is examined. A unified mathematical expression of the generating function of moments is presented for the fading coefficients in the communication channel in the frequency domain, distributed in accordance with the Nakagami-m law with non-uniform phase distributions. Thus, the classical methods for determining the generating function of moments can be directly used to determine the exact mathematical representation of the probability of error receiving signals for various types of modulation and diversity of signals.