The Probabilistic Characteristics of the Logarithmic Ratio of APSK Signal Adjacent Symbol Amplitudes

To implement high-speed systems for transmitting discrete information, amplitude and phase-shift keyed signals are widely used. Differential shift keying of the ratio of the amplitudes of adjacent symbols makes it possible to abandon the calibration of the amplitude characteristics of the reception path, while determining the probabilistic characteristics of this ratio and especially its log-rhyme is relevant. In this paper it is shown that the probabilistic characteristics of the logarithm of the ratio of the amplitudes of adjacent symbols under the influence of Gaussian noise do not depend on the absolute levels of the signal and noise, but are determined only by their ratio. The corresponding approximate expressions are obtained, and the influence of the type of amplitude and phase-shift keyed signal constellation is studied and its parameters. Statistical simulation is carried out. It is noted that the research results can be used in the design of communication systems.