Description: The article discusses the method for estimating the multiplicity M of the multilevel phase manipulation of the Multiple Phase-Shift Keying (MPSK) signal and its frequency by observation in white noise with an unknown distribution law. The properties of the nonparametric estimation of the multiplicity of the multilevel phase manipulation of the signal obtained using BDS statistics are studied, as well as the properties of the phase portraits of such signals. The dependences of the BDS statistics on the multiplicity of the multilevel phase shift keying and frequency at different signal-to-noise values are given. As the signal-to-noise ratio increases, the probability of correctly estimating the multiplicity of the multilevel phase manipulation reaches one for M = 2.4.8 already with values of q ≥ 0.6 (-4.5 dB), the greatest sensitivity to the noise level is observed at M = 16 . At the same time, to estimate the frequency, with the same order of phase manipulation, it is necessary to have a larger signal-to-noise ratio. It is shown that in the structure of the set of points of the MPSK phase portrait, isolated points appear due to violations of the continuity of the process of the second kind at the time of its phase jumps. In addition, at a moderate level of noise, the phase portrait contains signs of the multiplicity of phase manipulation, which are insensitive to the initial phase of the process. The study of phase portraits, multipositional phase shift keyed signals based on the analysis of the complex envelope, after transferring the Multiple Phase-Shift Keying oscillations to a low frequency, is being conducted. The results of the paper can be used to automate the approach to the "blind" determination of signal parameters with unknown properties of observation noise.
Keywords: MPSK process, Multiple Phase-Shift Keying, estimate of the multiplicity of manipulation, estimate of the frequency of manipulation BDS-statistics, probability of a correct assessment, phase portrait, isolated points
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