DETERMINATION OF STATISTICAL CHARACTERISTICS OF NON-GAUSSIAN ENVELOPE RELATIONS SIGNALS AND MIXTURES OF THE GAUSSIAN PROCESS WITH NON-GAUSSIAN
V. M. Artyushenko1, V. I. Volovach2,3
1Moscow State University of Geodesy and Cartography, Moscow, Russia
2Volga Region State University of Service, Togliatti, Russia
3MIREA - Russian Technological University, Moscow, Russia
Keywords: non-Gaussian signal, envelope ratio statistics, average number of outliers, incoherent processing, joint probability density, signal polarization parameters, generalized non-Gaussian distribution
Abstract
Statistical characteristics of the envelope ratios of two non-Gaussian signals and a mixture of two random processes with given distribution laws were determined. One-dimensional Density of Probability Distribution (DPD) for the ratio of envelopes of two independent non-Gaussian signals during incoherent processing, joint DPD of envelopes and their derivatives, as well as the average number of outliers were found. It is shown that one-dimensional DPD depends on the parameters characterizing the shape, scale and center of distribution of signal envelopes. Special cases of DPD calculations for Rayleigh and Rice distributions are given. Statistical characteristics of the polarization parameters of the signal, such as the DPD and the average number of emissions of the ellipticity coefficient, are obtained. Statistical characteristics are defined for the mixture ratio of two random processes with a normal distribution law and with a generalized non-Gaussian distribution. In particular, expressions were obtained for determining the DPD of a mixture of the two above processes, v-initial moments and an integral distribution function of the mixture of processes were found. The expressions DPD of the envelope of the useful signal in the presence of normal interference, DPD of the ratio of two statistically independent mixtures, DPD of the polarization phasor module, joint DPD of the mixture of two independent stationary processes and the average number of emissions are obtained.
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