Analysis of Statistical Characteristics of Probability Density Distribution of the Signal Mixture and Additive-multiplicative non-Gaussian Noise

It is noted that in real cases, as a rule, observed random processes have non-Gaussian nature of distribution. Statistical characteristics of the probability density function (PDF) of instantaneous values of the signal under the influence of the multiplicative noise, leading to amplitude and phase distortion are considered. Statistical characteristics of the envelope of the mixture of additive Gaussian noise and the signal under the influence of the multiplicative noise with Nakagami PDF are considered. Such combination is typical for many practically important cases. Statistical characteristics of the envelope of the additive mixture of a deterministic signal and non-Gaussian noise are considered. The expressions of generalized conditional and unconditional PDF of the envelope of the additive mixture are given. The PDF of the amplitude (PDFA) expression of non-Gaussian signal in the presence of non-Gaussian noise is given. It is determined by three parameters of the depth of signal fluctuations and two noise parameters. The PDFA expression is obtained when deterministic signal amplitude is absent. For these PDFs a family of curves is presented; impact of the distribution parameters on their shape is analyzed. The expression to determine the v-th initial moments of PDFA is presented. It is shown that the PDFA of the mixture of non-Gaussian signal and additive-multiplicative noise is fully determined by the distribution parameters characterizing depth of fluctuations of the signal and additive noise.