Definition of the Statistical Characteristics of the Signal under Influence of Additive and Multiplicative Noise

Abstract

The issues associated with the influence of multiplicative (modulating) (otherwise amplitude distortions) and additive noises on the processed signal are considered. Statistical characteristics of the probability density function of instantaneous values of the signal under the influence of multiplicative (modulating) noise are considered. Expressions are obtained to determine the probability density function of the instantaneous values of the useful signal, as well as a mixture of the signal and additive noise under the action of multiplicative noise. It is shown that the obtained mathematical expressions make it possible to simulate the probability density function of the said mixture at an arbitrary distribution law of the envelope signal. The issues also associated with the analysis of statistical characteristics of the envelope of the mixture of non-Gaussian periodically non-stationary signal and additive noise in the case when the envelopes of elementary reflected signals are described by a Rayleigh distribution are considered. The expression to determine the joint probability density function of quadrature components of a signal reflected from an area of an extended object in the form of a two-dimensional normal distribution is obtained. It is shown that these components are correlated and are determined by non-Gaussian probability density functions with different variances of quadrature components and thus the sum signal does not satisfy the necessary stationarity conditions. The condition of the initial moment values of the signal is given under which the square of the processed signal is not time-dependent. The analysis showed that the statistical characteristics of the periodically non-stationary signal in the presence non-Gaussian noise are completely determined by the parameters characterizing the statistical properties of the signal and the influencing noise. It is shown that the statistical characteristic of non-Gaussian periodically non-stationary signal in the presence of non-Gaussian noise is completely determined by the parameters characterizing the statistical properties of the signal and the affecting noise.