Estimating the Influence of Modulating Noise on Broad-band Noise-like Signals

Mathematical modeling of multidimensional probability distribution density (PDD) under the influence of non-Gaussian fluctuating multiplicative noise is considered, on the basis of which the effect of modulating noise on broad-band noise-like signals is estimated. Cases are considered where a useful signal is exposed only to phase distortions, as well as to simultaneous effects of phase and amplitude distortions, for which multidimensional (N-dimensional) PDD are determined. A special case of determining a two-dimensional PDD of a useful signal is given. It is show that the desired PDD can be determined through one-dimensional PDD when a number of conditions are met. In particular, these conditions may be an increase in dispersion or depth of phase distortion of the signal. It has been show that N-dimensional PDD can also be expressed through PDDs of independent signal samples. It is noted that for a signal distorted by modulating noise, the uncorrelation of its samples means at the same time the independence of the latter. It has been shown that multiplicative noise affects the extraction of a useful signal mainly by changing the characteristics of said signal. It is show that the method of extracting a signal by exceeding a predetermined detection threshold in practically significant cases is the most acceptable. Dependencies of probability of correct and false detection of useful signal on parameters of fluctuating multiplicative noise are obtained. It is noted that when the signal level is significantly exceeded relative to the level of additive noise, multiplicative noise is the main source of distortion of useful information.