Modeling of Correlated Two-Dimensional Non-Gaussian Noises

Abstract

The article describes and analyzes mathematical models of multiplicative and additive non-Gaussian noises affecting the useful signals. For synthesis and analysis, and, hence, the effective design of information systems and radio devices operating in conditions of intense perturbations it is necessary to choose not only the adequate mathematical model of the useful signals and information processes, but also the corresponding models of random effects, possessing in general non-Gaussian multiplicative and additive character. To describe the arbitrary non-Gaussian noises, which are quasiharmonic processes whose spectrum is close (or narrowband) to the band of the desired signal, the authors used a two-dimensional elliptic symmetric probability density function, including two extreme cases: Gaussian processes and a sinusoidal signal with random initial phase distributed uniformly in the interval [0, 2 π]. Model of correlated non-Gaussian narrowband noises of elliptically symmetric two-dimensional probability density function allows you to make a synthesis of information systems and devices based only on a priori knowledge of one-dimensional probability density function and the correlation function. Because knowing one-dimensional probability density function of the instantaneous values, we can determine the probability density function of the envelope; this makes it possible to use the elliptically symmetric probability density function to describe not only additive, but multiplicative (baseband) noises. To describe the real density of probability density function of the non-Gaussian process, the authors propose to approximate its a priori known one-dimensional probability density function and a specially designed transitional probability density function, and show the adequacy of this approximation of the real two-dimensional probability density function of correlated noises.