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Envelope statistical characteristics for mixture of non-Gaussian periodically non-stationary signal and additive noise

Keywords:

V.M. Artyushenko – Dr. Sc. (Eng.), Professor, Head of Department of Information Technology and Management Systems, Technological University (Korolyov, Moscow region) E-mail: artuschenko@mail.ru V.I. Volovach – Dr. Sc. (Eng.), Associate Professor, Head of Department of Information and Electronic Service, Volga Region State University of Service (Togliatti) E-mail: volovach.vi@mail.ru


The statistical characteristics of the envelope of the mixture of non-Gaussian periodically non-stationary radio signal and non-Gaussian additive noise typical for short-range radiolocation when a sensed reflection signals from extended objects are considered and analyzed. The expression to determine the joint probability density function (PDF) 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 PDFs 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. Expressions to determine the PDF of the envelope of the signal (including fluctuating signal) and expressions for the ν-th initial moments are obtained. 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 by setting different values of these parameters it is possible to obtain statistical characteristics of the envelope of the additive mixture of a large class of combinations of probabilistic models of the useful signal and noise, widely used in the synthesis and analysis of short-range electronic systems and devices.
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