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HARMONIC LAW DISTRIBUTION RAYLEIGH-RICE IN THE COMMUNICATION CHANNELS WITH FADING
Aleksandr A. Smirnov, North-Caucasus Federal University, Stavropol, Russia, shursun@mail.ru
Victoria V. Bondar, North-Caucasus Federal University, Stavropol, Russia, viktori-bondar@yandex.ru
Olga D. Rozhenko, North-Caucasus Federal University, Stavropol, Russia, r.o.d@mail.ru
Anna D. Darjania, North-Caucasus Federal University, Stavropol, Russia, anna22051@yandex.ru
Marina V. Mirzoyan, North-Caucasus Federal University, Stavropol, Russia, vaganovna73@mail.ru
Lyudmila V. Belokon, North-Caucasus Federal University, Stavropol, Russia, lyu64133670@yandex.ru
Abstract
One of the main indicators of the quality of communication channels is noise immunity. This is an indicator that characterizes the probability of erroneous reception of an elementary symbol. Evaluation of this parameter is determined by the law of distribution of amplitudes, which is formed depending on the presence of noise in the communication channel. To determine the type of noise and distribution laws, radio-physical models of signal propagation are developed depending on the parameters of the propagation medium. At the same time, in modern radiophysical models of wave propagation in real media, the problem of determining the distribution of signal amplitudes at the receiving end point is posed. If there are no amplitude fluctuations in the models, the distribution of amplitudes in most problems is considered to be harmonic with an indefinite phase distributed uniformly. However, in addition to phase fluctuations as a result of various physical processes in the propagation of waves there are additional amplitude fluctuations in the wave front. Fluctuations can be caused by both additive amplitude oscillations caused by attenuation and as a result of in-terference processes and multiplicative noise caused by them. In most models, the distribution of amplitudes in a single beam is considered to be subject to the rice distribution or the Rayleigh distribution in the limiting case without a regular amplitude component. The article describes a new law of the distribution of amplitudes at the receiving end based on the averaging of the distribution of the amplitudes of the harmonic distribution law of distribution of amplitude of the regular component of rice. For this purpose, the article applies the method of integration with the hyperbolic cosine substitution. In addition, the article proposes a method for obtaining a number of harmonic laws of distribution of amplitudes with fading caused by wave interference. The paper presents graphical dependences of the obtained law of distribution of amplitudes. Also on the basis of numerical calculations according to the obtained expression the graphs of noise immunity estimation are presented. A recommendation to provide the required noise immunity index is proposed. It is shown that the presence of a second discrete beam significantly reduces the quality of the communication channel. The reliability of the obtained result is confirmed by the fact that in particular cases the obtained distribution is reduced to known expressions. Numerical calculations are consistent with theoretical ones.
Keywords: distribution law, rice distribution, Rayleigh distribution, one-way normal distribution, radio wave propagation models.
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Information about authors:
Aleksandr A. Smirnov, associate Professor, doctor of technical Sciences, Professor of the Department: Higher mathematics, Institute of mathematics and natural Sciences North-Caucasus Federal University, Stavropol, Russia
Victoria V. Bondar, associate Professor, candidate of physical and mathematical Sciences, head of the Department of Higher mathematics, Institute of mathematics and natural Sciences of the North Caucasus Federal University, Stavropol, Russia
Olga D. Rozhenko, candidate of pedagogical Sciences, associate Professor of Higher mathematics, Institute of mathematics and natural Sciences of the North Caucasus Federal University, Stavropol, Russia
Anna D. Darjania, candidate of pedagogical Sciences, associate Professor of mathematics, Institute of mathematics and natural Sciences North-Caucasus Federal University, Stavropol, Russia
Marina V. Mirzoyan, candidate of pedagogical Sciences, associate Professor of mathematics, Institute of mathematics and natural Sciences North-Caucasus Federal University, Stavropol, Russia
Lyudmila V. Belokon, candidate of technical Sciences, associate Professor of mathematics, Institute of mathematics and natural Sciences North-Caucasus Federal University, Stavropol, Russia