A. A. Smirnov – Dr.Sc. (Eng.), Associate Professor, Professor,

North-Caucasus Federal University (Stavropol)

E-mail: shursun@mail.ru

M. A. Solchatov – Ph.D. (Eng.), Associate Professor,

North-Caucasus Federal University (Stavropol)

V. V. Bondar – Ph.D. (Phys.-Math.), Associate Professor, Head of Department,

North-Caucasus Federal University (Stavropol)

O. D. Rozhenko – Ph.D. (Ped.), Associate Professor,

North-Caucasus Federal University (Stavropol)

A. D. Darjania – Ph.D. (Ped.), Associate Professor,

North-Caucasus Federal University (Stavropol)

L. V. Belokon – Ph.D. (Eng.), Associate Professor,

North-Caucasus Federal University (Stavropol)

In modern conditions of urban development and distribution of multi-channel and broadband communication channels such as Wi-Fi, 4G or perspective 5G, multipath signal propagation is increasingly observed. This leads to significant fading at the receiving point. The most effective way to combat fading is diversity reception. At the same time, with the increase in the number of subscribers and, accordingly, communication lines, there is a need for electromagnetic compatibility of communication devices. For the most accurate recommendations on the use and placement of stations for receiving and transmitting of signals, the most accurate calculation of the quality indicators of such lines is necessary. At the same time, the existing models for N-multiple diversity have numerical mathematical methods for calculating quality indicators. Thus, the question of obtaining strict analytical dependences of the quality parameters of communication channels on the energy, geometrical and other parameters of the communication line remains relevant.

The article deals with the issues of accurate analytical calculation of noise immunity or the probability of erroneous reception of an elementary symbol in the binary communication channels for triple signal reception. The given technique can be extended to quadruple reception.

For communication channels with more than double diversity, numerical calculations of mathematical models are used to assess their quality. In most cases the amplitude fading of the Rayleigh nature are observed in the communication channels. Therefore, the model of the communication channel with this type of signal fading has been considered. The model of triple incoherent signal reception has been considered. The analytical expression for estimation of error probability of incoherent reception of signals in the communication channel of the triple reception with a various degree of correlation in the branches of diversity in the conditions of Rayleigh fading has been derived in the work. The solution has been obtained by calculating the eigenvalues of the matrix of correlation dependences of the diversity branches. It has been assumed that different degrees of signal correlation can be observed in the diversity branches. The obtained results have been used to calculate the noise immunity of the communication channel. A comparison with computer simulation based on numerical calculation has been given.

The reliability of the result is confirmed by the fact that in particular cases the obtained expression is reduced to known ones. Graphical dependences of both numerical and analytical calculation of noise immunity of triple reception have been presented. The results have a sufficiently exact match acceptable for assessing the quality of such a communication channel. Analytical expressions allow to carry out mathematical (differential, integral, limit, etc.) analysis of communication channel models of triple signal reception. Using this technique, you can get similar expressions for quadruple signal reception. In addition, in the future in the models of communication channels one can consider more general Rician fading or four-parametric fading or even deeper one-way-normal fading, which are often found in dense urban development.

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