S.A. Yakushenko 1, S.V. Dvornikov 2, A.F. Kryachko 3, E.A. Popov 4, A.V. Zabelo 5

1 Institute of Radio Engineering, Electronics and Communications,

St. Petersburg State University of Aerospace Instrumentation (Saint-Petersburg, Russia)

2,5 Military Academy of Communications (Saint-Petersburg, Russia)

3 St. Petersburg State University of Aerospace Instrumentation

4 Graduate School of Applied Physics and Space Technology,

Peter the Great St. Petersburg Polytechnic University (Saint-Petersburg, Russia)

1 was16@mail.ru; 2 practicdsv@yandex.ru; 3 alex_k34.ru@mail.ru; 4 popov@spbstu.ru; 5 zabelo_an@mail.ru

Assessment and forecasting of indicators of stability of complex systems to external destructive factors is an urgent task. There are many ways to assess the multichannel system to the impact of destructive factors, which are based on the assessment of the stability parameters of the fixed states of the communication system and the impact. However, a multichannel radio communication system, depending on the number of means of action and their capabilities, can be in different states, differing in the values of the parameters of the quality of information transmission and resistance to impact. Existing approaches are limited in predicting the state of stability in the dynamics of temporary changes in the states of systems. Therefore, the article has developed a scientific and methodological apparatus that allows assessing the state of a multi-channel radio communication network in the conditions of the dynamics of changes in the process of exposure to destructive factors and its subsequent restoration through the use of a protective resource. The paper proposes an approach to predicting stability indicators by describing states with a Markov process. The mathematical apparatus allows us to obtain the dependence of the average stability of the network on time and find the probabilities of staying in a state based on the Markov process, and taking into account the results obtained, we can determine the average stability for given values of stability in each state.

The concept of a step includes time intervals of exposure to destructive factors and time periods of recovery of a multichannel radio communication system after exposure. In this case can be solved the problem of determining the values of the probability of being in a state in each time period from the moment of impact and the task of determining the probabilities stay in the status of each step control for fixed effects.

The paper assumes that the Markov process, which characterizes the functioning of a multichannel radio communication system, is homogeneous with known transition probability densities for all pairs of states. This allows us to apply an approach to estimating the probabilities of staying in a state based on a system of Kolmogorov differential equations, which together represent a mathematical model of the dynamics of changes in the functioning of a multichannel radio communication system, i.e. the Cauchy problem for a system of ordinary differential equations of the first order. To solve it, the article uses a difference method based on an iterative procedure. A numerical solution is obtained by the Runge-Kutta method. The probabilities of staying in acceptable conditions are generalized and presented in the form of an average probability that determines stability under the influence of destructive factors. the proposed approach makes it possible to predict the stability of a multichannel radio communication system to destructive factors in the dynamics of temporary changes in their states, and therefore, to determine the potential functioning of a multichannel radio communication system with given impact and protection resources..

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