THEORETICAL STUDY OF ESTIMATING THE PROBABILITY OF A CONNECTION IN SYSTEMS WITH BROADBAND SIGNALS AND FHSS

The article is devoted to a theoretical study of the probabilistic characteristics of communication systems with broadband signals and pseudorandom tuning of the operating frequency in a complex electromagnetic environment. An analytical tool for calculating the communication probability is presented, taking into account the complex effects of multipath propagation, frequency-selective fading, and intentional interference. The dependence of the communication probability on the signal-to-noise ratio is investigated using integral expressions that take into account the normal power distribution at the input of the receiving device. A mathematical analysis of the transmission function of the communication channel as a complex characteristic describing the amplitude-frequency and phase distortions during signal propagation is performed. Theoretical models of synchronization processes are developed, including the stages of signal search, capture, and tracking, using the Markum function to describe the probability of signal detection against the background of Gaussian noise. Methods for optimizing the key parameters of the RFP system, such as the frequency tuning period, the total number of frequency channels, and the width of the protective frequency interval, are proposed. The theoretical foundations of adaptive control based on the maximum likelihood method and recursive filtering for estimating the parameters of the channel\are described. The energy efficiency of systems with RFP is studied, taking into account the frequency tuning losses and the necessary adjustment of the signal-to-noise ratio. A comprehensive indicator of the quality of a communication system combining probabilistic, energy, and time characteristics of the system is proposed. Analytical expressions are developed for estimating the intensity of synchronization failure based on statistical analysis of experimental data and calculation of the covariance matrix of measurement noise. The expediency of using reference signals to increase the reliability of measurements of communication channel parameters in adaptive control of the system is justified. Relations are derived for determining the duration of the synchronization window, taking into account the maximum allowable time of entering synchronism and the margin factor, which takes into account possible frequency instabilities of the reference generators.  The influence of the protective frequency interval on preventing inter-channel interference and ensuring electromagnetic compatibility of neighboring channels is analyzed. The presented theoretical results provide a scientific basis for the design of radio systems with increased noise immunity and can be used in the development of adaptive algorithms for controlling RF control systems in a dynamically changing electromagnetic environment, ensuring a balance between the reliability of information transmission and the efficiency of using frequency-time resources of the communication system.