SIMULATION OF A MULTIPATH COMMUNICATION CHANNEL

Abstract

In the article, the simulation of a multipath communication channel with two bands or subbands (intervals) of frequencies, the system function of which is expressed in a closed form through elliptic functions. A multipath communication channel is a linear system with time various parameters. Multipath leads to the fact that there is always a certain number of errors. They characterize the lower limit of the probability of errors, regardless of the applied methods of error-correcting coding and an unlimited increase in the energy potential of the radio link. Mathematical simulation of a multipath communication channel provides the joint consideration of time delays and Doppler frequency shift of the received signal. The correlation between the transfer function 퐻 (휔,푡) and the system function 푆 ̃(휏,휔 ̃) is shown. Іn the article at the first time, the mathematical theory of elliptic functions and elliptic integrals is applied to the definition of a system function, which in known literature sources is determined using the mathematical methods of statistical analysis. In article is shown the application an approach to mobile radio systems, which are operating in several frequency bands, such as a combined mobile digital troposcatter-radiorelay station or a digital troposcatter station. Their work is carried out in two frequency bands or two frequency subbands (transmit / receive). Therefore, in this case it becomes very difficult to create a mathematical model of a multipath communication channel with the definition of system functions. This situation is complicated if a frequency adaptation system is used. At the same time, several frequency intervals are used to combat fading and interferences, in the simplest case – two intervals. The article describes the approach to the representation of system functions through elliptic functions. This allows to have close form of the transfer function for the multipath communication channel. For the considered case of two-frequency intervals, the final expression is written in terms of theta-functions and the complete elliptic integral of the first kind.