Razvoj metoda i algoritama za procenu performansi komunikacionih sistema primenom aproksimacija specijalnih funkcija

Abstract

The intensive development of wireless communication systems has been accompanied by the need to develop methods and algorithms for implementing appropriate approximations of special functions in order to efficiently estimate the corresponding performance of these services through their application. In order to evaluate the behavior of digital communications systems, it is necessary to estimate standard performance measures for the observed wireless communications systems, various modulation types application, detection types, as well as channel models, and observe relations between performance and key values of system parameters. The analysis of the average bit error rate at reception for the applied modulation format is one of the tools for assessing service performance, that describes the nature of the wireless communication system in the best manner. In order to analytically evaluate the average bit error rate for the applied modulation format, it is necessary to perform the most accurate implementation of the approximation of special functions erfc(x), erf (x), Marcum Q, in the widest input range values. The dissertation will present composite methods of the special functions’ approximations. In addition to the simplicity of realization in approximating the observed functions, the aspect of robustness of approximations absolute and relative error values in a wide range of input parameters values will be considered. The advantages of the proposed solutions will be highlighted by direct comparison with the absolute and relative errors obtained by using the known special functions’ approximations from the literature. Furthermore, when transferring information through fading communication channels, for cases of application of proposed special functions’ approximations, it will be proved that system performance can be determined more easily by applying solutions proposed in the dissertation. In this way, it would be easier to determine the probability of the error of communication systems due to different types of fading existance in the channel. By comparing predicted values of the average bit error rate at reception, when transmitting signals through various communication channels medias, for cases of application of existing, previously proposed special functions’ approximations, with the average bit error rate at reception obtained by calculation based on the proposed approximation solutions, it will be shown that communication performances can be calculated more precisely. Proposed approximations could also be used in the source coding of the signal and could simplify design and realization of the quantizers.