Oleksiuk V. Mathware and software for bit error rate research of digital modems with noise signals

The urgency of the development of mathware and software research of digital modems with noise signals is caused by the need to improve the results of bit error rate (BER) estimation characteristics of digital modems with complex signals. Over the last few decades, researchers have been drawn to ultra-wide signal communication systems, including the use of chaotic and noise signals as a carrier. The development of digital technologies has simplified the practical implementation of such systems. At the present stage, the underdevelopment of the methodology for estimating the potential BER of digital systems with noise carrier leads to the presence of significant errors in the calculations. In particular, this is manifested in significant differences between empirical and theoretical estimates of BER of such systems. Therefore, there is a need to develop new approaches to mathematical modeling and software design processes for analysis and simulation of digital modems to obtain a potential estimate of BER of such systems. The thesis is aimed at solving the current scientific and technical problem, which is to increase the accuracy of estimating the characteristics of digital modems' demodulators with noise signals through the development of mathware and software modeling of the estimating process their bit error rate. Development of appropriate mathware and software allows engineers to determine the prospects for the development of the system at the design stage, and at the implementation stage to select the optimal parameters of the system under conditions of interference of various origins. The work uses an object-oriented approach to describe the process of designing the software architecture for bit error rate research of digital modems with noise signals using a unified modeling language (UML). This approach allowed to improve the method of designing software for simulation of the estimating process the BER of digital modems with noise signals and to provide better simulation model support. Using the Java programming language, an object-oriented implementation of the studied models of digital modems was performed. A block diagram of a multiple access modem with correlation-time manipulation of the noise signal for K≥2 users is developed in integrated development environment and patented. The method of finding the minimum number of samples of the analog-todigital converter of a noise signal for the set level of the signal-to-noise ratio (SNR) is improved. This method allows increasing the efficiency of software implementation of a digital modem by applying exponential regression by reducing the probability of bit error and increasing the transmission rate for different levels of interference in a multiple access modem with correlated time manipulation of the noise signal. The increase transmission rate occurs by reducing the length of samples for the selected value of the SNR at the input of the demodulator. BER analysis is performed and methods of mathematical modeling of the BER estimation process of digital multiple access modems with correlation-time noise signal manipulation and binary modem with phase noise signal manipulation are developed. Software has been developed that simplifies the process of selecting the optimal parameters of these demodulators. For the listed modems as the information carrier the noise signal of type of white Gaussian noise and the autocorrelation method of reception of signals by the demodulator in the channel where the additive Gaussian noise operates is used. Investigations of BER of autocorrelation type systems in most cases are carried out using a Gaussian approximation of random variables (RV) in a demodulator. The influence of the presence of a non-Gaussian explosive distribution in a demodulator is considered for the first time to increase the accuracy of the theoretical assessment of the BER of the system. The study uses two methods for estimating BER, taking into account components with different laws of probability distribution in the functionality of the threshold detector: 1) Taking into account the non-Gaussian (quadratic) distribution in the demodulator of correlation time modems of binary and multiple accesses. In contrast to the existing methods, it takes into account the non-Gaussian law of component distribution, which makes it possible to obtain new analytical regularities for calculating the specified BER; 2) application of the characteristic function apparatus in the analysis of binary modems with correlation time and phase manipulation of the noise signal, which in contrast to the existing methods of Gaussian approximation of explosives allows to apply the laws of probability theory for functional transformations of explosives and obtain analytical expressions.