Mathematical models of simple signals modulation for algebraic separation of noise in information communication systems

Abstract

The article is a continuation of the work [1] about the separation of the useful signal from the noise and the works [2,3], in which a method for solving systems of linear algebraic equations using QR decomposition based on the Gram-Schmidt method was proposed. The work is relevant because on the frequency axis of information communication systems it is impossible to find a section free from interference, it is always necessary to count on the case that the noise is in the entire available frequency range, a description of some sources of this noise is given in the introduction to this article. The development of modern information and communication systems is impossible without the use of mathematical models, because this affects the cost of research and is a prerequisite for the creation of research stands. The goal of this work is to build models for representing useful signals, an important direction in this is compliance with the criteria of mathematical models: adequacy, flexibility, acceptable complexity. The benefit from modeling can be obtained only under conditions when the correct (adequate) reflection of the properties of the original is ensured, and the problem of the complexity of research on real objects is also removed. Therefore, the work is extended in the direction of constructing analytical mathematical models of simple signals using modulation methods: amplitude, frequency, phase. The work contains graphs with a time sweep of simple signals, construction formulas and parameters, which include frequency, symbol rate and transmission period of one symbol, and also provides a verbal description of the demodulation process to assess the correctness of the modulation graphs. Therefore, the result of the work is analytical mathematical models that have adequacy and acceptable complexity, they can also be used to construct more complex models, for example, constructing a quadrature modulation model, where a change in two parameters is observed: amplitude and initial phase. Based on the results of the work, it can be concluded that the work is relevant, has a goal, result and direction of further research, which will be determined by mathematical models for constructing an interference system based on Fourier series and sinc functions, their additive addition to the useful signal, with the subsequent use of matrices of systems of linear algebraic equations (SLAE) and a comparison of the results obtained with conventional methods of the demodulation process, which are based on the use of correlation integrals.