Volterra Filter Performance Analysis

At present,China is a leader in the fifth generation communications technology market(5G).The application of new standards in information transmission systems requires us to work with frequency bands whose frequency is tens of gigahertz.High-frequency communication lines cannot be designed without non-linear filters,it follows that without research in the field of non-linear filtering,it will be impossible to maintain and increase the rate of development of infocommunication systems.In addition to working on the development of new nonlinear filtering algorithms and solving purely applied problems,attention should also be paid to fundamental studies of filter charac-teristics.The most often applicable,in the theory of nonlinear filtering,are Voltaire filters,the adaptive and non-adaptive algorithms of which are based on finding.the kernels of the Voltaire-Wiener integral series.The study of the performance of adaptive algorithms based on the theory of Voltaire and the study of the methodology for determining the kernels of the Voltaire-Wiener integral series will allow the construction of more advanced high-frequency communication systems.The.aim of this work is to study the performance characteristics of adaptive(least means squares)LMS and Leaky-LMS.Voltaire filters,as well as to consider the methodology for de-termining Voltaire kernels using the method of purposeful systems and practical application in solving the problem of identifying a black box.using the example of determining the char-acteristics of a strongly nonlinear electric.circuit to compensate anti-traction currents railway tracks.Ideas for further development of the theory of identification and mathematical modeling of physical systems will also be proposed.This work is divided into three chapters:The first chapter is an introduction.It carried out a retrospective analysis of the develop-ment of Voltaire's theory,adaptive filtering methods,problems solved by non-linear filtering algorithms,substantiating the choice of the research topic and its significance.The second chapter is devoted to adaptive Voltaire filters,namely the analysis of the performance of LMS and Leaky-LMS Voltaire filters.The analysis was performed from the point of view of energy conservation and was demonstrated under various restrictions for the input signal.Cases of the Gaussian and non-Gaussian regressors are considered.In the third chapter,an algorithm for determining Voltaire kernels is considered using the example of a second-order Voltaire series.The problem of identifying a black box represented by an RLC-circuit and the described system of second-order differential equations is solved;examples of the practical application of such identification on railway tracks and in control systems for uncontrolled access to fiber-optic networks are illustrated.