UDC 621.391: 621.396: 621.369
DOI: 10.36871/2618-9976.2021.06.004

Authors

Valery A. Pakhotin
Doctor of Physical and Mathematical Sciences, Professor, Institute of Physical Technical Sciences and Information Technologies of the Immanuel Kant Baltic Federal University «IKBFU», Kaliningrad, Russia
Ksenia V. Vlasova
Candidate of Physical and Mathematical Sciences, Associate Professor, Baltic State Academy of the BGA RF fishing fleet, Kaliningrad, Russia
Roman V. Simonov
Postgraduate Student, Institute of Physical Technical Sciences and Information Technologies of the Immanuel Kant Baltic Federal University «IKBFU», Kaliningrad, Russia
Sergey V. Petrov
Postgraduate Student, Institute of Physical Technical Sciences and Information Technologies of the Immanuel Kant Baltic Federal University «IKBFU», Kaliningrad, Russia

Abstract

In this paper, the potential possibilities of the maximum likelihood method for solving statistical problems of radio engineering are analyzed. A condition is introduced for the correlation interval of a random vector of parameters of a set of signals, which expands the scope of the maximum likelihood method under conditions of a priori and parametric uncertainty. Proofs are given that the known methods of spectral, correlation analysis, and angular spectral analysis are special cases of the maximum likelihood method. The scope of their application for signal processing is limited. They determine the optimal estimates of the signal parameters only when the adopted implementation contains a single signal. The substantiation of the possibility of obtaining solutions to statistical problems of radio engineering in the field of nonorthogonality of signals, when spectral lines, correlation functions, radiation patterns partially coincide, is given. The issues of solving the problem of separate detection of a set of signals based on the proposed optimal receiver are discussed. The issues of separate estimation of signal parameters in the area of their nonorthogonality are discussed. The conditions of the maximum resolution of signals are analyzed. The possibility of creating maximum likelihood filters based on likelihood equations is discussed. It is shown that such filters allow separating signals in the area of their nonorthogonality. They are the basis for solving the problem of channel sealing in communication systems. They make it possible to develop communication systems with nonorthogonal carrier frequencies. A concrete example shows the possibility of exceeding the speed of information transmission in nonorthogonal communication systems in comparison with the maximum speed, which follows from the Shannon theorem. The paper presents the results of model calculations illustrating the provisions of the theory.

Keywords

Maximum likelihood method
Bayesian solution
Likelihood functional
Likelihood equations
Optimal solution
Maximum likelihood filters
Information transfer rate in communication systems