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Telecommunications and Radio Engineering
SJR: 0.202 SNIP: 0.2 CiteScore™: 0.23

ISSN 印刷: 0040-2508
ISSN オンライン: 1943-6009

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Telecommunications and Radio Engineering

DOI: 10.1615/TelecomRadEng.v75.i5.10
pages 383-400

SYMBOLIC MARKOV CHAINS WITH MULTILINEAR MEMORY FUNCTION

S. S. Melnyk
A. Usikov Institute of Radio Physics and Electronics, National Academy of Sciences of Ukraine 12, Academician Proskura Str., Kharkiv 61085, Ukraine
O. V. Usatenko
A. Usikov Institute of Radio Physics and Electronics, National Academy of Sciences of Ukraine 12, Academician Proskura Str., Kharkiv 61085, Ukraine

要約

Engineering of various radio devices such as filters, delay lines, random antennas with given radiation patterns requires new approaches to generate random sequences (i.e., the parameter values of such systems), possessing specified correlation properties, as the spectral characteristics of the named and similar systems are expressed in terms of the Fourier components of the correlation devices. An adequate mathematical apparatus for such problems are the higher-order Markov chains. Statistical characteristics of these objects are determined solely by their conditional probability function that, in general case, can be very complicated. The purpose of this paper is to present the decomposition procedure for the conditional probability function of random sequences with long-range correlations in a form convenient for their numerical generation. Here we restrict ourselves to the case of the state space, when random values of system's elements belong to the finite abstract set. The function of conditional probability is decomposed into independent components expressed through so-called matrixvalued memory function. The developed theory opens the way to build a more consistent and nuanced approach for the description of systems with long-range correlations. In the limiting case of weak (in terms of value, not distance) correlations the memory function is uniquely expressed in terms of higher-order correlation functions, allowing us to generate a random sequence with a given multiple long-range correlations. As an applicable example of the obtained analytical results we offer a numerical implementation of the random sequencing with specified competing matrix correlators of the second and third order.


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