Open AccessFormation of Minimax Ensembles of Aperiodic Gold Codes
Author(s) -
V. Yu. Zubarev,
Boris Victorovich Ponomarenko,
E. G. Shanin,
А. Г. Вострецов
Publication year - 2020
Publication title -
izvestiâ vysših učebnyh zavedenij rossii. radioèlektronika
Language(s) - English
Resource type - Journals
eISSN - 2658-4794
pISSN - 1993-8985
DOI - 10.32603/1993-8985-2020-23-2-26-37
Subject(s) - aperiodic graph , code (set theory) , minimax , computer science , algorithm , gold code , binary number , signal (programming language) , function (biology) , mathematics , mathematical optimization , combinatorics , evolutionary biology , biology , programming language , computer network , channel (broadcasting) , spread spectrum , arithmetic , set (abstract data type)
. Signals constructed on the basis of ensembles of code sequences are widely used in digital communication systems. During development of such systems, the most attention is paid to analysis, synthesis and implementation of periodic signal ensembles. Theoretic methods for synthesis of periodic signal ensembles are developed and are in use. Considerably fewer results are received regarding construction of aperiodic signal ensembles with given properties. Theoretical methods for synthesis of such ensembles are practically nonexistent. Aim . To construct aperiodic Gold code ensembles with the best ratios of code length to ensemble volume among the most known binary codes. Materials and methods . Methods of directed search and discrete choice of the best ensemble based on unconditional preference criteria are used. Results. Full and truncated aperiodic Gold code ensembles with given length and ensemble volume were constructed. Parameters and shape of auto- and mutual correlation functions were shown for a number of constructed ensembles. Comparison of the paper results with known results for periodic Gold code ensembles has been conducted regarding growth of minimax correlation function values depending on code length and ensemble volume. Conclusion . The developed algorithms, unlike the known ones, make it possible to form both complete ensembles and ensembles taking into account the limitation of their volume. In addition, the algorithms can be extended to the tasks of forming ensembles from other families, for example, assembled from code sequences belonging to different families.