Chaotic logistic map sequences with good auto-correlation properties

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Published: Jun 27, 2023
DOI: https://doi.org/10.22201/icat.24486736e.2023.21.3.1786
Keywords:
Auto-correlation goodness metric, chaotic logistic map sequences, frame synchronization, time synchronization.

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Gerardo Laguna-Sanchez
Universidad Autónoma Metropolitana
Daniela Aguirre-Guerrero
Department of Applied Mathematics at Universidad Autónoma Metropolitana
Ismael Ariel Robles-Martinez
Universidad Autónoma Metropolitana

Abstract

In this work, chaotic sequences with good auto-correlation properties are presented. The studied sequences are synthesized by means of the logistic map function and, been chaotic but fully deterministic, become a good alternative for well-known sequences, for example the Zadoff-Chu sequences, especially for small size sequences commonly used for frame synchronization purposes in digital communications systems. A new auto-correlation goodness metric is proposed, and it is employed as objective function in order to maximize the correlation goodness for short synchronization sequences synthesized by means the logistic map function.

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How to Cite
Laguna-Sanchez, G., Aguirre-Guerrero, D., & Robles-Martinez, I. A. (2023). Chaotic logistic map sequences with good auto-correlation properties. Journal of Applied Research and Technology, 21(3), 367–375. https://doi.org/10.22201/icat.24486736e.2023.21.3.1786
Issue
Vol. 21 No. 3 (2023)
Section
Articles
Author Biographies

Daniela Aguirre-Guerrero, Department of Applied Mathematics at Universidad Autónoma Metropolitana

Dr. Daniela Aguirre Guerrero holds a degree in Telematics Engineering from the Instituto Politécnico Nacional (IPN), a Master's degree in Information Sciences and Technologies from the Universidad Autónoma Metropolitana (UAM), both in Mexico, and a Ph.D. in Technology from the Universitat de Girona, Spain. She also completed a postdoctoral stay as part of the Interdisciplinary Data Science Program at Colegio de México (COLMEX). She has taught mathematics and computer science at the undergraduate and graduate levels at IPN, UAM, and COLMEX.

Ismael Ariel Robles-Martinez, Universidad Autónoma Metropolitana

Ismael Robles graduated in Telematics Engineering from the National Polytechnic Institute (IPN), Mexico. He has a Master of Science (Mathematics) from the Metropolitan Autonomous University (UAM), Mexico. He is currently finishing his PhD in Mathematics, also from the UAM. He has worked for almost a decade in the private sector as software consultant in several specialized projects and he is an active collaborator of open source projects for graph theory, like YAGS: Yet Another Graph System. He is member of the Society for Industrial and Applied Mathematics (SIAM).