Analysis of Self-Similar Binary Sequences

Authors

DOI:

https://doi.org/10.31861/sisiot2023.1.01003

Keywords:

self-similarity, momentum, coding, correlation

Abstract

Rectangular pulses are simple to form, including with the help of a modern radio element base. In the work, a calculation analysis of the base and correlation coefficient of a binary sequence with a length of eight rectangular pulses was carried out. The obtained calculations of the base of sequences were analyzed, and a conclusion was made about which of them is the most suitable for encoding information during data transmission over the radio channel. Based on the calculations of the correlation coefficient between the series of pulse sequences, it was concluded which of them could be separated in the channel. Based on the structure of the self-similar sequence of pulses, a mathematical model and an expression of the spectral density of the proposed signal are written. A new method of correlation analysis for sequences that are symmetrical was also proposed, which allowed for improved recognition of the useful signal at lower signal-to-noise ratios in the communication channel. The method is a combination of autocorrelation and cross-correlation functions. The right and left halves of the symmetrical sequence and the reference signal are compared. The ratio of the height of the main petal to the side petals in our proposed correlation function is greater than in the classical version. To obtain the greatest possible ratio of the height of the petals, it is advisable to choose symmetrical sequences that have the largest base. With the help of such sequences, it is planned to encode one bit of information, which should improve the recognition of transmitted information against the background of noise. The obtained results are planned to be used for the development of a transmitter and receiver with an improved coding method for recognizing a useful signal against a background of noise.

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Author Biographies

  • Andrii Veryha, Yuriy Fedkovych Chernivtsi National University

    Received BS and MS degrees in Radio Engineering from Yuriy Fedkovych Chernivtsi National University, Ukraine. He received a Ph.D. in Radio Engineering from Yuriy Fedkovych Chernivtsi National University. He is currently an assistant of the Radio Engineering Department of Yuriy Fedkovych Chernivtsi National University. His research interests include signal processing, development of electronic circuits.

  • Ruslan Politansky, Yuriy Fedkovych Chernivtsi National University

    Received MS degrees in applied mathematics and physics/qualification of an engineer-physicist from Moscow Institute Physics and Technologies, Russia, in 1994. He received a Ph.D. in solid state physics from Yuriy Fedkovych Chernivtsi National University. His research interests include signal processing, coding theory, pseudorandom sequence systems with chaotic dynamics (differential equations and circuits, including own invention) and their synchronization, fractal Brownian signals.

  • Marharyta Rozhdestvenska, Yuriy Fedkovych Chernivtsi National University

    Ph.D., lecturer at the department of Radio Engineering and Information Security in Institute of Applied-Physics and Computer Science at Yuriy Fedkovych Chernivtsi National University, Chernivtsi, Ukraine. Her research interests include radioengineering and information security.

  • Halyna Lastivka, Yuriy Fedkovych Chernivtsi National University

    Received BS and MS degrees in Radio Engineering from Yuriy Fedkovych Chernivtsi National University, Ukraine; Ph.D. She is currently an associate professor of the Radio Engineering Department of Yuriy Fedkovych Chernivtsi National University. Her research interests include methods and means of radio spectroscopy, their application for research of sensory properties, cybersecurity.

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Published

2023-06-30

Issue

Vol. 1 No. 1 (2023)

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
A. Veryha, R. Politansky, M. Rozhdestvenska, and H. Lastivka, “Analysis of Self-Similar Binary Sequences”, SISIOT, vol. 1, no. 1, p. 01003, Jun. 2023, doi: 10.31861/sisiot2023.1.01003.