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Using Families of Extremal Quasi-Orthogonal Matrices in Communication Systems

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Intelligent Decision Technologies

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 238))

Abstract

The evolution of knowledge about quasi-orthogonal matrices as a generalization of Hadamard matrices is briefly considered in the paper. We describe the origin of the names of quasi-orthogonal matrix families and the connection of their orders with known numerical sequences. The structured matrices, searching for which is of the greatest practical interest, are distinguished: symmetric, persymmetric, cyclic, structured according to Walsh. There are also features and characteristics of such matrices highlighted in the paper. Examples of the applicability of the matrices for various tasks of information transformation and processing are given: noise immune coding, masking, compression, signal coding.

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Acknowledgements

The reported study was funded by the Ministry of Science and Higher Education and of the Russian Federation, grant agreement No. FSRF-2020-0004.

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Authors and Affiliations

  1. Saint-Petersburg State University of Aerospace Instrumentation, 67 Bolshaya Morskaya Street, Saint-Petersburg, 190000, Russian Federation

    Anton Vostrikov, Alexander Sergeev & Yury Balonin

Authors
  1. Anton Vostrikov
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  2. Alexander Sergeev
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  3. Yury Balonin
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Editor information

Editors and Affiliations

  1. Gdynia Maritime University, Gdynia, Poland

    Ireneusz Czarnowski

  2. Bournemouth University, Poole, UK

    Robert J. Howlett

  3. KES International, Shoreham-by-Sea, UK

    Lakhmi C. Jain

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© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

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Vostrikov, A., Sergeev, A., Balonin, Y. (2021). Using Families of Extremal Quasi-Orthogonal Matrices in Communication Systems. In: Czarnowski, I., Howlett, R.J., Jain, L.C. (eds) Intelligent Decision Technologies. Smart Innovation, Systems and Technologies, vol 238. Springer, Singapore. https://doi.org/10.1007/978-981-16-2765-1_8

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