Modeling pseudo-random sequences
Authors: Sokolov T.D., Askerova N.A., Askerova A.A. | |
Published in issue: #2(67)/2022 | |
DOI: 10.18698/2541-8009-2022-2-771 | |
Category: Informatics, Computer Engineering and Control | Chapter: System Analysis, Control, and Information Processing, Statistics |
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Keywords: pseudo-random sequence M-sequence, Kasami codes, Gold codes, signals, cross-correlation of codes, autocorrelation function, comparative analysis, efficiency |
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Published: 25.02.2022 |
The paper presents a review of various pseudo-random sequences, such as the M-sequence, Gold codes and Kasami codes. For each type of pseudo-random sequence, methods of formation are presented, which are also described in examples using diagrams and mathematical calculations. Preferred pairs for the formation of Gold and Kasami sequences have been selected. The properties of pseudo-random sequences are considered. The autocorrelation function is investigated and its mathematical substantiation is given. The autocorrelation properties of the sequences have been studied using the example of the ratio of cross-correlation and lengths of code sequences. Recommendations on the use of codes are formed, taking into account their properties.
References
[1] Psevdosluchaynye posledovatel’nosti [Pseudorandom sequences]. siblec.ru: website (in Russ.). URL: https://siblec.ru/telekommunikatsii/teoreticheskie-osnovy-tsifrovoj-svyazi/12-metody-rasshirennogo-spektra/12-2-psevdosluchajnye-posledovatelnosti (accessed: 10.12.2021).
[2] Psevdosluchaynye posledovatel’nosti i ikh svoystva [Pseudorandom sequences and their properties]. studfile.net: website (in Russ.). URL: https://studfile.net/preview/9478149/page:17/ (accessed: 10.12.2021).
[3] Sadiq K.G. Performance comparison of various short codes in direct sequence spread spectrum (DS/SS) system. J. Techniques, 2011, vol. 24, no. 8, pp. E154–E167.
[4] Varakin L.E. Sistemy svyazi s shumopodobnymi signalami [Communication system noise-type signal]. Moscow, Radio i svyaz’ Publ., 1985 (in Russ.).
[5] Prozorov D.E., Smirnov A.V., Balanov M.Yu. Fast code synchronization algorithm of spread spectrum signals based on sequences with high structural complexity. Vestnik RGRTU [Vestnik of Ryazan State Radio Engineering University], 2015, no. 51, pp. 3–8 (in Russ.).
[6] Optimal’nye i asimptoticheski optimal’nye ansambli diskretnykh signatur [Optimum and asymptotically optimal signature ensemble]. siblec.ru: website (in Russ.). URL: https://siblec.ru/telekommunikatsii/shirokopolosnye-signaly-i-sistemy/12-optimalnye-i-asimptoticheski-optimalnye-ansambli-diskretnykh-signatur#12.3 (accessed: 10.12.2021).
[7] Posledovatel’nosti Golda [Gold sequences]. crypto.pp.ua: website (in Russ.). URL: http://crypto.pp.ua/2011/12/posledovatelnosti-golda-chast-1/ (accessed: 10.12.2021).
[8] Autocorrelation and cross-correlation for two half-cycle Wischmeyer sweeps generated using Kasami sequences. researchgate.net: website. URL: https://www.researchgate.net/figure/Autocorrelation-grey-only-the-peak-value-is-visible-and-cross-correlation-black-for_fig6_259544211 (accessed: 10.12.2021).
[9] Autocorrelation Function of PN sequence generated. researchgate.net: website. URL: https://www.researchgate.net/figure/Autocorrelation-Function-of-PN-sequence-generated_fig2_263464034 (accessed: 10.12.2021).