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Frequency-hopping sequence sets with no-hit-zone through Cartesian product

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Abstract

For quasi-synchronous (QS) frequency-hopping multiple access (FHMA) systems, relative time delay between different users can be allowed to vary in a domain around the origin. On the other hand, for frequency-hopping sequence (FHS) sets with no-hit-zone (NHZ), there will be no hit between different sequences in case their time delay does not exceed a certain region known as NHZ. In such circumstances, NHZ-FHS sets can be well applied in QS-FHMA systems to eliminate the mutual interference (MI) and have great practical significance. In this paper, based on Cartesian product theory, three designs of NHZ-FHS sets are presented. It turns out that the newly constructed NHZ-FHS sets have optimal periodic Hamming correlation (PHC) properties and can offer help in improving the corresponding communication system performances in practice.

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References

  1. Specification of the Bluetooth Systems-Core, The Bluetooth Special Interest Group (SIG), [online]. Available: http://www.bluetooth.com

  2. Golomb, S.W., Gong, G.: Signal Design for Good Correlation: For Wireless Communication, Cryptography and Radar. Cambridge University Press, Cambridge (2005)

    Book  Google Scholar 

  3. Fan, P.Z., Darnell, M.: Sequence Design for Communications Applications, Research Studies Press (RSP). Wiley, London (1996)

    Google Scholar 

  4. Lempel, A., Greenberger, H.: Families of sequences with optimal Hamming correlation properties. IEEE Trans. Inf. Theory 20, 90–94 (1974)

    Article  MathSciNet  Google Scholar 

  5. Peng, D.Y., Fan, P.Z.: Lower bounds on the Hamming auto- and cross correlations of frequency-hopping sequences. IEEE Trans. Inf. Theory 50, 2149–2154 (2004)

    Article  MathSciNet  Google Scholar 

  6. Kumar, P.V.: Frequency-hopping code designs having large linear span. IEEE Trans. Inf. Theory 34, 146–151 (1988)

    Article  MathSciNet  Google Scholar 

  7. Ding, C.S., Fuji-Hara, R., Fujiwara, Y., Jimbo, M., Mishima, M.: Sets of frequency hopping sequences: bounds and optimal constructions. IEEE Trans. Inf. Theory 55, 3297–3304 (2009)

    Article  MathSciNet  Google Scholar 

  8. Ding, C.S., Yang, Y., Tang, X.H.: Optimal sets of frequency hopping sequences from linear cyclic codes. IEEE Trans. Inf. Theory 55, 3605–3612 (2010)

    Article  MathSciNet  Google Scholar 

  9. Peng, D.Y., Fan, P.Z., Lee, M.H.: Lower bounds on the periodic Hamming correlations of frequency hopping sequences with low hit zone. Sci. China 49, 1–11 (2006)

    Article  MathSciNet  Google Scholar 

  10. Ye, W.X., Fan, P.Z.: Two class of frequency hopping sequences with no-hit zone. In: Proceedings of the 7th International Symposium on Communication Theory and Applications, pp 304–406 (2003)

  11. Ye, W.X., Fan, P.Z., Peng, D.Y., et al.: Theoretical bound on no hit zone of frequency hopping sequences. In: Proceedings of the 5th International Workshop in Signal Design and Its Applications in Communications (IWSDA2011), pp 115–117 (2011)

  12. Liu, X., Zhou, L., Zeng, Q.: No-hit-zone frequency hopping sequence sets with respect to aperiodic Hamming correlation. Electron. Lett. 54, 212–213 (2018)

    Article  Google Scholar 

  13. Peng, D.Y., Han, H.Y.: Frequency/time hopping sequences with no hit zone: bounds and designs. J. Chengdu Univ. Inf. Technol. 30, 1–6 (2015)

    Google Scholar 

  14. Zeng, Q., Liu, X.: Chaos theory-based NHZ-FH sequence set for quasi-synchronous FHMA system. Electron. Lett. 53, 1493–1495 (2017)

    Article  Google Scholar 

  15. Ye, W.X., Fan, P.Z., Gabidulin, E.M.: Construction of non-repeating frequency-hopping sequences with no-hit zone. Electron. Lett. 42, 681–682 (2006)

    Article  Google Scholar 

  16. Ye, W.X., Fan, P.Z.: Construction of frequency hopping sequences with no hit zone. J. Electron. (China) 24, 305–308 (2007)

    Article  Google Scholar 

  17. Chung, J.H., Han, Y.K., Yang, K.: No-hit-zone frequency-hopping sequence sets with optimal Hamming autocorrelation. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 93, 2239–2244 (2010)

    Article  Google Scholar 

  18. Chung, J.H., Yang, K.: New classes of optimal low-hit-zone frequency-hopping sequence sets by Cartesian product. IEEE Trans. Inf. Theory 59, 726–732 (2013)

    Article  MathSciNet  Google Scholar 

  19. Wang, C.Y., Peng, D.Y., Han, H.Y., et al.: New sets of low-hit-zone frequency-hopping sequence with optimal maximum periodic partial Hamming correlation. Sci. China Inf. Sci. 58, 1–15 (2015)

    Google Scholar 

  20. Zhou, L.M.N., Peng, D.Y., Liang, H.B., et al.: Generalized methods to construct low-hit-zone frequency-hopping sequence sets and optimal constructions. Cryptogr. Commun. 9, 707–728 (2017)

    Article  MathSciNet  Google Scholar 

  21. Zhou, L.M.N., Peng, D.Y., Han, H.Y., et al.: Construction of optimal low-hit-zone frequency hopping sequence sets under periodic partial Hamming correlation. Adv. Math. Commun. 12, 67–79 (2018)

    Article  MathSciNet  Google Scholar 

  22. Liu, X., Zhou, L.: New bound on partial Hamming correlation of low-hit-zone frequency hopping sequences and optimal constructions. IEEE Commun. Lett., accepted. https://doi.org/10.1109/LCOMM.2018.2810868

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Acknowledgements

This work was supported by Youth Innovative Talent Project of Guangdong Education Department (Grant No. 2017KQNCX242), The Sixth Zhongshan Innovation Team Programme – Flexible Internet of Things Enabled by Wireless Energy Transfer (Contract No. 180809162197874), High Level Talent Research Starting Project in University of Electronic Science and Technology of China, Zhongshan Institute (Grant No. 417YKQ06), National Science Foundation of China (Grant No. 61701331).

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Authors and Affiliations

  1. School of Electronic and Information Engineering, University of Electronic Science and Technology of China, Zhongshan Institute, Zhongshan, China

    Limengnan Zhou

  2. School of Computer Science, Sichuan Normal University, Chengdu, China

    Hongyu Han

  3. College of Electrical Engineering and Information Technology, Sichuan University, Chengdu, China

    Xing Liu

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  1. Limengnan Zhou
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  2. Hongyu Han
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  3. Xing Liu
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Correspondence to Limengnan Zhou.

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Zhou, L., Han, H. & Liu, X. Frequency-hopping sequence sets with no-hit-zone through Cartesian product. Cryptogr. Commun. 12, 485–497 (2020). https://doi.org/10.1007/s12095-019-00381-7

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  • DOI: https://doi.org/10.1007/s12095-019-00381-7

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