Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1
Chinese Journal of Engineering Mathematics

Chinese Journal of Engineering Mathematics ›› 2017, Vol. 34 ›› Issue (3): 221-231.doi: 10.3969/j.issn.1005-3085.2017.03.001

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New Classes of Optimal Frequency-hopping Sequence Set by Interleaving Techniques

XU Shan-ding1,2,3,   CAO Xi-wang1,   XU Guang-kui1   

  1. 1- Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016
    2- Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 211167
    3- Key Laboratory of Mathematics and Interdisciplinary Sciences, Guangdong Higher Education Institutes, Guangzhou University, Guangzhou 510006
  • Received:2014-09-22 Accepted:2016-12-05 Online:2017-06-15 Published:2017-08-15
  • Supported by:
    The National Natural Science Foundation of China (11371011; 11601177; 61572027); the Open Project of Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Hig-her Education Institutes, Guangzhou University (GDSXJCKX2016-07); the Natural Science Foundation of Jiangsu Province (BK20160771); the Jiangsu Provincial Innovation Program for Graduate Education (KYZZ15_0090); the Fund for Outstanding Doctoral Dissertation in NUAA (BCXJ16-08); the Research Fund of Nanjing Institute of Technology (CKJB201606).

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Abstract: Frequency-hopping spread spectrum (FHSS) systems, which have the properties of anti-jamming, anti-intercept, channel sharing and code division multiple access, have been widely applied to mobile communication, military radio communication, modern radar and sonar echo-location systems. An important subject in frequency-hopping (FH) multiple-access systems is to find optimal frequency-hopping sequence (FHS) sets, which are an indispensable part of FHSS systems. Based on the interleaving technique and the Chinese reminder theorem, two classes of FHS sets are constructed and the Hamming correlations of the new FHS sets are derived.  The results show that a large number of optimal FHS sets can be obtained recursively by choosing appropriate parameters and specific FHS sets.

Key words: frequency-hopping sequence, interleaving technique, Lempel-Greenberger bound, maximum Hamming correlation, average Hamming correlation

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