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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2017, Vol. 34 ›› Issue (3): 221-231.doi: 10.3969/j.issn.1005-3085.2017.03.001

• •    下一篇

由交织技术构建新的最优跳频序列族

徐善顶1,2,3,   曹喜望1,   许广魁1   

  1. 1- 南京航空航天大学数学系，南京  210016
    2- 南京工程学院数理部，南京  211167
    3- 广州大学数学与交叉科学普通高校重点实验室，广州  510006
  • 收稿日期:2014-09-22 接受日期:2016-12-05 出版日期:2017-06-15 发布日期:2017-08-15
  • 基金资助:
    国家自然科学基金(11371011; 11601177; 61572027)；广东省数学与交叉科学“普通高校重点实验室”开放课题项目(GDSXJCKX2016-07)；江苏省青年基金(BK20160771)；江苏省普通高校研究生科研创新计划项目(KYZZ15_0090)；南京航空航天大学博士学位论文创新与创优基金项目(BCXJ16-08)；南京工程学院校级科研基金项目(CKJB201606).

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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摘要： 跳频技术具有抗干扰、抗截获、频带共享和码分多址等优点，在民用移动通信、军事无线电通信、现代雷达和声纳等电子系统中具有广泛的应用．寻找和设计最优跳频序列族是研究跳频通信技术的重要议题，因为跳频序列是跳频系统中不可或缺的重要组成部分．本文基于交织技术和中国剩余定理，构造了两类新的跳频序列族，导出了新序列族的各类汉明相关性质．研究结果表明，通过选择恰当的参数和已知跳频序列族，本文所提方法可递归得到大量的最优跳频序列族．

关键词: 跳频序列, 交织技术, Lempel-Greenberger界, 最大汉明相关, 平均汉明相关

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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