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周期准互补序列集构造法

陈晓玉 彭秀英 王成瑞 崔莉

陈晓玉, 彭秀英, 王成瑞, 崔莉. 周期准互补序列集构造法[J]. 电子与信息学报, 2022, 44(11): 4034-4040. doi: 10.11999/JEIT210881
引用本文: 陈晓玉, 彭秀英, 王成瑞, 崔莉. 周期准互补序列集构造法[J]. 电子与信息学报, 2022, 44(11): 4034-4040. doi: 10.11999/JEIT210881
CHEN Xiaoyu, PENG Xiuying, WANG Chengrui, CUI Li. Constructions of Periodic Quasi-complementary Sequence Sets[J]. Journal of Electronics & Information Technology, 2022, 44(11): 4034-4040. doi: 10.11999/JEIT210881
Citation: CHEN Xiaoyu, PENG Xiuying, WANG Chengrui, CUI Li. Constructions of Periodic Quasi-complementary Sequence Sets[J]. Journal of Electronics & Information Technology, 2022, 44(11): 4034-4040. doi: 10.11999/JEIT210881

周期准互补序列集构造法

doi: 10.11999/JEIT210881
基金项目: 河北省自然科学基金(F2021203078),河北省高等学校科学技术研究项目(ZD2022026)
详细信息
    作者简介:

    陈晓玉:女,副教授,研究方向为信号设计、无线通信技术

    彭秀英:女,硕士生,研究方向为扩频序列设计

    王成瑞:男,硕士生,研究方向为扩频序列设计

    崔莉:女,博士生,研究方向编码理论、密码学、信号设计

    通讯作者:

    陈晓玉 chenxiaoyu@ysu.edu.cn

  • 中图分类号: TN911.2

Constructions of Periodic Quasi-complementary Sequence Sets

Funds: The Natural Science Foundation of Hebei Province (F2021203078), The Science and Technology Project of Hebei Education Department (ZD2022026)
  • 摘要: 该文基于2元序列支撑集和低相关序列集,提出一种新的周期准互补序列集构造框架。在此框架基础上,分别利用最优4元序列族A、族D和Luke序列集提出了3类渐近最优和渐近几乎最优周期准互补序列集,序列集参数由2元序列和低相关序列集共同决定。与传统的完备互补序列集相比,所构造的准互补序列集具有更多的序列数目,应用到多载波扩频通信系统中可以支持更多的用户。
  • 表  1  方法1周期准互补序列集参数

    $n$$M$$K$$N$${\delta _{\max }}$$\rho $
    664166354.01.9486
    712832127104.51.8851
    825664255204.01.8403
    9512128511400.91.8086
    1010242561023792.01.7862
    下载: 导出CSV

    表  2  方法2周期准互补序列集参数

    $n$$M$$K$$N$${\delta _{\max }}$$\rho $
    712832254152.71.9562
    825664510295.51.8888
    95121281.22577.01.8421
    10102425620461134.01.8095
    11204851240942240.01.7866
    下载: 导出CSV

    表  3  方法3周期准互补序列集参数

    $n$$M$$K$$N$${\delta _{\max }}$$\rho $
    28486.01.4882
    326132616.11.2374
    480408045.01.1249
    5242121242129.31.0685
    6728364728378.01.0385
    下载: 导出CSV

    表  4  准互补序列集参数比

    方法序列数目子序列数目序列长度$\delta_{\max} $$\rho $约束条件
    文献[11]方法1pnpn–1–1pn–1$\dfrac{1}{2}\left( p^{\frac{n}{2}+p^n}\right)$1$p=2 $
    文献[11]方法2pnpn–1–12(pn–1)$ p^{\frac{n}{2}}+ p^n$$ \sqrt {\frac{3}{2}}$$p=2 $
    文献[12]方法1p$\dfrac{p-1}{2}$p$\dfrac{p+\sqrt {p} }{2}$1p是奇素数且p≥5
    文献[12]方法2pKp$\sqrt {\dfrac{pK(p-K)}{p-1} }$1p是奇素数且p≥5
    文献[13]方法Apn–1Kpn–1$\sqrt {\dfrac{p^n K(p^n-K-1)}{p^n-2} }$1p是素数
    文献[13]方法Bpn–1$\dfrac{p^n}{4}$pn–13·2n–2$\sqrt {3} $p=2
    文献[13]方法Cpn–1$\dfrac{p^n-1}{2}$pn–1$\dfrac{1}{2}(p^n+p^{\frac{n}{2} })$1p是奇素数
    文献[13]方法Dpn–1pn–1pn–1$p^{n-\frac{1}{2}} $1p是素数
    文献[13]方法Ep2n–1pnp2n–1$p^{\frac{3n}{2}} $1p是素数
    本文方法1pnpn–2pn–1$3(p^{\frac{n}{2}-2}+p^{n-2}) $$\sqrt {3} $p=2
    本文方法2pnpn–22(pn–1)$3(p^{\frac{n}{2}-1}+p^{n-\frac{3}{2}}) $$\sqrt {3} $p=2
    本文方法3pn–1$\dfrac{p^n-1}{2}$pn–1$\dfrac{1}{2}(p^n+p^{\frac{n}{2} })$1p是奇素数
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-08-26
  • 修回日期:  2022-05-09
  • 网络出版日期:  2022-05-21
  • 刊出日期:  2022-11-14

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