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高斯整数零相关区序列集构造方法的研究

陈晓玉 李冠敏 孔德明 李玉博

陈晓玉, 李冠敏, 孔德明, 李玉博. 高斯整数零相关区序列集构造方法的研究[J]. 电子与信息学报, 2019, 41(6): 1420-1426. doi: 10.11999/JEIT180703
引用本文: 陈晓玉, 李冠敏, 孔德明, 李玉博. 高斯整数零相关区序列集构造方法的研究[J]. 电子与信息学报, 2019, 41(6): 1420-1426. doi: 10.11999/JEIT180703
Xiaoyu CHEN, Guanmin LI, Deming KONG, Yubo LI. Research on the Constructions of Gaussian Integer Zero Correlation Zone Sequence Set[J]. Journal of Electronics & Information Technology, 2019, 41(6): 1420-1426. doi: 10.11999/JEIT180703
Citation: Xiaoyu CHEN, Guanmin LI, Deming KONG, Yubo LI. Research on the Constructions of Gaussian Integer Zero Correlation Zone Sequence Set[J]. Journal of Electronics & Information Technology, 2019, 41(6): 1420-1426. doi: 10.11999/JEIT180703

高斯整数零相关区序列集构造方法的研究

doi: 10.11999/JEIT180703
基金项目: 国家自然科学基金(61601399, 61501395, 61501394),河北省自然科学基金(F2016203155),河北省高等学校科学研究计划(QN2016120)
详细信息
    作者简介:

    陈晓玉:女,1983年生,副教授,研究方向为扩频序列设计

    李冠敏:女,1993年生,硕士生,研究方向为扩频序列设计

    孔德明:男,1983年生,副教授,研究方向为数字信号处理技术

    李玉博:男,1985年生,副教授,研究方向为无限通信中的序列设计

    通讯作者:

    孔德明 demingkong@ysu.edu.cn

  • 中图分类号: TN911.2

Research on the Constructions of Gaussian Integer Zero Correlation Zone Sequence Set

Funds: The National Natural Science Foundation of China (61601399, 61501395, 61501394), The Natural Science Foundation of Hebei Province (F2016203155), The Science Research Programs of Hebei Educational Committee (QN2016120)
  • 摘要: 该文提出两类高斯整数零相关区(ZCZ)序列集的构造方法。方法1以ZCZ序列集为基础,利用插零滤波法构造高斯整数ZCZ序列集,并给出了所构造的高斯整数ZCZ序列集度的计算方法。方法2提出了两种高斯整数正交矩阵的构造方法,进而基于正交矩阵构造最优高斯整数ZCZ序列集。该文所构造的高斯整数ZCZ序列集可以应用于准同步码多分址(QS-CDMA)、正交频分复用(OFDM)和多输入多输出(MIMO)等多种通信系统中,在抑制干扰的同时,提高系统的频谱效率。
  • 表  1  ${c\,^0}$${c\,^1}$序列元素

    $\begin{aligned}{c\,^0} =& [6 + 11j,6 + 2j, - 6 + 10j,6 + 11j, - 6 - 2j,\\& \quad 6 - 10j, - 6 - 11j, - 6 - 2j, - 6 + 10j,6 + 11j, - 6 - 2j,\\& \quad - 6 + 10j,6 + 11j,6 + 2j, - 6 + 10j, 6 + 11j,6 + 2j,\\& \quad 6 - 10j, - 6 - 11j,6 + 2j, - 6 + 10j,6 + 11j, - 6 - 2j,\\& \quad - 6 + 10j, - 6 - 11j,6 + 2j, - 6 + 10j, - 6 - 11j,6 + 2j,\\& \quad 6 - 10j,- 6 - 11j,6 + 2j,6 - 10j,6 + 11j, - 6 - 2j,\\& \quad 6 - 10j, - 6 - 11j,6 + 2j, - 6 + 10j, - 6 - 11j,- 6 - 2j,6 - 10j,\\& \quad - 6 - 11j, - 6 - 2j,{6 - 10j,6 + 11j, - 6 - 2j,6 - 10j]}\end{aligned} $
    $\begin{aligned}{c\,^1} =& [ - 6 - 11j, - 6 - 2j, - 6 + 10j, - 6 - 11j, - 6 - 2j,6 - 10j,\\& \quad 6 + 11j, - 6 - 2j,6 - 10j, - 6 - 11j, - 6 - 2j,6 - 10j,6 + 11j,\\& \quad 6 + 2j,6 - 10j,6 + 11j, - 6 - 2j, - 6 + 10j, - 6 - 11j, - 6 - 2j,\\& \quad - 6 + 10j,6 + 11j,6 + 2j, - 6 + 10j,6 + 11j, - 6 - 2j, - 6 + 10j,\\& \quad {6 + 11j,6 + 2j,6 - 10j,6 + 11j,6 + 2j, - 6 + 10j, - 6 - 11j,}\\& \quad { - 6 - 2j, - 6 + 10j, - 6 - 11j,6 + 2j,6 - 10j, - 6 - 11j,6 + 2j,}\\& \quad { - 6 + 10j, - 6 - 11j,6 + 2j,6 - 10j,6 + 11j,6 + 2j,6 - 10j]}\end{aligned}$
    下载: 导出CSV

    表  2  正交矩阵的构造实例

    矩阵构造方法参数矩阵实例
    ${{\text{H}}_2}$基于多电平$\begin{array}{l} a = (1 + j) \\ b = (1 - j) \\ \end{array} $${{\text{H}}_2} = \left[ {\begin{array}{*{20}{c}} 2&{2j} \\ {2j}&2 \end{array}} \right]$
    ${{\text{H}}_3}$基于DFT变换$\begin{array}{l} {m_i} = (18,1,6) \\ {a_i} = ( - 1, - 1, - 3) \\ {b_i} = (3, - 4,3) \\ \end{array} $${{\text{H}}_3} = \left[ {\begin{array}{*{20}{c}} {18 + 6j,18 - 6j,18} \\ {1 - 8j,1 + j,1 + 7j} \\ {6 + 6j,6 - 12j,6 + 6j} \end{array}} \right]$
    ${{\text{H}}_5}$基于多电平$\begin{array}{l} a = (1 + j, - 1 + j) \\ b = (1 - j, - 1 - j) \\ c = (2 + j) \\ \end{array} $${{\text{H}}_5} = \left[ {\begin{array}{*{20}{c}} {1 + 5j,1 - 5j, - 4, - 4, - 4,} \\ {5 + j, - 5 + j, - 4j, - 4j, - 4j} \\ {4,4, - 1 + 5j, - 1 - 5j,4} \\ { - 4j, - 4j, - 5 + j,5 + j, - 4j} \\ { - 4 - 2j, - 4 - 2j, - 4 - 2j, - 4 - 2j,6 + 3j} \end{array}} \right]$
    ${{\text{H}}_6} = {{\text{H}}_2} \otimes {{\text{H}}_3}$Kronecker积同${{\text{H}}_2}$和${{\text{H}}_3}$的参数${{\text{H}}_6} = \left[ \begin{array}{l} 36 + 12j,36 - 12j,36, - 12 + 36j,12 + 36j,36j; \\ 2 - 16j,2 + 2j,2 + 14j,16 + 2j, - 2 + 2j, - 14 + 2j; \\ 12 + 12j,12 - 24j,12 + 12j, - 12 + 12j,24 + 12j, - 12 + 12j; \\ - 12 + 36j,12 + 36j,36j,36 + 12j,36 - 12j,36; \\ 16 + 2j, - 2 + 2j, - 14 + 2j,2 - 16j,2 + 2j,2 + 14j; \\ - 12 + 12j,24 + 12j, - 12 + 12j,12 + 12j,12 - 24j,12 + 12j \\ \end{array} \right]$
    下载: 导出CSV

    表  3  高斯整数ZCZ序列集参数比较

    文献定理构造基础序列集参数$\eta $
    文献[10] 定理32元正交矩阵${\rm{ZCZ}}(L,N,Z - 1),\gcd (N,Z) = 1$
    ${\rm{ZCZ}}(L,N,Z - 2),\gcd (N,Z) > 1$
    $\eta \le 1$
    文献[11] 定理1多元${\rm{ZCZ}}(L,N,K)$序列集${\rm{ZCZ}}(L,N,K)$$\eta \le 1$
    文献[14] 定理1移位序列和完备高斯整数序列${\rm{ZCZ}}(2N,2M,Z)$$\eta \le 1$
    文献[19] 定理12元伪随机序列${\rm{ZCZ}}(2N,2M,Z),N = {2^n} - 1$$\eta \le 1$
    本文 定理1${\rm{ZCZ}}(N,M,Z)$序列集和完备高斯整数序列${\rm{ZCZ}}(NK,M,ZK)$$\eta \le 1$
    本文 构造法2高斯整数正交矩阵${\rm{ZCZ}}(NK,N,K)$$\eta = 1$
    下载: 导出CSV
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出版历程
  • 收稿日期:  2018-07-13
  • 修回日期:  2019-01-28
  • 网络出版日期:  2019-02-20
  • 刊出日期:  2019-06-01

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