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具有最佳相关特性和极大线性复杂度的序列

黄泽明1, 李 超1,2   

  1. 1.国防科技大学 数学与系统科学系,湖南 长沙410073；
    2．东南大学 移动通信国家重点实验室，江苏 南京 210096

  • 收稿日期:2005-12-12 修回日期:2006-11-24 出版日期:2007-07-30 发布日期:2007-07-30

CDMA Sequences with Optimal Correlation and Large Linear Span

HUANG Ze-Ming 1, LI Chao1,2   

  1. 1 Department of Mathematics and System Sciences, National University of Defense Technology, Changsha 410073 China;
    2 National Mobile Communications Research Laboratory ,Southeast University,Nanjing 210096,China
  • Received:2005-12-12 Revised:2006-11-24 Online:2007-07-30 Published:2007-07-30

摘要：

Helleseth－Gong（HG）序列是一类具有理想相关性的无线通信系统码分多址（CDMA）序列，对奇素数p和整数n,m,d满足n=2(2d+1)m，本位利用有限域上的二次型理论和迹变换的性质HG序列基础上构造一类序列数目众多，具有最佳相关性的非平衡p元CDMA序列族，其最佳相关性用Welch下届来衡量。同样，对偶数n=2(2d+1)m，在改进非平衡p元CDMA序列族基础上利用有限域上的迹变换构造了一类序列数目众多，具有最佳相关性的非平衡p元CDMA序列族。 文章证明了这两类CDMA序列族中的序列都具有大的周期和线性复杂度，适合在无线通信信道上传输。

关键词: p元序列, 最佳相关性, 平衡序列, 线性复杂度

Abstract: The Hellseth-Gong(HG) sequence is a kind of CDMA sequences used in wireless communication systems with ideal autocorrelation. For an odd prime p and integers n,m,d satisfying n=2(2d+1)m , using the theory of quadratic forms and properties of trace transform over finite field, a new unbalanced p -ray CDMA sequence family with large family size and optimal correlation property is constructed based on HG sequences.which means the family has optimal correlation in terms of Welch’s lower bound.Similarly,for an even number n=2(2d+1)m , using the trace transform,a family of balanced p -ray CDMA sequences with large family size has the property of optimal correlation,which is constructed from the unbalanced p-ray CDMA sequence family.It is shown that the two CDMA sequence families have large period and linear span,and are sutable for transmission in wireless communication systems.

Key words: p-ray sequence , optimal correlation, balanced sequence, linear spannel