最优高斯整数周期组间互补序列集的构造

Construction of Optimal Gaussian Integer Periodic Inter-Group Complementary Sequence Sets

本文在高斯整数集上,基于完备高斯整数序列和正交矩阵,构造了一类最优周期组间互补序列集,可实现任意长度的零相关区内互补码数量和互补码集数量的灵活选择.通过设计2阶和3阶核正交矩阵,将其对角拼接与完备高斯整数过滤,得到一类任意阶正交矩阵.利用该正交矩阵,结合任意长完备高斯整数序列,可构造零相关区与完备序列等长的周期组间互补序列集,其参数达到理论界.构造结果与已有文献比较,参数可在无条件限制下实现最优.组间互补序列集应用于多载波系统可消减邻区间的通信串扰并提升用户容量.

Based on perfect Gaussian integer sequences and orthogonal matrices,a class of optimal periodic intergroup complementary(IGC)sequence set is constructed on the Gaussian integer set,which can realize the flexible number of complementary codes and complementary code sets within any zero-correlation zone length.By designing 2-order and 3-order kernel orthogonal matrices,splicing them on the diagonal way and filtering with perfect Gaussian integer sequences,a class of orthogonal matrices of arbitrary order is obtained.By using the orthogonal matrices and perfect Gaussian integer sequences of arbitrary length,the periodic inter-group complementary sequence set can be constructed,in which the length of zero correlation zone equals to that of perfect sequence and the set parameters reach the theoretical bound.Compared with the existing literature,the construction results show that the parameters can be optimized without any restriction.IGC sequence sets can be applied to the multi-carrier code division multiple access communication system to reduce adjacent cell interference and increase user capacity.