沃尔什序列组的两个新性质及其推论  

Two New Properties and Corresponding Deductions of Walsh Sequence Set

作　　者：郭黎利[1] 刘明夺[1] 姜晓斐[2] 

机构地区：[1]哈尔滨工程大学信息与通信工程学院,黑龙江哈尔滨150001 [2]中国电子科技集团公司第54研究所,河北石家庄050001

出　　处：《华南理工大学学报（自然科学版）》2013年第6期35-41,共7页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(61271263)

摘　　要：利用沃尔什(Walsh)序列现有的性质,推导并证明了L×L阶完备Walsh序列组的新性质,即组中任意三条或四条序列均存在L/4列的列同性.依据序列的列同性又推导出完备Walsh序列组中四条序列列同性的二进制Walsh编号之和为0,以及三条序列等幅叠加生成序列正交映射后与组中序列部分正交的推论.仿真结果验证了完备Walsh序列组中叠加生成序列与原序列组中序列的部分相关性.最后,将叠加序列的部分相关性应用于并行组合扩频通信系统中,简要介绍了在并行组合扩频通信系统QPSK调制中使用完备Walsh序列组来实现接收解调的软判决.Based on the present properties of Walsh sequences,a new property of an L × L-order complete Walsh sequence set is derived,i.e.there exists sequence identity of L/4 columns of arbitrary three or four sequences.According to this property,it is deduced that the sum of binary Walsh numbers in the identical columns of four sequences is zero,and that,the mapping sequences of three superposition sequences are orthogonal to a certain number of sequences in the sequence set.Moreover,the partial correlation between the superposition sequences and the original sequences is verified by simulations and is applied to a parallel combinatory spread spectrum communication system.Finally,the soft decision for QPSK modulation of the spread spectrum system is briefly analyzed.

关 键 词：沃尔什序列 列同性 部分相关性 定理证明 并行组合扩频 

分 类 号：TN914.42[电子电信—通信与信息系统]