论文标题
关于“具有零自相关区域的最佳无干扰序列”的注释
A Note on "Optimum Sets of Interference-Free Sequences With Zero Autocorrelation Zone"
论文作者
论文摘要
在本文中，通过精心设计的有限Zak Transform晶格镶嵌，提出了简单的无干扰零相关区（IF-ZCZ）序列集的简单结构。每个集合的特征是序列$ km $，设定尺寸$ k $的时间周期和零相关区的长度$ M-1 $，这对于Tang-Fan-Matsufuji绑定而言是最佳的。其次，给出了保持最佳IF-ZCZ序列集的属性的转换，并根据这些转换定义了最佳IF-ZCZ序列集的等效关系。然后，证明由Popovic提出的最佳IF-ZCZ序列集的一般结构等同于最佳IF-ZCZ序列集的简单结构，这表明可以简化最佳IF-ZCZ序列集的生成。此外，可以指出的是，最佳IF-ZCZ序列集的特殊情况的字母大小可能是该时期的一个因素。最后，最佳的IF-ZCZ序列集及其特殊情况的简单结构都有稀疏且结构高度的Zak Spectra，这可以大大降低实现匹配的滤镜库的计算复杂性。
In this paper, a simple construction of interference-free zero correlation zone (IF-ZCZ) sequence sets is proposed by well designed finite Zak transform lattice tessellation. Each set is characterized by the period of sequences $KM$, the set size $K$ and the length of zero correlation zone $M-1$, which is optimal with respect to the Tang-Fan-Matsufuji bound. Secondly, the transformations that keep the properties of the optimal IF-ZCZ sequence set unchanged are given, and the equivalent relation of the optimal IF-ZCZ sequence set is defined based on these transformations. Then, it is proved that the general construction of the optimal IF-ZCZ sequence set proposed by Popovic is equivalent to the simple construction of the optimal IF-ZCZ sequence set, which indicates that the generation of the optimal IF-ZCZ sequence set can be simplified. Moreover, it is pointed out that the alphabet size for the special case of the simple construction of the optimal IF-ZCZ sequence set can be a factor of the period. Finally, both the simple construction of the optimal IF-ZCZ sequence set and its special case have sparse and highly structured Zak spectra, which can greatly reduce the computational complexity of implementing matched filter banks.
