This paper introduces a novel finite Zak transform (FZT)-aided framework for constructing multiple zero-correlation zone (ZCZ) sequence sets with optimal correlation properties. Specifically, each sequence is perfect with zero auto-correlation sidelobes, each ZCZ sequence set meets the Tang-Fan-Matsufuji bound with equality, and the maximum inter-set cross-correlation of multiple sequence sets meets the Sarwate bound with equality. Our study shows that these sequences can be sparsely expressed in the Zak domain through properly selected index and phase matrices. Particularly, it is found that the maximum inter-set cross-correlation beats the Sarwate bound if every index matrix is a circular Florentine array. Several construction methods of multiple ZCZ sequence sets are proposed, demonstrating both the optimality and high flexibility. {Additionally, it is shown that excellent synchronization performance can be achieved by the proposed sequences in orthogonal-time-frequency-space (OTFS) systems.

翻译：本文提出了一种新颖的有限Zak变换辅助框架，用于构造具有最优相关特性的多组零相关区序列集。具体而言，每个序列均为自相关旁瓣为零的完美序列，每个ZCZ序列集均以等式形式满足Tang-Fan-Matsufuji界，且多组序列集之间的最大互相关值以等式形式满足Sarwate界。研究表明，通过适当选取索引矩阵和相位矩阵，这些序列可在Zak域中实现稀疏表示。特别地，当每个索引矩阵均为循环Florentine阵列时，最大互相关值可突破Sarwate界。本文提出了多种多组ZCZ序列集的构造方法，证明了其最优性与高度灵活性。此外，研究还表明所提序列在正交时频空间系统中能够实现优异的同步性能。