New sets of low-hit-zone frequency-hopping sequence with optimal maximum periodic partial Hamming correlation

Abstract

Recently, Chung et al. gave a general method to construct frequency-hopping sequence set (FHS set) with low-hit-zone (LHZ FHS set) by the Cartesian product. In their paper, Theorems 5 and 8 claim that k FHS sets whose maximum periodic Hamming correlation is 0 at the origin result in an LHZ FHS set based on the Cartesian product, and Proposition 4 presented an upper bound of the maximum periodic Hamming correlation of FHSs. However, their statements are imperfect or incorrect. In this paper, we give counterexamples and make corrections to them. Furthermore, based on the Cartesian product, we construct two classes of LHZ FHS sets with optimal maximum periodic partial Hamming correlation property. It is shown that new FHS sets are optimal by the maximum periodic partial Hamming correlation bound of LHZ FHS set.

摘要

创新点

基于笛卡尔积, Chung 等提出了一种构造低碰撞区跳频序列集的方法. 在他们的论文中, 定理 5 和定理 8 阐述表明: k 个在零时延时的最大周期汉明相关为 0 的跳频序列集的笛卡尔积

产生一个低碰撞区跳频序列集; 同时命题 4 给出了一个关于这种方法构造的跳频序列的最大周期汉明相关上界. 但是, 经过研究, 我们发现这种构造方法或观点存在不足. 本文的主要创新点为:

• (1) 针对定理 5、, 定理 8 以及命题 4, 我们分别给出了相应的反例以及正确的定理和命题;

• (2) 给出利用笛卡尔积构造传统跳频序列集的一般方法;

• (3) 在各个候选跳频序列的最大周期汉明相关呈阶梯状均匀分布的条件下, 对于笛卡尔积构造的跳频序列, 给出了一个关于最大周期汉明相关的上界;

• (4) 给出了两类具有最优最大周期部分汉明相关特性的低碰撞区跳频序列集的构造方法并分析其在低碰撞区内的最大周期部分汉明相关特性. 关于低碰撞区跳频序列集最大周期部分汉明相关 理论界, 新构造的序列集是最优的.