具有最优部分汉明相关的低碰撞区跳频序列设计研究

The Hamming correlation of the frequency hopping sequence is a significant indicator to meature the performance of sequences. They have a negligible impact on the anti-interference performance of the system.To analysis and design frequency hopping sequence with excellent performance is one of the important topic of frequency hopping communication system. The frequency hopping sequence with low hit zone is a research direction emerging in recent years has caused the attention of many scholars at home and abroad, which has attracted many attentions of the scholars in the world. In this project, we will study the partial Hamming correlation of low hit zone frequency hopping sequences. The research topics include: (1) the design of low hit zone frequency hopping sequences with optimal partial Hamming correlation based on the interleaving technology; (2) the design of low hit zone frequency hopping sequences with optimal partial Hamming correlation based on the cyclotomy theory; (3) the design of low hit zone frequency hopping sequences with optimal partial Hamming correlation over a polynomial residue class ring. The output of this project will provide improtant criteria for judging the performance of low hit zone frequency hopping sequences from the viewpoint of partial Hamming correlation, and provide more low hit zone frequency hopping sequences with optimal partial Hamming correlation.

跳频序列的汉明相关是衡量序列性能的重要指标，对系统抗干扰性有着不可忽视的影响。分析与设计具有优异性能的跳频序列是研究跳频通信系统的重要课题之一。低碰撞区跳频序列是近年新提出的研究方向，关于低碰撞区跳频序列汉明相关性能的研究已引起国内外许多学者的重视。本课题针对具有优异部分汉明相关的低碰撞区跳频序列设计进行研究，主要研究内容包括：(1) 基于交织理论构造具有优异部分汉明相关的低碰撞区跳频序列；(2) 基于分圆理论构造具有优异部分汉明相关的低碰撞区跳频序列；(3) 多项式剩余类环上构造具有优异部分汉明相关的低碰撞区跳频序列。本课题的研究成果将为低碰撞区跳频序列的部分汉明相关的优劣提供重要的参考标准，同时构造出更多具有最优部分汉明相关的低碰撞区跳频序列。

跳频序列的汉明相关是衡量序列性能的重要指标，对系统抗干扰性有着不可忽视的影响。分析与设计具有优异性能的跳频序列是研究跳频通信系统的重要课题之一。本项研究主要针对低碰撞区跳频序列集部分汉明相关特性进行研究，在低碰撞区跳频序列部分汉明相关理论界和序列设计方面取得了一系列研究成果。（1）建立了跳频序列集非周期部分汉明相关的理论界，理论界给出了跳频序列集的序列数目，频隙集大小，相关窗大小以及非周期部分汉明相关函数所满足的约束关系；（2）基于交织技术构造了几类低碰撞区跳频序列集，新序列集具有新的灵活参数，且序列数目大，可以满足工程应用中更多用户的需求。（3）基于笛卡尔积、中国剩余定理和分圆理论给出了几类低碰撞区/常规跳频序列集，这些集合关于部分汉明相关理论界是最优的或者几乎最优的。(4)基于跳频序列的相关结果，构造了几类性能优异的互补序列。本课题主要对低碰撞区跳频序列的部分汉明相关性的理论界和序列设计进行了研究，填补了跳频序列非周期部分汉明相关领域的研究空白，丰富了低碰撞区跳频序列的研究成果。该研究不但具有重要的理论意义，而且对于推动准同步扩频通信系统的实际应用，具有关键作用。