二元和四元序列的自相关性质研究

发布时间：2018-06-10 06:31

本文选题：四元序列 + 自相关　；参考：《西安电子科技大学》2014年硕士论文

【摘要】：自相关性质良好的伪随机序列在软件测试、无线通信、雷达导航和密码学等领域占有十分重要的角色。具有良好自相关性质的序列可以从它们自己的移位序列集合中分离出来。二元和四元序列在通信系统中的作用使得它们在伪随机序列的设计方面越来越受到关注。本文研究了基于交织结构和逆格林映射的二元及四元序列的性质及构造方法,得到了如下四个方面的结果:(1)本文根据唐小虎和丁存生利用交织技术和逆格林映射提出的具有良好自相关性质的二元序列的构造,推广构造了一类周期为4N的四元序列,并证明了其具有几乎平衡性和良好的自相关性质。对构造出来的四元序列通过一些取值不同的参数进行了分类和讨论,并找出了它们之间存在的等价关系。(2)根据平衡的四元序列和逆格林映射的性质,发现了两类置换方法:第一类可以由一个具有平衡性质的四元序列得到另一个同样具有平衡性的四元序列,它们的自相关性质完全相同;第二类可以由一个四元序列得到另外四个自相关值实部相同,虚部相反的四元序列。然后简要的分析和证明了这些置换方法,并且用计算机验证了任意选取一个大周期的四元序列的自相关值。(3)姜志雄和唐小虎等人近期先后构造了具有最优自相关性质的四元序列,本文详细地分析了这两种构造方法,发现当n值固定时,采用所有周期为2-1n的m序列来进行以上两种构造得到的四元序列集合是相同的,找到了这两种方法构造出的四元序列的交集。(4)根据唐小虎和丁存生构造四元序列的方法,本文得到了一类新的四元序列,这类四元序列的自相关值决定于它的构造参数,总结出了参数与自相关值的变化规律并给出证明。最后,通过计算机编程验证了其自相关值。
[Abstract]:Pseudorandom sequences with good autocorrelation play an important role in software testing, wireless communication, radar navigation and cryptography. Sequences with good autocorrelation properties can be separated from their own set of shift sequences. The role of binary and quaternion sequences in communication systems makes them pay more and more attention to the design of pseudorandom sequences. In this paper, we study the properties and construction methods of binary and quaternion sequences based on interleaved structure and inverse Green mappings. In this paper, we generalize a class of quaternion sequences with a period of 4N based on the construction of binary sequences with good autocorrelation properties proposed by Tang Xiaohu and Ding Cunsheng by using interleaving technique and inverse Green mappings. It is proved that it has almost equilibrium and good autocorrelation property. The quaternion sequences are classified and discussed by some parameters with different values, and the equivalent relation between them is found out. (2) according to the properties of the equilibrium quaternion sequences and inverse Green mappings, Two kinds of permutation methods are found: the first kind can obtain another quaternion with equilibrium property from one quaternion sequence with equilibrium property and their autocorrelation properties are identical; In the second class, four other quaternions with the same autocorrelation values and the opposite imaginary parts can be obtained from one quaternion sequence. And then briefly analyze and prove these permutation methods, And it is verified by computer that the autocorrelation value of a large period quaternion sequence is chosen arbitrarily.) Jiang Zhixiong and Tang Xiaohu have recently constructed quaternion sequences with optimal autocorrelation properties. In this paper, the two construction methods are analyzed in detail. It is found that when n values are fixed, the set of quaternion sequences obtained by using all m sequences with a period of 2-1n for the above two kinds of structures is the same. Find the intersection of the quaternion constructed by these two methods.) according to the method of constructing quaternion sequence by Tang Xiaohu and Ding Cunsheng, we obtain a new kind of quaternion sequence, whose autocorrelation value is determined by its construction parameters. The variation of parameters and autocorrelation values is summarized and proved. Finally, the autocorrelation value is verified by computer programming.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN918.1

【共引文献】