满映射Logistic数字混沌序列的产生及性能分析  

Generation and Performance Analysis of Digital Chaotic Sequence from Surjective Logistic-Map

作　　者：余金峰 杨文革 路伟涛 王金宝 

机构地区：[1]装备学院光电装备系,北京101416 [2]洛阳电子装备试验中心,河南洛阳471003

出　　处：《电讯技术》2013年第2期140-145,共6页Telecommunication Engineering

摘　　要：Logistic映射形式简单,但表现出了复杂的动态性能。以满映射Logistic混沌序列为对象,讨论了混沌序列数字化的两种方法,推导了数字混沌序列比特位分布概率,计算了截短数字混沌序列的相关性能。结果表明,在不变分布偶对称的情况下,两种方法得到的数字化混沌序列都是"0""1"等概率的,截短序列的自相关函数旁瓣方差和互相关方差均等于序列长度N的倒数。对数字化Logistic混沌序列进行了数值仿真,所得结果与结论相吻合;仿真结果还显示,自相关旁瓣和互相关均服从高斯分布。研究结果使得能够从理论上对一类数字混沌序列的特性进行整体把握,超越了经验性的结论,便于在有关系统中进行应用分析。Logistic-Map is a widely studied typical discrete time non-linear dynamic system. Based on the surjective Logistic-Map, this paper discusses two methods to digitalize chaotic sequences, induces the statistical properties of the occurrence of ＂0＂ and ＂1＂ of the digital chaotic sequences, and investigates the correlation characteristics of the cut-down sequences. The result shows： ＂0＂and＂ 1＂ have equal probabilities in digital chaotic sequences generated by both digitalization methods when a map has symmetrical invariant distribution; the variance of correlation equals to the reciprocal of sequence length N. The theoretical conclusions are verified by numerical simulations based on surjective Logistic-Map. The simulations result also shows the correlation obeys Gauss distribution. The theorical conclusions in this paper, rather than experiential formulars, are helpful to understand the correlation properties of digital chaotic sequences.

关 键 词：LOGISTIC映射 混沌序列 数字化 扩频序列 相关特性 

分 类 号：TN911[电子电信—通信与信息系统] TN914.4[电子电信—信息与通信工程]