基于分段线性映射的混沌扩频序列设计

The Design of Chaotic Spreading Sequences Using Piecewise Linear Maps

在异步DS-CDMA系统中,白噪声序列并非是最佳扩频序列,而具有符号交替、指数衰减部分自相关函数的扩频序列有着更为优良的性能,它相对于白噪声序列可以提高约15%的系统容量。基于上述事实,对反Baker变换和Tent映射两类分段线性映射所产生的序列的性能进行了分析,并利用具有特定分岔参数的反Baker变换和Tent映射,产生具有符号交替、指数衰减的部分自相关函数的扩频序列,并对分岔参数为2的整数次方的分段线性映射提出了一种有限精度实现方法,从而可以很好的近似实现这类混沌序列。经仿真表明由上述方法产生的序列性能明显优于白噪声序列和Gold码,更适合用作异步DS-CDMA系统的扩频码。

White sequences are not the optimal spreading sequences for asynchronous DS-CDMA systems. Those sequences with alternating signs and exponentially decaying partial auto-correlation function are 15% better than white sequences in terms of system capacity. Based on that fact,the performances of sequences generated by two classes of piecewise linear maps,i.e. inverse Baker transform and Tent map,are analyzed. Sequences with alternating signs,exponentially decaying partial auto-correlation function can be generated by using inverse Baker transformation and Tent map with some class of bifurcation parameters. Moreover,a new approach of implementation of spreading sequences using piecewise linear maps whose bifurcation parameter is some integer power of 2 is proposed so that this kind of chaotic sequences can be implemented approximately. According to the simulation,the performances of these sequences are superior to those of white sequences and Gold codes.They are the better candidates of spreading sequences for asynchronous DS-CDMA systems.