相空间法对混沌序列的自相关特性研究

Research on Chaotic Sequence Autocorrelation by Phase Space Method

混沌序列已作为伪随机序列得到广泛应用,但如何判断混沌序列的相关特性、调制后相关特性的好坏,以及其理论依据,至今尚无定论,使其应用受到限制。该文给出了判断混沌序列自相关特性好坏的一个简单有效的方法。用相空间法对混沌序列的自相关特性作了研究,发现相空间轨迹是否具有轴对称性与其自相关函数好坏相对应,证明了相空间轨迹具有轴对称结构的序列有好的自相关函数,并通过仿真予以了证实。

Chaotic sequences have been widely used as pseudorandom sequences.But the problem of how to judge the performances of their autocorrelation functions,up to now,has not yet been solved completely.Because of this,the applications of chaotic sequences are limited.In the paper,by method of phase space,we prove that the autocorrelation performance of a chaotic sequence is determined by whether its phase space trajectory is axis symmetrical,and we deduce a theorem that a sequence which phase space trajectory is axis symmetrical has good autocorrelation performance.The theorem is verified by simulations.