Abstract: Chaotic sequence, as a spreading code in spread spectrum systems, has the characteristics of rich sequences and good confidentiality. The autocorrelation of traditional two-dimensional maps has great defects, with its high sidelobes and nonzero means. To solve those problems, this paper proposes an improved symmetrical two-dimensional Logistic map with two levels based on phase space reconstruction, which greatly optimizes the correlation property. The simulation results prove that the algorithm mentioned in this paper is effective. Furthermore, the power spectral density, maximum Lyapunov exponent and the cross-correlation are analyzed, which show that the new method is consistent with the requirements of spread spectrum sequences.

Key words: chaotic, Logistic sequence, correlation, spread spectrum communication

摘要： 混沌序列作为扩频系统中的扩频码，具有序列丰富，保密性好等特性，二维映射较一维映射的安全性更高。针对传统二维Logistic映射归一化自相关特性差，副瓣高，且在相关间隔非零时均值不为零的缺点，提出一种基于相空间重构的改进型二维Logistic映射，有效地改善了映射的相关特性，仿真实验验证了算法的有效性。进一步分析了映射的功率谱密度、最大Lyapunov指数和序列互相关性，实验结果表明，该算法较传统二维Logistic映射更适合于扩频通信。

关键词: 混沌, Logistic序列, 相关性, 扩频通信