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为探讨混沌的雷达波形适用性,着重研究分析不同混沌映射、不同调制方式下混沌调制雷达波形的混沌行为。介绍了混沌调频和混沌相位编码雷达信号模型,重点从数学上推导了混沌调制后雷达信号的混沌特性关系,认为调制后信号的混沌性不能从理论得到保证,信号的混沌性具有不确定性。为获取调制信号较好的自相关函数性能,在分析李亚普洛夫指数求取的基础上,进一步强化条件,给出了混沌保留的充分条件。应用四类离散混沌映射分别产生频率调制和二相编码混沌雷达信号,分析比较了各情况下信号的相关函数性能,从仿真角度验证了理论分析,指出Bernoulli映射具有最佳的混沌频率调制性能,而Congruent混沌映射不适合混沌相位编码信号使用。该分析方法对于实际工程中指导混沌雷达波形设计具有重要现实意义。
In order to explore the applicability of the chaotic radar waveform, the chaotic behavior of the chaotic modulation radar waveform with different modulation schemes is studied emphatically. The signal model of chaotic FM and chaotic phase coded radar is introduced. The chaotic characteristic of the radar signal after chaotic modulation is deduced mathematically. The chaos of the modulated signal can not be guaranteed from theory and the chaos of the signal is uncertain. In order to obtain better performance of the autocorrelation function of the modulated signal, the condition is further strengthened by analyzing the Lyapunov exponents, and sufficient conditions for the preservation of chaos are given. Four types of discrete chaotic maps are used to generate frequency modulated and two - phase coded chaotic radar signals respectively. The correlation function performance of each signal is analyzed and compared. The theoretical analysis is validated from the simulation point of view. The results show that the Bernoulli map has the best chaotic frequency modulation performance, The Congruent chaotic map is not suitable for chaotic phase coded signal. The analysis method has important practical significance for the guidance of chaotic radar waveform design in practical engineering.