Foundational Research On Applications Of Chaos To Time-Varying Parameter Secure Communication And Radar Signal Design

With the development of chaos research, chaos is more and more widely applied to many areas. In this paper, we will research the applications of chaos to secure communication and radar signals.Chaotic synchronized secure communication, wants to reach communication security by shelter character of chaotic systems. But the emergence of many attacking methods aiming to chaotic systems, such as: general synchronization method, phase figure or mending phase figure method, parameter auto-adaptive estimating arithmetic, fixed point method, makes chaotic communication systems no longer secure. To remedy the defect, academe have presented many methods to improve secure performance of chaotic communication systems. But to a chaotic synchronized communication system, because of the existence of conflict between security and robustness, it isn't advisable that only single side performance is improved, and the research of chaotic synchronized secure communication is hard to develop for a time. The attracted differential chaos shift keying (DCSK), its security performance is low. To make chaotic synchronized secure communication become practicable, We must consider both sides of security and robustness at the same time. To solve these problems, we have done following work.1.In the paper, we present time-varying parameter, continuous time-varying parameter methods for chaotic synchronized secure communication. On one hand, the security performances of both methods are high. Especially continuous time-varying parameter method is hard to be broken in theory, and we have proved it in the paper, and there almost has no method which can attack continuous time-varying parameter method efficiently in theory, so the known attacking methods are not efficient to continuous time-varying parameter method. On the other hand, both methods have no negative effect on robustness, and they hold robustness. Therefore, by the methods, the security performance has been improved greatly, and robustness performance is good too, the conflict between security and robustness has been settled now.2. We have researched time-varying parameter, continuous time-varying parameter methods in theory, built its theoretic base, satisfied its theoretic requirement, and guided its practice by the theory. Presently, the sufficient conditions of chaos synchronization which can determine evolution areas of state variables are lacked. In the paper, we have done many work to research these sufficient conditions and have built some theories about them. Because of the requirement of practicable, this kind of sufficient conditions of chaos synchronization must be undemanding, and is easy to reach. To the chaos systems which parameters often change, we have done many work to research their evolution rule and state.3. To time-varying parameter method for chaotic synchronized communication, because its work mode is different from normal fixed parameter method, so need some arithmetics to support its work, such as synchronization arithmetic of time-varying parameters. In the paper, we have done many work to exploit these arithmetics, and verify these arithmetics can work properly.4. We have verified chaotic synchronized secure communication systems based on time-varying parameter or continuous time-varying parameter method in two sides. On one hand, confirm these communication systems hold very high security performance. We have proved that the security performance of continuous time-varying parameter method is so high that the method is hard to be broken in theory, therefore, there almost exists no method that can attack the method effectively, and the known chaos attacking methods have no effect to systems based on continuous time-varying parameter method. On the other hand, these methods have no any negative effect on robustness of communication systems, and systems hold good robustness performance. In the paper, we present some schemes to realize these chaotic synchronized secure communication systems based on time-varying parameter or continuous time-varying parameter method.Totally, by time-varying parameter and continuous time-varying parameter methods, the security and robustness problems of chaotic synchronized communication systems are well settled now, and it makes chaotic secure communication more and more practicable.Chaos is more and more widely applied to radar signals, too.Pulse compressing radar is widely utilized, because it holds both virtues between detecting distance and distance resolution, in addition, it has certain Doppler resolution. Noise radar is similar to pulse compression radar. Samely, noise radar holds both virtues between detecting distance and distance resolution, and holds fine distance ambiguity compression characteristic, in addition, it holds certain anti-detection and anti-disturbing abilities, has attracted abroad attention of academe.Because chaos series hold pseudo-random characteristic, in many references, people have attempted to make chaos series as noise sources, and apply it to noise radar. To many chaos series, their auto-correlation functions are resemble toδfunction, and inter-correlation functions are approach zero, so chaos series are seem to be ideal noise sources. But a chaos system is a deterministic system, and many chaos systems have strong inner structures. Under some radar modulation, their structures are revealed, so the correlation performances of their radar signals become very bad, and ambiguity function performances become bad, too. Because the performances of chaotic noise source are instable under many kinds of radar modulations, applications of chaos to radar signal source are embarrassed. Noise signals are random, have no inner structure, and have no this problem. But comparing with noise signals, chaos signals hold many virtues, such as: controllable, easy to produce and easy to use, so people want to maintain chaos signals' virtues, overcome their defects, and apply them to radar as noise sources. In the paper, we do following work in this aspect.1.By analyzing different characteristics between chaos and noise, we point out inner structure of chaos system is the reason that cause performances of chaos signals instable under some radar modulations. The combination of its inner structure with some radar modulation, can decrease the performance of radar signals after radar modulation. To overcome the defect, we need to decrease inner structure of chaos systems, or choose chaos systems with weak inner structure.2. In the paper, we come up with weak structure characteristic which some chaos systems hold. We use MSPL chaos system to verify this theory. MSPL system is a chaos system, but by adjusting its parameter k, it can transform to noise system gradually. When parameter k is in certain area, MSPL system is chaos system with weak structure characteristic. It was confirmed that, chaos series with weak structure characteristic can endure all sorts of radar modulations, their radar signals after radar modulation hold good and stable correlation and ambiguity function performance, in addition, they have chaos systems' virtues of controllable, easy to produce and use. Therefore, chaos series with weak structure characteristic are better than common chaos series and noise series, and can be applied to noise radar acting as good noise sources.