Chaotic Systems Based On Digital-Analog Hybrid Method And Its Application

Chaos is a complex dynamic behavior of nonlinear dynamic systems.It describes the inherent randomness of deterministic nonlinear systems,which are commonly found in the operation of biological,meteorological and electronic systems.Chaotic system is one of the important content of chaotic theory.The study of chaotic phenomena and chaotic systems provides theoretical support for various engineering applications from the perspective of mathematics,promoting the innovation of engineering technology.The focus of this dissertation is on the digital-analog hybrid realization scheme of chaotic systems and its application to the design of digital-analog hybrid random number generators,as well as the transmission and reconstruction of Multiple Input Multiple Output(MIMO)radar transmitting signal.Random numbers with good property are widely used as keys in cryptographic protocols,digital signatures,identity authentication,data encryption,and Monte Carlo methods.Besides,radar transmitting waveform design and optimization directly effects the MIMO radar resolution,measurement accuracy,the ability of suppressing clutter.In view of the above research priorities,the main work of this dissertation is summarized as follows:1.A new Chen-like system is proposed based on the Chen system by introducing nonlinear terms,making the Chen system a particular case of Chen-like system.Moreover,based on the chaotic system flow with single linear terms proposed by Li,we further generalize the flow model which which summarizes all 3D chaotic systems with cubic terms.Through the dynamic analysis of the new systems,many unique properties were discovered,such as the existence of multi-stable and infinite equilibrium.In addition,we also discussed the amplitude control method of chaotic systems.When implementing chaotic system circuits,the digital method based on Field Programmable Gate Array(FPGA)is employed.FPGA has the advantages of programmability,parameter controllability,portability and robustness,and it is also very convenient to implement complex calculations with it.In order to ensure the utilization efficiencies of system resources,we code FPGA over the register transfer level instead of using DSP-Builder to automatically generate HDL code.Besides,the 32-bit fixed-point operation is used to ensure the effectiveness and efficiency of the system.More importantly,a total of 16 chaotic systems,including the chaotic system flow proposed by Li,are realized on a single FPGA platform at the same time,which is rarely considered in previous studies.By programming the parameter setting and output method of the control system,the output of the whole system is diversified,greatly improving the application prospects of the system in the fields of secure communication,digital image encryption,cryptographic security and radar waveform design to achieve the required waveform characteristics.Moreover,the thesis also studies a special chaotic system with product terms of symbolic functions,discussing the analog circuit realization with specific digital logic elements.2.To tackle the problem that digital systems are inevitably affected by limited precision effects,causing system dynamic degradation,a digital-analog hybrid system scheme is proposed and a random number generator is designed based on that.We combine digital systems with few analog devices to construct a digital-analog hybrid system,overcoming the shortcomings of analog devices being susceptible to environmental influences,complex,and having poor controllability of device parameters.Moreover,the introduction of analog variable mitigates the limited precision effects in digital systems.To verify the effectiveness of the proposed digitalanalog hybrid system,a capacitor and a memristor are respectively used as the only analog component of the whole system,constructing two different digital-analog hybrid systems.The numerical simulations with the classic chaotic mapping and the proposed Chen-like system reveal that the digital-analog hybrid system does solve the dynamic degradation in pure digital systems.Based on our proposed digital-analog hybrid system,a random number generator is constructed with the complex coupled lattice mapping.To verify that the generated random number sequences are qualified to the practical application demands,the NIST test suite is employed.All the generated sequences successfully pass each test.Given enough scale of the FPGA,it is easy to obtain random number streams with a throughput of up to Gbit/s,which reaches a relatively high level compared to similar research.The proposed digital-analog hybrid system has very good property of integration,providing a strategy for solving the finite precision effects in other digital systems.3.The scheme of generating,transmitting and reconstructing transmitting signal for distributed MIMO radar system is proposed.Traditional wired transmission methods of transmitting signal greatly limit the flexibility of the system,while the inherent characteristics of the wireless transmission methods are always facing security threat.Therefore,we propose a solution based on the nonlinear dynamic network,which can be used to design,transmit and reconstruct radar transmitting signal.The scheme consists of three parts,including the optimal waveform dictionary,the signal generation module and the signal reconstruction module.First,according to the specific application characteristics,a suitable waveform design method is chosen to generate a series of base waveforms to construct the optimal waveform dictionary.Second,through bifurcation analysis,the nonlinear feedback function in the signal generation module is designed,which guarantees the chaotic property and convergence of the whole system.The nonlinear control function is mainly used to calculate the position information of the output signal in the optimal waveform dictionary for the next moment according to the output signal of the previous moment,ensuring the signal generating module outputs a continuous transmitting signal.Besides,random phases are introduced to the output transmitting signal to ensure a good confidentiality of the output transmitting signal.The proposed Chen-like system is also employed into the feedback control function.Last,in the reconstruction module,the receivers obtain all the compressed signals sent by the transmitters.With the prior information such as the known optimal waveform dictionary and the nonlinear feedback function,the transmitting signal reconstruction can be completed in real time.In addition,we perform a complete performance analysis of the signals and feedback control functions involved in the scheme,including correlation functions,energy spectral density,ambiguity functions,and bifurcation diagrams and so on,all of which have satisfied results.Signal reconstruction can be finished in real time at the receiving ends with no theoretical error.It is noticeable that the previously proposed digital-analog hybrid scheme can also be applied to realize the scheme for distributed MIMO radar systems.