Research On Power Spectral Density Constraint Of Chaotic Signal

With the continuous innovation of information technology,the security issue of information system becomes more and more important.The characteristics of broadband and inherent random of chaotic signals is key factor that can be used to encrypt information in the field of communication.The unsatisfactory power spectrum distribution leads to the chaotic signal can not be used as a communication carrier to achieve the signal wireless transmission,and this is one of the important reasons that currently restricting the development of chaotic signal in wireless communication.So,it is of great significance to improve the performance and achievability of chaotic communication system by studying the factors influencing the power spectrum density of chaotic signal and finding out the design method which can obtain the specific power spectrum density.Firstly,the chaotic characteristics of four existing chaotic systems that includes Lorenz chaotic system,Lü chaotic system,Xü chaotic system and Zhou chaotic system is analyzed in this thesis.By comparing the dynamic differential equations and the state of motion of the system,the influence of the different parameters and the structure of the nonlinear term on the chaotic attractor,the attract domain and the signal power spectrum density is analyzed so that the inherent relationship between the chaotic attraction region of the system and the power spectral density of the signal is obtained.Secondly,according to different influencing factors,the corresponding method of changing the power spectrum density of chaotic signal is found.Based on the existing chaotic system,the three methods of parameter method,nonlinear constraint method and parameter nonlinear constraint method are used to respectively design a new chaotic system with parameters.The range of the parameters in the new system is determined by theoretical analysis and the numerical simulation,and the chaos characteristics of the new system is researched by the direct observation method,the Lyapunov exponent method and the Poincaré section method.The experimental result shows that the state variables of the chaotic system are defined in a circular motion and the signal power spectrum density in a certain frequency range.Then,from the view of experimental results and practical application,the advantages and disadvantages of the three methods are compared and analyzed.Finally,according to the relationship between the attract domain of the chaotic system and the signal power spectrum density,a chaotic signal with the specific power spectrum is obtained by superimposing a chaotic system and a two-dimensional circular system and adjusting the parameters based on superposition principle,which verifies the feasibility of the proposed method.