Improved auxiliary particle filter‐based synchronization of chaotic Colpitts circuit and its application to secure communication

In this paper, we propose a synchronization scheme based on an improved auxiliary particle filter (IAPF) for chaotic Colpitts circuit and conduct an experimental study on the synchronization performance with application to secure communications. Specifically, with the synchronization scheme, when the chaotic signals generated by an analog Colpitts circuit are transmitted through a nonideal channel, the distorted signals are processed digitally by the novelly designed IAPF at the receiver, in order to obtain the synchronized signals of the transmitter circuit. Experimental results indicate that synchronization can be achieved over both the additive white Gaussian noise channel and the multipath fading channel with low signal‐to‐noise ratio, even if there exist severe circuit parameter mismatches between the transmitter and the receiver. Furthermore, a chaos‐masking secure communication system is constructed and verified over both the additive white Gaussian noise channel and the multipath fading channel, and the bit error rate is evaluated versus different signal‐to‐noise ratios and symbol periods. It is shown that the achievable bit error rate can reach the order of magnitude of 10 ^{− 4} without error correction coding techniques. In addition, security analysis demonstrates that the proposed chaotic secure communication system is resistant to the brute‐force attack. Copyright © 2013 John Wiley & Sons, Ltd.     

基于广义观测器实现混沌系统的同步及信息传输

将保密通信问题看成是信息信号同步问题,从全新的角度提出了一种基于广义观测器的保密通信系统.首先在不改变混沌发送系统的混沌特性的前提下,将信息信号注入到混沌发送系统中,并将其看作系统的状态量;然后在接收端设计广义观测器;最后根据发送端传来的隐藏有信息信号的混沌输出信号同步出混沌系统的状态和信息信号.此方法不需要单独设计加密解密算法,而是将收发端混沌系统的同步与信息传输用同步方法一次实现.对系统的仿真证明了该方法的有效性.     

一种网格多涡卷混沌Colpitts振荡器及其电路实现

基于单涡卷混沌Colpitts振荡器模型,提出了一种网格多涡卷混沌Colpitts振荡器模型。利用阶跃函数代替单涡卷混沌Colpitts振荡器模型中的非线性函数,以及增加一个饱和函数,构造了一个能产生网格多涡卷混沌吸引子的Colpitts振荡器模型。通过数值仿真与电路实验,验证了该网格多涡卷混沌Colpitts振荡器的可行性。     

Additive mixing modulation for public key encryption based on distributed dynamics

We introduce a public key encryption scheme that is based on additive mixing of a message with chaotic nonlinear dynamics. A high-dimensional dissipative nonlinear dynamical system is distributed between transmitter and receiver. The transmitter dynamics is public (known to all) and the receiver dynamics is private (known only to the authorized receiver). Bidirectional signals that couple transmitter and receiver are transmitted over a public channel. Once the chaotic dynamics which is initialized with a random state converges to the attractor, a message is mixed with the chaotic dynamics at the transmitter. The authorized receiver who knows the entire dynamics can use a simple algorithm to decode the message. An unauthorized receiver does not know the receiver dynamics and needs to use computationally unfeasible algorithms in order to decode the message. Security is maintained by altering the private receiver dynamics during transmission. We show that using additive mixing modulation is more efficient than the attractor position modulation distributed dynamics encryption scheme. We demonstrate the concept of this new scheme by simulating a simple coupled map lattice.     

Multi-scroll hyperchaotic system based on colpitts model and its circuit implementation

Based on the framework of Colpitts oscillator, a four-dimensional multi-scroll hyperchaotic system is proposed, which generates (2M+1)×(2N+1)-scroll chaotic and hyperchaotic attractors. The key strategy is to increase the number of index-2 equilibrium points by introducing two unit saw-tooth functions to extend and modify the Colpitts oscillator model. By using bifurcation diagram and phase portrait, the dynamical characteristics of the multi-scroll hyperchaotic system are briefly studied. Moreover, micro-controller based circuit realization is introduced and the experimental results demonstrate that 7×5-scroll chaotic and hyperchaotic attractors can be obtained in the digital circuit.     

Robust Chaotic Communication Based on Indirect Coupling Synchronization

This paper proposes a chaotic communication approach using indirect coupled synchronization scheme with high power encrypted signals. The proposed scheme is carefully designed so that the encrypted signal does not deteriorate the synchronization unlike in traditional communication methods. The synchronization problem is solved using observer-based controller. The advantages of this approach are the general and systematic feedback observer design methodology suitable for convergence rate of synchronization; flexibility in selection of chaotic signals for cryptosystem secure key generator; and improvement of the frequency-domain characteristics of the transmitted message. Computer simulations show that the synchronization between the transmitter and the receiver is more robust for different amplitude values of the information signal, even in the presence of external disturbances.     

基于考毕兹振荡器的宽带混沌电路设计

针对某些雷达、通信等系统在应用中对混沌信号频域带宽的要求,设计了一种基于考毕兹振荡器电路的宽带混沌信号发生器。该混沌信号产生电路由考毕兹振荡器为基本谐振电路、级联若干容阻串并联单元的选频网络构成,混沌信号的上下限频率分别由基本谐振电路和第一节容阻串并联网络参数决定,通带频谱的平坦性受其他级联选频网络影响。根据初步分析和仿真试验,该混沌电路组成结构简单,能够产生带宽超过60MHz较为平坦的宽带混沌信号。     

Secure Communication via Synchronization of Lur’e Systems Using Sampled-Data Controller

In this paper, synchronization of chaotic Lur’e systems using sampled-data control is applied to the secure communication problem. The message is transmitted and masked by the techniques of n-cipher and a public key obtained by the chaotic Lur’e system. The decryption of the transmitted encrypted message to recover the original message at the receiver can be achieved by synchronizing the transmitter and receiver chaotic systems. Sampled-data feedback control is used for synchronization, and a sufficient condition for obtaining feedback gain is derived in terms of linear matrix inequalities using a discontinuous Lyapunov functional. The secure communication system is simulated via Matlab along with the Chua system to show the effectiveness of the proposed result.     

Colpitts振荡电路动力学特性的PSPICE仿真分析

以Colpitts振荡器电路为例,在建立Colpitts电路模型的基础上,对其进行PSpice仿真研究,观察状态变量分别在时域和频域中的变化.通过调整电路元件的参数,观察Colpitts电路中动力学行为的演变过程,得到了与理论分析相吻合的结果.可以发现,电路处于混沌态和准周期态的参数组合不是唯一的.     

Chaotic dynamics of delayed feedback klystron oscillator and its control by external signal

Complex nonlinear dynamics and applications of a microwave klystron oscillator with delayed feedback are studied in this paper on the basis of a system of delayed differential equations. Results of numerical simulation of self-modulation and chaotic regimes are presented, unveiling a complex bifurcation pattern in a wide range of parameters. Various types of chaotic attractors and transition to chaos scenarios are described. Experimental results for the five-cavity klystron oscillator are presented as well, showing good qualitative agreement with numerical simulations. Special attention is paid to application of the oscillator in direct chaotic communications. Information transmission using chaos shift keying (CSK) modulation and coherent reception is demonstrated via numerical simulation. The driving by an external signal is used to control the chaotic states of the transmitter oscillator for the purpose of generation of CSK basis functions.     

Colpitts混沌电路的研究

对典型Colpitts振荡电路进行分析,并进行了Pspice仿真,观察状态变量随参数变化的动力学行为及频谱分布情况.对改进型Colpitts电路进行仿真,对比仿真结果可知正是寄生电容CCB影响了典型Colpitts电路产生高频混沌信号.     

借助EWB仿真软件分析混沌电路

通过虚拟电子实验室EWB软件仿真了非线性系统产生的混沌现象,以Colpitts振荡器电路为例,讨论了在电路中设置不同的元件参数值时产生的不同混沌,并介绍了这种动态混沌在通信系统中作为信息载体的重要应用.     

Two-stage chaotic Colpitts oscillator

A novel version of the chaotic Colpitts oscillator is proposed. It contains two bipolar junction transistors coupled in series. The resonance loop consists of an inductor and three capacitors. The two-stage oscillator, compared with the classical circuit, enables the fundamental frequency of chaotic oscillations to be increased by a factor of three. The PSpice simulations performed with 9 GHz threshold frequency transistors demonstrate that the highest fundamental frequencies of chaotic behaviour are 1 and 3 GHz for the classical and the two-stage Colpitts oscillator, respectively     

Optical Chaotic Communication Using Generalized and Complete Synchronization

We propose a secure optical communication system based on the principles of generalized and complete chaotic synchronization. A transmitter and a receiver both composed by two chaotic external-cavity semiconductor lasers are coupled in a master-slave configuration to provide generalized synchronization, while the master lasers in the transmitter and in the receiver are completely synchronized through the synchronization channel via an optical fiber. A message is added to the transmitter slave laser and sent to the receiver through the information channel to be compared with the output of the receiver slave laser. The system is robust to a small mismatch of the laser parameters or of the coupling between the master and slave lasers, unavoidable in a real system, and can even enable a good communication up to a 5 Gb/s transmission rate using the chaos masking encryption method, when the master laseres are coupled bidirectionally.      

混沌电路同步及其在通信中的应用研究

混沌在实际系统中是很常见的，但直到最近工程人员大都把它作一种无用的东西并极力去避免它。本文给出了一个蔡氏电路系统在固有的混沌模式下实现同步的可能性。     

Enhancing Chaotic Communication Performances by Manchester Coding

A numerical analysis of an optical chaotic transmission system, based on the synchronization of two chaotic lasers, in a master-slave closed loop configuration is presented. At the transmitter, the master chaotic wave is superposed on the information message; at the receiver, the message is recovered by subtracting the synchronized slave chaotic wave from the received signal. The performances are analyzed in terms of the Q-factor, considering two different message modulation formats: the nonreturn-to-zero and the Manchester coding. The Manchester coding shows enhanced performances due to the shift of the signal spectrum to higher frequencies.     

短信终端的SOC设计及系统实现

实现了基于兼容MCS51的8位处理器的PSTN固定电话短信终端的SOC设计.阐述了短信终端的SOC解决方案,包括双音多频信号的编解码、频移键控信号的调制解调、输入信号的1比特量化、输出信号的脉宽调制和滤波,降低了功耗和设计复杂度,减少了数模接口的数量.     

A second-order Markov model to synchronize a quasi-chaotic sequence: application of synchronization and decoding problem with belief propagation

The use of chaotic codes in transmission systems presents many advantages, not only in term of security, but also to combat multi-path propagations and to allow multiple access. Nevertheless, the main problem of communication with chaos is the design of an experimental and real-time synchronization decoder between transmitter and receiver. In this paper, we suggest to use the belief propagation algorithm as a new approach for synchronizing quasi-chaotic signals. In this approach, the transmitter contains a digital chaotic oscillator which is perturbed by the information signal. The receiver consists in a dual system augmented with a belief propagation processing, whose aim is to recover the information signal. We suppose that the channel is Gaussian and synchronization is forced in a first step. Once synchronization is achieved, the information signal modulated the chaotic system and is transmitted on the Gaussian channel. An adaptative belief propagation algorithm is processed to recover the signal information.     

一种新的混沌调制和线性解调方法

提出一种新的用于保密通信的混沌调制和线性解调方法.发送端和接收端各有一个相同的混沌电路,将有用信号接入发送端混沌电路的线性子电路,使其对该混沌电路进行调制.调制后的混沌信号传送到接收端的混沌电路,检测该电路中某一电流或电压变量,经线性滤波器解调可恢复原始有用信号.基于这一调制、解调方法的混沌通信系统保密性强且电路简单.对两个混沌保密通信系统的仿真实验取得了满意的结果.     

宽带连续混沌波形信号的研究与设计

针对现代战场对信息信号低截获概率的要求,分析研究了宽带连续混沌信号的低截获性,并对失谐耦合型考必兹宽带混沌电路进行研究,并分析比较了不同耦合方式的Colpitts振荡器电路,同时对该混沌电路产生的连续混沌波形信号做出分析,最后仿真出了该混沌信号的模糊函数图。仿真结果显示该混沌信号基底分布均匀,近似于理想的"图钉型",具有良好的距离和速度分辨率的同时,也具有更强的杂波抑制能力。