一种混沌映射的相空间去噪方法

对于混沌映射来说,它们的频谱比混沌流的频谱更广阔,与噪声频谱的重叠率更高,所以混沌流的去噪方法对它们并不适用. 在半盲分析法的框架下,混沌系统的参数估计问题终将归结为最小二乘估计问题. 本文从最小二乘拟合的角度出发估计混沌映射的演化参数,进而通过相空间重构以及投影操作,实现对观测信号的噪声抑制. 实验结果表明,该算法的去噪效果优于扩展卡尔曼滤波器（extended Kalman filter,EKF）和无先导卡尔曼滤波器（unscneted Kalman filter,UKF）,并且能够较大程度地将信号源的混沌特征量还原. 关键词： 混沌 噪声抑制 相空间重构 投影     

Noise-resistant chaotic maps

Synchronized chaotic systems are highly vulnerable to noise added to the synchronizing signal. It was previously shown that chaotic circuits could be built that were less sensitive to this type of noise. In this work, simple chaotic maps are demonstrated that are also less sensitive to added noise. These maps are based on coupling a shift map to a digital filter. These maps are simple enough that they should help lead to an understanding of how noise-robust chaotic systems work. (c) 2002 American Institute of Physics.     

输入受限的混沌系统同步控制

在混沌系统的同步控制中, 由于混沌系统对初始状态的敏感性, 一旦两个混沌系统的状态初值偏差大, 其状态同步往往需要高幅值的控制律来达到, 这给同步控制实现带来了困难, 并且在同步控制中, 两个混沌系统的初始值通常是未知的. 本文考虑控制输入受限情况下的混沌同步控制问题, 基于符号函数的近似表示式, 将受限的控制输入建模为连续可微的光滑函数, 在每一个采样点将同步控制误差系统近似为局部最优线性模型并设计连续型线性二次型调节器(LQR)最优控制律. 为降低混沌同步控制律的幅值和维持同步系统采样时刻之间的动态, 设计了等价的离散最优控制律, 并通过调整LQR性能加权矩阵值, 确保同步控制信号不会超出其受限的上界. 最后对统一混沌模型下的三种不同混沌系统同步控制进行了仿真研究. 仿真结果验证了方法的有效性. 关键词： 统一混沌模型 符号函数 输入受限 同步控制     

Complexity and synchronization in stochastic chaotic systems

We investigate the complexity of a hyperchaotic dynamical system perturbed by noise and various nonlinear speech and music signals. The complexity is measured by the weighted recurrence entropy of the hyperchaotic and stochastic systems. The synchronization phenomenon between two stochastic systems with complex coupling is also investigated. These criteria are tested on chaotic and perturbed systems by mean conditional recurrence and normalized synchronization error. Numerical results including surface plots, normalized synchronization errors, complexity variations etc show the effectiveness of the proposed analysis.     

SENSITIVE ERROR ANALYSIS OF CHAOS SYNCHRONIZATION

We study the synchronizing sensitive errors of chaotic systems for adding other signals to the synchronizing signal. Based on the model of the Henon map masking, we examine the cause of the sensitive errors of chaos synchronization. The modulation ratio and the mean square error are defined to measure the synchronizing sensitive errors by quality. Numerical simulation results of the synchronizing sensitive errors are given for masking direct current, sinusoidal and speech signals, separately. Finally, we give the mean square error curves of chaos synchronizing sensitivity and three-dimensional phase plots of the drive system and the response system for masking the three kinds of signals.     

Chaotic synchronization of coupled ergodic maps

With few exceptions, studies of chaotic synchronization have focused on dissipative chaos. Though less well known, chaotic systems that lack dissipation may also synchronize. Motivated by an application in communication systems, we couple a family of ergodic maps on the N-torus and study the global stability of the synchronous state. While most trajectories synchronize at some time, there is a measure zero set that never synchronizes. We give explicit examples of these asynchronous orbits in dimensions two and four. On more typical trajectories, the synchronization error reaches arbitrarily small values and, in practice, converges. In dimension two we derive bounds on the average synchronization time for trajectories resulting from randomly chosen initial conditions. Numerical experiments suggest similar bounds exist in higher dimensions as well. Adding noise to the coupling signal destroys the invariance of the synchronous state and causes typical trajectories to desynchronize. We propose a modification of the standard coupling scheme that corrects this problem resulting in robust synchronization in the presence of noise.     

不确定自催化反应扩散时空混沌系统的延时同步

设计了一种延迟同步控制器实现了时空混沌系统之间的同步控制.基于Lyapunov稳定性定理,确定了延迟同步控制器的结构以及系统状态变量之间的误差方程.以自催化反应扩散时空混沌系统为例,仿真模拟验证了该控制器的有效性.进一步设计了参量辨识器,对不确定自催化反应扩散时空混沌系统中的参量进行了有效辨识.通过研究有界噪声影响下系统的同步效果,表明该同步方法具有较好的抗干扰能力. 关键词： 时空混沌 延时同步 参量辨识 有界噪声     

Least mean square error difference minimum criterion for adaptive chaotic noise canceller

The least mean square error difference (LMS-ED) minimum criterion for an adaptive chaotic noise canceller is proposed in this paper. Different from traditional least mean square error minimum criterion in which the error is uncorrelated with the input vector, the proposed LMS-ED minimum criterion tries to minimize the correlation between the error difference and input vector difference. The novel adaptive LMS-ED algorithm is then derived to update the weights of adaptive noise canceller. A comparison between cancelling performances of adaptive least mean square (LMS), normalized LMS (NLMS) and proposed LMS-ED algorithms is simulated by using three kinds of chaotic noises. The simulation results clearly show that the proposed algorithm outperforms the LMS and NLMS algorithms in achieving small values of steady-state excess mean square error. Moreover, the computational complexity of the proposed LMS-ED algorithm is the same as that of the standard LMS algorithms.     

混沌系统的时间延迟同步误差分析

对Pecora和Carroll的混沌自同步方案的延迟同步误差进行了研究.在计算机上对Lorenz混沌系统伪装的延迟同步误差进行了模拟:给定系统参数,对应不同延迟时间,得出了均方误差与采样步长的关系曲线;给定系统参数和延迟时间,对应不同采样步长,得到了混沌时间序列的误差曲线;给定采样步长,对应不同的系统参数,获得了混沌时间序列的尺度效应和均方误差与采样步长的关系曲线.提出了减小延迟同步误差的一些方法,得到一些对混沌同步和混沌控制应用有意义的结果. 关键词： 混沌同步 时间同步 误差分析     

一种分数阶混沌系统同步的自适应滑模控制器设计

针对分数阶混沌系统的同步问题, 基于滑模控制理论和自适应控制理论, 设计了一个具有较强鲁棒性的分数阶积分滑模面, 并提出了一种自适应滑模控制器在不消除非线性项的情况下实现一类三维分数阶混沌系统同步的方法. 利用所设计的自适应滑膜控制器实现了分数阶Chen系统、分数阶Liu系统以及分数阶Arneodo系统的混沌同步. 数值模拟仿真结果验证了所设计的控制器的有效性和可行性.     

Chaotic secure communication based on strong tracking filtering

A scheme for implementing secure communication based on chaotic maps and strong tracking filter (STF) is presented, and a modified STF algorithm with message estimation is developed for the special requirement of chaotic secure communication. At the emitter, the message symbol is modulated by chaotic mapping and is output through a nonlinear function. At the receiver, the driving signal is received and the message symbol is recovered dynamically by the STF with estimation of message symbol. Simulation results of Holmes map demonstrate that when message symbols are binary codes, STF can effectively recover the codes of the message from the noisy chaotic signals. Compared with the extended Kalman filter (EKF), STF has a lower bit error rate.     

Closed-form MSE and achievable rate for indirect learning DPD

The digital pre-distortion (DPD) signal processing is an effective way to mitigate the power amplifier (PA) nonlinearity effect. For communication systems containing DPD and PA, it is difficult to acquire performance metrics closed-forms for any DPD architecture since there was no mathematical expression for each DPD coefficient. Usually, researchers look for more efficient DPD algorithms for DPD coefficients (compared to the existing ones) in terms of computational complexity, delay, power consumption, etc. Consequently, the performance is evaluated through intensive simulation. In this paper, we show how one can exploit the results of our recent work to mathematically model the indirect learning architecture (ILA) DPD and efficiently derive important measures in communication systems, e.g. normalized mean square error (NMSE), achievable rate, and signal-to-noise plus distortion ratio (SNDR). The author would like to clarify that this work might be the first one to provide closed-form analysis for DPD systems. We think the provided framework/analysis will open the door to other researchers/engineers to plug their own assumptions and derive the performance metrics. The derived expressions of the performance metrics (NMSE, SNDR, and achievable rate) are validated through Monte Carlo simulations. We also derive a closed-form expression for the achievable rate bound for the transmit chain. Moreover, we analytically study the effect of the thermal noise and the quantization noise, in the analog-digital conversion (ADC) process, on the NMSE and achievable rate. The analytical expressions are validated through numerical simulations.     

Estimating model parameters in nonautonomous chaotic systems using synchronization

In this Letter, a technique is addressed for estimating unknown model parameters of multivariate, in particular, nonautonomous chaotic systems from time series of state variables. This technique uses an adaptive strategy for tracking unknown parameters in addition to a linear feedback coupling for synchronizing systems, and then some general conditions, by means of the periodic version of the LaSalle invariance principle for differential equations, are analytically derived to ensure precise evaluation of unknown parameters and identical synchronization between the concerned experimental system and its corresponding receiver one. Exemplifies are presented by employing a parametrically excited 4D new oscillator and an additionally excited Ueda oscillator. The results of computer simulations reveal that the technique not only can quickly track the desired parameter values but also can rapidly respond to changes in operating parameters. In addition, the technique can be favorably robust against the effect of noise when the experimental system is corrupted by bounded disturbance and the normalized absolute error of parameter estimation grows almost linearly with the cutoff value of noise strength in simulation.     

Synchronization of reconstructed dynamical systems

The problem of constructing synchronizing systems to observed signals is approached from a data driven perspective, in which it is assumed that neither the drive nor the response systems are known explicitly but have to be derived from the observations. The response systems are modeled by utilizing standard methods of nonlinear time series analysis applied to sections of the driving signals. As a result, synchronization is more robust than what might be expected, given that the reconstructed systems are only approximations of the unknown true systems. Successful synchronization also may be accomplished in cases where the driving signals result from nonlinearly transformed chaotic states. The method is readily extended and applied to limited real-time predictions of chaotic signals.     

Synchronization of Chaotic Optical Systems by Remote Feedback Controlling

A dynamical variable feedback scheme is proposed to synchronize chaotic motion of two identical and nearly identical laser systems with an injected signal. The feedback synchronization method works well while the conventional variable-replacement synchronization methods are not realizable. Various practical situations for synchronizing two chaotic laser systems located distance away from each other are taken into account. The application of this synchronization approach to wide range of practical systems is emphasized.     

Further results on complete synchronization for noise-perturbed chaotic systems

In this Letter, a class of general systems which covers several famous chaotic systems is studied in complete synchronization with noise perturbation. Special nonlinear coupling techniques as well as LaSalle-type invariance principle of stochastic differential equations are employed to deduce our sufficient conditions for complete synchronization without involving the boundedness of chaotic systems. Furthermore, the correlative numerical simulations are given to illustrate the effectiveness of our theoretic results.     

混沌噪声背景下微弱脉冲信号的检测及恢复

构建了一种在混沌噪声背景下检测并恢复微弱脉冲信号的模型.首先,基于混沌信号的短期可预测性及其对微小扰动的敏感性,对观测信号进行相空间重构、建立局域线性自回归模型进行单步预测,得到预测误差,并利用假设检验方法从预测误差中检测观测信号中是否含有微弱脉冲信号.然后,对微弱脉冲信号建立单点跳跃模型,并融合局域线性自回归模型,构成双局域线性(DLL)模型,以极小化DLL模型的均方预测误差为目标进行优化,采用向后拟合算法估计模型的参数,并最终恢复出混沌噪声背景下的微弱脉冲信号.仿真实验结果表明本文所建的模型能够有效地检测并恢复出混沌噪声背景中的微弱脉冲信号.     

Deep-BiGRU based channel estimation scheme for MIMO–FBMC systems

Deep Learning (DL)–based wireless communication systems have the potential to improve the conventional functions and current architecture of communication systems. In this paper, we propose a novel DL-based channel estimation scheme for multiple-input multiple-output filter bank multicarrier with offset quadrature amplitude modulation (MIMO-FBMC/OQAM) systems called deep bidirectional gated-recurrent unit (BiGRU) scheme. This scheme can easily be applied to a single-input single-output (SISO) system. The proposed scheme is divided into two stages: offline and online. The network is first trained in the offline stage. The prediction of channel information and estimation of the channel matrix using the trained network is then performed in the online stage. The simulation results in terms of the normalized mean square error (NMSE) and bit error rate (BER) demonstrate that, under different time-varying channel models, the proposed DL scheme significantly improves the channel estimation performance of FBMC for single and multiple antennas compared to conventional interference approximation method (IAM) channel estimation methods.     

Impulsive control for synchronization of nonlinear Rossler chaotic systems

This paper reports that an impulsive control theory for synchronization of nonlinear R?ssler chaotic systems is developed. A new framework for impulsive synchronization between such chaotic systems is presented, which makes the synchronization error system a linear impulsive control system. Therefore, it is easy to derive the impulsive synchronization law. The proposed impulsive control scheme is illustrated by nonlinear R?ssler chaotic systems and the simulation results demonstrate the effectiveness of the method.     

Partial phase synchronization for multivariate synchronizing systems

Graphical models applying partial coherence to multivariate time series are a powerful tool to distinguish direct and indirect interdependencies in multivariate linear systems. We carry over the concept of graphical models and partialization analysis to phase signals of nonlinear synchronizing systems. This procedure leads to the partial phase synchronization index which generalizes a bivariate phase synchronization index to the multivariate case and reveals the coupling structure in multivariate synchronizing systems by differentiating direct and indirect interactions. This ensures that no false positive conclusions are drawn concerning the interaction structure in multivariate synchronizing systems. By application to the paradigmatic model of a coupled chaotic Roessler system, the power of the partial phase synchronization index is demonstrated.