Blind Extraction of Chaotic Signals by Using the Fast Independent Component Analysis Algorithm

We report the results of using the fast independent component analysis （FastICA） algorithm to realize Mind extraction of chaotic signals. Two cases are taken into consideration： namely, the mixture is noiseless or contaminated by noise. Pre-whitening is employed to reduce the effect of noise before using the FastICA algorithm. The correlation coefficient criterion is adopted to evaluate the performance, and the success rate is defined as a new criterion to indicate the performance with respect to noise or different mixing matrices. Simulation results show that the FastICA algorithm can extract the chaotic signals effectively. The impact of noise, the length of a signal frame, the number of sources and the number of observed mixtures on the performance is investigated in detail It is also shown that regarding a noise as an independent source is not always correct.     

Stochastic resonance of bias signal-modulated noise in a single-mode laser＊

Stochastic resonance (SR) for bias signal modulation is studied in a single-mode laser system. By investigating a gain-noise model driven by correlated pump noise and quantum noise, we find that, whether the correlation coefficient between both the noises is positive or negative, SR always appears in the dependence of signal-to-noise ratio (SNR) upon the noise correlation time and the frequency of the modulation signal. However, only when the correlation coefficient between both noises is negative can SR occur in the dependence of SNR upon the quantum noise intensity and pump noise intensity, while when the correlation coefficient between both noises is positive, it shows monotonically.     

Stochastic Resonance in a Bistable System Subject to Non-Gaussian and Gaussian Noises

In this paper, we consider the phenomenon of stochastic resonance （SR） in a quartic bistable system under the simultaneous action of a multiplicative non-Gaussian and an additive Gaussian noises and a weak periodic signal. The expression of the signal-to-noise ratio R is derived by applying the two-state theory in adiabatic limit. We discuss the effects of the parameter q indicating the departure of the non-Gaussian noise from the Gaussian noise, the correlation time r of the non-Gaussian noise, and coupling intensity A between two noise terms on the stochastic resonance. It is found that the signM-to-noise ratio of the system, as a function of the additive noise intensity, undergoes the transition from having one peak to having two peaks, and then to having one peak again when the parameter q or the noise correlation time τ is increased. The parameter q and τ play opposite roles in the SR of the system.     

Stochastic resonance in with additive noises a stochastic bistable system and square-wave signal

<正>This paper considers the stochastic resonance in a stochastic bistable system driven by a periodic square-wave signal and a static force as well as by additive white noise and dichotomous noise from the viewpoint of signal-to-noise ratio.It finds that the signal-to-noise ratio appears as stochastic resonance behaviour when it is plotted as a function of the noise strength of the white noise and dichotomous noise,as a function of the system parameters,or as a function of the static force.Moreover,the influence of the strength of the stochastic potential force and the correlation rate of the dichotomous noise on the signal-to-noise ratio is investigated.     

Synchronization in a Mutualism Ecosystem Induced by Noise Correlation

Understanding the cause of the synchronization of population evolution is an important issue for ecological improvement. Here we present a Lotka-Volterra-type model driven by two correlated environmental noises and show, via theoretical analysis and direct simulation, that noise correlation can induce a synchronization of the mutualists. The time series of mutual species exhibit a chaotic-like fluctuation, which is independent of the noise correlation, however, the chaotic fluctuation of mutual species ratio decreases with the noise correlation. A quantitative parameter defined for characterizing chaotic fluctuation provides a good approach to measure when the complete synchronization happens.     

Effect of Time Delay on Binary Signal Detection via a Bistable System

The effect of time delay on binary signal detection via a bistable system in the presence of white or colored Gaussian noise is investigated. By defining the bit error rate based on the solution of the approximated Fokker- Planck equation, the detector performance is investigated theoretically and is verified by Monte Carlo simulation. It is shown that, when the system parameter or noise intensity is optimally chosen, the increasing time delay generally improves the system performance. It is also shown that it is more difficult to accurately predict the system performance with a larger time delay and correlation time. This may inspire more thorough investigations in cooperative effects of a nonlinear system and time delay on signal processing.     

Intensity Correlation Time of a Single-Mode Laser Driven by Two Coloured Noises with Coloured Cross-Correlation with Bias Signal Modulation

The intensity correlation time T is studied by employing a gain-noise model of a single-mode laser driven by coloured pump noise τ1 and coloured quantum noise τ2 with coloured cross-correlation τ3 with a bias signal modulation. By using the linear approximation method, we detect that a maximum （i.e. resonance） exists in the curves of the intensity correlation time T versus the noise intensities D and Q when the noise correlation coefficient A is positive; and a minimum （i.e. suppression） exists in the T - D and T - Q curves when A is negative. When A is zero, T increases monotonously with increase of D and decreases monotonically with increase of Q. Furthermore, the curve of T versus the pump noise self-correlation time τ1 is also studied. Our study shows that, no matter what the value of A is, there exist one maximum and one minimum in the T - τ1 curve.     

Resonance, Multi-resonance, and Reverse-resonance Induced by Multiplicative Dichotomous Noise

A constant-potential system driven by multiplicative dichotomous noise and subject to an input oscillatory signal is investigated. Two phenomena of stochastic resonance are observed. One is the response as a function of the noise＇s parameters; the other is that as a function of the input signal frequency. A phenomenon of multi-resonance （there are three or four peaks） is found for the response as a function of a parameter of the noise. A phenomenon of reverse-resonance is found, for which the response of the system to the signal can be weakened by the presence of the noise （there is an optimal minimum）. These results help in studies of the systems with multiplicative dichotomous noise, such as the semiconductor, the proteins motor, the chemical reaction, and so on.     

The statistical fluctuation of a single-mode laser system driven by coloured pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts

Using the linear approximation method, this paper studies the statistical property of a single-mode laser driven by both coloured pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts, and calculates the steady-state mean normalized intensity fluctuation and intensity correlation time. It analyses the influences of the modulation signal, the net gain coefficient, the noise and its correlation form on the statistical fluctuation of the laser system respectively. It is found that the coloured pump noise modulated by the signal has a great suppressing action on the statistical fluctuation of the laser system; the pump noise self-correlation time and the specific frequency of modulation signal have the result that the statistical fluctuation tends to zero. Furthermore, the ＇colour＇ correlation of pump noise has much influences on the statistical fluctuation of the laser system. Increasing the intensity of pump noise will augment the statistical fluctuation of the laser system, but the intensity of quantum noise and the coefficient of cross-correlation between its real and imaginary parts have less influence on the statistical fluctuation of the laser system. Therefore, from the conclusions of this paper the statistical property can be known and a theoretical basis for steady operation and output of the laser system can be provided.     

Influence of net gain on the statistical fluctuation in a single-mode laser system

Using linear approximation method, we calculate the intensity correlation time of a single-mode laser driven by both colored pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts, and analyze the influence of the net gain coefficient a0 on the statistical fluctuation of the laser system. It is found that for the case that the colored pump noise is long time correlated, the main factor influencing the statistical fluctuation of the laser system is a0, and the frequency of the modulation signal has negligible effect on the statistical fluctuation of the laser system.     

混沌信号的压缩感知去噪

对非线性时间序列进行噪声抑制是从中提取有效信息的前提. 混沌信号的去噪算法不仅要使滤波后的信号具有较高的信噪比, 也要具有较好的不确定性. 从压缩感知的角度出发,提出了一种新的噪声抑制方法. 该方法包括估计噪声方差, 以及依据动态的稀疏度将观测值往确定的过完备字典上投影. 仿真实验表明, 该方法比常用的小波阈值法和局部曲线拟合法具有更高的输出信噪比, 而原始信号的混沌特性也能得到较大程度的恢复.     

距离无关的高精度混沌激光测距

研究了利用类噪声混沌激光的相关特性实现目标距离的测定方法.数值分析了混沌激光自相关曲线的半峰全宽和旁瓣水平与表征其混沌状态的最大李雅普诺夫指数及关联维数的关系.同时,模拟研究了波形误差对混沌激光测距的影响,并分析了不同混沌态的波形误差的临界值.结果表明,具有窄半峰全宽和低旁瓣水平的自相关曲线的高维混沌激光序列是理想的测距激光,其测量分辨率可达1.5 cm以下,且波形误差容忍度大,测量范围大.在测量范围内,精度与距离无关.     

基于广义窗函数和最小二乘支持向量机的混沌背景下微弱信号检测

为了从混沌背景中检测微弱信号,研究分析了复杂非线性系统的相空间重构理论,提出了一种基于广义窗函数的最小二乘支持向量机的预测法. 该方法以广义嵌入窗为基础,利用自关联函数法确定Lorenz系统的嵌入维数和时间延迟, 实现相空间重构,结合最小二乘支持向量机建立Lorenz系统的误差预测模型, 检测微弱目标信号(瞬态和周期信号).仿真实验表明,该方法的预测模型具有较小的误差, 能够有效地从混沌背景噪声中检测出微弱目标信号,减小噪声对目标信号的影响. 与传统方法相比,在降低检测门限的同时,能够有效地提高预测的精度, 在混沌噪声下信噪比为-87.41 dB的情况下,相对于传统支持向量机方法所得的均方根误差0.049(-54.60 dB时)降低近两个数量级至0.000036123(-87.41 dB时).     

毫米级高分辨率的混沌激光分布式光纤测温技术

近年来,随着分布式光纤传感技术在各大基础设施健康监测领域的广泛应用,人们对能够实现毫米量级精准定位和监测技术的需求日益增长.本文提出了一种基于宽线宽混沌激光的高分辨率分布式光纤测温技术.实验通过改变光反馈混沌源的偏振匹配态和反馈强度等外部参数,产生了–3 dB线宽约为7.5 GHz的宽线宽混沌激光,并在300 m传感光纤实现了空间分辨率为7.05 mm的分布式温度测量.同时,为了抑制光源线宽增加造成的布里渊增益谱恶化,在泵浦路中引入了时间门控技术,其中经脉冲调制后的泵浦光峰值功率提高了约9.5 dB,同时脉冲调制使混沌互相关锁定于脉冲持续时间内,从而布里渊增益谱的信号背景噪声比由约2.28 dB提升为4.55 dB,最终实现了空间分辨率为3.12 mm的分布式温度测量.     

基于Gabor变换的TDLAS检测信号的降噪研究

可调谐二极管激光吸收光谱(TDLAS)技术结合波长调制光谱(WMS)技术是用于痕量气体检测的重要技术手段。通过锁相放大器进行谐波检测,对解调得到的二次谐波信号进行分析可获得气体吸收的信息。但由于二次谐波信号受到噪声的影响,降低了检测系统的精度和稳定性。为了提高TDLAS检测系统的信噪比(SNR),提出了一种基于Gabor变换对二次谐波信号进行数字滤波降噪的方法。以CH₄在1 653.72 nm处的吸收光谱为例,通过仿真和实验对该降噪方法的有效性进行了验证。仿真结果表明,通过Gabor变换对信噪比为0dB的二次谐波信号进行处理后,系统的信噪比可提高15.73 dB。实验结果表明,基于Gabor变换进行降噪处理后,CH₄浓度在0.001%～0.02%区间内与二次谐波峰值的线性相关系数r达到了0.996 59,且系统的检测精度和稳定性明显提高。     

一种混沌海杂波背景下的微弱信号检测方法

基于复杂非线性系统的相空间重构理论,提出了一种基于遗传算法的支持向量机预测方法.利用改进的自相关法和饱和关联维数法确定混沌信号的时间延迟和嵌入维,从而实现相空间重构.通过遗传算法优化支持向量机中的惩罚系数和核函数参数,并结合支持向量机建立混沌序列的单步预测模型,从预测误差中检测出淹没在混沌背景中的微弱信号(包括瞬态信号和周期信号).以Lorenz系统和加拿大McMaster大学利用IPIX雷达实测得到的海杂波数据作为混沌背景噪声进行仿真实验,结果表明该方法能够有效地从混沌背景噪声中检测出微弱目标信号,所得的均方根误差为0.00049521(信噪比为-89.7704 dB),这比传统支持向量机方法的均方根误差(0.049,信噪比为-54.60 dB)降低了两个数量级.     

金属互连电迁移噪声的相关维数研究

针对金属铝互连中噪声信号随电迁移过程变化规律及其所反映的内部失效机理问题，提出将相关维数用于对电迁移噪声时间序列的分析.通过对互连电迁移噪声实验数据的相关维数计算，发现随着电迁移的进行，金属铝互连噪声由随机性成分占主导变为确定性成分占主导，反映出噪声由随机信号转变为混沌动力学信号.应用散射理论解释上述现象，在金属互连电迁移中，空位扩散阶段噪声主要产生机制是空位随机散射；在空位聚集到空洞成核这一过程中，噪声产生机制逐渐从随机散射转变到弹道混沌腔输运机制为主.通过与传统表征参量的对比，证明相关维数可用于预测金 关键词： 电迁移 噪声 相关维数 混沌     

基于分数阶可停振动系统的周期未知微弱信号检测方法

本文建立了分数阶可停振动系统, 其可停振动状态的改变对周期策动力敏感, 对零均值随机微小扰动不敏感, 这事实上为周期未知微弱信号检测提供了一种新的高效检测方法和判别标准. 与现有的利用混沌系统的大尺度周期状态变化检测周期未知弱信号的方法 需逐一尝试设置不同频率内置信号以便期望与待检周期信号发生共振不同, 利用分数阶可停振动系统的可停振动状态变化检测周期未知微弱信号的方法, 除了同样具有因为状态变化对周期信号的敏感性而能够实现极低检测门限的特点外, 还具有混沌系统信号检测所不具有的优点: 1)无需预先估计待检信号的周期; 2)无需计算系统状态的临界阈值; 3)可停振动状态可由本文设计的指数波动函数可靠地进行判断; 4)通过系统微分阶数的变化, 将检测系统层次化, 从而可得到比整数阶检测系统更低的检测门限, 特别是在色噪声环境下, 通过选取合适的微分阶数, 基于分数阶可停振动系统的微弱周期信号检测法能够大幅度的降低检测门限, 在本文的仿真试验中, 检测门限可达-182 dB. 关键词： 分数阶非线性系统 Duffing振子 弱信号检测     

Instability control in microwave-frequency microplasma

This paper introduces comprehensive large-signal analyses of modulation dynamics and noise of a chaotic semiconductor laser. The chaos is induced by operating the laser under optical feedback (OFB). Control of the chaotic dynamics and possibility of suppressing the associated noise by sinusoidal modulation are investigated. The studies are based on numerical solutions of a time-delay rate equation model. The deterministic modulation dynamics of the laser are classified into seven regular and irregular dynamic types. Variations of chaotic dynamics and noise with sinusoidal modulation are examined in both time and frequency domains over wide ranges of the modulation depth and frequency. The results showed that chaotic dynamics can be converted into five distinct dynamic types; namely, continuous periodic signal (CPS), continuous periodic signal with relaxation oscillations (CPSRO), periodic pulse (PP), periodic pulse with relaxation oscillations (PPRO) and periodic pulse with period doubling (PPPD). The relative intensity noise (RIN) of these types is characterized when the modulation frequencies are much lower, comparable to, and higher than the resonance frequency. Suppression of RIN to a level 8 dB/Hz higher than the quantum limit was predicted under the CPS type when the modulation frequency is 0.9 times the resonance frequency and the modulation depth is 0.14.     

基于最优滤波器的强混沌背景中谐波信号检测方法研究

强混沌背景中的微弱谐波信号检测有重要的工程研究意义. 目前的检测方法主要是基于Takens理论的混沌相空间重构方法, 然而这些方法往往对信干噪比要求高, 且对高斯白噪声敏感等. 本文注意到混沌信号的二阶统计特性是不变的, 根据这个特点提出了一种基于最优滤波器的强混沌背景中的微弱谐波信号检测方法. 该方法首先构建一个数据矩阵, 在频域上对每个频率通道分别检测谐波信号, 从而将信号检测问题转化为最优化问题, 然后利用最优化理论设计滤波器, 使待检测频率通道的信号增益保持不变, 而尽量抑制其他频率通道的信号, 最后通过判断每一频率通道的输出信干噪比来检测谐波信号. 与传统方法相比, 本文方法有如下优点: 1)可以检测更低信干噪比下的微弱谐波信号; 2)可检测的信号幅度范围更大; 3)抗白噪声性能更强. 仿真结果证明了本文方法的有效性.