关联噪声和周期信号驱动的非对称双稳系统的稳态分析

运用Liouville equation和诺维科夫原理,解出了关联噪声和周期信号共同驱动的非对称双稳系统的近似福克-普朗克方程,并求解了其稳态概率密度函数.在此基础上,分析了乘性噪声强度 、加性噪声强度 、噪声间关联系数 ,周期信号振幅 、频率 以及系统非对称参数 等对稳态概率密度分布曲线的影响.结果表明:(1)噪声强度及其关联、周期信号振幅、系统非对称参数的改变均能引起稳态概率密度分布曲线单峰结构和双峰结构之间的转换,即能够诱导非平衡相变产生;(2)周期信号频率改变时,没有非平衡相变发生;(3)当系统非对称参数为零时,稳态概率密度分布曲线具有关于 的对称结构;当系统非对称参数不等于零时,其对称结构被破坏.     

交叉关联噪声驱动的单模激光模型稳态分析：修正的郎之万方程情形

本文对具有加性和乘性白噪声关联的单模激光模型的统计性质进行了研究。从一个具有交叉关联噪声与单模激光与立方模随机等价郎之万方程，计算了稳态激光光强度的平均值、协方差和偏斜率。并与早期结果比较，阐明了考虑郎之万方程修正项对描述激光系统统计性质的重要性。     

Experimental study of the effect of parametric noise on the Andronov–Hopf bifurcation in brusselator

Specific features of the Andronov–Hopf bifurcation in the model of brusselator in the presence of parametric noise are numerically and experimentally studied. Regularities of evolution of the probability distribution with an increase in the noise intensity are typical of the additive and multiplicative effect of the Gaussian white noise. The existence of bifurcation interval corresponding to the gradual transition to the generation regime is experimentally revealed for both additive and multiplicative noise.     

The method of separating harmonic signals from multiplicative and additive noises

This paper focuses on the extraction of a harmonic signal from multiplicative and additive noises. A method is proposed in two stages: (1) to square the original discrete time series, which in- cludes both signals and noises, and form a new time series. By this means, the multiplicative noise is converted to additive noise; and (2) to filter out the noise by using existing noise removal schemes. With a large amount of simulation, experimental results demonstrated the efficiency and effective- ness of this newly developed method in terms of Signal-to-Noise Ratio (SNR) and other criteria. From the experiment, it is also found that: the two kinds of noises affect the SNR differently. In gen- eral, the SNR is not influenced by multiplicative Gaussian noise regardless of its variance. However, if both kinds of noise exist, the SNR decreases with the incensement of the Variance of Additive Noise to Multiplicative Noise Ratio (VAMNR). This analysis is also supported by simulation work.     

乘性色噪声和加性双值噪声作用下延迟双稳系统中的随机共振

研究了在乘性和加性色噪声以及加性非对称双值噪声作用下方波信号驱动的延迟双稳系统中的随机共振现象。基于小延迟近似,在绝热近似条件下推导出了系统输出信噪比(Signal-to-Noise Ratio, SNR)的解析形式。分析结果表明,随着双值噪声强度与非对称性参数、方波信号幅度以及乘性和加性色噪声强度的变化,SNR表现出了随机共振行为。随着延迟时间、色噪声相关时间和系统参数的增大,SNR作非单调变化。     

Harmonics in multiplicative and additive noise: parameterestimation using cyclic statistics

The problem of concern here is parameter estimation of harmonics in the presence of multiplicative and additive noise. Cyclic statistics are employed to estimate the frequencies and phases, after which the time series is demodulated and cumulants of the noise processes are estimated. The latter are then supplied to linear or nonlinear cumulant-based algorithms to identify ARMA model parameters for the noises. Cyclic statistics and higher order spectra-based approaches are shown to yield the same frequency estimates. Simulation examples illustrate the algorithms     

乘性和复加性噪声中复谐波的循环估计量的性能分析

从通信和探测系统需要的频率估计出发,文中研究了实乘性和复加性随机噪声中复谐波的恢复问题,表明循环均值和循环相关函数可用来对不同分布的有色实乘性和复加性随机噪声中的谐波进行恢复,分别对于非零均值和零均值乘性噪声情形分析了循环估计量的性能.证明了循环估计量与一定意义下的最小二乘估计量渐近等价,并给出了循环估计量的大样本方差表达式.模拟结果验证了大样本性能分析.     

On the error probability of linearly modulated signals on Rayleighfrequency-flat fading channels

Consideration is given to optimal detection of linearly modulated signals subject to multiplicative Rayleigh-distributed distortion and additive white Gaussian noise. For coherent detection, regenerated amplitude and phase references are employed at the receiver to compensate for amplitude and phase deviations from the correct values. A system model is formulated under the assumption of perfect symbol timing and in the absence of intersymbol interference, producing a final additive noise term, applied just before the detection, which contains the effects of the original additive and multiplicative distortions and of the errors in the phase and amplitude references. By determining the probability density function of this final noise term for arbitrary types of linear modulation, it is possible to perform exact calculations of error probabilities     

Noise spectra and noise correlation functions of the single-modelaser with a low-Q cavity

The noise characteristics of a single-mode laser with a low-Q cavity are investigated theoretically. After the electric field is adiabatically eliminated from the Maxwell-Bloch equations, coupled Langevin equations with both additive and multiplicative white noises are examined. The equations are solved using Rice's method in a framework of quasilinear Fourier analysis. Noise spectral densities are calculated analytically to study the dependence of the relative intensity noise (RIN) on the pumping. Through an investigation of the auto- and cross-correlations of the light intensity and population noises, their variances are obtained in order to compare their properties to the good-cavity case. The stationary intensity cumulants, the photon counting coefficient, and the photon counting probability are explicitly derived and compared with the results of a Fokker-Planck analysis previously carried out for both the good- and bad-cavity cases     

由统计特性分析激光主动成像系统图像的噪声性质

激光主动成像系统具有分辨率高、抗干扰能力强、能成三维像等一系列优点，因而应用越来越广泛，但它的图像同时受到散斑噪声和其他一些高斯噪声的影响。散斑噪声为一种乘性噪声，高斯噪声则为一种加性噪声，这两种噪声哪种占据主要地位对于图像噪声抑制噪声模型的建立具有重要的意义，分析了受到散斑噪声和高斯噪声污染图像的概率曲线及灰度均值方差比等统计特性，找出在两种噪声分别作用下的不同统计特性，以此为判别标准，对激光主动成像系统图像进行分析，得出了此图像所受噪声的主要成分为散斑噪声的结论。同时，算出了此图像的散斑噪声方差。     

Performance analysis of cyclic statistics for the estimation ofharmonics in multiplicative and additive noise

The problem of estimating the frequencies of harmonics in multiplicative and additive noise is addressed. The cyclic mean (CM) can be used if the multiplicative noise has nonzero mean; the cyclic variance (CV) can be used whether or not the multiplicative noise has zero mean. This paper answers the following question: under what conditions should we use the CV instead of the CM? The criteria used are the ease of detection and the accuracy of estimation. The CV is preferable to the CM if the coherent to noncoherent harmonic power ratio is less than a threshold that depends on the first four cumulants; when the noises are colored, this threshold becomes frequency dependent. Third- and fourth-order cyclic statistics are also studied, and it is shown that they will always be outperformed either by the CM or CV when the multiplicative noise is symmetric     

基于二维循环统计量的二维谐波信号参数估计

本文利用二维循环统计量方法对二维平稳乘性噪声与二维平稳加性噪声共存情况下的二维谐波信号参数估计问题进行了讨论.利用二维循环统计量能够有效地抑制二维平稳乘性噪声和二维平稳加性噪声的特点,有效地从噪声中提取出信号参数.仿真实验对算法作了说明.     

复高斯乘性和加性噪声中复谐波的Cramer—Rao界

本文考虑了在白的复高斯乘性和白的复高斯加性噪声中观测的多个复谐波的恢复问题，导出了频率估计以及乘性噪声的样本均值的可计算的Ｃｒａｍｅｒ－Ｒａｏ界（ＣＲＢ）表达式，模拟结果验证了所得结果的正确性。     

Harmonics in multiplicative and additive noise: performanceanalysis of cyclic estimators

Multiplicative noise causes smearing of spectral lines and thus hampers frequency estimation relying on conventional spectral analysis. In contrast, cyclic mean and correlation statistics have proved to be useful for harmonic retrieval in the presence of multiplicative and additive noise of arbitrary color and distribution. Performance analysis of cyclic estimators is carried through both for nonzero and zero mean multiplicative noises. Cyclic estimators are shown to be asymptotically equivalent to certain nonlinear least squares estimators, and are also compared with the maximum likelihood ones. Large sample variance expressions of the cyclic estimators are derived and compared with the corresponding Cramer-Rao bounds when the noises are white Gaussian. It is demonstrated that previously well established results on constant amplitude harmonics are special cases of the present analysis. Simulations not only validate the large sample performance analysis, but also provide concrete examples regarding relative statistical efficiency of the cyclic estimators     

A study of phase noise in CMOS oscillators

This paper presents a study of phase noise in two inductorless CMOS oscillators. First-order analysis of a linear oscillatory system leads to a noise shaping function and a new definition of Q. A linear model of CMOS ring oscillators is used to calculate their phase noise, and three phase noise phenomena, namely, additive noise, high-frequency multiplicative noise, and low-frequency multiplicative noise, are identified and formulated. Based on the same concepts, a CMOS relaxation oscillator is also analyzed. Issues and techniques related to simulation of noise in the time domain are described, and two prototypes fabricated in a 0.5-μm CMOS technology are used to investigate the accuracy of the theoretical predictions. Compared with the measured results, the calculated phase noise values of a 2-GHz ring oscillator and a 900-MHz relaxation oscillator at 5 MHz offset have an error of approximately 4 dB     

Quantization and roundoff noises in fixed-point FIR digital filters

The errors in a fixed-point finite impulse response (FIR) filter due to quantization (analog-to-digital conversion) and roundoff are considered. Expressions for the exact moments of the filter output noise are derived. It is well known that, when the input signal satisfies certain conditions, the popular additive white noise model can be valid in describing the quantization noise. The characteristics of multiplicative roundoff noises, however, differ from what this model predicts, even under conditions where the roundoff noises are white. Hence the additive white noise model does not provide accurate results on the characteristics of the output error in an FIR filter. Using the exact formulas for the moments, the author computes the exact power spectrum of the filter output error. These results agree well with those obtained from simulation     

Estimating random amplitude polynomial phase signals: acyclostationary approach

Modeling of a class of nonstationary signals with randomly time-varying amplitude and parametric polynomial phase is addressed. A novel approach is proposed for the estimation of the time-varying phase by exploiting the higher order cyclostationarity of these signals. The method does not require nonlinear search, is easy to implement, and yields consistent estimates for the parameters. The resulting algorithms are theoretically tolerant to a large class of noises including additive stationary non-Gaussian noise and any Gaussian noise. Simulation examples supporting the theory are provided     

Stochastic Resonance in Bistable System Subject to Multiplicative and Additive Noise

In this paper, a simulation model of bistable system subject to multiplicative and additive noise is built on the basis of the theory of stochastic resonance(SR). SR phenomenon appears in the system subject to multiplicative and additive noise when a single signal transmits in the system. The output waveforms and the power spectrums at different frequencies are compared. The impact of the intensity of multiplicative and additive noise on the bistable system is discussed. It is found that this simulation model can upgrade the quality of the signal processing and the noise intensity can be effectively used for improving the effect of SR.     

相位噪声对时差估计的影响分析

在到达时间差(TDOA)测量中,两异地接收站所配备的本振都会存在相位噪声,该相位噪声会影响时差测量的性能。该文分析了相位噪声对经典的互相关法时差估计无偏性的影响,同时推导了仅考虑相位噪声时TDOA估计精度的克拉美罗下限(CRLB)。并进一步得到了相位噪声与加性噪声都存在时的CRLB及其相对于加性噪声环境下的CRLB退化系数。仿真结果验证了理论分析的结果。     

Transmitted-reference techniques for random or unknown channels

In this paper, a particular approach to the problem of communicating in certain random or unknown channels is considered. A particular set of signals is chosen, each member of which is partitioned into a known reference or sounding signal and a message signal. The channel is assumed to be linear, and is divided into a multiplicative and an additive portion. The multiplicative portion is assumed to have the same response to both message and reference components, while the additive noises associated with these components are assumed to be independent. The channel outputs and the additive noises are further assumed to be Gaussian. Under these circumstances, the optimum receiver is shown to cross-correlate the message portion of the received signal with a filtered version of the posterior mean of the channel output, which is merely a filtered combination of the prior mean and the perturbed reference signal. This is an interesting extension of the optimum receiver for known signals in additive Gaussian noise. Several special cases are considered which yield additional insight into the operation of the optimum receiver.