基于Fisher信息量的弱信号处理增益问题研究

发布时间：2018-03-16 23:20

本文选题：随机共振　切入点：弱信号　出处：《青岛大学》2014年博士论文　论文类型：学位论文

【摘要】：随机共振是研究一些非线性系统中噪声的积极建设性作用的一类物理现象。本文在深入研究随机共振和循环平稳理论的基础上,在弱周期信号条件下,利用信噪比和费舍尔信息量进一步研究随机共振现象,并且找到了二者之间的关联。费舍尔信息量能够描述几个重要非线性处理过程中的性能；一个局部最优处理器能够获得最大输出输入信噪比,最大输出输入信噪比增益是由标准噪声分布的费舍尔信息量给定的,并且最大信噪比增益是静态非线性元素组成的阵列的信噪比增益的上限。在本论文中,又进一步的对静态和动态非线性系统的随机共振现象进行了对比。论文的主要研究成果如下： 1.最初费舍尔信息量是作为参数估计的性能指标。我们将它扩展并且表明费舍尔信息量能够描述几个重要非线性处理过程中的性能。对于加性白噪声中的弱信号,费舍尔信息量能决定如下四个方面：(i)周期信号的最大输出信噪比；(ii)信号检测的最优渐近性能；(iii)信号传输的最优互相关系数；(iv)无偏估计值的最小均方差。通过费舍尔信息量不等式,这个统一的结论用于建立通过噪声改善随机共振是否可行的条件。 2.通过噪声概率密度和噪声强度能精确地决定一个局部最优处理器,并且局部最优处理器的输出输入信噪比增益是由标准噪声分布的费舍尔信息量给定的。基于这个关联,我们发现对于局部最优处理器,能够获得比一任意大的信噪比增益。对于随机共振,考虑向已知信号中加入额外噪声时,我们证明了通过费舍尔信息量不等式,和新噪声完全匹配的更新的局部最优处理器,不能改进输出信噪比以超过无额外噪声时所对应的初始值。这个结果印证了一个以前只对高斯噪声存在的定理。此外,在参数不可调处理器的情况下,比如由噪声概率密度描述的局部最优处理器的结构不能完全适应噪声强度时,表明了可以恢复随机共振的一般条件,通过添加额外声提高输出信噪比的可能性来证明。 3.研究了为传输在加性白噪声中的弱周期信号,由任意的静态非线性元素组成的非耦合并联阵列的输出输入信噪比增益。在小信号的限制条件下,推导出信噪比增益的一个渐近表达式。并且证明了对任意给定的非线性系统和噪声环境,信噪比增益是关于阵列大小的单调递增的函数。由局部最优非线性系统所对应的信噪比增益,是静态非线性元素组成的阵列的信噪比增益的上限。在局部最优非线性系统中,随机共振不能发生,也就是说,在阵列中加入内部噪声不能改善信噪比增益。然而,在一个由次优但易实现的阈值非线性系统组成的阵列中,我们证明了随机共振发生的可行性,也证明了对于各种内部噪声分布,信噪比增益大于一的可能性。 4.利用输出信噪比作为测量方法,比较了静态和动态非线性系统的随机共振现象。对于给定的含噪弱周期信号,通过调谐内部噪声强度,静态和动态非线性并联阵列都能提高输出信噪比。静态非线性系统容易实现,而动态非线性系统有较多参数需要调整,存在不能利用内部噪声的有利作用的风险。并且外部噪声是非高斯类型时,可以观察到动态非线性系统是优于静态非线性系统,可以获得一个更好的输出信噪比,证明了加入额外白噪声以提高输出信噪比的可能性。
[Abstract]:Stochastic resonance is a physical phenomenon of some noise in nonlinear systems, a positive and constructive role. Based on the study of stochastic resonance and cyclostationary theory, the weak periodic signal conditions, the SNR and Fisher information to further study the stochastic resonance phenomenon, and find the correlation between the two. Fisher information to describe the performance of several important nonlinear process; a local optimal processor can obtain maximum output SNR, maximum output SNR gain is the amount of information given by the standard Fisher noise distribution, and the maximum SNR gain is a nonlinear static element array noise than the gain limit. In this paper, compared further on the static and dynamic nonlinear systems with stochastic resonance phenomenon. The main research The results are as follows:
1. of the original Fisher information is as the performance parameter estimation. We expand it and show that Fisher information can describe the performance of several important nonlinear process. For weak signal of additive white noise, Fisher decided the volume of information in four aspects as follows: (I) periodic signal maximum output signal-to-noise ratio; (II) the optimal asymptotic performance of signal detection; (III) optimal signal transmission cross correlation coefficient; (IV) an unbiased estimate of the minimum variance. By Fisher information inequality, the unified conclusion for establishing through noise improved stochastic resonance is feasible conditions.
2. the noise probability density and noise intensity can accurately determine a local optimal processor and local optimal processor output SNR gain is the amount of information given by Fisher standard noise distribution. Based on this association, we found that the local optimal processor, can earn more than a arbitrarily large signal-to-noise ratio gain. For stochastic resonance, consider adding additional noise to the known signals, we show that the amount of information through the Fisher inequality, the local optimal processor and new noise, completely updated, can improve the output SNR with no additional noise exceeds the initial value corresponding. This result confirms a previously only on Gauss noise existence theorem. In addition, the parameter adjustable processor case, such as local optimal processor structure can not be described by the noise probability density of fit In the case of noise intensity, the general condition of restoring the random resonance is shown, and the possibility of increasing the output signal to noise ratio by adding extra sound is proved.
3. studies for the weak periodic signal in additive white noise in transmission, non coupled parallel arrays composed of a nonlinear static element of arbitrary input and output SNR gain. Constraints on the small signal, the signal-to-noise ratio is derived. An asymptotic expression for the gain and the nonlinear system and noise environment for any given, the SNR gain is a function of the size of the array is monotonically increasing. The signal-to-noise ratio gain corresponding by local optimal nonlinear systems, nonlinear static element array is SNR gain limit. In local optimal nonlinear systems, stochastic resonance can occur, that is to say, adding the internal noise in the array can improve the signal-to-noise ratio gain. However, in an array composed of threshold nonlinear suboptimal but easy to implement in, we demonstrate the feasibility of stochastic resonance, also proved For all kinds of internal noise distribution, the gain of signal to noise ratio is more than one possibility.
4. the output signal-to-noise ratio as a measurement method, compare the stochastic resonance phenomenon of the static and dynamic nonlinear systems. For a given noisy weak periodic signal, by tuning the internal noise intensity, the static and dynamic nonlinear parallel array can improve the output SNR. The static nonlinear system is easy to implement, and dynamic nonlinear system many parameters need to be adjusted, there can not use risk beneficial effects of internal noise and external noise. The non Gauss type, can be observed in the nonlinear dynamic system is superior to static nonlinear system, and can obtain a better output signal-to-noise ratio, it is proved that adding additional white noise probability to improve the output SNR.

【学位授予单位】：青岛大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN911.7

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