混合高斯模型下的信号相关分析研究

发布时间：2018-07-10 05:51

本文选题：脉冲噪声 + Middleton　；参考：《广东工业大学》2016年博士论文

【摘要】：相关分析始于统计学的开创时期,是统计学的一个重要分支。时至今日,相关分析仍然是多个领域内的研究热点,这其中就包括了统计信号处理。在雷达和通信系统的信号检测和参数估计中,发射信号与接收信号之间的相关度是经常需要度量的。为了定量的描述随机变量或者信号之间关联程度的强弱,相关系数经常被作为相关关系的量化工具。在相关系数的家族里,Pearson相关系数一直占据着统治地位,这是因为Pearson相关系数对线性相关关系具有强大的识别能力,理论证明相对完备,而且其算法实现简单高效。而根据人们的使用经验,Spearman相关系数和Kendall相关系数在处理一些非线性的相关关系上有着独特的优势。除了上述三种经典的相关系数以外,研究者们还提出了其他的相关系数,如基尼相关和Pearson秩变量相关系数等。目前对Pearso n相关系数、S pearman相关系数和Kendall相关系数的理论研究基本建立在相对理想化的二元高斯模型的数据之上；基尼相关在数据服从二元高斯模型时的渐近统计特性近年见报；对Pearson秩变量相关系数的研究一直停滞。即使相关系数的使用已经非常的普遍,但是目前对这些相关系数的理论研究还存在急需填补的空白。除了相关分析中的一般性问题,针对发射信号与接收信号之间进行相关分析的场景,一些特定的因数也需要被纳入到考虑的范围内。对两路信号进行相关分析是信号处理的一种技术,而信号处理的很大一部分工作可以归纳为从噪声中提取感兴趣的信息,信号的相关分析也不例外。因此,噪声的特性是对信号进行相关分析时必须要考量的一个重要因数。目前绝大多数关于信号处理中噪声成分的研究工作都集中在加性高斯白噪声模型上。但是,这一模型已经被证明无法很好的拟合一些常见的噪声环境。这是因为加性高斯白噪声模型的适用需要满足一些假设条件。然而随着电磁环境的复杂化,噪声源之间不均衡的概率大大增加,一些高斯白噪声的假设条件难以被满足,实际噪声数据经常表现出脉冲的特性。所以,对基于脉冲噪声模型的信号相关分析问题进行研究就显得很有必要。为此,本文从以下几个方面对脉冲噪声下的信号相关分析问题进行了探讨：1.对脉冲噪声的建模。参考Middleton's Class A模型,利用二项高斯混合模型对脉冲噪声进行建模；进而建立混合高斯模型用于描述单通道脉冲噪声环境下发送信号与接收信号之间的关系,建立系统模型。2.基于混合高斯模型对多种相关系数的统计特性进行分析。首先对Pearson相关系数、Spearman相关系数和Kendall相关系数等三种经典相关系数在混合高斯模型下的统计特性进行分析；基于三种经典相关系数分析的结果进一步探讨基尼相关和Pearson秩变量相关系数在混合高斯模型下的工作性能,以获得更合适的信号相关分析工具。3.通过对基尼相关和Pearson秩变量相关系数定义表达式的改写,提出适合进行并行运算的实施架构,为其应用奠定基础。4.基于对多种相关系数在混合高斯模型下的理论结果和数据实验结果,作为相关系数在信号检测应用方面的一次探索,本文提出了一种适用于单通道脉冲干扰环境下的基于基尼相关的信号检测方法,并通过实验验证其性能。基于以上内容,本文的贡献有两个方面。在理论研究方面,本文的内容填补了多种相关系数在混合高斯模型下统计特性的部分理论空白。这可以为后续的理论研究提供参考,也可以为相关系数的应用提供必要的理论指导。在应用方面,本文针对脉冲噪声下的信号检测问题提出了一种基于基尼相关的信号检测方法。该方法是一种非参数的渐近局部最优的解决方案,其结构简单,使用方便,性能良好。另外,本文还提出了基尼相关和Pearson秩变量相关系数的并行运算架构,使得这两种相关系数在处理海量数据时的快速计算成为可能。
[Abstract]:The correlation analysis begins at the beginning of statistics and is an important branch of statistics. To today, the correlation analysis is still a hot spot in many fields, including statistical signal processing. In the signal detection and parameter estimation of radar and communication systems, the correlation between the transmitted signal and the received signal is often needed. In order to quantify the intensity of the correlation between random variables or signals, the correlation coefficient is often used as a quantifying tool for the correlation. In the family of correlation coefficients, the Pearson correlation coefficient has always dominated, because the Pearson correlation coefficient has a strong recognition ability for linear correlation. The proof is relatively complete and its algorithm is simple and efficient. According to the experience of people, the Spearman correlation coefficient and the Kendall correlation coefficient have unique advantages in dealing with some nonlinear correlation. In addition to the above three classical correlation coefficients, the researchers also put forward other correlation coefficients, such as Gini phase. The correlation coefficient of the Pearson rank variable and so on. The current theoretical research on the correlation coefficient of Pearso n, the correlation coefficient of S pearman and the correlation coefficient of Kendall is based on the data of the relatively idealized two element Gauss model; the asymptotic statistical properties of Gini correlation in the two yuan Gauss model are reported in recent years; and the Pearson rank variable is found in recent years. The study of the correlation coefficient has been stagnant. Even if the use of the correlation coefficient is very common, there is still an urgent gap in the theoretical study of these correlation coefficients. In addition to the general problems in the correlation analysis, some specific factors are also needed for the scene of the phase correlation analysis between the transmitted signal and the received signal. The correlation analysis of the two signals is a technique for signal processing, and a large part of the signal processing can be induced to extract the information of interest from the noise, and the correlation analysis of the signal is no exception. Therefore, the characteristic of the noise is one that must be considered when the signal is analyzed. Important factor. At present, most of the research work on noise components in signal processing is focused on the additive Gauss white noise model. However, this model has been proved to be unable to fit some common noise environment well. This is because the application of additive Gauss white noise model needs to satisfy some assumptions. However, with electricity, with electricity The complexity of magnetic environment, the probability of unbalance between noise sources is greatly increased, some of the hypothesis conditions of Gauss white noise are difficult to be satisfied. The actual noise data often show the characteristics of the pulse. Therefore, it is necessary to study the signal correlation analysis based on the impulse noise model. The problem of signal correlation analysis under impulse noise is discussed: 1. modeling of impulse noise. Reference Middleton's Class A model, using two Gauss hybrid model to model the impulse noise, and then establish a hybrid Gauss model to describe the relationship between the transmitted signal and the received signal under the single channel impulse noise environment. A system model.2. is established to analyze the statistical properties of various correlation coefficients based on the mixed Gauss model. First, the statistical properties of three classical correlation coefficients, such as Pearson correlation coefficient, Spearman correlation coefficient and Kendall correlation coefficient, are analyzed in the mixed Gauss model, and the results based on the analysis of the three classical correlation coefficients are advanced. The performance of Gini correlation and Pearson rank variable correlation coefficient under the mixed Gauss model is discussed step by step, so as to obtain a more appropriate signal correlation analysis tool.3., by rewriting the definition expression of the correlation coefficient of Gini correlation and Pearson rank variables, the implementation architecture suitable for parallel operation is proposed, and the foundation for its application is based on the pair The theoretical results of the multiple correlation coefficients and the results of the data experiment under the mixed Gauss model are used as an exploration of the correlation coefficient in the application of signal detection. This paper presents a method of signal detection based on Gini correlation in the environment of single channel pulse interference, and proves its performance through experiments. Based on the above content, this paper There are two aspects of contribution. In theoretical research, the content of this paper fills the theoretical gap of the statistical properties of a variety of correlation coefficients under the mixed Gauss model. This can provide reference for subsequent theoretical research, and also provide the necessary theoretical guidance for the application of correlation coefficients. In application, this paper is aimed at impulse noise. A signal detection method based on Gene correlation is proposed in this paper. This method is a non parametric asymptotic local optimal solution. It is simple in structure, convenient in use and good in performance. In addition, this paper also proposes a parallel operation architecture of the correlation between Gene correlation and Pearson rank variables, which makes these two correlation coefficients. It is possible to calculate quickly when dealing with massive data.
【学位授予单位】：广东工业大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TN911.6

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