本文選題：脈沖噪聲 + Middleton��； 參考：《廣東工業(yè)大學(xué)》2016年博士論文

【摘要】：相關(guān)分析始于統(tǒng)計(jì)學(xué)的開創(chuàng)時(shí)期,是統(tǒng)計(jì)學(xué)的一個(gè)重要分支。時(shí)至今日,相關(guān)分析仍然是多個(gè)領(lǐng)域內(nèi)的研究熱點(diǎn),這其中就包括了統(tǒng)計(jì)信號(hào)處理。在雷達(dá)和通信系統(tǒng)的信號(hào)檢測和參數(shù)估計(jì)中,發(fā)射信號(hào)與接收信號(hào)之間的相關(guān)度是經(jīng)常需要度量的。為了定量的描述隨機(jī)變量或者信號(hào)之間關(guān)聯(lián)程度的強(qiáng)弱,相關(guān)系數(shù)經(jīng)常被作為相關(guān)關(guān)系的量化工具。在相關(guān)系數(shù)的家族里,Pearson相關(guān)系數(shù)一直占據(jù)著統(tǒng)治地位,這是因?yàn)镻earson相關(guān)系數(shù)對線性相關(guān)關(guān)系具有強(qiáng)大的識(shí)別能力,理論證明相對完備,而且其算法實(shí)現(xiàn)簡單高效。而根據(jù)人們的使用經(jīng)驗(yàn),Spearman相關(guān)系數(shù)和Kendall相關(guān)系數(shù)在處理一些非線性的相關(guān)關(guān)系上有著獨(dú)特的優(yōu)勢。除了上述三種經(jīng)典的相關(guān)系數(shù)以外,研究者們還提出了其他的相關(guān)系數(shù),如基尼相關(guān)和Pearson秩變量相關(guān)系數(shù)等。目前對Pearso n相關(guān)系數(shù)、S pearman相關(guān)系數(shù)和Kendall相關(guān)系數(shù)的理論研究基本建立在相對理想化的二元高斯模型的數(shù)據(jù)之上；基尼相關(guān)在數(shù)據(jù)服從二元高斯模型時(shí)的漸近統(tǒng)計(jì)特性近年見報(bào)；對Pearson秩變量相關(guān)系數(shù)的研究一直停滯。即使相關(guān)系數(shù)的使用已經(jīng)非常的普遍,但是目前對這些相關(guān)系數(shù)的理論研究還存在急需填補(bǔ)的空白。除了相關(guān)分析中的一般性問題,針對發(fā)射信號(hào)與接收信號(hào)之間進(jìn)行相關(guān)分析的場景,一些特定的因數(shù)也需要被納入到考慮的范圍內(nèi)。對兩路信號(hào)進(jìn)行相關(guān)分析是信號(hào)處理的一種技術(shù),而信號(hào)處理的很大一部分工作可以歸納為從噪聲中提取感興趣的信息,信號(hào)的相關(guān)分析也不例外。因此,噪聲的特性是對信號(hào)進(jìn)行相關(guān)分析時(shí)必須要考量的一個(gè)重要因數(shù)。目前絕大多數(shù)關(guān)于信號(hào)處理中噪聲成分的研究工作都集中在加性高斯白噪聲模型上。但是,這一模型已經(jīng)被證明無法很好的擬合一些常見的噪聲環(huán)境。這是因?yàn)榧有愿咚拱自肼暷Ｐ偷倪m用需要滿足一些假設(shè)條件。然而隨著電磁環(huán)境的復(fù)雜化,噪聲源之間不均衡的概率大大增加,一些高斯白噪聲的假設(shè)條件難以被滿足,實(shí)際噪聲數(shù)據(jù)經(jīng)常表現(xiàn)出脈沖的特性。所以,對基于脈沖噪聲模型的信號(hào)相關(guān)分析問題進(jìn)行研究就顯得很有必要。為此,本文從以下幾個(gè)方面對脈沖噪聲下的信號(hào)相關(guān)分析問題進(jìn)行了探討：1.對脈沖噪聲的建模。參考Middleton's Class A模型,利用二項(xiàng)高斯混合模型對脈沖噪聲進(jìn)行建模；進(jìn)而建立混合高斯模型用于描述單通道脈沖噪聲環(huán)境下發(fā)送信號(hào)與接收信號(hào)之間的關(guān)系,建立系統(tǒng)模型。2.基于混合高斯模型對多種相關(guān)系數(shù)的統(tǒng)計(jì)特性進(jìn)行分析。首先對Pearson相關(guān)系數(shù)、Spearman相關(guān)系數(shù)和Kendall相關(guān)系數(shù)等三種經(jīng)典相關(guān)系數(shù)在混合高斯模型下的統(tǒng)計(jì)特性進(jìn)行分析；基于三種經(jīng)典相關(guān)系數(shù)分析的結(jié)果進(jìn)一步探討基尼相關(guān)和Pearson秩變量相關(guān)系數(shù)在混合高斯模型下的工作性能,以獲得更合適的信號(hào)相關(guān)分析工具。3.通過對基尼相關(guān)和Pearson秩變量相關(guān)系數(shù)定義表達(dá)式的改寫,提出適合進(jìn)行并行運(yùn)算的實(shí)施架構(gòu),為其應(yīng)用奠定基礎(chǔ)。4.基于對多種相關(guān)系數(shù)在混合高斯模型下的理論結(jié)果和數(shù)據(jù)實(shí)驗(yàn)結(jié)果,作為相關(guān)系數(shù)在信號(hào)檢測應(yīng)用方面的一次探索,本文提出了一種適用于單通道脈沖干擾環(huán)境下的基于基尼相關(guān)的信號(hào)檢測方法,并通過實(shí)驗(yàn)驗(yàn)證其性能�；谝陨蟽�(nèi)容,本文的貢獻(xiàn)有兩個(gè)方面。在理論研究方面,本文的內(nèi)容填補(bǔ)了多種相關(guān)系數(shù)在混合高斯模型下統(tǒng)計(jì)特性的部分理論空白。這可以為后續(xù)的理論研究提供參考,也可以為相關(guān)系數(shù)的應(yīng)用提供必要的理論指導(dǎo)。在應(yīng)用方面,本文針對脈沖噪聲下的信號(hào)檢測問題提出了一種基于基尼相關(guān)的信號(hào)檢測方法。該方法是一種非參數(shù)的漸近局部最優(yōu)的解決方案,其結(jié)構(gòu)簡單,使用方便,性能良好。另外,本文還提出了基尼相關(guān)和Pearson秩變量相關(guān)系數(shù)的并行運(yùn)算架構(gòu),使得這兩種相關(guān)系數(shù)在處理海量數(shù)據(jù)時(shí)的快速計(jì)算成為可能。
[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.
【學(xué)位授予單位】：廣東工業(yè)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：TN911.6

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