臺灣博碩士論文加值系統

通訊系統的雜訊是指在傳送和接收的正常訊號過程中所受到干擾的影響。影響通訊系統的雜訊來源有很多種，一般可以區分為系統內部的雜訊和系統外部的雜訊。大氣雜訊和人為的雜訊屬於前者，因為自然的電流或電壓震盪而使得電路或其原件所產生的散粒(shot)雜訊和熱雜訊則屬於後者。
在通訊系統中，當傳送端送出訊號經過通訊通道到接收端時，在現實的環境中，訊號會受到雜訊的影響和干擾。因此，當我們在模擬通訊系統時，通常會加入一個『可加性白色高斯雜訊』到訊號裡，用來模擬當訊號受到雜訊的影響和干擾。而傳統上都是使用軟體來產生『可加性白色高斯雜訊』，但是利用軟體來產生高斯雜訊需要耗費較多的時間。因此，為了能夠更有效率地去模擬雜訊的影響，近年來研究如何利用硬體來產生高斯雜訊也就越來越多。
本篇論文採用Box-Muller、Wallace和中央極限定理這三種方法，並且利用兩個不同的時脈來實現本篇論文的硬體架構。不同於過去都需要利用許多複雜的算術電路來產生高斯雜訊，本篇論文所提出來的主要架構只會用到簡單的加減法和位移，所以能很快速地產生白色高斯雜訊。此外，為了確認所產生的雜訊呈現高斯分佈，我們還利用了統計的最適度檢定法中的卡方檢定和K-S檢定來證明這個架構所產生出來的雜訊的確是高斯分佈。

Combining the Box-Muller method, Central Limit Theorem, and the Wallace method, a hardware white Gaussian noise generator (WGNG) is proposed to simulate the noise effect appeared in the communication channel and is synthesized in a 0.18um CMOS process. Passing two statistical tests of chi-square test and Kolmogorov-Smirnov (K-S) test, the proposed noise generator can generate high-quality 666.667 million Gaussian random variables per second.
It is different from the existing methods that require complex calculations. The proposed design only requires additions, subtractions, and shift operation in the major part. Because of only having simple operations, it is easy to achieve high performance.
In addition, the proposed architecture is not only applied to generate the additive white Gaussian noise (AWGN), but also applied to generate the random variables with other distributions such as exponential distributions.

摘要 I
誌謝 II
目錄 III
第一章 概論 1
第二章 文獻討論 2
第三章 理論架構 3
第四章 統計檢定 4
第五章 模擬結果與比較 5
第六章 結論 6
英文附錄 7
Abstract

Contents I
List of Figures III
List of Tables IV

Chapter 1 Introduction 1
1.1. Applications 1
1.2. Motivation 2
1.3. Thesis Organizations 3
Chapter 2 Methods Overview 5
2.1. Central Limit Theorem 5
2.2. Box-Muller method 6
2.3. Polar method 8
2.4. Wallace method 10
2.5. Ziggurat method 12
2.6. Comparisons of Previous Methods 16
Chapter 3 Proposed Architectures 17
3.1. The original architecture 17
3.2. The modified architecture 18
3.2.1. The first stage of Box-Muller 20
3.2.2. The second stage of Box-Muller 22
3.2.3. The third stage of Box-Muller 27
3.2.4. The forth stage of Box-Muller 28
3.2.5. The architecture of Wallace 28
Chapter 4 Statistic Tests 31
4.1. Chi-square test 31
4.2. Kolmogorov-Smirnov test 32
4.3. The results of the statistic tests 34
Chapter 5 Simulation Results and Comparisons 45
Chapter 6 Conclusions 49
Bibliography 51

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