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研究生: 傅弘聖
Fu, Hung-Sheng
論文名稱: 基於最大概似估測線性近似求解通道係數、干擾大小及雜 訊能量
Linear Approximation for the Measurement of Channel Coefficient, Interference Level, and Noise Power Based on Maximum Likelihood Estimation
指導教授: 卿文龍
Chin, Wen-Long
學位類別: 碩士
Master
系所名稱: 工學院 - 工程科學系
Department of Engineering Science
論文出版年: 2013
畢業學年度: 101
語文別: 中文
論文頁數: 80
中文關鍵詞: 干擾大小通道係數雜訊能量最大概似估測牛頓-瑞夫生法
外文關鍵詞: Interference Level, Channel Coefficient, Noise Power, Maximum-Likelihood Estimation, Newton-Raphson Method
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  • 在許多不同工程領域中處理訊號問題時,時常會操作在擁有固定干擾的衰減通道模型下。故本篇論文在此環境下,提出了一個演算法來量測觀察訊號中的干擾大小、通道係數及雜訊能量。此演算法是基於最大概似估測法(maximum-likelihood estimation),先求出干擾大小、通道係數及雜訊能量的估測器,由於以上估測器皆無封閉式的解(closed form solution),故使用近似線性估測器解得初始值,再利用迭代法逼近最佳解。為了效能比較,我們亦求得牛頓-瑞夫生法(Newton-Raphson method)最大概似估測。根據模擬結果,我們提出的概似函數(likelihood function)具有全域最大值且收斂是被保證的。模擬結果也顯示了,我們提出的近似線性演算法具有快速收斂的能力,以及在不同情況下,都比傳統方法有較佳的效能。

    The model of memoryless Gaussian channel with deterministic interference is commonly adopted in various engineering applications. In the thesis, we propose an algorithm for the measurement of channel coefficient, interference level, and noise power by observed signals over the memoryless Gaussian channel. This algorithm applies an iterative approach based on maximum-likelihood estimation for channel coefficient, interference level, and noise power. However, there isn’t a closed-form solution for these estimators. So the proposed algorithm applies an iterative approach with the initial point determined by the linear approximation of the hyperbolic tangent function. In the thesis we also use Newton-Raphson method to obtain another maximum-likelihood estimation for comparison. According to simulations, the proposed likelihood function has a global maximum and its convergence is guaranteed. Simulation results also demonstrate that, under many different situations, the proposed approach has faster convergence speed and better performance than closed-form approximation estimation.

    中文摘要. . . . . . . . i 英文摘要. . . . . . . . ii 誌謝. . . . . . . iii 目錄. . . . . . . iv 表目錄. . . . . . vii 圖目錄. . . . . . viii 符號說明. . . . . xi 第一章、緒論. . . . . 1 1.1 基礎知識. . . . 1 1.1.1 雜訊. . . . . . . 1 1.1.2 干擾. . . . . . . 3 1.1.3 通道. . . . . . . 4 1.2 研究動機. . . . . . 10 1.3 文獻探討. . . . . . 11 1.4 論文架構. . . . . . 13 第二章、系統架構. . . . 14 2.1 二位元相位鍵移. . . . . 14 iv 2.2 訊號模型. . . . 15 2.3 模擬與討論. . . . . . . 18 第三章、最大概似估測. . . . 27 3.1 干擾大小的估測. . . . . 27 3.2 通道係數的估測. . . . . 29 3.3 雜訊能量的估測. . . . . 30 3.4 近似封閉式估測. . . . . 31 3.5 近似線性估測. . . . . . . 34 3.6 模擬與討論. . . . . . . . . 38 3.6.1 近似封閉式估測. . . 38 3.6.2 近似線性估測. . . . 44 第四章、牛頓-瑞夫生法分析最大概似估測解. . . . 50 4.1 一維牛頓-瑞夫生法. . . . . 50 4.2 多維牛頓-瑞夫生法. . . . . 52 4.3 模擬與討論. . . . . . . . 54 4.3.1 單參數變動之牛頓-瑞夫生法迭代. . . 54 4.3.2 雙參數變動之牛頓-瑞夫生法迭代. . . 57 4.3.3 三參數變動之牛頓-瑞夫生法迭代. . . 63 4.3.4 比較不同變數參數之牛頓-瑞夫生法迭代. . . 66 v 4.3.5 牛頓-瑞夫生與最大概似估測法複雜度比較. . . . 69 第五章、模擬與討論 . . . . . 73 第六章、結論與未來展望. . . . . . 78 參考文獻. . . 79 vi

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