在無線通訊的系統之中通道的資訊可以說是最重要的訊息，對於雜訊變異數估測器而言通道的資訊也扮演著重要的角色，然而幾乎所有的雜訊變異數估測器都把通道設定為完美已知的條件，但是很不幸的就實際上而言通道估測的誤差卻是不能避免的，在這篇論文中我們在正交分頻多工系統(orthogonal frequency division multiplexing, OFDM)下討論通道估測誤差對於最大概似法則(maximum likelihood, ML)的雜訊變異數估測器的影響，同時我們也討論當我們的系統的同步沒有完美的完成所產生出來的載波頻率偏移對於我們估測器的影響，我們將算出雜訊估測器的平均值跟變異數，並且去模擬我們算出的結果跟實際上是否能相符合。

Noise variance estimator is very important in communication system which could control the transmission power and help system to reach the maximum capacity. But almost every kind of noise variance estimators assume that channel status is perfectly. Unfortunately the estimation error is always existence. This paper discuss that the maximum likelihood noise variance estimator (ML-NVE) in orthogonal frequency division multiplexing (OFDM) system with estimated channel. We take two kinds of the most popular channel estimation (CE) schemes Least Square (LS) and Modified-Least Square (MLS) as our consideration. And we investigate the situation that the ML-NVE suffered by carrier frequency offset (CFO) due to imperfect synchronization. As result we will show off the mean and variance of ML-NVE in those situations.

Chapter 1 Introduction………………………………………………………………1
1.1 SNR Estimation…………………………………………………………………2
1.2 Channel…………………………………………………………….……………3
Chapter 2 System Model …………………………………………………………….5
2.1 OFDM System…………………………………………………………………..5
2.2 Signal Model...………………………...………………………………………10
2.3 CFO ………..………………………………………………………………….11
2.4 ML-NVE………………………………………………………………………12Chapter 3 Channel Estimator ……………………………………...……...………14
3.1 LS Channel Estimator…………………………………..……………………..14
3.2 MLS Channel Estimator…………………………….…………………………20
Chapter 4 Training Based ML-NVE under CE Error and CFO...........................21
4.1 LS Channel Estimation Errors...………………………………………….…....21
4.2 MLS Channel Estimation Errors..………………………………………..….22
4.3 LS Channel Estimation Errors and CFO ………………….…….…………….23
4.4 MLS Channel Estimation Errors and CFO.…………………….…..…………24
Chapter 5 Pilot Based ML-NVE under CE Error and CFO…….…….………..27
5.1 Pilot System Model…………………………………………….…….………..27
5.2 Piloted LS Channel Estimation Errors…………………………….….……….27
5.3 Piloted MLS Channel Estimation Errors………………………………………28
5.4 Piloted LS Channel Estimation Errors and CFO………………….…………...30
5.5 Piloted MLS Channel Estimation Errors and CFO………….………………...31
Chapter 6 Simulation Results……………………………………………………….34
Chapter 7 Conclusion.................................................................................................45
Abbreviations..............................................................................................................47 References...................................................................................................................48

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