本論文主要針對正交分頻多工(Orthogonal Frequency Division Multiplexing，OFDM)系統中常見的兩種訊雜比(Signal to Noise Ratio，SNR)估測器，在同步不完美的情況下進行效能分析。這兩種估測器分別是最大可能性估測器(Maximum Likelihood Estimator，MLE)及二階與四階動差估測器(Second-and Fourth-Order Moments Estimator，MME)。由數學分析可以看出當時間同步點落在循環字首(Cyclic Prefix)內，最大可能性估測器會產生偏差，二階與四階動差估測器則不會受到時間誤差的影響。另一方面，同樣的頻率偏差會使得最大可能性估測器與二階與四階動差估測器兩者產生不同的偏差，而且二階與四階動差估測器在有頻率偏移下，估測結果的變動太大，不適合用來估測訊雜比。因此在本論文之中，我們專注於分析最大可能性估測器在進行訊雜比估測時，同時修正頻率偏差與時間偏差的效能。最後我們使用Argument 找出最接近的頻率與時間偏差量。

In this thesis, two signal-to-noise-ratio (SNR) estimators are analyzed for orthogonal frequency division multiplexing (OFDM) systems with imperfect
synchronization. The two SNR estimators under investigation are the maximum likelihood estimator (MLE) and the second- and fourth-order moments estimator (MME). Mathematical analysis shows that the performance of MME is not affected by the advanced timing offset while a fixed bias of MLE is induced. Mathematical analysis also shows that the same frequency offset induces different bias for the two estimators under investigation. Finally, a novel carrier frequency offset and timing offset tracking scheme based on SNR estimation is proposed in this thesis.

Chapter1 Introduction …………………….…………………1
1.1 Application of OFDM System ...……………………………1
1.2 SNR Estimation in OFDM System …………….….…………...2
1.3 Content about This Thesis ………….…………………………3
Chapter 2 System Model ……………………..………………5
2.1 OFDM System Description ………………………...………5
2.2 Signal model ………………………………………………….11
2.2.1 Signal Model in Timing Offset ……………………….12
2.2.2 Signal Model in Carrier Frequency Offset ………………13
2.3 Maximum Likelihood SNR Estimator ……………………14
2.4 Second-and Fourth-Order Moments Estimator ……………16
Chapter 3 Second-and Fourth-Order Moments Estimator in Imperfect Synchronous Situation ……………………………18
3.1 MME with Advanced Timing Offset ………………………..18
3.2 MME in Carrier Frequency Offset …………………………….19
Chapter 4 Maximum Likelihood Estimator with Imperfect Synchronous Situation ………………………………………23
4.1 MLE in Advanced Timing Offset ……………………………….23
4.2 MLE in Carrier Frequency Offset ……………………………25
4.3 MLE in Timing Offset & Carrier Frequency Offset …………….26
Chapter 5 ATO and CFO Correction …………………….28
Chapter 6 Simulations ………………………………………32
6.1 MME and MLE in Flat Fading Channel ……………………….32
6.2 MLE in Frequency Selective Fading Channel …………………34
6.3 Argument Method Performance ………………………………41
Chapter 7 Conclusion …………………………………44
References ……………………………………………45

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