正交分頻多工系統是新的調變技術用來抵抗多路經衰減效應。IEEE802.11a將OFDM定為標準規格。OFDM系統的一些優點：如降低計算複雜度、對抗窄頻干擾的能力、頻率分級的利用等等。在這篇論文中，我們考慮聯合頻率偏移和通道估測，但是我們先假定時間同步化的工作已經完成了。OFDM系統是在一個頻率平坦的環境下所做的。在這裡我們提出使用最大概似（ML）估計演算法來做聯合頻率偏移和通道估測。模擬的步驟：我們利用梯度圖來求得頻率偏移估測，再根據頻率偏移估測來求得通道頻率反應。然後在矯正頻率偏移後，我們再以合理假設運用最小平方法(least squares)求得通道估測做一比較。最後再將理論值跟模擬作比較。

Orthogonal frequency division multiplexing (OFDM) is a new generation modulation technique. OFDM system is robust against the fading effects of multipath propagation. The IEEE 802.11a applies OFDM for wireless local area networks (WLAN) as standard specification. OFDM has several advantages ：reduced computational complexity、exploitation of frequency diversity、and robust against narrowband interference. In this paper, we consider joint frequency offset and channel estimation assuming timing synchronization has been completed .Flat fading channels are considered. We use a maximum-likelihood (ML) algorithm to jointly estimate the frequency offset and the channel frequency response (CFR). By first obtaining the frequency offset estimation using gradient plot, then the CFR estimation is obtained from the frequency offset estimation result. Further, an alternative approach using a least squares formulation for channel estimation is also presented based on completion of the frequency offset correction. Simulations are performed to compare with theoretical predictions.

CONTENTS

ACKNOWLEDGENMENT	I
CHINESE ABSTRACT	II
ENGLISH ABSTRACT	III
CONTENTS   	IV
LIST OF FIGURES	VI
CHAPTER 1  INTRODUCTION	1
CHAPTER 2  MOBILE WIRELESS CHANNELS	4
2.1 Doppler Spread and Channel Coherence Bandwidth	4
2.2 The Rayleigh Fading Model	6
CHAPTER 3  PRINCIPLES AND STRUCTURE OF ORTHOGONAL FREQUENCY DIVISION MULPLEXING SYSTEMS	8
3.1 The Multicarrier System Model	9
CHAPTER 4  MAXIMUM LIKELIHOOD ESTIMATION	14
CHAPTER 5  FREQUENCY SYNCHRONIZATION AND CHANNEL ESTIMATION	18
5.1 Signal and System Models	18
5.2 The Joint Maximum-likelihood Estimation Algorithm	21
5.3 A Least Squares Channel Estimation	25
5.4 Channel Estimator Performance	27
CHAPTER 6  NUMERICAL SIMULATIONS	29
CHAPTER 7  CONCLUSIONS  	39
REFERENCES	         40

LIST OF FIGURES

Figure 3.1  The OFDM system structure…………………………………………………13
Figure 5.1  Gradient curve………………………………………………………………..24
Figure 6.1  Estimated frequency offset vs. true frequency offset for two SNR values	31
Figure 6.2  Estimated frequency offset vs. SNR for a true offset of 0.2.	32
Figure 6.3  ML Frequency offset estimation variance vs. SNR for  .	33
Figure 6.4  Variance of the ML frequency offset variance vs. true offset. SNR 40dB …..34 
Figure 6.5  ML estimate of   vs. SNR……………….……………………………….35
Figure 6.6  LS estimate of   vs. SNR…………………………..…………………….36
Figure 6.7  Comparison of the ML channel estimation variance and the theoretical LS 
estimation variance…………….…………………………………………..…37
Figure 6.8  Comparison of the LS channel estimation variance and the theoretical LS estimation variance…………………………………...………………………38

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