一般應用於正交分頻多工系統中的無線通道預測技術， 無論是採用最大可能估計法(maximum-likelihood estimation)或是最小平方法(least squares)來預測通道，大多是擷取通道脈衝響應為參數而不是通道頻率響應為參數來做預測。因為在多路徑散射通道中的通道脈衝響應係數是沒有相關聯性，而各子載頻之間的通道頻率響應則是具有相當程度相關聯性的，但是在正交分頻多工系統中被用於單頭(one tap)頻域等化器上所需的通道資訊必須是通道頻率響應。因此一般實際上的做法都是先得到通道脈衝響應的預估值，再利用離散傅利葉將結果轉換成通道頻率響應的預估值。在本論文中提出了只要當通道是屬於慢速衰減通道，就可以設計出最小平方演算法來利用重複的正交多頻分工系統的訓練符塊(training symbol block)，直接估計通道頻率響應的結果，而不用先得到通道脈衝響應的預估值。理論的分析及模擬的結果對於通道預估的表現將會呈現於後，而預估效果是利用均方誤差(mean square error)來評估。

For channel estimation in orthogonal frequency division multiplexing (OFDM) systems operated over wireless channels, either by maximum-likelihood (ML) or least squares (LS) criterion, one usually must choose the channel impulse responses (CIRs) rather than the channel frequency responses (CFRs) as the parameters to be estimated. This is because CIR taps of a multipath dispersive channel are uncorrelated while the subcarrier CFRs are correlated. But the ultimate channel information needed in OFDM should be the CFRs which are used for the one-tap frequency-domain equalizers. Thus, the usual practice is to first get the CIR estimates and then convert them into CFR estimates by discrete Fourier transforms (DFTs). In this paper, we show that, when channel fading is slow, one can scheme a least-squares (LS) algorithm using repeated OFDM training blocks to directly estimate the subcarrier CFRs without first obtaining the CIR estimates. Theoretical analysis accompanied by simulation results will be given for the estimation performance in terms of estimator mean square error (MSE).

TABLE OF CONTENTS

CHAPTER 1	 INTRODUCTION..........1
CHAPTER 2	 THE OFDM SYSTEM..........3
2.1	The Signal Model..........4
2.2	The Channel..........6
2.3	Cyclic Prefix..........7
2.4	The Receiver..........7
CHAPTER 3	 PRINCIPLE OF LEAST SQUARES METHOD...........10
3.1	History of Least Squares Method..........10
3.2	The Basic Theory of Least Squares Method........11
CHAPTER 4	 LEAST SQUARES ESTIMATION FOR CFR IN OFDM   SYSTEMS..........14
4.1	OFDM Channel Estimation..........14
4.2	The Novel LS CFR Estimation Algorithm for OFDM..15
4.3      The Estimator Performance..........21
CHAPTER 5	 SIMULATION RESULTS..........18
CHAPTER 6	 CONCLUSION..........22
REFERENCES..........23

LIST OF FIGURES
	
Figure 2.1   Spectrum of a single OFDM subcarrier...3
Figure 2.2   OFDM spectrum of several adjacent subcarriers	...4
Figure 2.3   OFDM block diagram...8
Figure 2.4   Concept of a cyclic prefix...9
Figure 5.1   MSE of LS CFR estimator vs. SNR....19
Figure 5.2   MSE of LS CFR estimator vs. SNR....20
Figure 5.3   MSE of LS CFR estimator vs. SNR....21

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