壓縮感知是一項被應用在許多領域的訊號處理技術。透過壓縮感知，可以由較少量的資訊高機率地復原未知數，藉此達成資源的節省。在無線通訊領域上，由於多重路徑通道的稀疏特性，我們可以藉由以壓縮感知為基礎的方法來處理在正交分頻多工中的稀疏通道估測問題。其中在領航信號的樣式的設計上，有別於一般藉由最小化測量矩陣的最大相關性值的方法，本文提出了新的設計準則，藉此有較高的機率能挑選出正交性較高的測量矩陣。模擬結果顯示，相對於被廣泛採用的準則，由本文提出的設計準則所產生的領航信號，在稀疏通道估測上可以有更低以及更穩定的均方誤差表現。

Compressed sensing (CS) is a signal processing technique which has been applied in lots of fields. Through CS, unknown parameters can be recovered with high probability from smaller amounts of information so that resources are saved. Due to the sparse nature of multipath channels, we settle the channel estimation problem in orthogonal frequency division multiplexing (OFDM) systems using CS -based method. On the design of pilot patterns, instead of a general way of minimizing the mutual coherence of the measurement matrix, a novel criterion is proposed by which measurement matrices with higher orthogonality can be picked with higher probability. Simulation results display that, in comparison to the widely used criterion, the pilot patterns generated by proposed criterion give better and more stable mean square error (MSE) performances in sparse channel estimation.

口試委員會審定書 #
誌謝 2
中文摘要 i
ABSTRACT ii
CONTENTS iii
LIST OF FIGURES v
LIST OF TABLES vii
Chapter 1 Introduction 1
1.1 Background 1
1.2 Related Works 4
Chapter 2 Problem Statement 6
2.1 An Overview of Compressed Sensing 6
2.2 OFDM System Model 10
2.3 Sparse Channel Estimation via Compressed Sensing 13
Chapter 3 Proposed Method 15
3.1 Effects from Eigenvalues of Measurement Matrices 15
3.2 Derivation for Bounds of Reconstruction Errors 17
3.3 Proposed Design Criterion 24
Chapter 4 Simulation Results 27
4.1 MSE Results 28
4.2 Results of Support Errors 33
4.3 Stability Results 37
4.4 Different Estimations of Sparsity 41
4.5 Another Channel Case 44
Chapter 5 Discussions 49
5.1 Distribution of Pilot Positions 49
5.2 Other Pilot Search Schemes 51
Chapter 6 Conclusion 52
References 53

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