在過去幾年來的發展下，正交分頻多工調變 (OFDM) 技術已經十分成熟，並已經應用在許多無線與有線的通訊系統上。然而，我們仍試著透過部分響應波形和超取樣技巧來提升系統可靠性。
回顧正交分頻多工調變系統的發展史，正交分頻多工調變系統由 R.W. Chang 於1966年發表，主要透過使用大量緊鄰的正交子載波，將每個子載波採用傳統的調變來產生類比訊號。然而，因傳輸者與接收者的混頻器必須完全同步，所以在硬體的實現上有相當難度。直到1970年，Weinstein and Ebert 提出透過離散傅立葉轉換來產生正交分頻多工調變的離散訊號，才使得正交分頻多工調變較易透過 VLSI 技術實現，如今才能被大量採用於現今的通訊系統。

近年來，頻譜資源越來越珍貴，如何做最有效率的頻譜利用變成一個相當重要的課題。在本篇論文中，我們採用部分響應波形來降低訊號頻寬，並推導在採用部分響應波形下正交分頻多工調變系統的功率譜密度函數。除此之外，亦模擬了不同部分響應波形所對應的頻寬與系統傳輸效率。接著我們針對多重路徑衰退通道提出一種超取樣接收器並對其做性能分析。從性能分析我們可以得到採用不同部分響應波形與超取樣率會有不同的分集增益。最後，我們參考 IEEE 802.11 ac 的實際規格來進行系統模擬並與傳統接收器比較，發現超取樣接收器擁有較好的分集增益與錯誤率性能。

In this thesis, we consider an OFDM system with partial-response signaling over a frequency selective fading channel. We employ the oversampling method to the received OFDM signal and derive the diversity gain. Both theoretical analysis and simulation results show that our proposed scheme outperforms the conventional OFDM system.

Abstract ii
Contents iii
List of Figures v
List of Tables ix
1 Introduction 1
2 Preliminary 3
2.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 An Overview of the OFDM System . . . . . . . . . . . . . . . . . . . 6
2.2.1 The Original Continuous-time OFDM System . . . . . . . . . 6
2.2.2 The Equivalent Discrete-time OFDM System . . . . . . . . . 9
2.2.3 The Contemporary OFDM System . . . . . . . . . . . . . . . 12
2.2.4 Complex Representation . . . . . . . . . . . . . . . . . . . . . 17
3 Power Spectral Density Functions of OFDM Signals with CP 20
3.1 Derivation of Power Spectral Density (PSD) Functions . . . . . . . . 21
3.2 The PSD of Pulse Shaping Functions . . . . . . . . . . . . . . . . . . 27
3.2.1 Rectangular Pulse Shaping Function . . . . . . . . . . . . . . 28
3.2.2 Half-cosine Pulse Shaping Function . . . . . . . . . . . . . . . 30
3.2.3 Raised-cosine Pulse Shaping Functions . . . . . . . . . . . . . 33
3.2.4 Truncated Sinc Pulse Shaping Functions . . . . . . . . . . . . 37
4 OFDM System over Frequency-Selective Fading Channel 45
4.1 Reciever without Oversampling . . . . . . . . . . . . . . . . . . . . . 47
4.2 Reciever with Oversampling . . . . . . . . . . . . . . . . . . . . . . . 51
5 Performance Analysis 59
5.1 Maximum Likelihood (ML) Decision Rule . . . . . . . . . . . . . . . 59
5.2 Minimum Distance Decision Rule . . . . . . . . . . . . . . . . . . . . 61
6 Simulation Results 68
6.1 An Overview of Channel Estimation . . . . . . . . . . . . . . . . . . 68
6.2 IEEE 802.11ac and Channel Model . . . . . . . . . . . . . . . . . . . 70
6.2.1 IEEE 802.11ac . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.2.2 Channel Model and Delay Power Profile . . . . . . . . . . . . 71
6.3 Effective Dimension of the Signal Space . . . . . . . . . . . . . . . . . 72
6.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.4.1 Performance Comparsion over Multipath Rayleigh Fading Channel
of the Rural Area . . . . . . . . . . . . . . . . . . . . . . . 73
6.4.2 Performance Comparsion over Multipath Rayleigh Fading Channel
of the Rural and Urban Areas . . . . . . . . . . . . . . . . 78
6.4.3 Performance Comparsion of Perfect Channel State Information
(CSI) and Least-Square Estimated CSI over Multipath
Rayleigh Fading Channel of Rural Area . . . . . . . . . . . . 80
7 Conclusion 84
A Bandwidth and System Efficiency 85
A.1 Truncated Raised-Cosine Pulse Shaping Functions . . . . . . . . . . . 85
B Effective Dimension of Signal Space 91
C Delay Power Profile 94
C.1 Typical Rural Area Channel Model . . . . . . . . . . . . . . . . . . . 94
C.2 Typical Urban Area Channel Model . . . . . . . . . . . . . . . . . . . 94

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