多媒體設備與行動通訊對於我們的重要性越來越高。 使用多個天線來創造多輸出多輸出 (MIMO) 的無線通道可以有效的提高數據速率和可靠性來強化傳輸的品質。 傳輸通道的容量會依照傳送和接收的天線輸量而增加。 時空碼 (Space-Time Code) 為一種可以有效提高頻譜效率和降低錯誤率的技術。 可除性代數 (Division Algebra)為一種常見的數學工具用來設計時空碼。 分集與多工增益權衡是評估所用的碼之性能高低比較之公平法則。


在此論文中，我們推算了在頻率選擇快速衰減通道下線性調變的時空碼的設計準則。接著我們依照設計準則來建構一個時供碼。 此時空碼由一個迴旋編碼器和一個空間編碼器所組成。 此空間編碼器是利用可除性代數設計之最佳編碼器。 接著，推導出在頻率選擇快速衰減通道下之此時空碼之分集與多工增益的權衡。

In this thesis, we evaluate the design criterion of a space-time coding scheme for linear modulation over frequency-selective fast fading channels. Beside, we explicate a code construction for multipath channels. Then, we show that the tradeoff between diversity gain and multiplexing gain of our coding scheme will better than the traditional optimal one without a temporal code.

1 Introduction 3
2 Frequency-Selective Fading Channel Model 5
2.1 Time-Variant Linear Channel . . . . . . . . . . . . . . . . . . . . 5
2.2 Tapped-Delay-Line Channel Model . . . . . . . . . . . . . . . . 6
3 A Scheme for Space-Time Coding with Linear Modulation 12
3.1 A Space-Time Coding Scheme . . . . . . . . . . . . . . . . . . . 12
3.2 Space-Time Code Design Criteria for Linear Modulation . . . . . 16
4 Space-Time Encoder Design 25
4.1 Convolutional Encoder . . . . . . . . . . . . . . . . . . . . . . . 25
4.2 A Spatial Encoder for Full Rank Matrix Design . . . . . . . . . . 27
4.2.1 Division algebra . . . . . . . . . . . . . . . . . . . . . . 27
4.2.2 Embedding Field Extension into Mnn(F) . . . . . . . . 28
4.2.3 Code Design with Full Rank . . . . . . . . . . . . . . . . 29
1
CONTENTS
5 The Diversity and Multiplexing Tradeoff of Frequency Selective Fading
Channel 32
5.1 The Optimal Diversity and Multiplexing Tradeoff . . . . . . . . . 32
5.2 The DMT of the Space-Time Code Scheme with Approximately
Universal Spatial Codes . . . . . . . . . . . . . . . . . . . . . . . 33
5.2.1 The DMT of the Space-Time code Scheme with Approximately
Universal Codes over Frequency-Selective Fading
Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
6 Conclusion 45

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