本篇論文是研究正交互補碼性能之研究，其正交互補碼為完全互補碼、超級互補碼和Generalized pairwise complementary code(GPC code)，探討由產生方式去看正交互補碼的性能，了解從正交矩陣產生出來的正交互補碼之自相關函數與互相關函數是完美的。將正交互補碼用於直接序列展頻的分碼多工系統和位移堆疊傳輸的分碼多工系統，在這二種不同傳輸之中，正交互補碼在直接序列展頻的分碼多工系統下，具有完美的自互相關特性，所以可以有效的解決多路徑和多用戶間干擾。而在位移堆疊傳輸的分碼多工系統下，具有完美的互相關特性，但是適當的調整位移堆疊展頻的位移量，也可以有效的解決多路徑傳輸干擾。另外，GPC code是以提升系統用戶數以及保有次完美的自相關與互相關特性，也就是說以一段較長的IFW來取代完美的自相關與互相關特性，捨棄完美的特性來換取較多的用戶數的展頻碼。最後將討論的正交互補碼利用2D orthogonal variable spreading factor (OVSF) codes擴展方式來產生multi-rate之正交互補碼，讓正交互補碼也可以達到支持不同傳輸速率的用戶。
在本文的第二章，我們開始介紹完全互補碼之特性證明，再不同傳輸下的對抗干擾的能力。第三章介紹超及互補碼之特性證明，再不同傳輸下的對抗干擾的能力。第四章介紹GPC code之特性證明，說明此展頻碼是犧牲了完美的特性來換取較多的用戶數的展頻碼。第五章介紹multi-rate之正交互補碼的產生與完美特性。

This is a research on orthogonal complementary codes, including complete complementary codes, super complementary codes, and generalized pairwise complementary code(GPC code). I discuss the properties of orthogonal complementary codes by the generation of orthogonal matries and realize its auto-correlation and cross-correlation are perfect. Apply orthogonal complementary codes on direct-sequence spreading system and offset stacked spreading system. In these two kinds of transmission, orthogonal complementary codes have the ideal auto-correlation and cross-correlation by way of direct-sequence spreading system, so it can solve multipath interference and multi-access interference effectively. While in offset stacked spreading system, orthogonal complementary codes have ideal cross-correlation. Modulating the offset chip time of offset stacked spreading properly can also solve multipath interference effectively. Moreover, GPC code keeps sub-ideal auto-correlation and cross-correlation, and it forsakes its ideal property to exchange for spreading codes with more users.
In Chapter 2, we start to introduce complete complementary codes and its property to resist interferences in different transmission. Chapter 3 is the introduction of super complementary codes and its property to resist interferences in different transmission. Chapter 4 is the introduction of GPC code. We explain that GPC code forsakes its ideal property to exchange for spreading codes with more users. Chapter 5 is the introduce multi-rate orthogonal complementary codes and use 2D OVSF to suport different transmission speed.

中英文摘要 I
誌謝 III
目錄 IV
圖表目錄 VII
參數列表 VII

第一章 導論 1
1.1 研究動機 1
1.2 論文架構 2
1.3 基本理論介紹 3
1.3.1 互補碼(Complementary Code) 3
1.3.2 偶位移正交序列(Even Shift Orthogonal Sequence) 4
第二章 完全互補碼之One chip與 chip正交特性與頭尾偵測 7
2.1 完全互補碼產生方式 7
2.2 完全互補碼的完美正交特性證明 10
2.3 在不同的傳輸下超級互補碼的特性 17
2.3.1 直接序列展頻(Direct-sequence spreading)前後偵測之效益 17
2.3.2 位移堆疊展頻(Offset stacked spreading)前後偵測之效益 22
第三章 超級互補碼之互補正交特性與頭尾偵測 27
3.1 超級互補碼產生方式 27
3.2 超級互補碼的完美正交特性證明 29
3.2.1 由維度為2的正交矩陣產生超級互補碼 29
3.2.2 由維度為 的正交矩陣產生超級互補碼 37
3.3 在不同的傳輸下超級互補碼的特性 46
3.3.1 直接序列展頻(Direct-sequence spreading)前後偵測之效益 46
3.3.2 位移堆疊展頻(Offset stacked spreading)前後偵測之效益 48
3.4 附錄 53
第四章Generalized Pairwise Complementary Code (GPC code)的特性證明 57
4.1 GPC code的產生方法 57
4.1.1 產生偶位移正交序列 57
4.1.2 產生GPC code 66
4.2 GPC code特性證明 67
第五章Multi-Rate之正交互補碼 77
5.1 Multi-Rate之正交互補碼產生過程 77
5.2 Multi-Rate正交互補碼之自相關與互相關完美證明 81
第六章 結論 85
附錄A：零相關區(Zero Correlation Zone)與最大用戶數 87
參考文獻 93
作者簡歷 95

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