本篇論文是介紹一種新的展頻碼(spreading code)—超級互補碼(super
complementary code)，超級互補碼如果用於分碼多工(code division multiple
access)系統中，可以有效的解決多用戶間干擾(multiple access interference)以及
多重路徑傳輸干擾(multipath interference)的問題，而這是因為超級互補碼本身
具有自相關函數以及互相關函數正交互補的特性，而這樣的特性是因為超級互
補碼是由正交矩陣所變化產生出來的，因此像超級互補碼這樣的展頻碼非常適
合運用於分碼多工系統中。
在論文的第三章中，我們會詳盡地說明超級互補碼的產生方式以及超級互
補碼的完美正交性並證明出為何超級互補碼會有自相關函數以及互相關函數的
正交互補特性；接著我們會在第四章中說明如何將超級互補碼運用到分碼多工
系統中，並且會介紹發射端和接收端的運作架構，並且會用圖解的方式說明超
級互補碼是如何克服多用戶干擾以及多重路徑傳輸干擾，我們也會分析在這樣
的分碼多工系統下的誤碼率，最後會利用Matlab來做超級互補碼相關的模擬
並且會將超級互補碼和其他比較常見的展頻碼做個比較，從模擬結果中我們可
以發現超級互補碼的性能因為本身的完美正交性而不會受到多用戶以及多重路
徑傳輸的干擾，所以性能要比其他的展頻碼要來的好，尤其是在多用戶以及多
重路徑傳輸的情況下。

In this thesis, a new spreading code - super complementary code is defined and
discussed. A general method of generating this code is also discussed. Super
complementary code has a orthogonal complementary property of auto-correlation
and cross-correlation. We designed a multi-carrier CDMA system architecture
according to the orthogonal-complementary property of super complementary code.
The proposed CDMA architecture can offer an MAI(multiple access interference)-free
operation in both down-link (synchronous channel) and up-link (asynchronous
channel) transmission under the AWGN channel, because of the orthogonal
complementary property of the super complementary codes. The proposed CDMA
architecture can also offer an MI(multipath interference)-free operation in both
downlink (synchronous channel) and uplink (asynchronous channel) , because of the
orthogonal-complementary properties of the super complementary codes.

中文摘要……………………………………………………………………………Ⅰ
英文摘要……………………………………………………………………………Ⅱ
誌謝 …………………………………………………………………………………Ⅲ
目錄…………………………………………………………………………………Ⅳ
變數表………………………………………………………………………………Ⅵ
圖目錄和表目錄……………………………………………………………………Ⅶ
第一章 導論………………………………………………………………………1
第二章 分碼多工系統上的相關研究……………………………………………3
第三章 超級互補碼………………………………………………………………5
3.1 前言…………………………………………………………………5
3.2 產生方式……………………………………………………………5
3.2.1 完全互補碼的產生方式…………………………………………5
3.2.2 擴展完全互補碼的產生方式……………………………………7
3.2.3 超級互補碼的產生方式…………………………………………8
3.3 完美正交性…………………………………………………………16
3.3.1 完全互補碼和超級互補碼的完美正交性………………………16
3.3.2 完全互補碼的完美正交性證明…………………………………18
3.3.3 擴展完全互補碼的完美正交性證明……………………………28
3.3.4 超級互補碼的完美正交性證明…………………………………31
第四章 使用超級互補碼的分碼多工系統架構………………………………43
4.1 前言…………………………………………………………………43
4.2 使用超級互補的分碼多工系統架構………………………………43
4.3 使用超級互補碼的分碼多工系統之圖解分析……………………49
4.4 使用超級互補的分碼多工系統之理論分析………………………55
4.4.1 非整數chip延遲下的分析………………………………………56
4.4.2 訊號連續傳送情況下的分析……………………………………57
4.4.3 多用戶以及多重路徑傳輸下的性能分析………………………58
4.5 Matlab模擬結果……………………………………………………63
第五章 結論以及未來的研究工作……………………………………………72
參考文獻……………………………………………………………………………74

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