本篇論文是研究完美的位移堆疊展頻碼，用於位移堆疊傳輸的分碼多工(code division multiple access, CDMA) 系統，和傳統的分碼多工系統比較，具有更高的展頻效率 (spreading efficiency)、頻寬效率 (bandwidth efficiency) 等。同時又因為碼組在堆疊傳輸系統下，具有完美的互相關特性，所以可以有效的解決多用戶間干擾 (multiple access interference, MAI)。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 (multipath interference, MI)的問題。此外本文對零干擾窗有深入的探討，將自、互相關函數的零干擾窗分開討論，可以解釋抗多用戶間干擾及多路徑干擾的能力，並提出零干擾窗 (IFW)、用戶數 (K)及處理增益 (PG) 的關係式
在本文第二章，我們會先介紹此篇論文中所用到的線性代數原理、Welch界限和直接序列展頻的完美展頻碼組產生方法。接著第三章對直接序列展頻的完美展頻碼組作後續的分析，包括碼組的相關特性，互相關函數零相關窗、用戶數及處理增益關係，以及在位移堆疊展頻的應用分析。第四章是全文的重心，我們會提出一種更適用於位移堆疊傳輸架構的完美位移堆疊展頻碼，可以改善完美展頻碼的頭尾檢測問題，更能操作在任何位移堆疊展頻，並分析抗干擾能力。

In this thesis, a new spreading code -- complete offset-stacked spreading code (OSC) is designed and discussed. OSC has a orthogonal complementary property of auto-correlation and cross-correlation. According to the interference-free windows of cross-correlation (CC_IFW) of OSC, the proposed CDMA architecture can offer an MAI-free operation in both down-link (synchronous channel) and up-link (asynchronous channel) transmission under the AWGN channel. According to the interference-free windows of auto-correlation (AC_IFW) of OSC, the proposed CDMA architecture can also offer a part of MI-free operation in both downlink (synchronous channel) and uplink (asynchronous channel). Furthermore, the range of AC_IFW is restricted by the number of offset chips.

目 錄 I
圖 目 錄 III
表 目 錄 V
參 數 列 表 VI

第一章 導論 1
第二章 相關的碼理論及搜尋完美展頻碼的方法介紹 6
2.1 Welch bound 6
2.1.1 單一序列零位移相關函數推導 6
2.1.2 單一序列任何位移相關函數推導 9
2.2 碼組設計的方法 11
2.3 線性代數理論 15
第三章 完美展頻碼的後續分析 17
3.1 完美展頻碼相關函數的推導 17
3.2 互相關函數的零干擾窗、用戶數及處理增益的關係式 21
3.2.1 互相關函數非對稱的零干擾窗展頻碼 24
3.2.2 互相關函數對稱的零干擾窗展頻碼 27
3.3 運用於位移堆疊傳輸的可行性 34
3.4 位移堆疊傳輸系統抗干擾能力 38
3.4.1 位移1個切片 38
3.4.2 位移2個切片 39
3.4.3 位移n個切片 39
3.5 結論 42
第四章 利用解相關函數方程組設計完美位移堆疊展頻碼 43
4.1完美位移堆疊展頻碼設計 44
4.1.1 非線性方程式組求解 44
4.1.2 線性方程式組求解 51
4.2 位移堆疊傳輸系統抗多路徑及多用戶干擾能力 62
4.2.1 位移1個切片 62
4.2.2 位移2個切片 64
4.2.3 位移n個切片 66
4.2.4 圖示位移堆疊展頻範例 69
4.3 適用於堆疊傳輸的完美展頻碼 73
4.4 結論 74
第五章 結論及未來的研究工作 75
附錄A 完美展頻碼的最大支援用戶數證明 78
附錄B 設計抗多路徑干擾的完美位移堆疊展頻碼 87
B.1 多路徑通道，位移1個切片堆疊展頻 87
B.2 多路徑通道，位移n個切片堆疊展頻 89
附錄C 以空間正交向量觀念證明完美位移堆疊展頻碼的支持用戶數 92
參 考 文 獻 100

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