光分碼多工展頻碼設計有兩大重點 : 一為展頻碼相關函數表現，另一為碼組所支援的用戶數。展頻碼相關函數表現會直接反映在系統性能表現上，而用戶數的多寡則表現出使用此展頻碼系統的用戶容量。由於在光通訊分碼多工系統中，我們所使用的展頻碼是由0、1所組成的序列，所以在展頻碼相關特性表現上沒辦法達到完全理想的相關表現，我們將在後面證明這個結論。再根據所得到的結論，以最佳相關函數表現來重新對光通訊展頻碼作定義。最佳光通訊展頻碼應為在自相關表現上為一理想的自相關函數 ，而在互相關表現上雖不能達到完全理想，但我們將旁瓣數降到最低，且旁瓣幅度最大為1 。
根據此最佳光通訊展頻碼的要求，我們先求出最佳決策值為何值並證明其值是可以讓錯誤率為最小。然後根據最佳相關性的特質來建構出光通訊質數波長跳動互補碼的產生方式，並證明符合我們對最佳光通訊展頻碼的要求( )。接著建構出使用此展頻碼的傳送器和接收器，然後在分碼多工系統上的性能做分析。在光通訊分碼多工系統中，影響性能表現最大的因素便是用戶間的干擾(MAI)，但由於光通訊互補碼是使用並列傳送比傳統的串列傳送來的好。因為可以減少用戶間碰撞的機率，且傳輸速度可以大大增加。所以我們可以從結論中清楚的看出在性能表現上優於一般光通訊展頻碼。
然後由於碼中權重的增加會影響我們設定的決策值，所以如何取得最佳決值使得錯誤率為最小也是我們討論的重點。

The most two important concern in CDMA code design, one is the properties of spreading codes correlation, and another one is the number of users. The correlation properties will influence BER (bit error rate) of the system directly, and the number of users will express the system capacity.
In optical-CDMA system, optical spreading code is impossible to achieve idea correlation properties. Because of the optical sequence is consisted of ”0”、”1”. We prove it after. According to the result we can define the best properties of correlation of the optical complementary codes. The ideal of auto-correlation is 0( ) and the optimum cross-correlation is 1( ).
According to the requirement of the optimum complementary codes we must first to decide the value of the best threshold and prove it. The properties of correlation are satisfied with optical prime-hopping complementary codes that we architecture.
We analysis the performance of the prime-hopping complementary codes in optical CDMA. Because of the hits of MAI decrease we can support most number of users, so we can clearly find the system with the prime-hopping complementary codes has the better performance.

中文摘要.............................................I
英文摘要.............................................II
誌謝.................................................III
目錄.................................................IV
變數列表.............................................VI
圖表目錄.............................................VII
第一章 導論..........................................1
1.1 研究動機.........................................1
1.2 論文架構.........................................3
第二章 光通訊分碼多工系統及展頻碼簡介................5
2.1 光通訊分碼多工系統介紹...........................5
2.1. 1 光分碼多工(OCDMA)使用直接序列展頻編碼.........5
2.1. 2 光分碼多工(OCDMA)結合其他系統.................6
2.2 光通訊展頻碼介紹.................................6
2.2. 1 光正交碼 (Optical Orthogonal Codes)...........6
2.2. 2 質數碼 (Prime Code)...........................9
2.2. 3 不等碼長編碼 (multilength code)...............9
第三章 光通訊展頻碼之相關函數特性....................11
3.1 光通訊單一展頻碼之相關函數分析...................11
3.1.1 自相關函數.....................................11
3.1.2 互相關函數.....................................14
3.2 光通訊直序展頻碼.................................15
3.3 光通訊多子碼展頻碼之相關函數分析.................17
3.4 光通訊多子碼展頻碼之子碼個數限制.................23
第四章 最佳光通訊互補碼..............................27
4.1 參數介紹.........................................27
4.2 最佳光通訊互補碼之相關性證明.....................28
4.2.1 光通訊互補碼自相關的分析.......................28
4.2.2 光通訊互補碼互相關的分析.......................30
4.3 最佳光通訊互補碼產生方式.........................32
4.3.1 對於自相關特性的要求...........................32
4.3.2 對於互相關特性的要求...........................33
4.3.3 光通訊互補碼的編碼方式.........................36
4.3.4 質數波長跳動互補碼的產生方法...................40
第五章 光通訊互補碼的分碼多工系統之性能分析..........57
5.1 傳統光纖分碼多工(FO-CDMA)系統....................57
5.1.1 光正交碼(OOCs)的系統架構.......................58
5.1.2 光通訊正交碼的分碼多工系統之理論分析...........58
5.1.3 光通訊正交碼(OOCs)的錯誤率分析.................73
5.2 光質數波長跳動互補碼架構.........................78
5.2.1 光質數波長跳動互補碼接收端的系統架構圖.........79
5.2.2 光質數波長跳動互補碼分碼多工系統之圖解分析.....81
5.2.3 光質數波長跳動互補碼的錯誤率分析...............87
5.3 各種光通訊編碼架構的比較.........................104
第六章 結論..........................................105
6. 1 光纖分碼多工使用互補碼的優點....................105
參考文獻.............................................107
附錄A 週期性與非週期性相關函數討論...................109
A-1 週期性相關函數與非週期性相關函數.................109
A-2 自相關函數.......................................110
A-2-1 週期性自相關...................................110
A-2-2 非週期性自相關.................................112
A-3 互相關函數.......................................115
A-3-1 、 週期性互相關...............................116
A-3-2 、 非週期性互相關推導.........................117
附錄B 推導決策值為任意值的錯誤率分析.................119
B-1 權重大於用戶數...................................119
B-2 權重小於用戶數...................................122
附錄C 最佳決策值的證明...............................133
C-1 光正交碼的最佳決策值的證明.......................133
C-2 光質數波長跳動互補碼的最佳決策值的證明...........136
作者簡歷.............................................139

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