這篇論文的研究方向主要分為兩個：其一是正交互補碼方面的相關研究，提出了columnwise complementary codes；其二是MIMO系統中space diversity方面的研究，提出了random complementary codes。
在這裡提出了一個新的正交互補碼，稱為columnwise complementary codes，它的優點為：
(1) 擁有完美的自相關與互相關函數來克服因為多路徑(multipath)以及多用戶(multi access)所產生的干擾旁瓣。
(2) 子碼長度最小可達到1，PG值遠小於完全互補碼，改善完全互補碼支持用戶
數受限於碼長(code family size)的缺點，減小了整個硬體實現的複雜度。
(3) 從碼矩陣的行向量(column vector)來觀察整個碼組的正交互補特性，使得columnwise complementary codes的產生方式非常直觀以及易於了解。
(4) 可以依照環境的不同選取所需要的columnwise complementary codes，例如對頻率選擇性衰減效應嚴重的通道，我們選取時域正交互補較多的columnwise complementary codes；對於時間選擇性衰減效應嚴重的通道，我們就選取頻域正交互補較多的columnwise complementary codes來更細部地抵抗時選和頻選效應。
(5) 對於multi rate transmission system，不同用戶間傳輸速率不相同，因此所需要的展頻碼子碼長度也不相同，運用columnwise complementary codes的產生觀念，可以依照不同傳輸速率，設計出不同長度的正交互補碼碼組。
(6) columnwise complementary codes由於它的產生方式的靈活，它具有很大的廣泛性，廣泛程度涵蓋了完全互補碼以及2D OVSF codes。
另一方面我們嘗試使用random complementary codes，將不同的random complementary codes分配到不同的發射天線上，而這些random complementary codse彼此之間是互相獨立的，也就是利用碼組的隨機性來移除發射天線間的相關性，讓發射天線可以靠得更近，藉此舒緩尺寸上的要求。

In thesis, we design a new orthogonal complementary codes- columnwise complementary codes. Its advantage is:
(1)As traditional orthogonal complementary codes, it has perfect orthogonal complementary property of auto-correlation and cross-correlation.
(2)We can choose different type of columnwise complementary codes to restrain frequency selective fading and time selective fading.
(3)Compared with complete complementary codes, it can support more users.
(4)The generating method of columnwise complementary codes is easy to understand.
(5)It can be used in multi-rate transmission system.
(6)The generality: complete complementary codes and 2D OVSF codes are subsets of columnwise complementary codes.
We also discuss its bit error rate in a frequency selective Rayleigh fading channel
and a time selective fading channel by computer simulation.

中文摘要 I
誌謝 II
目錄 III
圖目錄 V
表目錄 VII
變數列表 IX
第一章 導論 1
1.1 研究動機 1
1.1.1 正交互補碼方面的研究動機 1
1.1.2 Space Diversity方面的研究動機 3
1.2 論文架構 5
1.3 參考文獻 6
第二章 MIMO系統與正交互補碼之簡介 9
2.1 前言 9
2.2 空時系統(space-time)系統之簡介 9
2.3 空頻系統(space-frequency)系統之簡介 12
2.4 正交互補碼之簡介 16
2.5 參考文獻 20
第三章 位移正交序列 23
3.1 前言 23
3.2 偶位移正交序列 23
3.2.1 序列長度為4的偶位移正交序列 24
3.2.2 序列長度為8的偶位移正交序列 29
3.2.3 序列長度為N的偶位移正交序列 36
3.3 四位移正交序列 37
3.3.1 序列長度為8的四位移正交序列 37
3.3.2 序列長度為16的四位移正交序列 38
3.3.3 序列長度為N的四位移正交序列 44
3.4 位移正交序列 46
3.4.1 序列長度為 的 位移正交序列 46
3.4.2 序列長度為 的 位移正交序列 48
3.4.3 序列長度為L的 位移正交序列 50
3.5 參考文獻 62
第四章 Columnwise Complementary Codes 63
4.1 前言 63
4.2 概念簡介 63
4.3 -Columnwise Complementary Codes 67
4.3.1 -Columnwise Complementary Codes 67
4.3.2 -Columnwise Complementary Codes 68
4.3.3 -Columnwise Complementary Codes 73
4.3.4 -Columnwise Complementary Codes 78
4.4 -Columnwise Complementary Codes 79
4.4.1 -Columnwise Complementary Codes 80
4.4.2 -Columnwise Complementary Codes 82
4.4.3 -Columnwise Complementary Codes 84
4.4.4 -Columnwise Complementary Codes 89
4.4.5 -Columnwise Complementary Codes 95
4.5 -Columnwise Complementary Codes 100
4.5.1 -Columnwise Complementary Codes的完美自相關函數證明 102
4.5.2 -Columnwise Complementary Codes的完美互相關函數證明 107
4.7 Multi-rate Complementary Codes的設計 116
4.7.1 Combined Multi-rate Complementary Codes的設計 117
4.7.2 Multi-rate Columnwise Complementary Codes的設計 129
4.7.3 Advanced Multi-rate Columnwise Complementary Codes的設計 135
4.7.4 四種Multi-rate Complementary Codes的比較 142
4.8 參考文獻 146
第五章 Random Complementary Code 147
5.1 前言 147
5.2 Random Complementary Code產生方式 147
5.2.1 用戶數為2的Random Complementary Code產生方式 148
5.2.2 用戶數為4的Random Complementary Code產生方式 151
5.3 Random Complementary Code正交互補特性證明 158
5.3.1 Random Complementary Code在二位元（binary）情況下的正交互補特性證明 158
5.3.2 Random Complementary Code的正交互補特性證明 164
5.4 Random Complementary Code應用在MIMO系統的diversity分析 175
5.5 參考文獻 190
附錄A 週期與非週期完美相關函數互為充要條件之證明 195
附錄B Scrambling Operator之定義及特性證明 203
附錄C Spreading Operator之定義及特性證明 209
作者簡歷 213

[1] Golay, M.; “Complementary series”, Information Theory, IEEE Transactions on Volume 7, Issue 2, Apr 1961 Page(s):82 – 87
[2] Turyn, R.; “Ambiguity functions of complementary sequences (Corresp.)”, Information Theory, IEEE Transactions on Volume 9, Issue 1, Jan 1963 Page(s):46 - 47
[3] Taki, Y.; Miyakawa, H.; Hatori, M.; Namba, S.; “Even-shift orthogonal sequences”, Information Theory, IEEE Transactions on Volume 15, Issue 2, Mar 1969 Page(s):295 – 300
[4] Suehiro, N.; Hatori, M.; “N-shift cross-orthogonal sequences”, Information Theory, IEEE Transactions on Volume 34, Issue 1, Jan. 1988 Page(s):143 – 146
[5] Hsiao-Hwa Chen; Jun-Feng Yeh; Suehiro, N.; “A multicarrier CDMA architecture based on orthogonal complementary codes for new generations of wideband wireless communications”, Communications Magazine, IEEE Volume 39, Issue 10, Oct. 2001 Page(s):126 – 135
[6] Hsiao-Hwa Chen; Hsin-Wei Chiu; “Design of perfect complementary codes to implement interference-free CDMA systems”, Global Telecommunications Conference, 2004. GLOBECOM '04. IEEE Volume 2, 29 Nov.-3 Dec. 2004 Page(s):1096 - 1100 Vol.2
[7] Hsiao-Hwa Chen; Hsin-Wei Chiu; “Generation of perfect orthogonal complementary codes for their applications in interference-free CDMA systems”, Personal, Indoor and Mobile Radio Communications, 2004. PIMRC 2004. 15th IEEE International Symposium on Volume 1, 5-8 Sept. 2004 Page(s):734 - 738 Vol.1
[8] Chia-Ming Yang; Pei-Hsuan Lin; Guu-Chang Yang; Kwong, W.C.; “2D orthogonal spreading codes for multicarrier DS-CDMA systems”, Communications, 2003. ICC '03. IEEE International Conference on Volume 5, 11-15 May 2003 Page(s):3277 - 3281 vol.5
[9] 林金賢, “互補碼分碼多工系統之研究,” 國立中山大學電機工程學系研究所碩士論文, 2002
[10] Frank, R.; “Polyphase complementary codes”, Information Theory, IEEE Transactions on Volume 26, Issue 6, Nov 1980 Page(s):641 – 647
[11] Liru Lu; Dubey, V.K.; “Extended orthogonal polyphase codes for multicarrier CDMA system”, Communications Letters, IEEE Volume 8, Issue 12, Dec. 2004 Page(s):700 – 702
[12] Sivaswamy, R.; “Multiphase Complementary Codes”, Information Theory, IEEE Transactions on Volume 24, Issue 5, Sep 1978 Page(s):546 – 552
[13] Alamouti, S.M.; “A simple transmit diversity technique for wireless communications”, Selected Areas in Communications, IEEE Journal on Volume 16, Issue 8, Oct. 1998 Page(s):1451 - 1458
[14] Tarokh, V.; Jafarkhani, H.; Calderbank, A.R.; “Space-time block codes from orthogonal designs”, Information Theory, IEEE Transactions on Volume 45, Issue 5, July 1999 Page(s):1456 – 1467
[15] Tarokh, V.; Seshadri, N.; Calderbank, A.R.; “Space-time codes for high data rate wireless communication: performance criterion and code construction”, Information Theory, IEEE Transactions on Volume 44, Issue 2, March 1998 Page(s):744 – 765
[16] Rupp, M.; Mecklenbrauker, C.F.; “On extended Alamouti schemes for space-time coding”, Wireless Personal Multimedia Communications, 2002. The 5th International Symposium on Volume 1, 27-30 Oct. 2002 Page(s):115-119 vol.1
[17] Wonil Roh; Paulraj, A.; “MIMO channel capacity for the distributed antenna”, Vehicular Technology Conference, 2002. Proceedings. VTC 2002-Fall. 2002 IEEE 56th Volume 2, 24-28 Sept. 2002 Page(s):706 - 709 vol.2
[18] Siwamogsatham, S.; Fitz, M.P.; Grimm, J.H.; “A new view of performance analysis of transmit diversity schemes in correlated Rayleigh fading”, Information Theory, IEEE Transactions on Volume 48, Issue 4, April 2002 Page(s):950 - 956
[19] Fitz, M.P.; Grimm, J.; Siwamogsatham, S.; “A new view of performance analysis techniques in correlated Rayleigh fading”, Wireless Communications and Networking Conference, 1999. WCNC. 1999 IEEE 21-24 Sept. 1999 Page(s):139 - 144 vol.1
[20] Bolcskei, H.; Paulraj, A.J.; “Performance of space-time codes in the presence of spatial fading correlation” Signals, Systems and Computers, 2000. Conference Record of the Thirty-Fourth Asilomar Conference on Volume 1, 29 Oct.-1 Nov. 2000 Page(s):687 - 693 vol.1
[21] Weifeng Su; Safar, Z.; Liu, K.J.R.; “Diversity analysis of space-time modulation over time-correlated Rayleigh-fading channels”, Information Theory, IEEE Transactions on Volume 50, Issue 8, Aug. 2004 Page(s):1832 – 1840