在本論文中，我們針對時空區塊碼(Space-Time Block Code, STBC)編碼技術使同一個用戶間的天線是可分的與隨機互補碼(Random Complementary Code, RCC) 使不同用戶間是可分。並對時空區塊碼(Space-Time Block Code, STBC)編碼技術與隨機互補碼(Random Complementary Code, RCC)分碼多工(Code Division Multiple Access, CDMA)系統的整合架構做分析。此種整合架構有如下的特性
(1) 時空編碼技術可以透過多天線的配置結合編碼技術，可以在接收端提高接收訊號的天線分集，而隨機互補碼分碼多工技術可以擁有互補碼的完美相關特性下，在接收端降低訊號所受到的干擾，而兩者整合後的系統可以同時具有時空編碼技術的與隨機互補碼分碼多工技術的特性。
(2) 由於隨機互補碼是利用碼與碼之間的相關值互補特性來達到干擾消除，本論文中透過多載波的方式來實現隨機互補碼分碼多工技術，進而達到不僅僅是分用戶，同時兼具分天線的效果與干擾消除。因此設計兩種接收端(Receiver)，訊號合成式接收端(Signal Synthesis Receiver)與分天線式接收端(Distributed Antennas Receiver)。考慮在單一路徑的情況下，可以因為碼彼此間的正交達道零干擾的效果。然而，多路徑情況的頻率選擇性衰減通道中，使用多載波的隨機互補碼分碼多工系統在不同頻率上所造成的不同的通道響應破壞了隨機互補碼的碼結構，使得干擾無法有效地消除。
(3) 隨著用戶數的增加，在完全相關的子載波通道的情況下，系統的效能絲毫不受影響，但在完全獨立的子載波通道的情況下，系統的效能隨著用戶數增加而降低。同時在可解析的路徑數越多的情況下，完全相關的子載波通道的效能會因為能夠有效地利用到無干擾的多路徑分集增益，因此其性能逐漸優於完全獨立的子載波通道環境下的性能。同時我們將系統的參數變化至更加一般化，並嘗試分析出不同參數環境下系統的效能最佳值。

This is a research on Performance Analysis of Random Complementary Code Based MIMO-CDMA System. In the first instance we discuss the produce method of random complementary codes by the basic matrix and pole matrix. Pole matrix is the produce method of Walsh Hadamard matrix. We discuss the properties of random complementary codes by the pole matrix and realize its auto-correlation and cross-correlation are perfect. Apply random complementary codes on Distributed Users and Antennas. Random complementary codes have the ideal auto-correlation and cross-correlation by way of direct-sequence spreading system, so it can solve multi-path interference and multi-access interference effectively. Apply Space-Time Block Codes on Distributed time and Antennas in the same user. Systems combine RCC with STBC. I design STBC RCC-CDMA System and two receivers. We discuss Signal Synthesis Receiver and Distributed Antennas Receiver with Rayleigh fading channel.

In Chapter 2, we start to introduce random complete complementary codes and its property to resist interferences in different transmission. Chapter 3 is the introduction Performance Analysis of Random Complementary Code Based MIMO-CDMA System with full correlated Rayleigh fading channel. Chapter 4 is the introduction Performance Analysis of Random Complementary Code Based MIMO-CDMA System with multi-path Rayleigh fading channel. Chapter 5 is the introduce conclusion and to research a goal in the future.

Abstract--------------------------------------------------------------------------------------------------------------------------------------I
中文摘要------------------------------------------------------------------------------------------------------------------------------------II
誌謝------------------------------------------------------------------------------------------------------------------------------------------III
目錄-----------------------------------------------------------------------------------------------------------------------------------------IV
變數列表----------------------------------------------------------------------------------------------------------------------------------VII
圖、表目錄-------------------------------------------------------------------------------------------------------------------------------XI
第一章 導論-------------------------------------------------------------------------------------------------------------------------------1
1.1研究動機-------------------------------------------------------------------------------------------------------------------------------1
1.2論文架構-------------------------------------------------------------------------------------------------------------------------------2
1.3系統基本架構------------------------------------------------------------------------------------------------------------------------2
1.3.1時空區塊碼-------------------------------------------------------------------------------------------------------------------------2
1.3.2 互補碼運作原理------------------------------------------------------------------------------------------------------------------4
第二章 隨機互補碼----------------------------------------------------------------------------------------------------------------------9
2.1前言-------------------------------------------------------------------------------------------------------------------------------------9
2.2隨機互補碼產生方式---------------------------------------------------------------------------------------------------------------9
2.2.1用戶數為2的隨機互補碼產生方式------------------------------------------------------------------------------------------9
2.2.2用戶數為4的隨機互補碼產生方式-----------------------------------------------------------------------------------------12
2.3隨機互補碼正交互補特性證明------------------------------------------------------------------------------------------------18
2.3.1隨機互補碼在二位元情況下的正交互補特性證明--------------------------------------------------------------------18
2.3.2隨機互補碼的正交互補特性證明------------------------------------------------------------------------------------------22
2.4基本矩陣的探討-------------------------------------------------------------------------------------------------------------------33
2.4.1取得最佳的隨機值--------------------------------------------------------------------------------------------------------------34
第三章 空時直接序列式隨機互補碼分碼多工系統於單一路徑之完全相關Rayleigh衰減通道-----------------42
3.1前言-----------------------------------------------------------------------------------------------------------------------------------42
3.2系統架構圖--------------------------------------------------------------------------------------------------------------------------42
3.3系統分析-----------------------------------------------------------------------------------------------------------------------------48
3.3.1系統各個部分分析-------------------------------------------------------------------------------------------------------------48
3.3.1.1 STBC Decoder--------------------------------------------------------------------------------------------------------------48
3.3.1.2隨機互補碼--------------------------------------------------------------------------------------------------------------------50
3.3.1.3 QPSK Modulator------------------------------------------------------------------------------------------------------------51
3.3.1.4傳送訊號分析-----------------------------------------------------------------------------------------------------------------52
3.3.1.5通道模型-----------------------------------------------------------------------------------------------------------------------53
3.3.2訊號合成式接收端-------------------------------------------------------------------------------------------------------------53
3.3.2.1沒有多重路徑干擾下的接收訊號---------------------------------------------------------------------------------------54
3.3.2.2 QPSK Demodulator--------------------------------------------------------------------------------------------------------54
3.3.2.3 STBC Decoder的輸入端-------------------------------------------------------------------------------------------------56
3.3.2.4 STBC Decoder的輸出端-------------------------------------------------------------------------------------------------59
3.3.3分天線式接收端-----------------------------------------------------------------------------------------------------------------61
3.3.3.1分天線式接收端(未加Symbol Interchange的部分)-----------------------------------------------------------------61
3.3.3.2 STBC Decoder的輸入端(未加Symbol Interchange的部分)----------------------------------------------------62
3.3.3.3 STBC Decoder的輸出端(未加Symbol Interchange的部分)----------------------------------------------------66
3.3.3.4分天線式接收端加入Symbol Interchange-----------------------------------------------------------------------------67
3.3.3.5 STBC Decoder的輸入端(加入Symbol Interchange)--------------------------------------------------------------68
3.3.3.6 STBC Decoder的輸出端(加入Symbol Interchange)--------------------------------------------------------------69
3.4 理論分析---------------------------------------------------------------------------------------------------------------------------70
3.4.1分析結果--------------------------------------------------------------------------------------------------------------------------70
3.4.2雜訊方差--------------------------------------------------------------------------------------------------------------------------73
3.4.3 SNR分析------------------------------------------------------------------------------------------------------------------------75
3.4.4 BER分析-------------------------------------------------------------------------------------------------------------------------76
3.5 理論結果圖-------------------------------------------------------------------------------------------------------------------------81
第四章 空時直接序列式隨機互補碼分碼多工系統於多路徑Rayleigh衰減通道------------------------------------85
4.1前言----------------------------------------------------------------------------------------------------------------------------------85
4.2系統架構圖-------------------------------------------------------------------------------------------------------------------------85
4.3系統分析----------------------------------------------------------------------------------------------------------------------------91
4.3.1系統各個部分分析-------------------------------------------------------------------------------------------------------------91
4.3.1.1 STBC Decoder--------------------------------------------------------------------------------------------------------------91
4.3.1.2隨機互補碼--------------------------------------------------------------------------------------------------------------------92
4.3.1.3 QPSK Modulator------------------------------------------------------------------------------------------------------------93
4.3.1.4傳送訊號分析-----------------------------------------------------------------------------------------------------------------95
4.3.1.5通道模型(Channel Model)------------------------------------------------------------------------------------------------96
4.3.1.6通訊系統的正規化(normalize)-------------------------------------------------------------------------------------------97
4.3.1.7隨機互補碼經過多路徑通道----------------------------------------------------------------------------------------------98
4.3.2訊號合成式接收端-------------------------------------------------------------------------------------------------------------99
4.3.2.1沒有多重路徑干擾下的接收訊號----------------------------------------------------------------------------------------99
4.3.2.2多重路徑干擾下的接收訊號--------------------------------------------------------------------------------------------100
4.3.2.3 QPSK Demodulator------------------------------------------------------------------------------------------------------102
4.3.2.4 STBC Decoder的輸入端------------------------------------------------------------------------------------------------104
4.3.2.5 STBC Decoder的輸出端------------------------------------------------------------------------------------------------114
4.3.3分天線式接收端---------------------------------------------------------------------------------------------------------------115
4.3.3.1 STBC Decoder的輸入端(加入Symbol Interchange)------------------------------------------------------------115
4.3.3.2 STBC Decoder的輸出端(加入Symbol Interchange)------------------------------------------------------------125
4.4理論分析--------------------------------------------------------------------------------------------------------------------------126
4.4.1分析結果------------------------------------------------------------------------------------------------------------------------126
4.4.2雜訊方差------------------------------------------------------------------------------------------------------------------------130
4.4.3 SNR分析------------------------------------------------------------------------------------------------------------------------131
4.4.4 BER分析------------------------------------------------------------------------------------------------------------------------134
4.5理論結果圖------------------------------------------------------------------------------------------------------------------------140
第五章 結論與未來展望------------------------------------------------------------------------------------------------------------145
附錄A雜訊的方差推導-------------------------------------------------------------------------------------------------------------147
附錄B證明任意兩個均值為零的複數隨機變數，其變異數乘機可拆成個別變異數相乘-----------------------148
附錄C任意複數的變異數與共軛複數的變異數相等-----------------------------------------------------------------------150
附錄D說明將訊號合成式接收器的平均錯誤率利用Q-function乘上動差生成函數去積分----------------------151
附錄E說明分天線式接收器(加入Symbol Interchange的部分)的平均錯誤率利用Q-function
乘上動差生成函數去積分---------------------------------------------------------------------------------------------------------153
附錄F證明利用互補碼特性簡化兩個接收器幹擾的部分-----------------------------------------------------------------154
附錄G由高斯近似法得到干擾方差---------------------------------------------------------------------------------------------171
參考文獻--------------------------------------------------------------------------------------------------------------------------------174
作者簡歷--------------------------------------------------------------------------------------------------------------------------------176

[1]. 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

[2]. 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

[3]. 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

[4]. 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

[5]. 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

[6]. 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

[7]. 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

[8]. 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

[9]. 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

[10]. 陳冠廷, “互補隨機碼MIMO-CDMA系統設計及Columnwise Complementary Codes之設計” 國立中山大學通訊工程研究所碩士論文, 2005

[11]. 展頻及分碼多工技術通訊理論：數位通訊技術叢書，陳曉華 著作，全華科技，出版日期：2004/03/29


[12]. 蔡宗奇, “互補碼MIMO-CDMA系統在相關多載波通道中性能分析,” 國立中 山大學通訊工程研究所碩士論文, 2005


[13]. J.Proakis, Digital Communications, 4rd ed. New York, NY:McGraw-Hill, 2001.

[14]. Efthymoglou, G.P.; Piboongungon, T.; Aalo, V.A.; “Performance of DS-CDMA receivers with MRC in nakagami-m fading channels with arbitrary fading parameters,”Vehicular Technology, IEEE Transactions on Volume 55, Issue 1, Jan. 2006 Page(s):104 - 114 Digital Object Identifier 10.1109/TVT.2005.861204

[15]. Shamain, P.K.; Milstein, L.B.; “Acquisition of direct sequence spread spectrum signals with correlated fading,”Selected Areas in Communications, IEEE Journal onVolume 19, Issue 12, Dec. 2001 Page(s):2406 - 2419 Digital Object Identifier 10.1109/49.974606

[16]. Feng-Tsun Chien, Chien-Hwa Hwang, C.-C. Jay Kuo, “Analysis of asynchronous long-code multicarrier CDMA systems with correlated fading”, IEEE Trans. Commun., vol. 53, no. 4, Apr. 2005.