
系統識別號 
U00020401200617063300 
中文論文名稱

使用任意長方QAM調變之正交時空區塊碼於雷利衰退通道的精確錯誤率分析 
英文論文名稱

Exact Error Probability for Orthogonal SpaceTime Block Coded MIMO Systems Using Arbitrary Rectangular QAM Transmission over Rayleigh Fading Channels 
校院名稱 
淡江大學 
系所名稱(中) 
電機工程學系博士班 
系所名稱(英) 
Department of Electrical Engineering 
學年度 
94 
學期 
1 
出版年 
95 
研究生中文姓名 
劉鴻裕 
研究生英文姓名 
HongYu Liu 
學號 
889350053 
學位類別 
博士 
語文別 
英文 
口試日期 
20051202 
論文頁數 
70頁 
口試委員 
指導教授嚴雨田 委員陳金蓮 委員貝蘇章 委員丘建青 委員李揚漢

中文關鍵字 
正交時空區塊碼
多輸入多輸出
雷利衰退

英文關鍵字 
OSTBC
MIMO
Rayleigh fading
QAM

學科別分類 

中文摘要 
本篇論文中，我們提出”先平均法”推導正交時空區塊碼使用任意長方QAM於雷利衰退通道的精確錯誤率，並假設叢集子通道間為獨立的，而其子通道的功率可為均相異、均相同以及前兩者之混合等三種情況。再者，常見之正方QAM、一維PAM與BPSK調變方法均是本篇所考慮任意長方QAM的特例。特別要強調者，乃所有推導結果的最終公式均由最基本之數學式組成，無特殊高階的超越函數或尚未求出解的積分式，並且在討論混合均相異、均相同功率之雷利衰退通道時，我們亦說明如何將推導結果延伸至Nakagamim衰退通道。
我們推導的方法有別於文獻中所提供者，乃以估計誤差機率密度函數為基礎之分析法成功的得到精確錯誤率公式，並且在證明的過程中，得到多個新發現的性質與恆等式。我們亦將理論值模擬與蒙地卡羅電腦模擬比較，其結果顯示兩者非常契合。另外，從模擬曲線也得知均相同功率通道比均相異功率通道的錯誤率還低。又正方形QAM較長方形QAM有更佳之績效表現。另外，並深入討論一般化正交時空區塊碼的錯誤率特性，因為目前文獻中已提出或討論正交時空區塊碼的精確錯誤率分析，只限於一般化正交時空區塊碼的特例。我們發現，一般化正交時空區塊碼對於不同的字符，可能造成不等效錯誤率，這在已知的文獻中並未曾被提及與證明。雖然在公式推導的過程中，假設通道間為獨立的，我們亦說明如何將我們的方法應用於有關聯性的通道中。

英文摘要 
In this work, a preaveraging method is proposed for deriving theoretical symbol error probability (SEP) expressions for orthogonal spacetime block code (OSTBC) diversity systems employing arbitrary rectangular MQAM transmission over flat Rayleigh fading channels. Independent fading between diversity channels are assumed for simplicity as the technique of channel decorrelation has been proposed in the literature. Channel average powers may be distinctive, identical, or mixed with both. The rectangular MQAM results are extended to square MQAM, MPAM, and binary antipodal signaling. All derived expressions are in elementary forms without complicated high order transcendental functions and/or unevaluated integrals and hence are strictly exact and can be readily simulated by the computer with good accuracy. We delve into the error probability performance by proposing a new derivation method, from which many new equations and properties are shown and proved. Moreover, we show that mixed Rayleigh fading results can be readily extended to various Nakagamim fading results. We use a four transmit antenna system with a halfrate OSTBC for 16QAM signaling as the example to demonstrate that our theoretical results are in excellent agreements with the Monte Carlo simulated results. From simulation curves, we show that, under the independent channel fading condition, channels with identical powers have better error rate performance than channels with distinctive powers. Moreover, we discuss the performance of OSTBC with generalized complex orthogonal design (GCOD) in a rather general scope, which has not been explored in depth in the literature. Thus far, the SEP expressions for OSTBC found in the literature are only restricted to complex orthogonal design (COD) or some special GCOD cases. An important discovery is that OSTBC can produce different SEP performances for different information symbols. Although our derivation is presented based on the assumption of independent fading channels, we also provide an outline for the derivation for correlative fading channels. 
論文目次 
CONTENTS
CHINESE ABSTRACT I
ENGLISH ABSTRACT III
ACKNOWLEDGEMENTS V
CONTENTS VI
LIST OF FIGURES VIII
1 INTRODUCTION 1
2 THE OSTBC COMMUNICATION SYSTEM MODEL 5
2.1 The OSTBC Design……………………………………………5
2.2 Channel Model and Decoding Algorithm…………………6
3 SEP CALCULATION FOR ARBITRARY RECTANGULAR MQAM SIGNALS 10
3.1 Symbol Estimate Error PDF………………………………10
3.2 Channels with Distinctive Powers………………………12
3.3 Channels with Identical Power ………………………19
3.4 Channels Mixed with Distinctive and Identical Powers…………………………………………………………………24
4 SIMULATION RESULTS 29
5 CONCLUSIONS 40
APPENDIX A SYMBOL ESTIMATE ERROR PDF 42
APPENDIX B PROOF OF DECISION CORRECT PROBABILITIES FOR CHANNELS WITH DISTINCTIVE POWERS 44
APPENDIX C PROOF OF (B.4) 47
APPENDIX D PROOF OF (3.10) 49
APPENDIX E COMPARISON OF THE SQUARE QAM RESULT WITH THE ALOUINI/GOLDSMITH RESULT 53
APPENDIX F PROOF OF DECISION CORRECT PROBABILITIES FOR CHANNELS WITH IDENTICAL POWERS 55
APPENDIX G PROOF OF (3.36) 64
REFERENCES 66
LIST OF FIGURES
Figure 3.1 Illustrations for calculating correct probabilities in a 16QAM constellation, (a) integration region for , (b) integration region for , (c) integration region for ……………………………………………………….…………………………….15
Figure 3.2 vs. for 16QAM signaling in four transmitone receive antenna system with the rate 1/2 Tarokh code (eq. (38) in [8]) over Rayleigh fading channels with distinctive powers, , , , ……...….19
Figure 4.1 vs. for square 16QAM signaling in four transmitone receive antenna system with the rate 1/2 Tarokh code (eq. (38) in [8]) code over Rayleigh fading channels with distinctive powers. Curve (1) ; Curve (2) ; Curve (3)
…………………………………………………………………………………………30
Figure 4.2 vs. for 16QAM signaling in a four transmitone receive antenna system with the rate 1/2 Tarokh code (eq. (38) in [8]) over Rayleigh fading channels with identical powers. Various combinations……….…………………31
Figure 4.3 vs. for 256QAM signaling in a four transmitone receive antenna system with the rate 1/2 Tarokh code (eq. (38) in [8]) over Rayleigh fading channels with identical powers. Various combinations…………………..….…32
Figure 4.4 Comparison between theoretical SEP performance and Monte Carlo simulated performance for square 16QAM signaling in the same system as Figure 4.2…………………………………………………………………………….………..33
Figure 4.5 Comparison for square 16QAM signaling over Rayleigh fading channels with identical powers for two cases of four transmitone receive antenna systems. Curve (1) rate 1/2 Tarokh code (eq. (38) in [8]); Curve (2) rate 3/4 Tarokh code (eq. (40) in [8])……………………………………………………………………………………..35
Figure 4.6 Performance of rate 7/11 OSTBC/GCOD using five transmitone receive antenna system for square 16QAM signaling over Rayleigh fading channels with distinctive powers. ……………………..…37
Figure 4.7 Effect of channel correlation on SEP of the rate 1/2 GCOD code given by eq. (38) in [8] for square 16QAM signaling over correlative Rayleigh fading channels with distinctive powers for four transmitone receive antenna system. ……………………………………………………..39

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