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研究生： 賴冠綸
Lai, Guan-Lun
論文名稱： 互補碼跳碼多工系統之性能分析
Performance Analysis of Code Hopping Multiple Access Based on Complementary Code System
指導教授： 陳曉華
Chen, Hsiao-Hwa
學位類別： 碩士
Master
系所名稱： 工學院 - 工程科學系
Department of Engineering Science
論文出版年： 2019
畢業學年度： 107
語文別： 英文
論文頁數： 195
中文關鍵詞： 跳碼多址 、互補碼 、漢明相關 、碰撞概率 、卷積碼(摺積碼)
外文關鍵詞： Code hopping multiple access (CHMA), Complementary codes, Hamming correlation (HC), Collision probability, Convolutional codes
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    • 有別於傳統的碼分多址(CDMA)系統，跳碼多址(CHMA)是一種提供更高用戶容量的多址技術。我們搜尋了近十五年來關於跳碼多址的論文。在現有的CHMA系統方案中，在假設既不存在多徑干擾(MPI)也不存在多址干擾(MAI)的情況下，僅在同步信道中分析用戶信號之間的正交性。此外，任何用戶的展頻碼跳躍模式在其他論文中都是隨機的。為了克服現有CHMA方案中的MPI和MAI問題，首先我們提出利用互補碼(CC)在CHMA系統中擴頻，這裡稱為CC-CHMA。我們不僅考慮CC-CHMA系統中的單路徑而且考慮多徑方案。有別於其他的論文在高斯白雜訊通道分析，我們假設BPSK調製用於瑞利衰落信道上的發送編碼符號並分析其誤碼率(BER)性能。此外，還考慮了同步和異步信道。第二，我們提出了分配給活動用戶的周期性跳碼模式。之後藉由平均漢明相關(HC)來分析給定週期性跳碼模式的碼衝突概率。本文完整地推導了下行鏈路和上行鏈路CC-CHMA中誤碼率的解析公式。最後，我們還分析了卷積編碼環境中CC-CHMA系統的BER性能。仿真解析結果表示，在不同的操作場景下，具有信道編碼的CC-CHMA可以提供比CDMA系統高得多的用戶容量。特別是具有信道編碼的CC-CHMA在異步信道中具有優勢。

    Different from the traditional code division multiple access (CDMA) system, code hopping multiple access (CHMA) system is a kind of multiple access technique to offer higher user capacity. We survey papers about code hopping in recent fifteen years. In existing CHMA system schemes, orthogonality among user signals is only analyzed in synchronous channels under an assumption that neither multipath interference (MPI) nor multiple-access interference (MAI) exists. Additionally, code hopping pattern for any user is assumed random in other papers. In order to overcome MI and MAI problems in existing CHMA schemes, we first propose to utilize complementary codes (CCs) to spread spectrum in CHMA systems, which is called CC-CHMA here. We consider not only the single path but multipath scheme in CC-CHMA system. In addition, both synchronous and asynchronous channels are considered. Distinguish from the performance analysis in AWGN channel in other papers, we assume that BPSK modulation is used for transmitted coded symbols over a Rayleigh fading channel and analyze its bit error rate (BER) performance. Second, we propose the periodic code hopping pattern assigned to active users. Afterwards, average hamming correlation (HC) is introduced to analyze the code collision probabilities for given periodic code hopping patterns. Analytical formulae of bit error rate (BER) in both downlink and uplink CC-CHMA are completely derived in the thesis. Finally, we also analyze the BER performance for CC-CHMA system in convolutional coding environments with rayleigh fading. Simulation results show that the CC-CHMA with channel coding can provide much higher user capacity than CDMA systems in varying operational scenarios. Especially, CC-CHMA with channel coding has advantages in asynchronous channels.

    摘要vii Abstract ix Acknowledgements xi Table of Contents xiii List of Figures xvii List of Tables xxvii List of Abbreviations xxix List of Symbols xxxi Dedication xxxv 1 Introduction 1 1.1 Background and Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 A Brief Survey on Related Works . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2 Fundamentals of Code Hopping Multiple Access Systems 13 2.1 Complementary Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.1 Properties of Complementary Codes . . . . . . . . . . . . . . . . . . 14 2.1.2 Structure of Complementary Codes . . . . . . . . . . . . . . . . . . 17 2.2 Complementary-Coded Code Hopping Multiple Access (CC-CHMA) Systems 20 2.2.1 Overview of CHMA Based on Complementary Code . . . . . . . . . 20 2.2.2 Multiuser and Multipath Effect of CC-CHMA [10] . . . . . . . . . . 21 3 Performance Analysis of Synchronous CC-CHMA System 29 3.1 System Model of Complementary-Coded CHMA . . . . . . . . . . . . . . . 30 3.1.1 Definitions and Assumptions of CH Sequences . . . . . . . . . . . . 30 3.1.2 Transmitter and Receiver Models of CC-CHMA . . . . . . . . . . . 32 3.1.3 Channel Model of CC-CHMA . . . . . . . . . . . . . . . . . . . . . 35 3.2 Collision Probabilities of Synchronous CC-CHMA . . . . . . . . . . . . . . 36 3.2.1 Collision Probabilities in Single Path Synchronous Channels . . . . . 37 3.2.2 Collision Probabilities in Multipath Synchronous Channels . . . . . . 40 3.3 Bit Error Rate of Synchronous CC-CHMA . . . . . . . . . . . . . . . . . . . 47 3.3.1 Bit Error Rate in Synchronous Single Path Channels . . . . . . . . . 48 3.3.1.1 Uncoded Bit Error Rate in Synchronous Single Path Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.3.1.2 Bit Error Rate in Synchronous Single Path Channels with Convolutional Coding . . . . . . . . . . . . . . . . . . . . 54 3.3.2 Bit Error Rate in Synchronous Multipath Channels . . . . . . . . . . 61 3.3.2.1 Uncoded Bit Error Rate in Synchronous Multipath Channels 61 3.3.2.2 Bit Error Rate in Synchronous Multipath Channels with Convolutional Coding . . . . . . . . . . . . . . . . . . . . 69 4 Performance Analysis of Asynchronous CC-CHMA System 77 4.1 Collision Probabilities of Asynchronous CC-CHMA . . . . . . . . . . . . . 77 4.1.1 Collision Probabilities in Single Path Asynchronous Channels . . . . 78 4.1.2 Collision Probabilities in Multipath Asynchronous Channels . . . . . 82 4.2 Bit Error Rate of Asynchronous CC-CHMA . . . . . . . . . . . . . . . . . . 89 4.2.1 Bit Error Rate in Asynchronous Single Path Channels . . . . . . . . 89 4.2.1.1 Uncoded Bit Error Rate in Asynchronous Single Path Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.2.1.2 Bit Error Rate in Asynchronous Single Path Channels with Convolutional Coding . . . . . . . . . . . . . . . . . . . . 95 4.2.2 Bit Error Rate in Asynchronous Multipath Channels . . . . . . . . . 101 4.2.2.1 Uncoded Bit Error Rate in Asynchronous Multipath Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 4.2.2.2 Bit Error Rate in Asynchronous Multipath Channels with Convolutional Coding . . . . . . . . . . . . . . . . . . . . 109 5 Performance Simulations and Comparisons with Analytical Results 117 5.1 Uncoded Performance Simulations with Analytical Results . . . . . . . . . . 117 5.2 Coded Performance Simulations with Analytical Results of Convolutional Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 6 Conclusions and Future Works 147 6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 6.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 References 151 A Hamming Correlation Functions 157 A.1 Hamming Correlation functions of CH Sequences . . . . . . . . . . . . . . . 157 A.1.1 Definition of Hamming Correlation functions of CH Sequences . . . 158 A.1.2 Offset Property of HC functions of CH Sequences . . . . . . . . . . 161 B Overview of Convolutional codes 165 B.1 Encoding of Convolutional Codes . . . . . . . . . . . . . . . . . . . . . . . 165 B.2 Structural Property of Convolutional Codes . . . . . . . . . . . . . . . . . . 168 B.3 Viterbi Algorithm [39] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 B.4 Performance Bounds for Convolutional Codes . . . . . . . . . . . . . . . . . 176 C Derivation of Equations 179 C.1 Derivation of Equation in (3.33) . . . . . . . . . . . . . . . . . . . . . . . . 179 C.2 Derivation of Equation in (3.36) . . . . . . . . . . . . . . . . . . . . . . . . 180 C.3 Derivation of Equation in (3.81) . . . . . . . . . . . . . . . . . . . . . . . . 182 C.4 Derivation of Equation in (3.84) . . . . . . . . . . . . . . . . . . . . . . . . 183 C.5 Derivation of Equation in (4.32) . . . . . . . . . . . . . . . . . . . . . . . . 185 C.6 Derivation of Equation in (4.35) . . . . . . . . . . . . . . . . . . . . . . . . 186 C.7 Derivation of Equation in (4.82) . . . . . . . . . . . . . . . . . . . . . . . . 188 C.8 Derivation of Equation in (4.85) . . . . . . . . . . . . . . . . . . . . . . . . 191 D List of Complementary Codes 193

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