多天線暨正交載波多工通訊系統預先編碼器之設計

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研究生：	吳秋萍 Ciou-Ping Wu
論文名稱：	多天線暨正交載波多工通訊系統預先編碼器之設計 Efficient Precoder Design for MIMO-OFDM Communication Systems
指導教授：	吳仁銘 Jen-Ming Wu
口試委員:
學位類別：	碩士 Master
系所名稱：	電機資訊學院 - 通訊工程研究所 Communications Engineering
論文出版年：	2007
畢業學年度：	95
語文別：	英文
論文頁數：	71
中文關鍵詞：	預先編碼器、多天線系統
外文關鍵詞：	precoder, MIMO, LUD
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多天線系統(Multi-input Multi-output，常簡稱 MIMO) 是利用發射端的多個天線各自獨立發送信號，同時在接收端用多個天線接收並恢復原訊息；其中可利用多天線來抑制通道衰減（channel fading）。當此系統所處之傳輸環境為相當穩定，即通道以緩慢的速率改變時；若系統為分時多工系統(TDD)，則可藉由通道的交互原理或經由回授通道，使傳送端得到有關於通道的資訊，包含通道之衰減特性或其統計特性。預先編碼器(precoder)是指資料由天線被傳送之前，先將欲傳送信號進行處理，以提高傳輸品質或資料吞吐量(throughput)；系統則根據通道特性設計出適當的預先編碼器。預先編碼器根據接收端所提供的通道矩陣來調整各天線傳送功率的分布，以及將此多天線所構成之通道分解為各自獨立的子通道，以降低接收端偵測之複雜度；另外，依據輸入信號之間的相關性，做適度的調整，以提高資料吞吐量及降低傳送錯誤率。
在分解通道部份，傳統的預先編碼器是利用奇異分解 (SVD)，將通道矩陣轉為對角矩陣；但是由於奇異分解需要龐大的運算，而加大系統的複雜度。為了降低系統的負擔，我們試著找出較低複雜度的演算法來完成通道分解的部份；在本論文中，則利用LU Decomposition (LUD) 將通道矩陣轉換為對角矩陣。經由模擬的結果顯示，我們所提出的演算法相較於傳統利用奇異分解 (SVD) 的方式，擁有更好的效能且較低的複雜度。

Communications over multiple-input multiple-output (MIMO) wireless channels have been a subject of intense research over the past several years. For a MIMO communication system, if the communication environment is relatively stationary, the channel information is possible via feedback or the reciprocal principle when time division duplex (TDD) is used. The precoder designed by the channel information can
process the transmitting symbol before transmission. It can used to adjust the power of the singles and match the channel matrix H and the input-shaping matrix Q. The communication system can increase the transmission reliability and decrease the detection complexity by the precoder.
The conventional precoder is designed by singular value decomposition (SVD) which is exploited to diagonalize the channel matrix H. However the computational complexity of SVD is large, it will increase the cost of the system. In order to reduce the cost of the system, we try to find a novel algorithm to diagonalize the channel matrix H. In this thesis, LU decomposition (LUD) is utilized to diagonalize the channel matrix H. The simulation result shows that our proposed algorithm has better performance and lower complexity than the conventional SVD.

中文目錄
中文摘要………………………………………………Ⅰ
致謝……………………………………………………Ⅱ
附錄：英文論文本……………………………..……..Ⅲ

Contents

Contents…………………………………………………………………………...i
List of Figures………………………………………………………………….iii
List of Tables………………………………………………………………….viii
Abstract…………………………………………………………………………...ix
Chapter 1 Introduction………………………………………………………..1
Chapter 2 MIMO and OFDM System…………………………………..3
2.1    MIMO system…………………………………………………………...3
2.2    OFDM Basics…….. …….. …………………………………………….4
    2.2.1 OFDM introduction…….. ………………………………………... ..4
    2.2.2 The Transmitter and Receiver of OFDM System ………………….. 5
2.3 MIMO-OFDM System…………………………………………………6
Chapter 3 MIMO Channel and Precoder Design……………...…….9
3.1    The MIMO Channel………………………………………..………….9
    3.1.1 The Channel Model of the SISO System…………………...……….9
    3.1.2 The Channel Model of the MIMO System…………………………11
3.2    The Basic Structure of the Transceiver…………………………….13
3.3 The Precoder Design…………………………………………………...16
   3.3.1 Optimal Precoder Input-shaping Matrix……………………………..17
   3.3.2 Optimal power allocation…………………………………………….19
   3.3.3 Optimal beam directions……………………………………………..21
Chapter 4 Precoder design algorithms…………………..……………..24
4.1 The Algorithm of SVD…………………………….……………........24
4.2    Proposed algorithm to match channel matrix ……………............34
4.3 The Performance of SVD and LUD……………………………….39
4.4    Power Allocation of Precoder ……………………………………...52
Chapter 5 Simulation Results……………………………………………..61
5.1    The comparison of computational complexity………...................61
5.2    Simulation Result…………………………………………………..….63
    5.2.1 The Simulation of The Beam Directions……………………………64
    5.2.2 The Precoder : the Beam Directions and the Power Allocation…….67
Chapter 6 Conclusion ……………………………………………………….70















List of Figures

Figure 2-1 : Single input single output (SISO) system ……………………………....3
Figure 2-2 : Multiple input multiple output (MIMO) system………..……………….3
Figure 2-3 : The single carrier system v.s. the OFDM system…………..……………5
Figure 2-4 : The transmitter and the receiver of the OFDM system……………….....6
Figure 2-5A: The MIMO-OFDM system with the spatial diversity structure ………..7
Figure 2-5B: The MIMO-OFDM system with the spatial multiplexing structure…….8
Figure 3-1 : The MIMO communication system……………………………………..11
Figure 3-2A : The MIMO system A with MIMO Detector…..………………………14
Figure 3-2B : The MIMO system B with precoder and de-precoder………………...15
Figure 3-3 : The basic block diagram of the transmission system including the           precoder………………………………………………………………………………16
Figure 3-4 : The basic blocks of the precoder………………………………………..17
Figure 3-5A : The encoder with spatial multiplexing structure………………….…..18
Figure 3-5B : The encoder with space-time coding…………………..………….…..18
Figure 3-6 : The block diagram including the precoder and the decoder ……….…..19
Figure 3-7 : The block diagram of the beam directions and the MIMO channel…....22
Figure 3-8 : The block diagram of channel decomposition………………...………..23
Figure 3-9 : The basic structure of the precoder……………………………………..23
Figure 4-1 : The diagram of revised system…………………………………………35
Figure 4-2 : The block diagram of the precoder and the De-precoder of the purposed system………………………………………………………………………………..36
Figure 4-3 : The block diagram of the precoder, the de-precoder , and the MIMO channel……….............................................................................................................39
Figure 4-4 : The equivalent channel ………………………………………………...40
Figure 4-5A : The MIMO channel using SVD ….…..………………………………40
Figure 4-5B : The equivalent channel using SVD……………..…………………….42
Figure 4-6 : The MIMO channel using LUD ….…..…………..…………………….43
Figure 4-7 : The equivalent channel using LUD…………………………………......44
Figure 4-8 : The precoder including SVD and the power allocation…..…………….54
Figure 4-9 : The equivalent block diagram with SVD…………………………….....55
Figure 4-10 : The precoder including LUD and the power allocation……………….57
Figure 4-11 : The equivalent block diagram with LUD…………..………………….58
Figure 5-1 : The computational complexity of SVD and LUD……….……………..62
Figure 5-2 : The block diagram of the simulation…………………………………...63
Figure 5-3 : The perform without the power allocation in the 2 x 2 MIMO system…65
Figure 5-4 : The perform without the power allocation in the 4 x 4 MIMO system…66
Figure 5-5 : The perform without the power allocation in the 6 x 6 MIMO system…66
Figure 5-6 : The perform with the power allocation in the 2 x 2 MIMO system…….67
Figure 5-7 : The perform with the power allocation in the 4 x 4 MIMO system…….68
Figure 5-8 : The perform with the power allocation in the 6 x 6 MIMO system…….68







List of Tables

Table 4-1 : The number of operation for Householder transformation………………30
Table 5-1 : The computational complexity of SVD and LUD………....…………….62

                                

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