在多重路徑衰褪通道下編碼調變系統之反覆式解碼法

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研究生：	黃莨展 Lian-Jaan Huang
論文名稱：	在多重路徑衰褪通道下編碼調變系統之反覆式解碼法 Iterative Decoding for Coded Modulation Systems over Multipath Fading Channels
指導教授：	呂忠津 Chung-Chin Lu
口試委員:
學位類別：	碩士 Master
系所名稱：	電機資訊學院 - 電機工程學系 Department of Electrical Engineering
論文出版年：	2004
畢業學年度：	92
語文別：	英文
論文頁數：	48
中文關鍵詞：	反覆式解碼、多重路徑衰褪通道、等化器、因子圖
外文關鍵詞：	Iterative decoding, Multipath fading channels, Equalization, Factor graph
相關次數：	點閱：3 下載：0
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無線通訊是現在及未來的主要通訊技術，在無線通訊中，惡劣的傳輸環境使得傳送訊號被嚴重破壞，造成接收端無法解碼解調變時候的困難，而多重路徑干擾是最常見的現象。由於傳輸環境中地形和周遭物的影響，反射路徑及落後的路徑會夾雜在一起，加上傳輸速度越來越快，解決多重路徑干擾的問題就成了在無線通訊環境中傳輸的一個主要課題。
許多傳統解決多重路徑干擾的方法已經被提出。在此，我們將通道的記憶考慮進來，提出一種反覆的解碼方式(iterative decoding)來解決多重路徑干擾的問題。一個經過旋積編碼(convolutional coded)的訊號，傳送在多重路徑衰褪通道下，可以視為一個被兩次旋積編碼的訊號，一次是兩元的旋積編碼，另一次是實數旋積編碼。如同渦輪碼(turbo code)的解碼方式，引入因子圖(factor graph)及反覆解碼的觀念，即可得到我們的反覆式解碼法。另外，效能的評估也是我們所在意的，由於在多傳路徑衰褪通道下的傳輸，可以想成是一個延遲多樣性(delay diversity scheme)的傳輸，因此我們類比此傳輸方式的性能分析法，探討多重路徑衰褪通道下的傳輸性能。
從模擬的結果來看，跟傳統的解決多重路徑干擾方法比較，我們的方法提供了很大的效能改善。在穩定多重路徑干擾環境中(static ISI channel)，經由幾次的反覆解碼，多重路徑干擾的效應可以完全地被移除掉。在多重路徑衰褪通道下(multipath fading channel)，雖然多重路徑干擾無法完全消除，但卻引進了些許的多樣化增益(diversity gain)。值得一提的是，即使在有頻道估測錯誤下，此方法依然表現的比傳統的解碼方法好。在緩慢衰褪的通道中(slow fading)，此方法依舊能提供了時序上的多樣性增益(time diversity gain)。
頻道估測的不準確以及緩慢的衰褪通道環境是實際傳輸中主要的問題，此解碼法提供了一個解決這些問題的方法，性能表現也相當不錯。

An iterative decoding scheme for coded modulation systems over multipath fading channels is proposed to overcome the detrimental effects of intersymbol interference caused by the multipath channels. At the receiver, equalization and decoding process are jointly combined to apply the iterative decoding. The iterative decoding process is run over a factor graph, a cascade of the factor graph of a binary convolutional code and the graph a real-valued
convolutional code (corresponding to the multipath channel). As in turbo decoding, the extrinsic soft information is extracted from the symbol detector and from the decoder at each decoding step and is used in the next decoding step. Performance analysis for multipath fast Rayleigh fading channel is provided. Simulation results are presented both for static multipath channel (ISI channel) and multipath fading channels. For the ISI channel, the
intersymbol interference effect is completely overcome through the iterative decoding when SNR is high enough. For the multipath fading channel, although the ISI is not completely removed, the reduction of the intersymbol interference is remarkable and satisfactory for many practical applications.

Contents
Abstract i
Contents i
List of Figures iii

Introduction 1

Factor Graphs and Message Passing 3

1 A brief introduction to factor  graphs . . . . . . . . . . . . . . . . . . . . . . 3

2 Factor graphs for decoding problems with code trellis . . . . . . . . . . . . . 6

3 Sum-product algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4 Message passing schedules . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Iterative Decoding 13

1 Global function of the system factor graph . . . . . . . . . . . . . . . . . . . 13

2 Iterative decoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Performance Analysis 22

1 The delay diversity scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
i

2 Performance analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.1 The system model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2 Properties from linear algebra . . . . . . . . . . . . . . . . . . . . . . 24

2.3 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Simulation Results 28

1 ISI channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2 Multipath Rayleigh fading channels . . . . . . . . . . . . . . . . . . . . . . . 32

2.1 Perfect channel estimation . . . . . . . . . . . . . . . . . . . . . . . . 32

2.2 Decoding with channel estimation errors . . . . . . . . . . . . . . . . 43

Conclusion 46

Bibliography 47

ii

List of Figures

1 The tap delay line channel model. . . . . . . . . . . . . . . . . . . . . . . . . 2

1 A simple example of factor graph. . . . . . . . . . . . . . . . . . . . . . . . . 3

2 An example of a (2, 1) binary convolutional encoder. . . . . . . . . . . . . . . 5

3 The trellis of the convolutional encoder shown in Fig. 2.2. . . . . . . . . . . 5

4 The factor graph for the trellis of the (2, 1) binary convolutional code. . . . . 6

5 The factor graph for the decoding problem. . . . . . . . . . . . . . . . . . . . 7

1 The factor graph of the system model. . . . . . . . . . . . . . . . . . . . . . 14

2 Principle of the iterative decoding. . . . . . . . . . . . . . . . . . . . . . . . 17

1 The block diagram of a delay diversity transmitter. . . . . . . . . . . . . . . 23

1 Performance for interleavers of different size. . . . . . . . . . . . . . . . . . . 29

2 Performance evaluation for static multipath channel. . . . . . . . . . . . . . 31

3 Performance evaluation over 5-path fading channel with ECL=2 and  = 0.99. 34

4 Performance evaluation over 5-path fading channel with ECL=2 and  = 0.01. 35

5 Performance evaluation over 5-path fading channel with ECL=5 and  = 0.99. 36

6 Performance evaluation over 5-path fading channel with ECL=5 and  = 0.01. 37

7 Performance evaluation over 5-path fading channel with  = 0.99 and  = 0.01. 38
iii

8 Performance evaluation over 5-path fading channel for ECL=2 and ECL=5
with  = 0.01. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

9 Performance evaluation over 2-path fading channel with ECL=5 and  = 0.99. 40

10 Performance evaluation over 2-path fading channel with ECL=5 and  = 0.01. 41

11 Performance comparison for multipath fading channels with  = 0.01. . . . . 42

12 Performance evaluation for 5-path fading channel with channel estimation
errors for  = 0.01. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

13 Performance comparison for 5-path fading channel with channel estimation
errors for  = 0.01. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
iv

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