利用因子圖進行綜合反覆式檢測與估計於多重路徑衰退通道下之通訊

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研究生：	劉柏嶔 Pai-Chin Liu
論文名稱：	利用因子圖進行綜合反覆式檢測與估計於多重路徑衰退通道下之通訊 Joint Detection and Estimation over Multipath Fading Channels with Factor Graphs
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：	2005
畢業學年度：	93
語文別：	英文
論文頁數：	91
中文關鍵詞：	反覆式、因子圖、綜合檢測與估計
外文關鍵詞：	iterative, factor graph, joint detection and estimation
相關次數：	點閱：2 下載：0
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無線通訊在現今生活中是越來越重要，在無線通訊下，傳輸的訊號會遭受到不好的通道效應，使得訊號在接收端難以解碼。其中影響最大的是通道的衰退以及多重路徑干擾。多種的通道等化方法被利用來等化不好的通道效應，如最大可能序列估測（maximam likelihood sequence estimation）。在1993年，有一個重要的解碼方式被提出，也就是渦輪解碼法，也可以稱做是反覆式解碼法。此種解碼的方法可以運用在通道的等化上面。在資料傳輸到通道之前，我們可以先將資料編碼成迴旋碼（convolutional code），再將編碼完成的訊號做交叉存取，之後才傳輸到通道中。而多重衰退路徑通道可以把它視做為一種複數係數的迴旋碼，如此即可作反覆式解碼。
另外我們還討論另一種模組，是利用時空碼（space-time code）的方式傳輸資料。時空碼是一種多進多出的系統，傳送端與接收端都各有數目大於一的天線進行傳送與接收。在此假設時空碼是遭受到雷式衰退效應，而雷式衰退的量是一個高斯-馬可夫（Gaussian-Markov）的序列。而傳送端系統的設計如同第一段所描述，在時空碼之前，先將資料編碼成迴旋碼，再經過交叉存取，之後這份編碼才再經過時空碼的編碼。
在通道的估測方面，我們利用卡氏濾波器（Kalman filter）進行雷式衰退係數的估測。上述的模組我們都可以利用因子圖（factor graph）來表示之。利用因子圖，我們可以在多重衰退路徑（或時空碼）、迴旋碼以及卡氏濾波器間，進行三向的反覆式檢測與估計。在多重衰退路徑下，假設是同步狀態，則不需有事前的估測（training）。在多進多出的系統下，則必須要有已知的訊號（preamble）來輔助通道的估測。
此種反覆式檢測與估計方式，經由電腦模擬可以得知是可行且結果良好。因此我們可以歸納出，利用因子圖可以正確地進行通道的檢測與估計，來達成通道等化的效果。

In order to combat the channel selectivity and fading, we propose the iterative method to
execute the joint detection and estimation. Factor graph is our tool to model the whole sys-
tem in the thesis. Simulation results will show that joint detection and estimation performs
well in both SISO system and MIMO system.

Contents
Abstract i
Contents i
List of Figures v
List of Tables viii
1 Introduction 1
2 Factor Graph and Sum-Product Algorithm 4
2.1 Introduction of Factor Graph . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Sum-Product Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Message Passing Schedules . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.1 Generalized Forward/Backward(GFB) Schedule on a Tree . . . . . . 7
2.4 Factor Graphs of the Subsystem Models . . . . . . . . . . . . . . . . . . . . 8
2.4.1 Convolutional Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
i
2.4.2 Interleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4.3 Multipath Fading Channel: Tapped-Delay-Line Model . . . . . . . . 11
2.4.4 Space-Time Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.5 Gaussian-Markov Model . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4.6 Rayleigh Fading Channel . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.7 Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5 Message Passing of the System Models . . . . . . . . . . . . . . . . . . . . . 15
2.5.1 Code Trellis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5.2 Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3 Joint Detection and Estimation 19
3.1 Global Function of SISO system . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.1 Extrinsic Information of SISO System . . . . . . . . . . . . . . . . . . 20
3.1.2 Message Passing in SISO System . . . . . . . . . . . . . . . . . . . . 23
3.2 Kalman Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.1 Kalman Filter Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.2 Error-Covariance Matrix . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.3 Fixed-interval Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3 Scheduling of Iterative Decoding . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.1 First Scheduling Algorithm . . . . . . . . . . . . . . . . . . . . . . . 31
ii
3.3.2 Second Scheduling Algorithm . . . . . . . . . . . . . . . . . . . . . . 32
3.3.3 Third Scheduling Algorithm . . . . . . . . . . . . . . . . . . . . . . . 32
3.4 Global Function of MIMO System . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4.1 Extrinsic Information of MIMO system . . . . . . . . . . . . . . . . . 34
3.4.2 Message Passing in MIMO System . . . . . . . . . . . . . . . . . . . 36
4 Performance Analysis 37
4.1 Performance Analysis of Serially Concatenated Convolutional Code . . . . . 37
4.2 Performance Analysis of Space-Time Code . . . . . . . . . . . . . . . . . . . 40
5 Simulation Results 42
5.1 Multipath Fading Channel of SISO System . . . . . . . . . . . . . . . . . . . 43
5.2 Frequency-Nonselective Fading Channel of MIMO System . . . . . . . . . . . 55
5.2.1 Di□erent Transmit Antennas . . . . . . . . . . . . . . . . . . . . . . . 55
5.2.2 Di□erent Receive Antennas . . . . . . . . . . . . . . . . . . . . . . . . 60
5.2.3 Performance of Z4 Convolutional Code . . . . . . . . . . . . . . . . . 61
5.2.4 Performance of Joint Detection and Estimation . . . . . . . . . . . . 63
6 Conclusion 66
A Derivation of Gaussian-Markov model 68
iii
B Convergence of Kalman Filter 71
Bibliography 80
iv
List of Figures
2.1 Factor graph of global function g(x) . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 A (2; 1; 2) binary convolutional encoder . . . . . . . . . . . . . . . . . . . . . 9
2.3 Trellis of (2; 1; 2) binary convolutional code . . . . . . . . . . . . . . . . . . . 9
2.4 Factor graph of (2; 1; 2) binary convolutional code . . . . . . . . . . . . . . . 10
2.5 Factor graph of space-time code . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.6 Factor graph of Gaussian-Markov Model . . . . . . . . . . . . . . . . . . . . 13
2.7 Factor graph of Rayleigh fading channel . . . . . . . . . . . . . . . . . . . . 14
2.8 Factor graph of Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1 Factor Graph of the System . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 First Scheduling Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3 Second Scheduling Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4 Third Scheduling Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.5 Block diagram of a MIMO system . . . . . . . . . . . . . . . . . . . . . . . . 33
5.1 Slow fading and fast fading 2-path channel of perfect estimation . . . . . . . 44
v
5.2 Performance of di□erent ECL under independent fading condition . . . . . . 45
5.3 Performance of di□erent schedules . . . . . . . . . . . . . . . . . . . . . . . . 46
5.4 Comparison of perfect estimation and Kalman ‾ltering estimation . . . . . . 47
5.5 Di□erent forgetting factors under 2-path Kalman ‾ltering estimation . . . . . 48
5.6 Di□erent forgetting factors under 2-path Kalman ‾ltering estimation . . . . . 49
5.7 Di□erent forgetting factors under 3-path Kalman ‾ltering estimation . . . . . 50
5.8 Di□erent forgetting factors under 3-path Kalman ‾ltering estimation . . . . . 51
5.9 Di□erent forgetting factors under 4-path Kalman ‾ltering estimation . . . . . 52
5.10 Di□erent number of paths at □ = 0:99 . . . . . . . . . . . . . . . . . . . . . . 53
5.11 Di□erent number of paths at □ = 0:99 . . . . . . . . . . . . . . . . . . . . . . 54
5.12 Performance of di□erent iterations . . . . . . . . . . . . . . . . . . . . . . . . 56
5.13 Performance of di□erent fading conditions . . . . . . . . . . . . . . . . . . . 57
5.14 Performance of di□erent transmit antennas while ECL = 2 . . . . . . . . . . 58
5.15 Performance of di□erent transmit antennas while ECL = 5 . . . . . . . . . . 59
5.16 Performance of di□erent receive antennas . . . . . . . . . . . . . . . . . . . . 60
5.17 Performance of ECL=2 Z4 Convolutional Code . . . . . . . . . . . . . . . . 61
5.18 Performance of ECL=5 Z4 Convolutional Code . . . . . . . . . . . . . . . . 62
5.19 Partition of training symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.20 Performance of ECL=2 convolutional code . . . . . . . . . . . . . . . . . . . 64
vi
5.21 Performance of ECL=5 convolutional code . . . . . . . . . . . . . . . . . . . 65
B.1 Estimated error at SNR=0dB with training symbols. . . . . . . . . . . . . . 72
B.2 Estimated error at SNR=5dB with training symbols. . . . . . . . . . . . . . 73
B.3 Estimated error at SNR=10dB with training symbols. . . . . . . . . . . . . . 74
B.4 Estimated error at SNR=0dB after training with 1024 bits and QPSK mod-
ulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
B.5 Estimated error at SNR=5dB after training with 1024 bits and QPSK mod-
ulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
B.6 Estimated error at SNR=10dB after training with 1024 bits and QPSK mod-
ulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
B.7 Estimated error of di□erent training length at SNR=5dB with 1024 bits and
QPSK modulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
B.8 Estimated error of di□erent insert parts at SNR=5dB. . . . . . . . . . . . . . 79
vii
List of Tables
A.1 Mobile velocity = 0.5m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
A.2 Mobile velocity = 1.0m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
A.3 Mobile velocity = 15.0m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
A.4 Mobile velocity = 30.0m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
viii

                                

Bibliography
[1] J. G. Proakis, Digital Communications. McGraw-Hill, fourth ed., 2001.
[2] C. Berrou, A. Glavieux, and P. Thitimajshima, \Near shannon limit error-correcting
coding and decoding: Turbo-codes," IEEE Int. Conf. Communications, pp. 1064{1070,
May 1993.
[3] L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, \Optimal decoding of linear codes for
minimizing symbol error rate," IEEE Trans. Inform. Theory, vol. 20, pp. 284{287, Mar.
1974.
[4] C. Douillard, M. J□ez□equel, and C. Berrou, \Iterative correction of intersymbol interfer-
ence: Turbo-equalization," European Trans. Telecomm., vol. 6, pp. 507{511, Sep./Oct.
1995.
[5] V. Tarokh, N. Seshadri, and A. R. Calderbank, \Space-time codes for high data rate
wireless communication performance criterion and code construction," IEEE Trans.
Inform. Theory, vol. 44, pp. 744{765, Mar. 1998.
[6] S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollara, \Serially concatenation of inter-
leaved codes: Performance analysis, design, and iterative decoding," IEEE Transaction
on Information Theory, vol. 44, pp. 909{926, May 1998.
[7] R. E. Kalman, \A new approach to linear ‾ltering and prediction problems," Journal
of Basic Eng., vol. 82, pp. 35{45, March 1960.
80
[8] H. Stark and J. W.Woods, Probability and Random Processes with Application to Signal
Processing. Prentice Hall, third ed., 2002.
[9] G. N. Saridis, Stochastic Processes, Estimation, and Control: The Entropy Approach.
John Wiley and Sons, ‾rst ed., 1995.
[10] H. Runch, F. Tung, and C. Strielbel, \Maximum likelihood estimates of linear dynamic
systems," AIAA Journal, vol. 3, p. 1445, 1965.
[11] F. R. Kschischang, B. J. Frey, and H.-A. Loeliger, \Factor graph and the sum-product
algorithm," IEEE Trans. Inform. Theory, vol. 47, pp. 498{519, Feb. 2001.
[12] C.-L. Hsiao and C.-C. Lu, \An optimality test of Zp-convolutional coded CPFSK for
communications over Rayleigh fading channels,"
81

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