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Iterative estimation and detection for single carrier block transmission [Elektronische Ressource] / von Markus Alexander Dangl

159 pages
Iterative Estimation and Detectionfor Single Carrier Block TransmissionDISSERTATIONzur Erlangung des akademischen Grades einesDOKTOR-INGENIEURS(DR.-ING.)der Fakulta¨t fu¨r Ingenieurwissenschaftenund Informatik der Universita¨t UlmvonMARKUS ALEXANDER DANGLAUS HEIDENHEIMGutachter: Prof. Dr.-Ing. Ju¨rgen LindnerProf. Dr.-Ing. habil. Volker Ku¨hnAmtierenderDekan: Prof. Dr. rer. nat. Helmuth PartschUlm, 16. November 2007AcknowledgmentsThis thesis summarizes the results of the research that I conducted at the Institute ofInformation Technology, University of Ulm.I am most grateful to Prof. Ju¨rgen Lindner for the opportunity to work in his re-searchteam,theacademicfreedomhesupported,andthechancetodiscussinterestingscientific problems at international conferences and symposia. Furthermore, I wouldlike to express my gratitude to Prof. Volker Ku¨hn for the careful proof-reading of themanuscript and the co-supervision of this work.For the inspiring collaboration during my research visit at National ICT Australiain Canberra, I would like to thank Dr. Mark Reed and Dr. Zhenning Shi. In addition,I am indebted to Michael Anderson for exchanging ideas on soft iterative channelestimation.I am further grateful to all the persons who thoroughly cross-read the manuscriptand to the colleagues at the Institute for the friendly atmosphere. Especially, I wouldlike to thank Alexander Linduska, Ulrich Marxmeier, Ivan Periˇsa, Christian Pietsch,Dr.
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Iterative Estimation and Detection
for Single Carrier Block Transmission
DISSERTATION
zur Erlangung des akademischen Grades eines
DOKTOR-INGENIEURS
(DR.-ING.)
der Fakulta¨t fu¨r Ingenieurwissenschaften
und Informatik der Universita¨t Ulm
von
MARKUS ALEXANDER DANGL
AUS HEIDENHEIM
Gutachter: Prof. Dr.-Ing. Ju¨rgen Lindner
Prof. Dr.-Ing. habil. Volker Ku¨hn
AmtierenderDekan: Prof. Dr. rer. nat. Helmuth Partsch
Ulm, 16. November 2007Acknowledgments
This thesis summarizes the results of the research that I conducted at the Institute of
Information Technology, University of Ulm.
I am most grateful to Prof. Ju¨rgen Lindner for the opportunity to work in his re-
searchteam,theacademicfreedomhesupported,andthechancetodiscussinteresting
scientific problems at international conferences and symposia. Furthermore, I would
like to express my gratitude to Prof. Volker Ku¨hn for the careful proof-reading of the
manuscript and the co-supervision of this work.
For the inspiring collaboration during my research visit at National ICT Australia
in Canberra, I would like to thank Dr. Mark Reed and Dr. Zhenning Shi. In addition,
I am indebted to Michael Anderson for exchanging ideas on soft iterative channel
estimation.
I am further grateful to all the persons who thoroughly cross-read the manuscript
and to the colleagues at the Institute for the friendly atmosphere. Especially, I would
like to thank Alexander Linduska, Ulrich Marxmeier, Ivan Periˇsa, Christian Pietsch,
Dr. Werner Teich, Zoran Utkovski, and Matthias Wetz for the numerous discussions I
could benefit from.
Certainly, many of the findings in this thesis would not have been feasible without
the following three persons who shared their insights and ideas with me. Therefore,
I deeply appreciate the support of my former room-mate Dr. Achim Engelhart, for the
supervision of my diploma thesis and for sparking my interest in detection problems;
of my former and present colleague Dr. Jochem Egle, for our joint work on turbo
equalizationissues;andofmyformercolleagueDr.ChristianSgraja,forthefascinating
and fruitful conversations about estimationtheory and beyond.
Finally, I am most obliged to my parents for their assistance and patience.
Markus Dangl
Neu-Ulm, December 2007
iiiivAbstract
HIS thesis deals with efficient receiver design for digital point-to-point commu-
nications. A single carrier block transmission scheme, including channel cod-T ing, shall serve as a basis. At the receiver neither knowledge of the channel
impulse response (CIR) nor the signal-to-noise ratio (SNR) is assumed. Accordingly,
thoseparametershavetobeestimatedforpower-efficientdatadetection. Inparticular,
an iterative solution for joint parameter estimation and data detection based on the
turbo principle is investigated. As a result of an in-depth study of various decision-
directed SNR estimation techniques, a novel estimator using a priori probabilities of
data symbols is derived for Gaussian channels with binary modulation. The potential
of the algorithm is evaluated for the example of iterative decoding of concatenated
convolutional codes. In the case of multipath channels, the CIR has to be estimated,
too and equalization is additionally necessary. Iterative equalization and decoding
(turbo equalization) is chosen as a powerful technique for data detection with mod-
erate computational complexity. A decision-directed channel estimator based on the
least-mean-square (LMS) algorithm is suggested that adapts its step size according to
thequalityofthedataestimatesandthatdoesnot requireSNRknowledge. Numerical
resultsforaturboequalizationsetupsupportthattheproposedchannelestimatorper-
forms well for arbitrary signal constellations. Furthermore, the performance of turbo
equalizationitselfisaddressed. Anoptimizationalgorithmforbit-to-symbol mappings
is presented that enhances power efficiency by means of iterative demapping. The al-
gorithmcanbeappliedtoanyequalizationtechniqueiftheequalizer’soutputvariance
is known or can be estimated. Finally, the use of estimation error statistics is investi-
gated. Its advantage for turbo equalization and the relationship to decision-directed
channel estimation is shown by an extrinsicinformation transfer (EXIT) analysis.
vviContents
1 Introduction 1
2 Fundamentals 5
2.1 Model of a Digital Point-To-Point Communication System . . . . . . . . 5
2.1.1 Continuous-Time Representation . . . . . . . . . . . . . . . . . 5
2.1.2 Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.3 Discrete-TimeRepresentation . . . . . . . . . . . . . . . . . . . 9
2.2 Bit ErrorProbability, Log-Likelihood Ratios, and MutualInformation . . 14
2.3 IterativeReceiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3 SNR Estimation 23
3.1 A Note on Estimation Theory . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 Pilot-Aided Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3.1 Component-Wise Minimum Variance Unbiased Estimation . . . . 26
3.3.2 MaximumLikelihood Estimation . . . . . . . . . . . . . . . . . 26
3.3.3 Cramer-Rao Lower Bound . . . . . . . . . . . . . . . . . . . . . 28
3.3.4 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4 Blind Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.4.1 Estimation Using Second- and Fourth-OrderMoments . . . . . . 31
3.4.2 Estimation Using the Absolute Moment . . . . . . . . . . . . . . 32
3.4.3 Approximate MaximumLikelihood Estimation . . . . . . . . . . 33
3.4.4 Cramer-Rao Lower Bound . . . . . . . . . . . . . . . . . . . . . 34
3.4.5 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5 Decision-Directed Estimation . . . . . . . . . . . . . . . . . . . . . . . 37
3.5.1 Hard and Soft Decision-Directed Estimation . . . . . . . . . . . 40
3.5.2 Correction of Initial Estimate and Criterionfor Re-Estimation . . 41
3.5.3 Approximate MaximumLikelihood Estimation with Priors . . . . 44
3.5.4 Cramer-Rao Lower Bound . . . . . . . . . . . . . . . . . . . . . 46
3.5.5 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.6 Higher-OrderSignal Constellations . . . . . . . . . . . . . . . . . . . . 51
3.6.1 PSK Signal Constellations . . . . . . . . . . . . . . . . . . . . . 51
3.6.2 Multi-AmplitudeSignal Constellations . . . . . . . . . . . . . . 52
3.7 Multipath Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.8 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
viiContents
4 Channel Estimation 57
4.1 SystemModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2 Pilot-Aided Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.2.1 MaximumLikelihood Estimation . . . . . . . . . . . . . . . . . 59
4.2.2 Linear Minimum Mean-SquareError Estimation . . . . . . . . . 60
4.2.3 Least-Mean-SquareAlgorithm . . . . . . . . . . . . . . . . . . . 61
4.2.4 Cramer-Rao LowerBound . . . . . . . . . . . . . . . . . . . . . 62
4.2.5 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.3 Decision-Directed Estimation . . . . . . . . . . . . . . . . . . . . . . . 63
4.3.1 Least-SquaresEstimation . . . . . . . . . . . . . . . . . . . . . . 64
4.3.2 Least-Mean-SquareAlgorithm . . . . . . . . . . . . . . . . . . . 65
4.3.3 Cramer-Rao LowerBound . . . . . . . . . . . . . . . . . . . . . 70
4.3.4 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5 Turbo Equalization 75
5.1 Soft Interference Cancellation Combined with Linear Filtering . . . . . 76
5.1.1 Channel-Matched Filter . . . . . . . . . . . . . . . . . . . . . . 79
5.1.2 Minimum Mean-SquareError Filter . . . . . . . . . . . . . . . . 79
5.1.3 Minimum Variance Unbiased Filter . . . . . . . . . . . . . . . . 80
5.2 Special Case of Real-Valued Signal Constellations . . . . . . . . . . . . 81
5.3 OtherApproaches to Turbo Equalization . . . . . . . . . . . . . . . . . 86
5.4 Convergence Analysis Using the EXIT Chart . . . . . . . . . . . . . . . . 86
5.4.1 EXIT Function of the Decoder . . . . . . . . . . . . . . . . . . . 87
5.4.2 EXIT Function of the Equalizer. . . . . . . . . . . . . . . . . . . 89
5.5 Designof Symbol Mappings for Multipath Channels . . . . . . . . . . . 92
5.5.1 EXIT Functions Depending on the Symbol Mapping . . . . . . . 93
5.5.2 Optimizationof Symbol Mappings . . . . . . . . . . . . . . . . . 96
5.5.3 DesignExample . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.6 Equalizationwith Channel Uncertainty . . . . . . . . . . . . . . . . . . 100
5.6.1 ErrorModel for Imperfect Channel Estimation . . . . . . . . . . 101
5.6.2 EqualizationIncorporating Estimation Error Statistics . . . . . . 103
5.7 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6 Iterative Estimation and Detection 109
6.1 IterativeEstimation and Detection for the AWGN Channel . . . . . . . . 109
6.1.1 Receiver Structure . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.1.2 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.2 IterativeEstimation and Detection for Multipath Channels . . . . . . . 115
6.2.1 Receiver Structure . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.2.2 Performancefor Known SNR . . . . . . . . . . . . . . . . . . . . 118
6.2.3 Performancefor Estimated SNR . . . . . . . . . . . . . . . . . . 124
viiiContents
6.3 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7 Summary and Conclusions 129
A Proofs 131
A.1 Proof of Proposition 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
A.2 Proof of Proposition 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
A.3 Proof of Proposition 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
B Notation, List of Symbols, and Abbreviations 135
Bibliography 141
ixx

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