Coding and modulation for spectral efficient transmission [Elektronische Ressource] / vorgelegt von Nabil Sven Muhammad
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Coding and modulation for spectral efficient transmission [Elektronische Ressource] / vorgelegt von Nabil Sven Muhammad

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Coding and Modulation for SpectralEfficient TransmissionVon der Fakultät Informatik, Elektrotechnik und Informationstechnikder Universität Stuttgart zur Erlangung der Würde einesDoktor-Ingenieurs (Dr.-Ing.) genehmigte AbhandlungVorgelegt vonNabil Sven Muhammadaus FuldaHauptberichter: Prof. Dr.-Ing. J. SpeidelMitberichter: Prof. Dr.-Ing. B. YangTag der mündlichen Prüfung: 20. Juli 2010Institut für Nachrichtenübertragung der Universität Stuttgart2010AcknowledgementsThis dissertation is the outcome of my activities as a research assistant at the Institute ofTelecommunications (INÜ), University of Stuttgart, Germany.I would like to express my gratitude to Professor Joachim Speidel for giving me the oppor-tunity to work under his supervision. I owe him special thanks for having confidence in meand offering me the freedom to develop own ideas. His door was always open for fruit-ful discussions and advice. Furthermore, he sharpened my way of thinking towards a clearand scientific perspective. He constantly encouraged me in pursuing challenging tasks andenabled the publication of my research results.I would also like to thank Professor Bin Yang for the assessment of this thesis and his valu-able comments.Warm thanks go to all my former colleagues at the INÜ. I had a great time working withyou. Special thanks to Dr.

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Published 01 January 2010
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Coding and Modulation for Spectral
Efficient Transmission
Von der Fakultät Informatik, Elektrotechnik und Informationstechnik
der Universität Stuttgart zur Erlangung der Würde eines
Doktor-Ingenieurs (Dr.-Ing.) genehmigte Abhandlung
Vorgelegt von
Nabil Sven Muhammad
aus Fulda
Hauptberichter: Prof. Dr.-Ing. J. Speidel
Mitberichter: Prof. Dr.-Ing. B. Yang
Tag der mündlichen Prüfung: 20. Juli 2010
Institut für Nachrichtenübertragung der Universität Stuttgart
2010Acknowledgements
This dissertation is the outcome of my activities as a research assistant at the Institute of
Telecommunications (INÜ), University of Stuttgart, Germany.
I would like to express my gratitude to Professor Joachim Speidel for giving me the oppor-
tunity to work under his supervision. I owe him special thanks for having confidence in me
and offering me the freedom to develop own ideas. His door was always open for fruit-
ful discussions and advice. Furthermore, he sharpened my way of thinking towards a clear
and scientific perspective. He constantly encouraged me in pursuing challenging tasks and
enabled the publication of my research results.
I would also like to thank Professor Bin Yang for the assessment of this thesis and his valu-
able comments.
Warm thanks go to all my former colleagues at the INÜ. I had a great time working with
you. Special thanks to Dr. Frank Schaich and Robert Fritsch for all technical and even
more not-so-technical discussions we had (the same holds for all assistants at the INÜ —
also thanks for all the fun we had playing “Kicker”). I’m indebted to Torsten Freckmann for
carefully reading and correcting this thesis. Similarly, I thank Daniel Efinger for commenting
the thesis. Besides Torsten and Daniel, I frequently bothered Andreas Müller and Matthias
ABreuninger with questions about LT X. Thanks for all the tricks you taught me. I also likeE
to thank Dr. Hanns Thilo Hagmeyer for all prolific discussions I had with him. I always
left his room wiser than when I’ve entered it. Many thanks to the secretaries Dorothee
(Doro) Buchau and Jessica Driendl as well as to Agnes Schön-Abiry for daily support. Last,
but far from least I like thank (in German language) the “backbone” of the institute: to
Arnfried (Arnie) Eipper, Csaba Erdei, Günther Varady and Dieter Weber. Danke für Euere
Unterstützung (ganz besonders an Arnie), für die vielen guten und warmherzigen Gespräche
und für das gemeinsame Espresso trinken. Ich habe mich stets pudelwohl bei Euch gefühlt!
I would also like to appreciate the work of all students, who contributed to this dissertation
by their study, diploma or master theses. To highlight just some names would not be fair to
others, so I thank you all.
It is my pleasure also to thank my new colleagues at Sony. I am indebted to my big boss Dr.
Dietmar Schill for offering me the job position and for enabling my latest publication at the
VTC in Alaska. To Lothar Stadelmeier I bow down and express the warmest of thanks for
being such a great mentor. Finally (as promised, Bob) thanks to the Sony poker mates.
vThanks to Lars Sonnabend for being such a good friend and for all the (in)glorious parties
we had.
As my acknowledgment will exceed two pages anyway, I may as well thank Miss Ellie for
being the cutest cat in the world. Thanks for bringing me mice every night.
To my family I send my deepest gratitude (again in German): Danke an meine wunderbaren
Eltern, für all Euere Unterstützung. Nur durch Euch habe ich es so weit gebracht. Ihr seit
stets für mich da, habt mir alles ermöglicht, und dafür liebe ich Euch! Danke auch an meinen
Bruder und meine Schwester. Es ist gut zu wissen, dass Ihr immer ein offenes Ohr für mich
habt.
I saved the final thank-you’s for the sunshine of my life. Thank you, Andreea, my beloved,
for being the person you are. For your enduring support and your patience with me, es-
pecially in those times, when writing this thesis filled out my complete week. Thanks for
relieving me from most of the workload at home and even bringing me dinner to the office
once. But most of all, I thank you for all the love you have given me. You are my sunshine,
my only sunshine. You make me happy when skies are gray.
We shall not cease from exploration,
And the end of all our exploring,
Will be to arrive where we started,
And know the place for the first time.
(T.S. Elliot)
viContents
Acronyms and Abbreviations xi
Symbols xiii
Abstract xix
Kurzfassung xix
1 Introduction 1
2 Fundamentals 5
2.1 System Model for QAM . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Waveform Description of QAM . . . . . . . . . . . . . . . . . . . 5
2.1.2 Equivalent Baseband Description of Digital QAM . . . . . . . . . 11
2.1.3 QAM Mappings . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Channel Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.1 Additive White Gaussian Noise Channel . . . . . . . . . . . . . . . 17
2.2.2 Rayleigh Fading Channel . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.3 Multiple Input Multiple Output Channel . . . . . . . . . . . . . . . 18
2.2.4 Binary Erasure Channel . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 Error Control Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.1 Block Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.2 Convolutional Codes . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.3 Optimum Decoding . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.4 Concatenated Codes — The Turbo Principle . . . . . . . . . . . . 29
vii2.4 BICM with and without Iterative Demapping . . . . . . . . . . . . . . . . 31
2.5 Fundamentals of Information Theory . . . . . . . . . . . . . . . . . . . . . 32
2.5.1 Entropy and Mutual Information . . . . . . . . . . . . . . . . . . . 33
2.5.2 Capacity Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.6 EXIT Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3 Optimization of QAM Mappings 43
3.1 Prerequisites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1.2 Optimization Algorithm . . . . . . . . . . . . . . . . . . . . . . . 46
3.2 Mappings for Minimum Symbol Error Rate . . . . . . . . . . . . . . . . . 49
3.2.1 4-QAM for Minimum Symbol Error Rate . . . . . . . . . . . . . . 50
3.2.2 8-QAM for Minimum Symbol Error Rate . . . . . . . . . . . . . . 51
3.2.3 16-QAM for Minimum Symbol Error Rate . . . . . . . . . . . . . 53
3.2.4 32-QAM for Minimum Symbol Error Rate . . . . . . . . . . . . . 56
3.2.5 Summary for Minimum Symbol Error Rate Mappings . . . . . . . 59
3.3 Mappings for Maximum BICM Capacity . . . . . . . . . . . . . . . . . . . 60
3.3.1 Relation between Bit Error Rate and BICM Capacity . . . . . . . . 60
3.3.2 Enhanced Optimization Algorithm . . . . . . . . . . . . . . . . . . 62
3.3.3 8-QAM for Maximum BICM Capacity . . . . . . . . . . . . . . . 64
3.3.4 16-QAM for Maximum BICM Capacity . . . . . . . . . . . . . . . 68
3.3.5 32-QAM for Maximum BICM Capacity . . . . . . . . . . . . . . . 70
3.3.6 Summary for Maximum BICM Capacity Mappings . . . . . . . . . 73
3.4 Mappings for Maximum Signal Set Capacity . . . . . . . . . . . . . . . . 75
3.4.1 8-QAM for Maximum Signal Set Capacity . . . . . . . . . . . . . 76
3.4.2 16-QAM for Maximum Signal Set Capacity . . . . . . . . . . . . . 78
3.4.3 32-QAM for Maximum Signal Set Capacity . . . . . . . . . . . . . 79
3.4.4 Summary for Maximum Signal Set Capacity Mappings . . . . . . . 82
3.5 Maximum Exploitation of Perfect A Priori Information . . . . . . . . . . . 83
3.5.1 Closed-Form Expression of I (1) . . . . . . . . . . . . . . . . . . 83E1
viii3.5.2 Mappings for Maximum I (1) . . . . . . . . . . . . . . . . . . . 87E1
3.5.3 Summary for Maximum I (1) Mappings . . . . . . . . . . . . . . 89E1
3.6 Tradeoff between No and Perfect A Priori Knowledge . . . . . . . . . . . . 90
3.6.1 16-QAM Tradeoff Mappings . . . . . . . . . . . . . . . . . . . . . 90
3.6.2 Summary for Tradeoff Mappings . . . . . . . . . . . . . . . . . . . 94
4 Multidimensional Mappings for Iterative MIMO Detection 97
4.1 System Model for Multidimensional MIMO Mappings . . . . . . . . . . . 97
4.2 Generation of MdM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.3 Design Criteria and MdM Optimization . . . . . . . . . . . . . . . . . . . 101
4.3.1 MdM with BPSK and QPSK . . . . . . . . . . . . . . . . . . . . . 102
4.3.2 MdM with 16-QAM . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.4 Simulation Results of MdMs . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.4.1 Summary for Multidimensional Mappings . . . . . . . . . . . . . . 108
5 Inner Block Codes for Serial Concatenated Codes and Applications to BICM 111
5.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.2 System Model for SCC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.2.1 Transmitter for SCC . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.2.2 Receiver for SCC . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.2.3 Channel Models and Capacity Constraints . . . . . . . . . . . . . . 114
5.3 Transfer Characteristic of Inner Block Code . . . . . . . . . . . . . . . . . 114
5.4 Optimization of Irregular Inner Codes . . . . . . . . . . . . . . . . . . . . 119
5.4.1 Formulation of Design Target . . . . . . . . . . . . . . . . . . . . 119
5.4.2 Simulation Results for Irregular Inner Codes . . . . . . . . . . . . 120
5.5 Applications to BICM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.5.1 Bit Level Capacities . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.5.2 Transfer Characteristic of Demapper . . . . . . . . . . . . . . . . . 126
5.6 Summary for Inner Block Codes for Serial Concatenated Codes and Appli-
cations to BICM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
ix6 Conclusion 129
A Computation of Gradients 131
A.1 Gradient of Symbol Error Probability . . . . . . . . . . . . . . . . . . . . 131
A.2 Gradient of BICM Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . 132
A.3 Gradient of Signal Set Capacity . . . . . . . . . . . . . . . . . . . . . . . 134
A.3.1 General Expression for Gradient of Signal Set Capacity . . . . . . . 134
A.3.2 Optimality of BPSK . . . . . . . . . . . . . . . . . . . . . . . . . 135
A.4 Gradient of I (1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138E1
B Optimized Mapping Vectors 141
B.1 Mapping Vectors for Minimum Symbol Error Rate . . . . . . . . . . . . . 141
B.2 Mapping Vectors for Maximum BICM Capacity . . . . . . . . . . . . . . . 142
B.3 Mapping Vectors for Maximum Signal Set Capacity . . . . . . . . . . . . . 143
B.4 Mapping Vectors for Tradeoffs . . . . . . . . . . . . . . . . . . . . . . . . 143
x