Capacity Analysis of Spectrally Efficient Frequency Division Multiplexing DAVID ANDREW RAINNIE

125 Pages·2015·2.12 MB·English

Capacity Analysis of
Spectrally Efficient Frequency Division Multiplexing

DAVID ANDREW RAINNIE

Department of Electrical and Computer Engineering
McGill University
Montreal, Canada

April 2015

A thesis submitted to McGill University in partial fulfillment of the requirements of the
degree of Master of Engineering.
© 2015 David Andrew Rainnie
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Abstract
The increasing demand for wireless communication services is placing pressure on the
communication bandwidth available within a fixed electromagnetic spectrum resource.
Instead of traditional orthogonal signal transmission in both time and frequency domains,
non-orthogonal data transmission schemes have been proposed as a means to increase
data rates at the expense of introduced signal interference. Recently, Faster-Than-Nyquist
(FTN) Signaling and Spectrally Efficient Frequency Division Multiplexing (SEFDM)
have been the two main research directions in non-orthogonal communication when the
time and frequency orthogonality constraints are removed, respectively.

This thesis first provides a literature review of the FTN and SEFDN research areas
and derives corresponding information-theoretic channel models. The primary goal of
this work is to present a channel capacity analysis of the previously proposed multicarrier
SEFDM communication for different practical modulating pulses, i.e., rectangular and
square-root raised cosine with different roll-off factors. Consequently, the analysis is
extended when the concepts of time and frequency compression are employed jointly,
thus combining FTN with SEFDM. The presented numerical capacity results show that
there is a trade-off between realizable time and frequency compression capacity gains for
the different types of transmission pulses and explains the origin of these gains. Finally,
possible areas for future research are outlined.
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Sommaire
La demande croissante de services de communication sans fil exerce une pression sur la
bande passante de communication allouée dans une ressource de spectre
électromagnétique fixe. Au lieu de transmettre des signaux orthogonalement dans les
deux domaines temporel et fréquentiel, les systèmes de transmission de données non
orthogonaux ont été proposés comme un moyen d'augmenter les débits de données à la
charge de signal d'interférence introduite. Récemment, la Signalisation « Faster-Than-
Nyquist » (FTN) et le Multiplexage par division de fréquence efficace (SEFDM) ont été
les deux domaines de recherche principaux en communication non orthogonale lorsque
les contraintes d'orthogonalité du temps et de fréquence sont éliminées, respectivement.

Cette thèse fournit d'abord une révision de la documentation des domaines de
recherche FTN et SEFDM et dérive des modèles de canal correspondants d'une manière
d’information théorique. L'objectif principal de ce travail est de présenter une analyse de
la capacité du canal pour la communication multiporteuse de SEFDM précédemment
proposée pour différentes impulsions de modulation pratique : rectangulaire et la famille
des impulsions de la racine carrée de cosinus surélevé avec différents facteurs « roll-
off ». Par conséquent, l'analyse est étendue lorsque les concepts de compression de temps
et de fréquence sont utilisés conjointement, combinant ainsi FTN avec SEFDM. Les
résultats numériques de capacité présentés montrent qu'il existe un compromis entre les
gains de capacité réalisables pour la compression temporelle ainsi que fréquentielle pour
les différents types d'impulsions de transmission et explique l'origine de ces gains. À la

fin, des suggestions pour la recherche future seront présentées.
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Acknowledgements
First, I would like to thank my supervisor, Dr. Jan Bajcsy for welcoming me into his lab,
as well as for the discussions and guidance which enabled me to complete this thesis.
I must also thank Yi Feng and Dr. Yong Jim Daniel Kim for their support for and
valuable discussions about my research.
Lastly, I would like to thank my family for their support while I completed my
research and thesis over the past two and a half years. It is to them that I dedicate this
thesis.
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Table of Contents

Chapter 1. Introduction ..........................................................................................1
1.1. Recent Advances in Wireless Communication Systems .........................1
1.2. Technology for Data Transmission ..........................................................5
1.3. Non-Orthogonal Modulation Schemes: SEFDM & FTN ......................11
1.4. Thesis Objectives and Contributions .....................................................13
Chapter 2. Literature Review...............................................................................15
2.1. Early FTN Work ....................................................................................15
2.2. Recent FTN Work .................................................................................18
2.3. Multicarrier FTN Signaling and SEFDM ..............................................19
2.4. Chapter Summary ..................................................................................22
Chapter 3. Concepts for SEFDM and FTN .........................................................23
3.1. Preliminary Concepts for Modulation and Demodulation .....................23
3.2. Overview of FTN Signaling ..................................................................27
3.3. Frequency Compression ........................................................................30
3.4. Information Theory Concepts ................................................................41
Chapter 4. Channel Capacity Results ..................................................................49
4.1. The Discrete-Time SEFDM and FTN Channel Model ..........................49
4.2. SEFDM Channel Capacity Results ........................................................53
4.3. Single Carrier FTN Channel Capacity Results ......................................63
4.4. Joint SEFDM and FTN Capacity Results ..............................................71
4.5. Capacity Analyses for Other Pulses .......................................................77
4.6. Potential of Precoded SEFDM ...............................................................93
4.7. Chapter Summary ..................................................................................95
Chapter 5. Conclusion and Future Work .............................................................97
Appendix A Selected Proofs...............................................................................100
References ............................................................................................................104
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List of Figures
Figure 1. Increasing presence of wireless communication in consumer devices ........... 2
Figure 2. Projected mobile data usage increase ............................................................. 2
Figure 3. Projected mobile subscription breakdown ...................................................... 3
Figure 4. Electromagnetic Spectrum with usage examples ............................................ 5
Figure 5. Block diagram for general communications system ....................................... 6
Figure 6. (a) Block diagram of simple QAM modulator and (b) QAM constellation
with Grey code bit mapping ............................................................................ 8
Figure 7. Frequency domain depiction of the spectrum of 12 OFDM subcarriers (top)
and 12 SEFDM subcarriers (bottom) ............................................................ 10
Figure 8. Illustrative examples of interfering (a) pulses in the time domain for FTN
transmission and (b) subcarriers in the frequency domain for a generic
SEFDM system ............................................................................................. 12
Figure 9. Mazo’s minimum distance versus signalling rate plot from [44] for the sinc
pulse .............................................................................................................. 17
Figure 10. Time-frequency diagram showing symbol increase in (a) Nyquist OFDM, (b)
Nyquist SEFDM, (c) FTN OFDM, and (d) FTN SEFDM systems .............. 19
Figure 11. Normalized spectral efficiency for High-Compaction Multicarrier
modulation (HC-MCM). As reported by the author in [15]. ........................ 21
Figure 12. Minimum Euclidean distance for High-Compaction Multicarrier Modulation
(HC-MCM). As reported by the author in [15]............................................. 21
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Figure 13. (a) Matched filter architecture and (b) correlator architecture for a
multicarrier system with N carrier frequencies ......................................... 24
C
Figure 14. (a) Time domain and (b) frequency domain representations of rectangular
pulse .............................................................................................................. 25
Figure 15. (a)Frequency domain and (b)time domain representations of square-root
raised cosine pulse ........................................................................................ 27
Figure 16. Conceptual illustration of Nyquist pulse train .............................................. 28
Figure 17. Conceptual illustration of FTN pulse train for K = 2 ................................ 29
T
Figure 18. Frequency domain depiction of the spectrum of 12 OFDM subcarriers ...... 32
Figure 19. Diagram of an OFDM transmitter and receiver architecture ........................ 33
Figure 20. Diagram of an IDFT-based OFDM transmitter-receiver architecture .......... 34
Figure 21. Block diagram illustrating IDFT output samples.......................................... 35
Figure 22. Frequency domain depiction of the spectrum of 12 SEFDM subcarriers for
α=0.9, illustrating slight subcarrier compression .......................................... 37
Figure 23. Frequency domain depiction of the spectrum of 12 SEFDM subcarriers for
α=0.5, illustrating moderate subcarrier compression .................................... 37
Figure 24. Frequency domain depiction of the spectrum of 12 SEFDM subcarriers for
α=1/3. ............................................................................................................ 38
Figure 25. Frequency domain depiction of the spectrum of 12 SEFDM subcarriers for
α=0.1, illustrating severe subcarrier compression ........................................ 38
Figure 26. IDFT SEFDM implementation using zero padding to perform subcarrier
compression, whereN /and N((1)/)are integers ............................. 39
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Figure 27. Multiple IDFT SEFDM implementation using zero padding to perform
subcarrier compression ................................................................................. 40
Figure 28. Time-frequency diagram showing symbol increase in SEFDM and FTN
systems: (a) K 1,1 , (b) K 1,1/2, (c)
T T
K 1/2,1, (d) K 1/3,1/3 ..................................................... 51
T T
Figure 29. Channel capacity results for SEFDM using rectangular modulation pulses
with OFDM bandwidths c)N 20, d) N 100, and e) N 200. . 57
OFDM OFDM OFDM
Figure 30. Channel capacity results for SEFDM using square-root raised cosine
modulation pulses with roll-off factor 0.001 and OFDM bandwidth
N 20 ..................................................................................................... 59
OFDM
Figure 31. Channel capacity results for SEFDM using square-root raised cosine
modulation pulses with roll-off factor 0.22 and OFDM bandwidth
N 20 ..................................................................................................... 60
OFDM
Figure 32. Channel capacity results for SEFDM using square-root raised cosine
modulation pulses with roll-off factor 0.50 and OFDM bandwidth
N 20 ..................................................................................................... 61
OFDM
Figure 33. Channel capacity results for SEFDM using square-root raised cosine
modulation pulses with roll-off factor 0.999 and OFDM bandwidth
N 20 ..................................................................................................... 62
OFDM
Figure 34. Channel capacity results for FTN using rectangular modulation pulses with
Nyquist lengths c)N 20, d) N 100, and e) N 200 ................................. 65
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Figure 35. Channel capacity results for FTN using square-root raised cosine modulation
pulses with 0.001 and packet lengthN 20.......................................... 67
Figure 36. Channel capacity results for FTN using square-root raised cosine modulation
pulses with 0.22 and packet lengthN 20 ........................................... 68
Figure 37. Channel capacity results for FTN using square-root raised cosine modulation
pulses with 0.50 and packet length N 20 .......................................... 69
Figure 38. Channel capacity results for FTN using square-root raised cosine modulation
pulses with 0.999 and packet length N 20 ........................................ 70
Figure 39. Channel capacity results for SEFDM/FTN using rectangular modulation
pulses with OFDM bandwidth N 10 and packet length N 10 ....... 72
OFDM
Figure 40. Channel capacity results for SEFDM/FTN using square-root raised cosine
modulation pulses with 0.001, OFDM bandwidth N 20, and
OFDM
packet length N 20 .................................................................................... 73
Figure 41. Channel capacity results for SEFDM/FTN using square-root raised cosine
modulation pulses with 0.22, OFDM bandwidth N 20, and
OFDM
packet length N 20 .................................................................................... 74
Figure 42. Channel capacity results for SEFDM/FTN using square-root raised cosine
modulation pulses with 0.50, OFDM bandwidth N 20, and
OFDM
packet length N 20 .................................................................................... 75
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Figure 43. Channel capacity results for SEFDM/FTN using square-root raised cosine
modulation pulses with 0.999, OFDM bandwidth N 20, and
OFDM
packet length N 20 .................................................................................... 76
Figure 44. Channel capacity results for SEFDM using Hamming modulation pulses
with OFDM bandwidths c)N 20and d) N 100. ............................ 78
OFDM OFDM
Figure 45. Channel capacity results for FTN using Hamming modulation pulses with
Nyquist lengths a)N 20and b) N 100 ...................................................... 79
Figure 46. Channel capacity results for SEFDM using Phydyas (K=2) modulation
pulses with OFDM bandwidths c)N 20and d) N 100. ................. 81
OFDM OFDM
Figure 47. Channel capacity results for FTN using Phydyas (K=2) modulation pulses
with Nyquist lengths a)N 20and b) N 100 .............................................. 82
Figure 48. Channel capacity results for SEFDM/FTN using Phydyas (K=2) modulation
pulses with OFDM bandwidth N 10, and packet length N 10 ....... 83
OFDM
Figure 49. Channel capacity results for SEFDM using Phydyas (K=4) modulation
pulses with OFDM bandwidth N 20 ................................................... 84
OFDM
Figure 50. Channel capacity results for FTN using Phydyas (K=4) modulation pulses
with Nyquist length N 20 .......................................................................... 85
Figure 51. Channel capacity results for SEFDM/FTN using Phydyas (K=4) modulation
pulses with OFDM bandwidth N 10, and packet length N 10 ....... 85
OFDM