WIRELESS OFDM SYSTEMS How to make them work?

WIRELESS OFDM SYSTEMS
How to make them work?
THE KLUWER INTERNATIONAL SERIES
IN ENGINEERING AND COMPUTER SCIENCE
WIRELESS OFDM SYSTEMS
How to make them work?
edited by
Marc Engels
IMEC, Belgium
KLUWER ACADEMIC PUBLISHERS
NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW
eBook ISBN:
Print ISBN:
0-306-47685-1
1-4020-7116-7
©2002 Kluwer Academic Publishers
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Print ©2002 Kluwer Academic Publishers
Dordrecht
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Created in the United States of America
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In memory of my father who died
on 5 January 2002
How to make them work?
Contents
List of Figures
ix
List of Tables
xv
Preface
xvii
Contributors
xix
Acknowledgements
Introduction
1.1 A connected world emerges
1.2 Wireless OFDM: the next technology wave
1.3 Wireless OFDM systems
1.4 Structure of the book
xxiii
1
1
3
5
7
Understanding the indoor environment
2.1 Introduction
2.2 Propagation losses
2.3 Multipath propagation
2.4 Time variant channels
2.5 Conclusions
11
11
12
17
26
30
The OFDM Principle
3.1 The OFDM principle
3.2 The OFDM system model
33
33
38
viii
OFDM Systems
3.3
3.4
3.5
3.6
What if the channel is time-variant?
OFDM receiver performance
Coding: an essential ingredient
Summary
41
45
48
50
When people agree on OFDM
4.1 WLAN standards
4.2 HIPERLAN/2
4.3 Differences between HIPERLAN/2 and IEEE 802.11a
53
53
54
73
Beating the wireless channel
5.1 Introduction
5.2 Channel models and characteristics
5.3 One-Dimensional Channel Estimators
5.4 Two-Dimensional Channel estimators.
75
75
76
80
90
Avoiding a tower of Babel
6.1 Introduction
6.2 Effects of out of sync transmission
6.3 Timing synchronisation
6.4 Frequency synchronisation
95
95
96
100
106
Living with a real radio
7.1 Introduction
7.2 How the front-end impairs the OFDM modem
7.3 A system simulation tool
7.4 Analysis and simulation of the main front-end effects
7.5 Conclusions
113
113
115
122
127
149
Putting it all together
8.1 Introduction
8.2 The basedband signal processing ASIC
8.3 The discrete system set-up
8.4 Learning from results
151
151
155
171
178
Abbreviations
191
Variables
195
Notation
199
Index
201
How to make them work?
List of Figures
Figure 1.1. World-wide number of Internet users
1
Figure 1.2. World-wide number of mobile phones
2
Figure 1.3. Wireless Internet Technologies
3
Figure 1.4. Broad-band channel response
4
Figure 1.5. Single frequency network
5
Figure 2.1. Typical interference in 2.4 GHz ISM-band coming from a
microwave oven (a) or a Bluetooth hopper (b)
17
Figure 2.2. multipath propagation situation
18
Figure 2.3. Ray-tracing example (reflections in a corner)
22
Figure 2.4. Floorplan for ray tracing example 1
24
Figure 2.5. Power delay profile and baseband frequency response for ray
tracing example 1
24
Figure 2.6. Floorplan for ray tracing example 2
25
Figure 2.7. Power delay profile and baseband frequency response for ray
tracing example 2
25
Figure 2.8. Time correlation for different models of mobility
29
Figure 2.9. Doppler spectra for different mobility models
30
Figure 3.1. Subdivision of the bandwidth into subbands
33
Figure 3.2. multicarrier modulation
34
Figure 3.3. Spectrum of an OFDM signal
36
Figure 3.4. OFDM demodulation
37
Figure 3.5. Cyclic Prefix
37
Figure 3.6. Discrete-time baseband equivalent model of an OFDM system 38
Figure 3.7. Discrete-frequency representation for the Doppler multipath
channel and an OFDM receiver
44
Figure 3.8. OFDM performance for AWGN
45
x
OFDM Systems
Figure 3.9. OFDM-QPSK performance in a multi-path channel versus
signal-to-noise ratio for various speeds of the mobile,
subcarriers,
47
Figure 3.10. Forward error coding for OFDM
49
Figure 3.11. Coded OFDM performance in a multipath channel
50
Figure 4.1: HIPERLAN/2 protocol stack in the AP
55
Figure 4.2. Segmentation and reassembly operation
56
Figure 4.3. MAC frame structure
57
Figure 4.4. Broadcast PDU train with preamble
61
Figure 4.5. Downlink PDU train with preamble
61
Figure 4.6. Uplink PDU train with short preamble
62
Figure 4.7. Direct link PDU train with preamble
62
Figure 4.8. PHY layer reference configuration
63
Figure 4.10. Scrambler block diagram
65
Figure 4.12. Channel coder block diagram
65
Figure 4.13. Mother convolutional encoder block diagram
65
Figure 4.14. Mapping of data and pilot carriers
68
Figure 4.15. Payload section consisting of several OFDM symbols with CP
68
Figure 4.16. PHY burst format
69
Figure 4.17. Broadcast burst preamble structure
69
Figure 4.18. Overview of different PHY bursts: (a) broadcast burst, (b)
Downlink burst, (c) Uplink burst with short preamble, (d) Uplink burst
with long preamble, (e) Direct link burst
71
Figure 4.19. Transmit spectral mask
72
Figure 5.1. The OFDM system model
77
Figure 5.2. The "OFDM Channel" is a set of parallel Gaussian channels 78
Figure 5.3. Resampling a non-sample-spaced channel extends the channel
length
79
Figure 5.4. Early and Late Synchronisation result in a longer channel and
can lead to violation of the Cyclic Prefix condition
79
Figure 5.5. The ML estimator enables low complexity and time-frequency
interpretation
85
Figure 5.6. Comb Spectrum for
85
Figure 5.7. FFT-based approaches outperform the SVD-based approaches by
an order of magnitude for spectral shaping systems
86
Figure 5.8. Performance of ML and approximate LMMSE estimators
87
Figure 5.9. Simplified Time-Frequency grids in OFDM
91
Figure 6.1. Effect of early and late synchronisation
97
Figure 6.2. Principle of the Schmidl and Cox auto-correlation based timing
synchronisation circuit
101
How to make them work?
xi
Figure 6.3. A sequence of inverted training symbols followed by a sequence
of identical training symbols give a more accurate timing acquisition.
102
Figure 6.4. Principle of a cross-correlation frame synchronizer
103
Figure 6.5. Principle of a frame synchroniser based on the cyclic prefix.. 104
Figure 6.6. Transforming a training sequence into a cyclic prefix
105
Figure 6.7. Timing estimation accuracy in function of SNR, with the number
of training sequences M as a parameter
106
Figure 6.8. Principle of Moose auto-correlation based frequency
synchronisation circuit
107
Figure 6.9. Frame/frequency synchroniser based on the cyclic prefix
109
Figure 6.10. Frequency estimation accuracy in function of SNR, with the
number of training sequences M as a parameter
110
Figure 7.1. Simplified schematic of an OFDM transceiver
114
Figure 7.2. I/Q demodulation with I/Q imbalance
117
Figure 7.3. The implementation loss versus the difference between the
power of an additional Gaussian noise source and the channel noise
power resulting in a given BER
is described by a
119
unique curve
Figure 7.4. Implementation loss IL versus the noise power of an additional
Gaussian noise source, for powers ranging from 25 dBc to 45dBc. This
plot relates to 64 QAM transmission at BER of
and
120
Figure 7.5. BER curve for coded 64QAM, with coding rate
on an
AWGN channel without any front-end effect
121
Figure 7.6. Schematic of the full link model as modeled in MATLAB for
123
this study
Figure 7.7. BER curves for 52 non-zero 64QAM-modulated subcarriers with
a coding rate of 3/4, showing a 3dB implementation loss due to
corruption of the long training symbol not corrected in the equalizer.
124
Figure 7.8. The BER curve for uncoded 64QAM resulting from simulation
matches the theoretical one
126
Figure 7.9. The optimal clipping level depends on the word-length of the
128
transmitted symbols
Figure 7.10. BER curves, showing the implementation loss due to clipping
129
and quantization noise
Figure 7.12. Effect of phase noise on 1 OFDM symbol . Legend: *
transmitted symbol, received symbol
133
Figure 7.13. Effect of phase noise on all OFDM symbols in the same burst.
Legend: * transmitted symbol, received symbol
133
Figure 7.14. Phase noise spectrum
134
Figure 7.15. Effect of phase noise on BER for uncoded 64QAM
137
xii
OFDM Systems
Figure 7.16. Domains of clipping after
clipping operation (on magnitude
of I and Q separately) and after
clipping operation (on magnitude of
)
139
Figure 7.17. For an input signal clipped at
and with +6dBm average
power, the power amplifier is driven up to the limit of saturation for
141
Figure 7.19. The IL is 0.5 dB for
at
... 142
Figure 7.20. ADC clock jitter effects are included before conversion by an
ideal ADC
143
Figure 7.22. SIR versus synchronization location for three test cases: no
analog channel select filter, channel select filters A and B with similar
inband ripple (no adjacent channels). Only filter A shows fairly high
SIR for a large synchronization range
145
Figure 7.23. Influence of the filter impulse response on the BER
performances for the 3 filters already considered in Figure 7.22, with
synchronization on the sample that shows maximum SIR (uncoded
64QAM in AWGN channel). As expected, Filter B shows poor BER
145
performances
Figure 7.24. SIR performance of the filter architecture A in dispersive
channels: the SIR is quite insensitive to the multipath channel impulse
response
146
Figure 7.25. SIR performance of the filter architecture B in dispersive
channels: this architecture provides similar channel selection
performances, but shows much more sensitivity to the multipath
channel impulse response
146
Figure 7.26. BER performances evaluation for the example in a Gaussian
channel
148
Figure 8.1. A wireless webcam scenario was chosen as application scenario.
152
Figure 8 2. Detailed wireless webcam communication scenario
153
Figure 8.3. The design goals for the ASIC are divided upon concept,
implementation, and methodology to make sure that we arrive at an
implementable solution
155
Figure 8.4. Partitioning of the ASIC
157
Figure 8.5. A radix 2-2 scheme significantly reduces the arithmetic
complexity of the fast Fourier transform
159
Figure 8.6. The symbol-based sample reordering (SSR) unit essentially
allows a set of intra-symbol data transfer operations based on a generic
160
architecture
Figure 8.7. Robust
timing acquisition relies on preamble autocorrelation in combination with signal power monitoring
162
Figure 8.8. The carrier frequency offset estimate feeds a phase accumulator
and a CORDIC to limit CFO on the signal entering the FFT
163
How to make them work?
xiii
Figure 8.9. The Festival equalizer reveals a low-cost solution with feedforward channel estimation and feedback decision-directed tracking. 163
Figure 8.10. The Carnival equalizer requires an interpolator and divider in
addition to the Festival equalizer since modulation schemes up to 64QAM need to be processed
164
Figure 8.11. Simple, reference symbol-based channel estimation reveals
poor noise-influenced results. The interpolator improves the channel
estimate S/N by 2.5 to 3 dB
165
Figure 8.12. The impulse response is truncated and interpolated using a fully
programmable
transformation matrix operation
165
Figure 8.13. Clock offset is tracked by guard interval correlation and
averaging over multiple OFDM symbols
166
Figure 8.14. The receiver and transmitter token flow exploits a closed loop
token scheme
168
Figure 8.15. The object-oriented desing flow starts from C++ and ends in a
conventional HDL-based design flow
170
Figure 8.16. 5 GHz WLAN demonstration setup excluding the power
amplifier board
171
Figure 8.17. Software protocol stack for the webcam application (Windows)
and for file transfer or test purposes (Linux)
172
Figure 8.18. The FPGA contains a central processing unit (CPU) that
coordinates both data transfers (RX and TX) and signalling information
(serial protocol, MPI)
173
Figure 8.19. Digital baseband board. Different versions exist for the Festival
and Carnival ASICs because they are not pin-compatible
175
Figure 8.20. Baseband signal processing
175
Figure 8.22. Architecture of the digital IF implemented in an FPGA
176
Figure 8.23. The integrated front-end has a superheterodyne architecture.
The discrete board set-up uses a similar architecture
177
Figure 8.24. Carnival (
CMOS, left) outperforms Festival (
CMOS, right) at the cost of an 30 % area increase only
179
Figure 8.25. Non-compliant burst (lower) and preamble (upper) format in
Festival and Carnival ASICs
183
Figure 8.27. Proposed automatic gain control architecture
185
Figure 8.28. Signal-to-noise ratio and estimation error of the quantized ADC
output
185
Figure 8.29. Generic transmitter architecture
187
How to make them work?
List of Tables
Table 2.1. Channel characteristics for set-up 1 and set-up 2
26
Table 4.1. Number of OFDM symbols per transport channel excluding
physical layer preambles in function of the modulation and code rate R
62
Table 4.2. Mode dependent parameters
64
Table 4.3. OFDM parameters
67
Table 4.4. HIPERLAN/2 carrier frequencies and EIRP
72
Table 4.5. Comparison between HIPERLAN/2 and IEEE 802.11a
73
Table 7.1. Implementation Loss on uncoded 64QAM at a BER of
due to
quantizing and clipping for variable word-length b and clipping at
129
Table 7.2. Implementation Loss on uncoded 64QAM at a BER of
due to
I/Q imbalance
131
Table 7.4. Simulated Implementation Loss on uncoded 64QAM at a BER of
due to magnitude clipping, for different normalized clipping factors
(normalized to )
139
Table 8.1. Both Festival and Carnival shall be highly flexible, programmable
ASICs
154
Table 8.2. Carnival outperforms Festival with respect to spectral efficiency
and energy efficiency at a moderate increase in area despite a
significantly higher complexity
180
Table 8.3. There is an explosion in code size during top-down refinement
steps
180
Table 8.4. A fair reuse percentage between the two designs was obtained
despite significant algorithmic changes
181
How to make them work?
Preface
Wireless Local Area Networks (WLANs) experience a growing
popularity recently. Where WLANs were primarily used for niche
applications in the past, they are now deployed as wireless extensions to
computer networks. The increase of the datarates from 2 Mbps up to 11
Mbps for roughly a constant price has played a major role in this
breakthrough.
As a consequence, an even greater success can be envisioned for the
more recent OFDM-based WLAN standards in the 5 GHz band, which offer
up to 54 Mbps. At IMEC we have realised this potential already several
years ago and have established a successful research programme on OFDMbased WLAN.
In 1995, we started our research on wireless OFDM in the frame of a cooperation project with SAIT, a Belgian telecom company. The goal of the
project was to establish a robust network for industrial environments. This
resulted in a first OFDM chip, supporting QPSK, for wireless networking at
the end of the project (1999).
1999 was also the start of an intense co-operation with National
Semiconductor Inc., which resulted in a second generation ASIC in 2000.
This OFDM processor supports up to QAM-64 and has a more optimal
channel estimation algorithm.
Meanwhile, we have set-up a co-operation program, which currently
includes more then 10 partners. In the program we expanded our activities
from the digital baseband signal processing towards the 5GHz front-end and
the MAC implementation. We also defined a roadmap to realise WLAN
systems with an indoor range up to 100 meters and a capacity beyond 100
Mbps. The first goal requires for techniques like adaptive loading and turbo
xviii
OFDM Systems
coding. For increasing the network capacity, multiple antenna techniques
play an essential role.
To let a wider audience profit from our long-time experience with
implementing WLAN OFDM systems, we also developed a tutorial, which
has been delivered several times with great success. Recently, however, the
interest for wireless OFDM is spreading in new application domains with a
rapid increase of the interested audience as a consequence. For instance,
wireless access standards are adopting OFDM based solutions, it was
proposed for wireless personal area networks and it is heavily promoted as a
candidate for next generation mobile networks. This led us to the idea to put
our tutorial material down into a manuscript.
The result of this effort is in front of you. We hope that you enjoy reading
it and that it is useful in your professional work.
Marc Engels
How to make them work?
Contributors
Boris Come is the leader of the architecture design team in the mixedsignal and RF applications (MIRA) group of IMEC. Boris was born in
France in 1974. He graduated from the National Engineering School of
Electronics in Toulouse, ENSEEIHT, in June 1998. As part of his studies, he
performed two internships: the first one was a three-month summerstay in
ESA-ESTEC in 1997; the second one a four month internship, from March
to June 1998, at IMEC. After graduating, he started working in the MIRA
group at IMEC. His main research interests are in the design of mixed-signal
and RF front-ends for digital telecom system. For the past 2 years, he has
been working on system specification and architecture definition for
HIPERLAN/2 and IEEE 802.1la compliant WLAN transceivers. His main
focus was the RF module for which a single package solution is targetted.
Luc Deneire received the Engineering degree in Electronics from the
University of Liege (Belgium) in 1988, the Engineering degree in
Telecommunications from the University of Louvain-La-Neuve in 1994 and
the Ph.D. degree in Signal Processing at Eurecom, Sophia-Antipolis, France
in 1998. During this time, he was a Marie Curie Fellow. In 1999, he was
consultant for Texas Instruments, Villeneuve-Loubet, France, for the UMTS
base-station signal processing requirements. Since late 1999, he is a senior
researcher at IMEC, the largest European independent research institute in
Microelectronics. He is working on the signal processing algorithms
involved in wireless communications, specifically for third generation
mobile network, Wireless LANs and Wireless Personal Area Networks. His
main interests are blind and semi-blind equalisation and channel estimation,
modulation theory, multiple access schemes, smart antennas and link
adaptation. He is the author of more than 40 conference and journal papers.
xx
OFDM Systems
Wolfgang Eberle received the M.S. degree in Electrical Engineering
from Saarland University, Saarbruecken, Germany, in 1996 with
specialization in microwave engineering and telecommunication networks.
He joined the Wireless Systems Group of IMEC in 1997 working on
algorithm development and digital VLSI architecture design for OFDMbased wireless LAN modems. In 2000, he joined the Mixed-Signal and RF
Applications Group of IMEC where he now focusses on system-level mixedsignal aspects including digital compensation of receiver nonidealities,
power-efficient transmitters, and design methodologies, applied to wireless
LANs. He is also working towards the Ph.D. degree in Electrical
Engineering at the Katholieke Universiteit Leuven, Belgium.
Marc Engels is co-founder of LoraNet, a new company in fixed wireless
access, and responsible for research and product development. The company
will focus on sub 11 GHz systems that operate under non line-of-sight
conditions. Technologies involved are Orthogonal Frequency Division
Multiplexing (OFDM) and Space division multiple access (SDMA). Before,
Marc Engels was the director of the wireless department at IMEC, focussed
on the implementation of telecommunication systems on a chip. For these
systems, he overlooked research on the DSP processing, the mixed-signal
RF front-end and the software protocols. He was also active in design
methods and tools for implementing multi-disciplinary systems. Under his
supervision, several systems have been realised, including a 54 Mbps
WLAN terminal, a GPS-GLONASS receiver, a DECT-GSM dual mode
phone, a cable modem, etc. Previously, Marc performed research at the
Katholieke Universiteit Leuven, Belgium, Stanford University, CA, USA,
and the Royal Military School, Brussels, Belgium. Marc Engels received the
engineering degree (1988) and the Ph.D. (1993), both from the Katholieke
Universiteit Leuven, Belgium. Marc Engels is a visiting professor of telecom
system design at the Katholieke Universiteit Leuven and of embedded
system design at the University of Lugano, Switzerland. He is an active
member of the KVIV telecommunications society and URSI, secretary of the
IEEE Benelux chapter on vehicular technology and telecommunications and
member of the board of directors of SITEL. He is currently an associated
editor for the Wirelss Personal Communications journal and was associated
editor of IEEE transactions on VLSI in 1999-2000.
Bert Gyselinckx is heading the Wireless Systems group of IMEC. This
group performed projects in the fields of WLAN, broadband satellite
communication, navigation systems and cellular communication. His main
research interests are in spread-spectrum, wireless communications and
VLSI systems. Bert received the M.S. degree in Electrical Engineering from
How to make them work?
xxi
the Rijksuniversiteit Gent, Belgium, in 1992 and the the M.S. degree in Air
and Space Electronics from the Ecole Nationale Superieure de
l'Aeronautique et de l'Espace, Toulouse, France, in 1993. Previously he
worked for the Research and Development group of Siemens in Munich,
Germany.
Jean-Paul Linnartz is a Department Head with the Natuurkundig
Laboratorium (Nat.Lab.) of Philips Research, at Eindhoven, The
Netherlands. Here, as a Principal Scientist he studied the protection of audio
and video, in particular through the technology of electronic watermarking.
In 1992-1993,he was an Assistant Professor at the University of California at
Berkeley, where he worked on random access for wireless networks. In
1993, he was the first to use the name Multi-Carrier CDMA in one of the
first papers on the combination of OFDM with CDMA. In 1991, he received
his Ph.D. cum laude on multi-user mobile radio networks from Delft
University of Technology, The Netherlands. He has twenty (pending) patents
in the field of electronic watermarking, copy protection and radio
communications. He authored over 100 papers, he is founding Editor-inChief of "Wireless Communication, The Interactive Multimedia CD-ROM",
and he has been guest editor for two special journal issues on Multi-Carrier
Modulation.
Reto Ness received the engineering degree in Electrical Engineering
from the University of Karlsruhe, Germany and from the Ecole Nationale
Supérieure d”Electronique et de Radioélectricité de Grenoble, France, in
1999. He carried out his thesis in the Wireless Systems group at IMEC,,
Belgium, where he focussed on narrow-band interference cancellation in
OFDM-based WLANs. Currently, he works in the development department
of Tenovis GmbH & Co. KG, Germany.
Steven Thoen was born in Leuven, Belgium, in 1974. He received the
diploma of electrical engineering from the Catholic University of Leuven,
Leuven, Belgium in 1997. In October 1997 he joined IMEC where he is
currently finishing the Ph.D. degree from the Catholic University of Leuven,
Leuven, Belgium. During this period, he spent 6 weeks as a visiting
researcher at the Information Systems Lab, Stanford University, Palo Alto,
California, USA. His current research interests lie in the area of digital
communication theory including multiple antenna systems, OFDM
modulation, adaptive modulation and wireless systems. He has authored
several papers and one patent on these topics.
Jan Tubbax is a PhD student at the K.U.Leuven, Who performs its
research in the Wireless Systems (WISE) group of IMEC. The subject of his
xxii
OFDM Systems
Ph. D. research is the design of a high-performance, low-cost wireless LAN
system Jan Tubbax received his M.S. degree as Electrical Engineer,
telecommunications in 1998 from the Department of Electrical Engineering
(ESAT) at the Katholieke Universiteit Leuven, Belgium. The subject of his
M.S. thesis was a study on the performance of protocols for wireless and
mobile communications.
Patrick Vandenameele is the chief systems architect for Resonext
Communications, a fab-less semiconductor company based in San Jose, CA,
USA, developing and marketing end-to-end two-chip Wireless LAN
solutions. Patrick is responsible for the specifications and architectures of
both the PHY and MAC functions. Also, he leads the company’s systems
engineering team located in Leuven, Belgium. Before joining Resonext
Communications, he was a researcher in the Wireless Systems group at
IMEC. His research, funded by an IWT scholarship, resulted in lowcomplexity detection algorithms for OFDM/SDMA, including solutions to
real-world problems such as channel estimation, synchronization, power
control and the integration in a multiple-access protocol. Patrick received the
engineering degree (1996) and the Ph.D. degree (2000), both from the
Katholieke Universiteit Leuven, Belgium. His thesis, entitled Space Division
Multiple Access for Wireless LANs, was published by Kluwer Academic
Publishers. During his studies, he did internships at ST-Microelectronics,
Crolles, France; Sirius, Montpellier France; ENST, Paris, France; KTHElectrum, Kista, Sweden; and the Smart Antennas Research Group at
Stanford University, CA, USA.
Liesbet Van der Perre received the M.Sc. degree in Electrical
Engineering from the K.U.Leuven, Belgium, in 1992. She performed her
M.Sc. thesis research at the ENST in Paris, France. She received the Ph.D.
degree in Electrical engineering from the K.U.Leuven in 1997. Currently,
she is the director of IMEC’s wireless program. Her work focuses on system
design and digital modems for high-speed wireless communications. She
was a system architect in IMEC’s OFDM ASICs development, and the
leader of the turbo coding team. Also, she is a part-time professor at the
University of Antwerp, Belgium.
How to make them work?
xxiii
Acknowledgements
This book was only possible with the help and support of many people.
In the first place, I like to thank all the authors that contributed to the various
chapters. I am particularly indebted to Liesbet Van der Perre, who also
contributed to the concept of the book.
The material in the chapters is the result of the wireless program at
IMEC. I am grateful to all the people that worked with me in this program
during the last 7 years and realised these excellent results.
Finally, a word of thanks is due to my wife Els and my three daughters
Heleen, Laura and Hanne for their patience and support.
Marc Engels