Ultra-Wideband Radio Propagation Channels

Ultra-Wideband Radio Propagation Channels

A Practical Approach

Pascal Pagani Friedman Tchoffo Talom

Patrice Pajusco Bernard Uguen

Series Editor Pierre-Noël Favennec

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A Practical Approach

Pascal Pagani Friedman Tchoffo Talom

Patrice Pajusco Bernard Uguen

Series Editor Pierre-Noël Favennec

First published in France in 2007 by Hermes Science/Lavoisier entitled: “Communications ultra large bande : Le canal de propagation radioélectrique” First published in Great Britain and the United States in 2008 by ISTE Ltd and John Wiley & Sons, Inc. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd John Wiley & Sons, Inc. 27-37 St George’s Road 111 River Street London SW19 4EU Hoboken, NJ 07030 UK USA

www.iste.co.uk www.wiley.com © ISTE Ltd, 2008 © LAVOISIER, 2007 The rights of Pascal Pagani, Friedman Tchoffo Talom, Patrice Pajusco and Bernard Uguen to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Cataloging-in-Publication Data Communications ultra large bande. English Ultra-wideband radio propagation channels / Pascal Pagani ... [et al.]. p. cm. -- (A practical approach) Includes bibliographical references and index. ISBN 978-1-84821-084-4 1. Broadband communication systems. I. Pagani, Pascal. II. Title. TK5103.4.C6213 2008 621.382--dc22

2008030345 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN: 978-1-84821-084-4

Cover image created by Atelier Isatis, based on an original photograph by Denis Stenderchuck. Printed and bound in Great Britain by CPI Antony Rowe Ltd, Chippenham, Wiltshire.

Contents

Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Chapter 1. UWB Technology and its Applications . . . . . . . . . . . . . 21

1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211.2. Definition and historical evolution . . . . . . . . . . . . . . . . . . 22

1.2.1. Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221.2.2. Historical evolution . . . . . . . . . . . . . . . . . . . . . . . . 23

1.3. Specificities of UWB . . . . . . . . . . . . . . . . . . . . . . . . . . 241.4. Considered applications . . . . . . . . . . . . . . . . . . . . . . . . . 261.5. Regulation evolution . . . . . . . . . . . . . . . . . . . . . . . . . . 30

1.5.1. Regulation in the USA . . . . . . . . . . . . . . . . . . . . . . 311.5.2. Regulation in Europe . . . . . . . . . . . . . . . . . . . . . . . 321.5.3. Regulation in Asia . . . . . . . . . . . . . . . . . . . . . . . . . 33

1.6. UWB communication system and standardization . . . . . . . . . 341.6.1. Impulse radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

1.6.1.1. Pulse position modulation . . . . . . . . . . . . . . . . . 351.6.1.2. Pulse amplitude modulation . . . . . . . . . . . . . . . . 38

1.6.2. Direct sequence UWB . . . . . . . . . . . . . . . . . . . . . . 391.6.3. Multiband OFDM . . . . . . . . . . . . . . . . . . . . . . . . . 40

1.7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Chapter 2. Radio Wave Propagation . . . . . . . . . . . . . . . . . . . . . 43

2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.2. Definition of the propagation channel . . . . . . . . . . . . . . . . 43

2.2.1. Free space propagation . . . . . . . . . . . . . . . . . . . . . . 442.2.2. Multipath propagation . . . . . . . . . . . . . . . . . . . . . . 452.2.3. Propagation channel variations . . . . . . . . . . . . . . . . . 47

6 Ultra-Wideband Radio Propagation Channels

2.2.3.1. Spatial selectivity . . . . . . . . . . . . . . . . . . . . . . 482.2.3.2. Frequency selectivity . . . . . . . . . . . . . . . . . . . . 482.2.3.3. Doppler effect . . . . . . . . . . . . . . . . . . . . . . . . 50

2.3. Propagation channel representation . . . . . . . . . . . . . . . . . 512.3.1. Mathematical formulation . . . . . . . . . . . . . . . . . . . . 512.3.2. Characterization of deterministic channels . . . . . . . . . . 52

2.3.2.1. The time varying impulse response . . . . . . . . . . . . 532.3.2.2. The frequency domain function . . . . . . . . . . . . . . 532.3.2.3. The time varying transfer function . . . . . . . . . . . . 542.3.2.4. The delay-Doppler spread function . . . . . . . . . . . . 54

2.3.3. Characterization of linear random channels . . . . . . . . . . 542.3.4. Channel classification . . . . . . . . . . . . . . . . . . . . . . . 55

2.3.4.1. Wide sense stationary channels . . . . . . . . . . . . . . 552.3.4.2. Uncorrelated scattering channels . . . . . . . . . . . . . 562.3.4.3. Wide sense stationary uncorrelated scattering channels 57

2.4. Channel characteristic parameters . . . . . . . . . . . . . . . . . . 582.4.1. Frequency selectivity . . . . . . . . . . . . . . . . . . . . . . . 58

2.4.1.1. RMS delay spread . . . . . . . . . . . . . . . . . . . . . . 592.4.1.2. Coherence bandwidth . . . . . . . . . . . . . . . . . . . . 592.4.1.3. Delay window and delay interval . . . . . . . . . . . . . 602.4.1.4. Exponential decay constants . . . . . . . . . . . . . . . . 612.4.1.5. Cluster and ray arrival rates . . . . . . . . . . . . . . . . 61

2.4.2. Propagation loss . . . . . . . . . . . . . . . . . . . . . . . . . . 622.4.3. Fast fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 632.4.4. Spectral analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 64

2.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Chapter 3. UWB Propagation Channel Sounding . . . . . . . . . . . . . 67

3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673.2. Specificity of UWB channel sounding . . . . . . . . . . . . . . . . 673.3. Measurement techniques for UWB channel sounding . . . . . . . 70

3.3.1. Frequency domain techniques . . . . . . . . . . . . . . . . . . 713.3.1.1. Vector network analyzer . . . . . . . . . . . . . . . . . . 713.3.1.2. Chirp sounder . . . . . . . . . . . . . . . . . . . . . . . . 72

3.3.2. Time domain techniques . . . . . . . . . . . . . . . . . . . . . 733.3.2.1. Pulsed techniques . . . . . . . . . . . . . . . . . . . . . . 733.3.2.2. Correlation measurements . . . . . . . . . . . . . . . . . 753.3.2.3. Inversion techniques . . . . . . . . . . . . . . . . . . . . . 78

3.3.3. Multiple-band time domain sounder for dynamic channels . 783.3.3.1. Principle of multiple-band time domain sounding . . . 803.3.3.2. Description of the SIMO channel sounder . . . . . . . . 813.3.3.3. Extension towards UWB . . . . . . . . . . . . . . . . . . 813.3.3.4. Experimental validation . . . . . . . . . . . . . . . . . . 84

Contents 7

3.4. UWB measurement campaigns . . . . . . . . . . . . . . . . . . . . 853.4.1. Overview of UWB measurement campaigns . . . . . . . . . . 853.4.2. Illustration of channel sounding experiments . . . . . . . . . 91

3.4.2.1. Static measurement campaign over the 3.1–10.6 GHzband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

3.4.2.2. Static measurement campaign over the 2–6 GHz band 953.4.2.3. Dynamic measurement campaign over the 4–5 GHz

band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 953.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Chapter 4. Deterministic Modeling of the UWB Channel . . . . . . . . 99

4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994.2. Overview of deterministic modeling . . . . . . . . . . . . . . . . . 99

4.2.1. FDTD based approach . . . . . . . . . . . . . . . . . . . . . . 1004.2.2. MoM based approach . . . . . . . . . . . . . . . . . . . . . . . 1004.2.3. Ray based approach . . . . . . . . . . . . . . . . . . . . . . . . 101

4.3. Specificity of deterministic modeling in UWB . . . . . . . . . . . 1014.4. Overview of UWB deterministic modeling . . . . . . . . . . . . . 102

4.4.1. Qiu model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1024.4.2. Yao model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1024.4.3. Attiya model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1034.4.4. Uguen and Tchoffo Talom model . . . . . . . . . . . . . . . . 104

4.5. Illustration of a deterministic model formalism . . . . . . . . . . . 1044.5.1. Received signal synthesis . . . . . . . . . . . . . . . . . . . . . 1054.5.2. Ray impulse response without delay . . . . . . . . . . . . . . 1054.5.3. Ray channel matrix without delay . . . . . . . . . . . . . . . 1084.5.4. Described model results . . . . . . . . . . . . . . . . . . . . . 110

4.5.4.1. Emitted waveform and considered scenario . . . . . . . 1104.5.4.2. Channel matrix of each emitted waveform in the LOS

case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1134.5.4.3. Received signal with ideal antennas . . . . . . . . . . . 114

4.6. Consideration of real antenna characteristics in deterministicmodeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

4.7. Building material effects on channel properties . . . . . . . . . . . 1204.8. Simulation and measurement comparisons . . . . . . . . . . . . . 124

4.8.1. Evaluation of real antenna consideration . . . . . . . . . . . 1244.8.2. Evaluation of impulse response reconstruction . . . . . . . . 125

4.9. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

Chapter 5. Statistical Modeling of the UWB Channel . . . . . . . . . . 133

5.1. Experimental characterization of channel parameters . . . . . . . 1345.1.1. Propagation loss . . . . . . . . . . . . . . . . . . . . . . . . . . 134

5.1.1.1. Frequency propagation loss . . . . . . . . . . . . . . . . 134


5.1.1.2. Distance propagation loss . . . . . . . . . . . . . . . . . 1365.1.2. Impulse response characterization . . . . . . . . . . . . . . . 137

5.1.2.1. Delay spread . . . . . . . . . . . . . . . . . . . . . . . . . 1375.1.2.2. Power delay profile decay . . . . . . . . . . . . . . . . . 1415.1.2.3. Ray and cluster arrival rate . . . . . . . . . . . . . . . . 145

5.1.3. Study of small-scale channel variations . . . . . . . . . . . . 1485.1.4. Effect of moving people . . . . . . . . . . . . . . . . . . . . . . 151

5.1.4.1. Observation of temporal variations . . . . . . . . . . . . 1515.1.4.2. Slow fading . . . . . . . . . . . . . . . . . . . . . . . . . . 1525.1.4.3. Fast fading . . . . . . . . . . . . . . . . . . . . . . . . . . 1535.1.4.4. Spectral analysis . . . . . . . . . . . . . . . . . . . . . . . 156

5.2. Statistical channel modeling . . . . . . . . . . . . . . . . . . . . . . 1575.2.1. Examples of statistical models . . . . . . . . . . . . . . . . . 158

5.2.1.1. IEEE 802.15.3a model . . . . . . . . . . . . . . . . . . . 1585.2.1.2. IEEE 802.15.4a model . . . . . . . . . . . . . . . . . . . 1595.2.1.3. Other models . . . . . . . . . . . . . . . . . . . . . . . . . 160

5.2.2. Empirical modeling principles . . . . . . . . . . . . . . . . . . 1625.2.2.1. Propagation loss model . . . . . . . . . . . . . . . . . . . 1625.2.2.2. Modeling the channel impulse response over an infinite

bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . 1635.2.2.3. Modeling the channel impulse response over a limited

bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . 1665.2.2.4. Simulation results . . . . . . . . . . . . . . . . . . . . . . 166

5.3. Advanced modeling in a dynamic configuration . . . . . . . . . . 1695.3.1. Space variation modeling . . . . . . . . . . . . . . . . . . . . . 1695.3.2. Modeling the effect of people . . . . . . . . . . . . . . . . . . 172

5.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

Appendices

A. Baseband Representation of the Radio Channel . . . . . . . . . . . 177B. Statistical Distributions . . . . . . . . . . . . . . . . . . . . . . . . . 181

B.1. Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181B.1.1. Rayleigh distribution . . . . . . . . . . . . . . . . . . . . . 181B.1.2. Rice distribution . . . . . . . . . . . . . . . . . . . . . . . 182B.1.3. Nakagami distribution . . . . . . . . . . . . . . . . . . . . 183B.1.4. Weibull distribution . . . . . . . . . . . . . . . . . . . . . 184B.1.5. Normal distribution . . . . . . . . . . . . . . . . . . . . . . 184B.1.6. Log-normal distribution . . . . . . . . . . . . . . . . . . . 185B.1.7. Laplace distribution . . . . . . . . . . . . . . . . . . . . . 185

B.2. Kolmogorov-Smirnov goodness-of-fit test . . . . . . . . . . . . 186C. Geometric Optics and Uniform Theory of Diffraction . . . . . . . . 189

C.1. Geometric optics . . . . . . . . . . . . . . . . . . . . . . . . . . 189C.1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 189

Contents 9

C.1.2. Field locality principle . . . . . . . . . . . . . . . . . . . . 190C.1.3. Field expression in geometric optics . . . . . . . . . . . . 191C.1.4. Change of local basis . . . . . . . . . . . . . . . . . . . . . 192C.1.5. Incident field . . . . . . . . . . . . . . . . . . . . . . . . . . 192C.1.6. Reflected field . . . . . . . . . . . . . . . . . . . . . . . . . 193C.1.7. Refracted and transmitted field . . . . . . . . . . . . . . . 197

C.2. Uniform theory of diffraction . . . . . . . . . . . . . . . . . . . 200C.2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 200C.2.2. Diffracted field . . . . . . . . . . . . . . . . . . . . . . . . . 200C.2.3. UTD 2D coefficient . . . . . . . . . . . . . . . . . . . . . . 201C.2.4. UTD 3D coefficient . . . . . . . . . . . . . . . . . . . . . . 204

D. Ray Construction Techniques . . . . . . . . . . . . . . . . . . . . . . 209D.1. Ray launching . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209D.2. Ray tracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209D.3. Other techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 211

E. Description of the Time-Frequency Transform . . . . . . . . . . . . 213

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237


Foreword

Although the origins of distant signal transmission are ancient, thetheoretical foundations of modern telecommunication techniques areowed to Claude Shannon’s 1948 publications. Since then, the field oftelecommunications has not stopped evolving. In particular, spread spectrumtechniques enabled unprecedented improvements in the quality and security ofdigital communications under harsh transmission conditions.

Today, the main players in the telecommunication world are facing anincreasing demand for multimedia wireless applications, linked to a real needfor very high throughput radio communication systems. Among the most recentinnovations in this field, the scientific community is particularly interestedin ultra-wideband (UWB) technology. This technique consists of transmittingradio signals spreading over very large frequency bandwidths, typically in theorder of 500 MHz to several GHz. Initially developed in the field of radarlocalization, UWB technology is now seen as a promising candidate for futurewireless transmission systems. As such, it is considered with an increasinginterest in both scientific and industrial communities.

UWB technology undeniably offers numerous advantages andunprecedented possibilities in the design of radio systems. Its very largespectral bandwidth optimally exploits the benefits of spread spectrumtechniques, by increasing the transmission capacity and by improving thejamming immunity. Simultaneously, UWB presents a high resolution inthe time domain, which may be used to efficiently process the multiplepropagation paths or handle localization issues. In particular, the capacityof UWB pulses to travel through different materials allows us to considerthrough-wall imaging applications. It is also noteworthy that UWB systemspresent a low power spectral density, which not only increases the discretionand security of wireless communications, but also reduces the potentialjamming experienced by other spectrum users. Finally, the complexity of


UWB transceivers may be considerably reduced with respect to traditionalarchitectures.

These characteristics are unique to UWB technology and enable thedesign of communication systems offering very high data rates, up to severalhundred Mbps. In 2002, the Federal Communication Commission (FCC) –an American regulation body – authorized the transmission of UWB signalsin the 3.1–10.6 GHz band, encouraging the research efforts in this field inall continents. In Europe, a transmission mask for UWB signals has beendefined and the coexistence between UWB systems and other applications isunder study. In the current context of high demand for wireless multimediaapplications, UWB seems to be an innovative and attractive solution forfuture radio communication systems. As an illustration, important industrialconsortiums such as UWB Forum and WiMedia Alliance are currentlyinvolved in the design of UWB based equipment.

These systems are particulary well suited to ad hoc communicationnetworks, but a number of other applications may be envisioned by exploitingthe unique characteristics of UWB. The possibility of accurate localizationenable the development of sensor networks known as radio frequencyidentification (RFID), for industrial environment applications or for massmarket geographical information services. Radar identification techniquesbased on UWB signals may be exploited to design anti-collision systems forvehicles, but may also be used in the fields of civil engineering, medicine andimaging. Numerous applications still need to be explored, associating UWBwith advanced techniques such as multiple-input multiple-output (MIMO)antennas techniques or time reversal techniques.

In order to develop such systems, many challenges are still to beencountered. The short duration of UWB signals requires a high accuracy inthe system synchronization procedure. Also, electronic components need to beadapted in order to process such a wide frequency band, while maintaininga tractable complexity. In particular, the antenna characteristics largely varywith increasing frequency and require an accurate characterization.

Among these scientific challenges, a complete knowledge of the radiochannel properties is fundamental. Indeed, the performance of a wirelesstransmission system is directly linked to the propagation conditions betweenthe emitter and the receiver. These devices need to be designed in orderto benefit from the channel characteristics and to mitigate the channelimpairments. For instance, modeling the propagation loss allows us to estimatethe radio system coverage, while link level simulations may be used to assessthe communication robustness. Owing to the width of its frequency band, the

Foreword 13

UWB propagation channel is intrinsically different from traditional widebandchannels. For instance, the interactions between the radio waves and theirenvironment need to be described more accurately and the variations of thematerial properties with frequency need to be taken into account. It is thusnecessary to closely study the propagation channel in order to evaluate thepotential and the constraints attached to UWB communication systems.

This textbook results from an intense collaboration between FranceTelecom’s Research and Development Division and the IETR–UMR CNRS6164 (Institut d’Electronique et de Telecommunications de Rennes/Instituteof Electronics and Telecommunications in Rennes). These research teamsconducted joint studies on UWB techniques and on the impact of thetransmission channel on UWB communication systems. Through its didacticpresentation and the detailed illustration of the discussed topics, thisdocument is an excellent introduction for engineers and communicationsystems designers as well as for researchers and lecturers willing to expandtheir knowledge to the field of the UWB transmission channel. The originalityof this textbook lies in its experimental approach, which allows the readerto follow step by step the theoretical and practical aspects of radio channelcharacterization and modeling. This approach may easily be adapted todifferent contexts: for different applications, in other environments or indifferent frequency bands, such as the available bands around 17 GHz and60 GHz. It should also be noted that the accurate knowledge of the UWBchannel in the 3.1–10.6 GHz band gives access to all the useful information fordeveloping systems included in this frequency band, such as WiFi systemsoperating around 5 GHz.

This book is divided into five distinct parts.

Chapter 1 presents UWB technology. Its historical evolution, theenvisioned applications and its main characteristics are detailed. UWBspectrum regulation issues and the proposed communications techniques arealso discussed.

Chapter 2 describes the propagation of electromagnetic waves in general.All large scale and small scale radioelectric phenomena at play are highlighted.The reader is then introduced to the area of mathematical representation andits characteristic parameters. This didactic presentation covers both indoor andoutdoor environments and is applicable in both contexts of mobile radio andwireless networks.

Chapter 3 presents an overview of the channel sounding techniques adaptedto UWB technology. A distinction is made between frequency domain andtime domain techniques, with a discussion on the application domains and the


limitation of each solution. The main UWB channel measurement campaignsavailable in the literature, including those conducted by the authors, are listedand illustrated by a few examples.

For the study of the propagation phenomena and the design ofcommunication systems, the UWB propagation channel is simulated usingdeterministic or statistical models. These two modeling approaches are detailedand illustrated in the last two chapters. Chapter 4 focuses on deterministicUWB modeling. A literature review of the proposed deterministic modelsis given, comparing the advantages and drawbacks of each proposal. Thefundamental issues and the theoretical formalism of a UWB deterministicmodel are then detailed. To illustrate this presentation, some examples aregiven, where the authors describe a comprehensive deterministic simulator forthe UWB channel.

Chapter 5 is dedicated to the statistical modeling of the UWB transmissionchannel. The characterization of the most representative radio channelparameters is first presented. Different results available in the literatureare compared and commented upon, hence providing a rich experimentaldatabase on the UWB propagation channel characteristics. After a descriptionof different statistical models, the principles of statistical modeling and thedifferent related issues are presented following an experimental method. Thisapproach is illustrated using a model designed by the authors, allowing for thesimulation of the UWB channel in both static and dynamic environments.

Finally, the interested reader will find useful additional informationregarding channel analysis and modeling in the appendices. The discussedtechnical material includes the fields of signal processing, statistics, geometricaloptics and diffraction theory. It should also be noted that the numerousbibliographical references constitute an abundant source of information, whichmay easily be exploited to learn more about the last advances in this field.

This book examines all the characteristics of the UWB transmissionchannel and provides useful tools for designing efficient UWB systems.Non-specialists will be introduced to UWB technology in general and moreparticularly to the propagation channel, which is the key element in acommunication system. Specialists will find valuable information and apractical approach in order to design simulators, set-up measurements, studythe channel characteristics and define models for UWB or in other contexts.This reference document is also an excellent basis for further research onadvanced techniques, such as time reversal or UWB transmission in a MIMO

Foreword 15

configuration. I am convinced that this textbook will prove essential readingin future research in the field of UWB communications.

Professor Ghaıs El Zein

Deputy Director at IETR


Acronyms

ADC Analog-to-digital converterAGC Automatic gain controlBER Bit error rateBPSK Binary phase shift keyingCDF Cumulative density functionCDMA Code division multiple accessCEPT Conference of European Postal and TelecommunicationsDAA Detect and avoidDAC Digital-to-analog converterDCS Digital communication systemDOA Direction of arrivalDOD Direction of departureDSO Digital sampling oscilloscopeDS-UWB Direct sequence ultra-widebandECC Electronic Communication CommitteeEIRP Effective isotropic radiated powerESD Energy spectral densityETSI European Telecommunications Standards InstituteFCC Federal Communication CommissionFDML Frequency domain maximum likelihoodFDTD Finite difference time domainGO Geometrical opticsGPS Global positioning systemGSM Global system for mobilesGTD Geometrical theory of diffractionIDA Infocom Development Authority of SingaporeIEEE Institute of Electrical and Electronics EngineersIF Intermediate frequencyIMST Institut fur Mobil- und Satellitenfunktechnik


IR Impulse responseISB Incident shadow boundaryISM Industrial, scientific and medicalITU International telecommunication unionLDC Low duty cycleLNA Low noise amplifierLO Local oscillatorLOS Line of sightMB-OFDM Multiband orthogonal frequency division mutliplexingMIC Ministry of Internal Affairs and CommunicationsMIMO Multiple-input multiple-outputMoM Method of momentsNLOS Non-line of sightOFDM Orthogonal frequency division mutliplexingOOK On-off keyingPAM Pulse amplitude modulationPDA Personal digital assistantPDF Probability density functionPDP Power delay profilePLL Phase locked loopPN Pseudo-noisePPM Pulse position modulationPSD Power spectral densityQAM Quadrature amplitude modulationQPSK Quadrature phase shift keyingRF Radio frequencyRFID Radio frequency identificationRIR Ray impulse responseRSB Reflection shadow boundarySAGE Space alternating generalized expectationSHF Super high frequenciesSIMO Single-input multiple-outputSISO Single-input single-outputSWR Standing wave ratioUHF Ultra high frequenciesUMTS Universal mobile telecommunications systemUNII Unlicensed national information infrastructureUS Uncorrelated scatteringUTD Uniform theory of diffractionUWB Ultra-widebandVCO Voltage control oscillatorVNA Vector network analyzerWBAN Wireless body area network

Acronyms 19

WiFi Wireless fidelityWLAN Wireless local area networkWPAN Wireless personal area networkWSS Wide-sense stationaryWSSUS Wide-sense stationary uncorrelated scattering802.11 IEEE task group on WLAN802.15.3 IEEE task group on high rate WPAN802.15.4 IEEE task group on low rate WPAN


Chapter 1

UWB Technology and its Applications

1.1. Introduction

By the end of the 20th century, studies in the telecommunication field hadmade significant progress. The advent of new radiocommunication technologiesallowed telephony to change from a telegraphic transmission support to aradio transmission support. Over the last few years, the processing speed andstorage size of the computers have increased considerably. This explains thegeneral public’s passion for communicating objects, which require the highspeed transfer of a great amount of information.

One of the current scientific challenges, where significant research effortsare engaged, is related to the use of very high data rate radio transmissionstechniques on relatively short ranges. In this context, ultra-wideband (UWB)technology, initially used in radar, appears to be an ideal candidate for futurewireless communication systems.

This chapter presents the UWB technology and its applications for wirelesscommunication systems. After a definition of UWB and of its historicalevolution, its characteristics are first outlined, then the considered applicationsand the regulation spectrum in the USA, Asia and Europe are detailed. Thechapter ends by presenting the modulation techniques proposed for UWB andby a state of the art of standardization today.


1.2. Definition and historical evolution

1.2.1. Definition

The generic term UWB is used to represent a radio technique which wasstudied under various names. In the earliest writings on this field, we can findthe terms impulse radio, carrier-free radio, baseband radio, time domain radio,non-sinusoid radio, orthogonal function radio and large relative bandwidthradio [BAR 00]. The relative bandwidth is defined by:

Bf,3 dB = 2 · fH − fL

fH + fL[1.1]

where fH and fL respectively represent the upper and lower cut-off frequenciesof the band defined at −3 dB. Initially, UWB signals were defined by a relativebandwidth of 25% or more [TAY 95]. In 2002, the American regulationauthority, the Federal Communication Commission (FCC), extended thisdefinition to a broader category of signals, by including signals with a relativebandwidth Bf,10 dB higher than 20% or with a frequency band higher than500 MHz [FCC 02]. Typically, the bandwidth of UWB signals is about500 MHz to several GHz. Thus, the denomination UWB not only includesimpulse techniques, but also all the modulations presenting an instantaneousband higher than or equal to 500 MHz.

Pow

er sp

ectra

l den

sity

(dB

m.M

Hz-

1 )

-41.3 dB m.MHz -1

Bandwidth (Hz)

Ultra-wideband

Conventionalnarrowbandmodulation

Spreadspectrum

GHz

MHz

kHz

Figure 1.1. Comparison of various radio system spectrums

Figure 1.1 illustrates the comparison between conventional radio systems,which generally modulate a narrowband signal on a carrier frequency, wideband

UWB Technology and its Applications 23

systems, with spreading spectrum for example, and ultra-wideband systems,which show a weak power spectral density. As a comparison, the bandwidth ofUMTS signals is 5 MHz.

1.2.2. Historical evolution

The study of electromagnetism in the time domain began 40 years ago. Thefirst research was concentrated on radar applications because of the broadbandnature of the signals, which implies a strong resolution1 in the time domain.

It was in 1960 that impulse radars were developed by the American andSoviet armies. Indeed, impulse systems have good space resolution properties.The resolution in distance of a system is conversely proportional to itsbandwidth; the brevity of an impulse signal determines its spectrum width.

In the 1970s, Bennett and Ross presented a complete study of the firstresearch carried out on UWB [BEN 78]. Two decades later, Taylor describedthe bases of the UWB technology applied to radar [TAY 95]. Since the middleof the 1960s, research on this field regularly progressed, as mentioned in thehistorical bibliography published by Barrett [BAR 00]. However, the use ofUWB signals for radio communication was not really considered before the endof the 20th century. In 1990, the Department of Defense of the US governmentpublished the results of its evaluation of UWB technology. These results weremainly concentrated on radar systems, since no application of UWB technologyto communication systems was considered at that point [FOW 90].

More recently, research focused on UWB signals for radio communication[SCH 93, SCH 97a], by using the main characteristics of this technique: a timeresolution around one nanosecond due to the huge frequency bandwidth, a shortduty cycle allowing for modulations such as time hopping and the managementof multi-users, as well as a possible transmission without carrier, which canlead to a simplification of the radio system architecture [FOE 01a].

In 1998, the FCC launched the first study on UWB. In February 2002, afirst regulatory report was published, allowing particularly for the transmissionof signals in the 3.1–10.6 GHz band for wireless communications, with strongconstraints on the power spectral density [FCC 02]. From this date, intensiveacademic and industrial research was undertaken with the aim of proposing apowerful communication systems using UWB technology.

1. The resolution of a system is its capacity to separate very close energy paths.


1.3. Specificities of UWB

With the need for increasing the data rate of wireless systems, the UWBtechnology seems to be an ideal candidate for future radio communicationsystems in various types of networks, which can be residential, office, ad hoc,etc.

As shown in section 1.2.1, the main characteristic of the UWB signal is thewidth of the occupied frequency band, typically about 500 MHz to several GHz.Information theory teaches us that with the use of an appropriate code, it ispossible to transmit data with a binary error rate (BER) lower than a fixedarbitrarily low threshold, that is, if the data rate is lower than the theoreticalvalue of the transmission channel capacity. Thus, channel capacity C gives anindication of the theoretical maximum data rate reachable with a given channel.It can be obtained using Shannon’s theorem [SHA 49]:

C = Bw · log2

(1 +

S

N

)[1.2]

where C is the channel capacity (bit/s), Bw is the signal bandwidth (Hz), S isthe signal power level (W) and N is the noise power level (W).

We can note that for a given bandwidth the channel capacity increases in alogarithmic way with the signal to noise ratio. In the case of a constant signalto noise ratio, the capacity increases linearly with the signal bandwidth.2

In the context of an increasing demand for communication systems withhigh data rates, radio technologies using a broad spectral band are more ableto propose convenient data rates. So, with a frequency band reaching severalGHz, the UWB is well adapted to an increase of data rate than the systemsshowing a high constraint on the bandwidth [FOE 01a].

The main properties of UWB systems are described below:

• High temporal resolution capability

Because of their great bandwidth, UWB signals have a high temporalresolution, typically about one nanosecond. A first implication of thisproperty is related to the localization: knowing the delay of a signal with

2. We can note that for a given signal power level S, the capacity increases nonlinearlywith the bandwidth and reaches the asymptotic value of Clim = S

N0· log2(e), where

N0 is the noise power spectral density.


a precision of about 0.1 to 1 ns, it is possible to obtain information onthe position of the transmitter with an accuracy of 3 to 30 cm.

• Robustness against fading related to multipath propagation

In usual propagation channels, narrowband systems suffer from fadingrelated to the multipath which combine in a destructive way. In the case ofimpulse signals, the transmitted waveforms can have a great bandwidth,so the multipath presenting delays lower than one nanosecond can beresolved and added in a constructive way. This recombination causes somecomplications on the system implementation, as it leads to the design ofa receiver with a great number of diversity branches.

• Low power spectral density

This characteristic is not intrinsic to UWB signals as they were defined(see equation [1.1]), but it is imposed by the radio spectrum regulationauthorities. Indeed, as UWB signals present a wide spread spectrum,the occupied frequency band necessarily covers the frequencies alreadyallocated to existing radio systems. To allow a peaceful coexistence ofUWB with existing narrowband radio technologies, the FCC has limitedthe power spectral density of UWB signals to −41.3 dBm.MHz−1,which corresponds to the power spectral density limit of authorizednon-intentional radio transmissions.3 This low power spectral densityimproves the safety of UWB radio communications, since it becomesmore difficult to detect the transmitted signals. Another consequenceof this characteristic concerns the propagation distance, which is thuslimited to about ten meters. So, the applications considered for UWBsystems are short range and high data rate, and are particularly adaptedto the development of ad hoc networks.

• Less sensitivity to jamming

UWB systems offer a great processing gain.4 Thus, the interference UWBsystems may have on other systems is reduced, thanks to the low level ofthe power spectral density authorized by the FCC. On the contrary, theinterference caused by narrowband systems on UWB systems is a prioriminimized by the bandwidth covered by the impulse signals.

3. Thus, we can consider that UWB radio signals are transmitted “under the noiselevel”, although the imposed limits remain above the thermal noise.

4. The processing gain of a system is a parameter which gives an indication of theresistance of this system against the jamming caused by the other systems.


• Protected and secured communications

UWB signals are signals that are by nature difficult to detect. Indeed, theyare spread over a broad band and transmitted with a low power spectraldensity close to the noise floor level of traditional radiocommunicationreceivers. These characteristics enable secured transmissions with a weakprobability of detection and a weak probability of interception.

• Relative simplicity of the systems design

In terms of implementation, the conventional radio systems are generallyof heterodyne design: the signal which codes the transmitted data isgenerated in baseband and is then transposed to higher frequenciesbefore being emitted. The UWB technology allows the use of impulsegenerated in baseband and directly transmitted on the radio channelwithout modulation. This possibility of transmission without carrier maysimplify the architecture of the radio systems. Indeed, it is possible todesign UWB transmitter-receivers without any synthesizer using a phaselocked loop (PLL), any voltage control oscillator (VCO) or any mixer.Thus, this can lead to the design of systems with low manufacturing andmarketing costs.

• Good obstacle penetration properties

UWB signals offer good capabilities of penetration in the walls and theobstacles, in particular for the low frequencies part of the spectrum. Thismakes it possible to have a good precision in terms of localization andtracking [DEN 03b]. The American company Time Domain, pioneer inthe topic of UWB for communication, has developed a broad activityaround radar systems of vision through walls.

1.4. Considered applications

For a few years, the world of telecommunications has faced an increasingdemand for wireless numerical applications, in the industrial environment aswell as from the general public. Moreover, we can add to this tendency animportant need for total connectivity, the information having to be availablefor anybody, anywhere and at any time [POR 03b]. This increasing need forwireless connectivity leads to the development of many standards for wirelessand short range communication systems. We can mention Bluetooth, the WiFistandards family (IEEE 802.11 a, b and g), Zigbee (IEEE 802.15.4) and therecent standard 802.15.3. We may note that the majority of these technologiesfor wireless local area networks (WLAN) and personal area networks (WPAN)uses free frequencies in ISM and UNII bands, with a maximum bandwidths ofabout 10 MHz.

A comparative study of the characteristics of some wireless technologies ispresented in Table 1.1. Taking into consideration other wireless systems like


Bluetooth or WiFi, the UWB technology presents a very low level of emission.However, we can reach transmission data rates that are definitely higher thanthe two other technologies.

Figure 1.2 shows the position of UWB in comparison with the leadingWLAN and WPAN standards in terms of rate and maximum achievableranges. We can note that contrarily to WiFi standards, UWB technologymainly addresses short range WPAN networks. However, its potential datarate exceeds the performances of all current WLAN and WPAN standards.

UWB

Max

imum

bit

rate

(M

bps)

Maximum indoor range (m)

10 20 30 40 50 100

0.1

1000

100

10

1

WiFi 802.11a

WiFi 802.11b

WiFi 802.11g

Zigbee

Bluetooth

802.15.3

802.15.4a (Low rate UWB)

Figure 1.2. WLAN and WPAN main standards: rate and maximum ranges

In order to provide a high data rate anywhere, the future networks will haveto be designed considering an optimization of the space capacity, namely theglobal available data rate per unit of area.

In narrow band, we generally regard the spectral capacity of the systemsin (bps/Hz) as one of the main parameters for a transmission. The variouselements of a communication system, like the modulation, the coding, theimplementation, etc. make it possible to improve it. By increasing only thetransmission power or the signal band, the capacity also increases. However,the spectral resource for these systems is limited and their power cannot beincreased indefinitely. It is limited by medical or commercial considerations,for example the pollution of the spectrum or the life duration of the batteries.

For UWB systems, the transmission level or the transmitted power spectraldensity must be kept sufficiently low because these systems operate in already


Tec

hnol

ogy

Dat

ara

teFre

quen

cyban

dEIR

PM

odula

tion

Spec

ifica

tion

UW

B≥

100

Mbps

3.1

–10.6

GH

z−4

1.3

dB

m/M

Hz

PP

M,O

FD

M,C

DM

A,..

.IE

EE

802.1

5.3

a

≥500

kbps

3.1

–10.6

GH

z−4

1.3

dB

m/M

Hz

PP

M,O

FD

M,C

DM

A,..

.IE

EE

802.1

5.4

a

Blu

etoot

h≤

700

kbps

ISM

2.4

GH

zty

pe

1:20

dB

mty

pe

2:0

dB

mG

MSK

IEE

E802.1

5.1

WiF

i≤

54

Mbps

5G

Hz

0.2

–1

WB

PSK

,16-Q

AM

,Q

PSK

,64-Q

AM

IEE

E802.1

1a

≤11

Mbps

ISM

2.4

GH

z0.1

–2

WC

CK

,B

PSQ

,Q

PSK

,D

SS

IEE

E802.1

1b

≤54

Mbps

ISM

2.4

GH

z0.1

–1

WB

PSK

,16-Q

AM

,Q

PSK

,64-Q

AM

,O

FD

MIE

EE

802.1

1g

Tab

le1.

1.C

om

pari

son

ofso

me

wirel

ess

com

munic

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tech

nolo

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occupied bands. These low levels are compensated by the use of a broad band.So, compared to the existing wireless systems (see Table 1.2), UWB technologyhas a low spectral capacity. Thus, it is more correct to speak about the spatialcapacity [GHA 04b]. This parameter corresponds to the maximum data rate ofa system divided by the surface covered by this system.

Rate Distance Spatial Spectral

capacity capacity

(Mbps) (m) (kbps/m2) (bps/Hz)

UWB 100 10 318.3 0.013

IEEE 802.11a 54 50 6.9 2.7

Bluetooth 1 10 3.2 0.012

IEEE 802.11b 11 100 0.350 0.1317

Table 1.2. Comparison of the spatial and spectral capacity of some wireless systems

Wireless and very high data rate radio technologies like UWB will makeit possible to considerably increase the spatial capacity, by the developmentof dynamic ad hoc networks [POR 03b]. Finally, we can note that astandardization work is currently in progress in the IEEE 802.15.4a workgroup to use UWB spectrum within the framework of low data rate and shortrange radio links. The expected data rate is typically the same as that of theZigbee standard, with a range of about a hundred meters.

Thus, the potential applications of UWB radio technology are mainly relatedto two techniques: high data rate for short range systems (typically 200 Mbps upto 10 m), and low data rate for long range systems (typically 200 kbps at 100 m).

These two ways of using the UWB radio spectrum allow us to consider agiven number of typical applications for UWB systems [YAN 04, POR 03b].Firstly, UWB technology will make it possible to increase the data rate oftraditional personal wireless networks. So, it will be useful for WiFi networkswhich make wireless access to the Internet network possible, or for connectionsbetween various peripherals (printer, readers, etc.) in limited size environmentsof, for example, one or more rooms. Because of a potential of very high datarate in short range, applications requiring a higher data rate are also possiblewith a range from 1 to 4 meters, for example a high quality multi-media transferbetween a DVD player and a screen. In the same manner, the UWB promotersalso proposed a wireless alternative for the Ethernet standard.


In addition, UWB applications are expected to be used for houseautomation, where a great number of devices able to communicate at adistance of several dozen meters are deployed in an office or residentialenvironment. In this usage, the exploited characteristics of UWB systems arethe low costs of the equipment and the possibility of obtaining localizationinformation. Such potential house automation applications include detectionof intrusion, or the electronic reception (owner detection and launching ofservices like the unlocking of doors).

In outdoor scenarios, UWB technology will be used for point-to-pointcommunication applications. An example usage is the transfer of data betweenseveral personal devices. In addition, some studies are in progress concerningservices of multimedia contents diffusion from electronic kiosks. An exampleof application typical of such electronic kiosks is the download of stockmarketinformation on a portable digital assistant (PDA) every time the user iswaiting at his regular subway station.

Finally, UWB applications are also envisioned in the industrial context.By exploiting the possibilities of long range localization combined withinformation transfer, sensor networks could be deployed in the productionslines or warehouses, in order to follow-up and automatically manage theoperations. This kind of application is well suited for UWB low data rate andlong range communication. The main challenge to be raised for this type ofapplications is the control of radio communication under difficult propagationand interference conditions.

1.5. Regulation evolution

The bandwidth of UWB signals requires a strict regulation of theirtransmission spectrum. Indeed, many systems, whether licensed or not,are presented in UHF and SHF bands, which are very favorable for radiosystems deployment. To allow the use of UWB signals over several GHz,regulatory authorities imposed a strict limitation on the transmission power.Figure 1.3 shows some radio systems existing in UHF and SHF bands.We can note that there are reserved bands for several systems like thestandards of cellular telephony GSM (900 MHz), DCS (1.8 GHz) and UMTS(2 GHz). The global positioning system (GPS) also occupies a reserved bandaround 1.5 GHz. Other frequency bands are already used for unlicensedcommunication systems. For example, the ISM band is used by systems suchas Bluetooth, WiFi and DECT, and is also authorized for domestic devicessuch as microwave ovens. The UNII band is the frequency band where theWiFi 802.11a and HiperLAN standards operate.

In order to limit the UWB signals effects on the other radio systems, theregulatory agencies agree on the use of the 3.1–10.6 GHz band for UWB


signals [AIE 03b].5 This part of the radio spectrum allows us to use abandwidth as wide as 7.5 GHz, while avoiding telephony systems and GPS.The very low authorized power spectral density, located under the level ofunintentional emission fixed by the FCC (−41.3 dBm.MHz−1), is compensatedby the bandwidth, allowing it to emit a total power of 0.6 mW.

3.1 5 10.62.42.01.50.9

Pow

er s

pect

ral d

ensi

ty(d

Bm

.MH

z-1 )

Frequency (GHz)

Unintentionalradiation limit

(-41.3 dBm.MHz-1)

GS

M

GP

SD

CS

ISM

UN

II

UWB

Bluetooth, 802.11b,DECT,microwaveovens

802.11a, HiperLAN

1.8

UM

TS

Figure 1.3. Radio systems in UHF and SHF bands

1.5.1. Regulation in the USA

In the USA, the regulatory agency FCC launched its first works on UWBradio technology as early as 1998 [MOR 03, POR 03a]. In May 2000, a firstproposal for a regulation was published (Notice of Proposed Rule Making),which led to the current regulatory text Report & Order of February 2002[FCC 02].

The FCC rules of the UWB spectrum regulation enable it to emit signalsmainly in the frequency band 3.1–10.6 GHz, by respecting a power spectraldensity lower than the one applied to non-intentional radio transmissions. Threedifferent classes of equipment are considered:• Visualizing systems: ground penetrating radars, through-wall visualizing

systems, medical systems and monitoring systems.

5. We will see that in certain regions of the world (Europe, Asia), only a part of the3.1–10.6 GHz band is considered.


• On-board radar systems: for example, the radars for cars in the 24–29 GHzband.• Communication and measurement systems.

Each class of equipment has its own emission mask. Figure 1.4 presents theemission mask of the communication systems, for indoor use. The spectrumwas defined to ensure a protection of the sensitive systems, more particularlythe GPS (1.2–1.5 GHz), and the bands dedicated to civil aviation.

UW

B E

IRP

em

issi

onle

vel(

dBm

.MH

z-1 )

Frequency (GHz)

FCC (indoor)

CEPT

-75

-70

-65

-60

-55

-50

-45

-40

-35

1 10

1.61

GPS band

3.1

MIC(proposal)

6 8.5

3.8

7.25

2.7

Singapore (UWB FriendlyZone)

1.99

10.25

10.6

0.96

Figure 1.4. UWB systems emission masks

1.5.2. Regulation in Europe

In Europe, the European Telecommunications Standards Institute (ETSI)has operated since 2001 on the attribution of the frequencies in Europe for UWBsystems. The studies are carried out in close cooperation with group SE24 ofthe Conference Europeenne des Postes et Telecommunications (CEPT), whichmore particularly analyzes the possible impact of the UWB systems on theexisting ones [POR 03b]. Normally, these European authorities aim to reach agiven accord for all the European Union States, but each national regulatoryagency keeps the right to manage its radio spectrum independently.

Compared to the American regulation, a more restrictive position wasadopted by the CEPT. In a decision presented in March 2006 [ECC 06],the regulatory organization Electronic Communication Committee (ECC)proposed a spectral mask limiting the emission of UWB signals to the


6–8.5 GHz band with a power spectral density of −41.3 dBm.MHz−1, areshown in Figure 1.4. The emission is also authorized in the band 3.8–6 GHzwith a power spectral density of −70 dBm.MHz−1. However, we shouldnote that such a power limitation does not make it possible to carry outreliable communication systems for a distance of about one meter. Inorder to encourage a fast emergence of UWB systems in Europe, the ECCcurrently considers the possibility of using mitigation techniques to ensure thecompatibility of UWB systems with the other radio services in the 3.1–4.8 GHzband. Among these mitigation mechanisms, we can find the detection andavoidance (DAA) systems which allow us to avoid bands already used by othersystems and the use of low duty cycle (LDC). Hence, all UWB systems usingsatisfactory mitigation mechanisms could be authorized to emit with a powerspectral density of −41.3 dBm.MHz−1 in the 3.1–4.8 GHz band. Temporarily– until June 2010 – the ECC authorizes the emission in the 4.2–4.8 GHz bandwith a power spectral density of −41.3 dBm.MHz−1.

1.5.3. Regulation in Asia

In Asia, the regulation of UWB is particularly well advanced in Japan andSingapore.

In Japan, from September 2002, the Information and TechnologyCommunication Sub-Council working group presented its first investigationson UWB technology at the ministry for telecommunications, in order toprepare the regulation of UWB. Moreover, the Communications ResearchLaboratory (CRL) is developing a project with many industrial partnersin order to design marketable UWB systems. However, the emission maskproposed by their ministry of internal affairs and communications, MIC,remains more restricted than the American mask. As illustrated in Figure 1.4,a preliminary proposal presented in August 2005 suggests a limitation ofUWB emissions to the 7.25–10.25 GHz frequency bands with a power spectraldensity of −41.3 dBm.MHz−1.

At the beginning of 2003, the Singaporean regulatory agency namedInfocom Development Authority (IDA) created a UWB research area,called UWB Friendly Zone, which makes it possible to deploy tests anddemonstrators in Singapore with experiments using an emission power ofabout 10 dB above the FCC limit and a band spreading from 2 GHz to10 GHz [POR 03b]. With that, the IDA tries to give an significant advancein Singapore to new telecommunication technologies, in order to remainscientifically and economically competitive.

To conclude, it should be specified that the greatest constraint of regulationcomes from management of the interference. The problems of UWB regulation


do not come from the effect of only one UWB system, but from the aggregationof hundreds of devices using this technology, creating a sum of signals whichcan possibly interfere with other systems, like the navigation or safety systems.So, the UWB scientific community currently works to test and define systemswhich remain inoffensive, even when using several colocalized equipments.

1.6. UWB communication system and standardization

The emission mask of UWB radio signals established by the FCC allowsthe use of various signals. Figure 1.5 presents various solutions which canbe considered. For each approach, the used frequency band as well as theemission mask of the FCC are presented in the left-hand graph. In each case,the right-hand graph presents the time domain signal corresponding to theband represented in solid line. As we can observe, the duration of the obtainedimpulse is inversely proportional to the bandwidth used.

The mono-band approach consists of using all the frequency band available.It is characterized by very short impulses, therefore resistant to the effects ofsuperimposed multipaths, and the signals can be created from an arbitraryimpulse modeled by an adequate filter. However, this approach allows littleflexibility in the use of the radio spectrum, and requires us to use very powerfulradio frequency (RF) components.

Another solution consists of dividing the allocated UWB spectrum intotwo parts: it is the dual bands approach. It makes it possible to use cheaperintegrated circuit technologies, especially for the low band (typically 3–6 GHz),the high band being used according to the development of new RF components.The flexibility of the spectrum radio remains moderate, but this solution allowsit to avoid an arbitrarily sensitive band, as the UNII band around 5 GHz forexample.

Finally, the multiband approach consists of using frequency bands ofminimal width about 500 MHz. This solution has a very great flexibilityfor radio spectrum management. For example, if the emission mask ismore restricted in a given country, we can avoid the subbands which arenot authorized. The management of the multi-user communications is alsosimplified, as many frequency combinations or temporal multiplexings arepossible.

Many modulation techniques were developed from these various UWBsignals. Historically, the first form of modulation suggested for UWB was theimpulse radio [SCH 93]. Regarding standardization, the American instituteIEEE began the work of defining a high data rate communication system


using the UWB spectrum in 2002. The choice of the type of modulation forthis system was the subject of a procedure of very strict selection, within the802.15.3a work group. The debate for a single solution was mainly articulatedaround two proposals: Direct Sequence UWB (DS-UWB), proposed by theconsortium UWB Forum [FIS 04] and MultiBand Orthogonal FrequencyDivision Multiplexing (MB-OFDM), proposed by the consortium MultiBandOFDM Alliance/WiMedia Alliance [BAT 04b]. In January 2006, as noconsensus could be found for a single solution, the IEEE 802.15.3a groupwas disbanded. Today, only one industrial standard exists concerning UWBsystems: the standard ECMA-368 [ECM 05], developed by the consortiumWiMedia Alliance and based on MB-OFDM.

1.6.1. Impulse radio

The impulse radio concept, developed from radar studies, corresponds to theemission of impulses of very short duration (around 100 ps to 1 ns). Typically,this type of impulses occupies a very broad spectrum (about 1 to severalGHz). It is thus a mono-band approach. The impulse signals generally adoptedfor UWB communications include the Gaussian impulse, its first derivative(Gaussian monocycle), and its second derivative, as represented in Figure 1.6.The drawback of the Gaussian impulse lies in its non-zero mean value, whichcorresponds in the frequency domain to an important continuous component.Thus, the Gaussian impulse cannot be propagated without deformation, andwe generally prefer the Gaussian monocycle [BAT 03].

1.6.1.1. Pulse position modulation

Relation [1.3] gives the typical expression of a transmitted impulse radiosignal, using a pulse position modulation (PPM) [SCH 97a]:

s(t) =∑

j

w(t− j · Tf − cj · Tc −Δ · d� j

Ns�)

[1.3]

where w(t) represents the waveform of a transmitted monocycle, normallystarting from t = 0.

Thus, the transmitted signal corresponds to a sequence of impulsestransmitted at different times, the jth impulse being transmitted atj · Tf + cj · Tc + Δ · d� j

Ns�.

The term j ·Tf allows a uniform spacing of the impulses. Indeed, the signaldefined by:

s(t) =∑

j

w(t− j · Tf

)[1.4]


0 5 10 15-80

-70

-60

-50

-40

Pow

er sp

ectra

lde

nsity

(dB

m.M

Hz-1

)(a )

0 0.1 0.2 0.3 0.4-1

-0.5

0

0.5

1

Nor

mal

ized

sign

al

0 5 10 15-80

-70

-60

-50

-40

Pow

er sp

ectra

lde

nsity

(dB

m.M

Hz-1

)

(b)

0 0.5 1 1.5 2-1

-0.5

0

0.5

1N

orm

aliz

ed si

gnal

0 5 10 15-80

-70

-60

-50

-40

Frequency (GHz)

Pow

er sp

ectra

lde

nsity

(dB

m.M

Hz-1

)

(c)

0 2 4-1

-0.5

0

0.5

1

Time (ns)

Nor

mal

ized

sign

al

Figure 1.5. UWB spectrum and signals: mono-band approach (a), dual-bandapproach (b) and multiband approach (c)


0 0.2 0.4 0.6 0.8 1-1

-0.5

0

0.5

1

Time (ns)

Nor

mal

ized

sig

nal

Gaussianpulse

Gaussianmonocycle

Secondderivative

Figure 1.6. UWB impulse waveforms

corresponds to a sequence of impulses uniformly distributed, with a pulsespacing equal to Tf seconds.

The impulse sequence of relation [1.4] is represented in Figure 1.7(a). Tf isgenerally called “frame duration” and is about 100 to 1000 times the impulseduration. This makes it possible to obtain signals with a low duty cycle, andtherefore with a low power spectral density. However, we should note that theperiodicity of this signal generates parasitic spikes in the radio spectrum. Inaddition, impulses cyclically transmitted by the users of the network are verysensitive to collision when the signals access the channel.

These two problems are solved by the use of a temporal pseudo-randomhopping code. The frame of duration Tf is subdivided in a given numberof time intervals (chip) of duration Tc. Each user is provided with apseudo-random code {cj} of length Ns which indicates in which chip of eachframe the impulse must be transmitted. The use of a pseudo-random codemakes it possible to decrease the effect of appearance of spikes due to theperiodicity of the frame, and the spectrum appears much more smoothed[PEZ 03]. If the pseudo-random sequence is sufficiently long, the UWBsignal can be compared, on the occupied band, to a Gaussian white noise.In addition, the pseudo-random code allows the management of multi-userson the radio channel. The transmitted signal with the considered code isexpressed by:

s(t) =∑

j

w(t− j · Tf − cj · Tc

)[1.5]

and its shape is given by Figure 1.7(b).


Tf

Tc

(a)

(b)

(c)

t

t

t

Figure 1.7. Sequences of radio impulses: (a) sequence of uniformly distributedimpulses, (b) spreading code at position 0, and (c) spreading code at position 1

In relation [1.3], the modulation used to transmit data is PPM. Indeed, theterm Δ represents a time interval of about Tc

2 , and the dk terms are the 0 and1 symbols to be transmitted. The index d� j

Ns�, where �·� indicates the integer

part, shows that the same symbol is used over the whole length of the code.There is thus a redundancy of information, which makes it possible to increasethe processing gain. Under these conditions, when zero is transmitted, thereis no temporal shift in the emission of the data, while a duration shift of Δis applied over the entire code duration when one is transmitted. These twostates are shown in Figure 1.7(b) and (c). We can note that PPM modulationsusing a greater number of states are possible.

Concerning impulse radio, the signals reception is done by correlation. Thebasic idea is to multiply the received signal by a model signal, which makes itpossible to demodulate the transmitted data. So, the model signal correspondsto a given pseudo-random emitted code. Thus, the use of time codes allows themanagement of multi-access [SCH 93]. If several users emit simultaneously byusing orthogonal pseudo-random codes, only the signal corresponding to theselected code will be demodulated, the other users will appear as noise. Thisscheme corresponds to the traditional code multiple division access (CDMA).

1.6.1.2. Pulse amplitude modulation

The pulse amplitude modulation (PAM) is an alternative to the pulseposition modulation. This technique consists of varying the amplitude of thetransmitted impulses to code the different states.

Theoretically, an unlimited number of different values can be used for thesignal amplitude. In practice, the PAM modulation is often reduced to two


states, 1 and -1. Under these conditions, 2-PAM modulation may be regardedas a form of binary phase shift keying (BPSK). This BPSK modulation has agood robustness to the effects of the channel and simplifies the synchronization.Indeed, the position of the impulse remains fixed, and it is only its phase whichvaries.

Another alternative of the PAM modulation consists of transmitting twostates: 1 and 0. This corresponds to an on-off keying (OOK) modulation. In eachdefined transmission time-slot, an impulse is emitted to code 1, and nothing isemitted to code 0.

Finally, we may also consider hybrid modulations. We can for examplecreate a modulation of 512 states by using a combination of 256-PPM witha modulation 2-PAM.

The impulse radio modulation technique was implemented by the Americancompany Time Domain, and was marketed in an electronic chip, named PulsOn210. However, because of the difficulty of implementation and the low spectralflexibility of this type of system, the standardization authorities have chosenother types of modulations, presented in the following subsections.

1.6.2. Direct sequence UWB

The direct sequence ultra-wideband (DS-UWB) modulation is a solutionproposed by the industrial group UWB Forum [FIS 04]. This modulationuses the frequency band allocated to UWB under two dual bands coveringrespectively 3.1–4.85 GHz and 6.2–9.7 GHz. This configuration make itpossible to avoid the UNII band at 5 GHz used by WiFi systems. On thesedual bands, the transmitted impulses have a time duration of about 0.3–0.5 nsand present several cycles (see Figure 1.5(b)). In a first step, only the lowband is used, in order to simplify the architecture of the radio transmissionsystems.

As with the PPM modulation, the DS-UWB modulation uses a framedivided in chips. However, an impulse can be transmitted in each chip ofthe frame. So, the signal is transmitted continuously and there is no lowduty cycle as in the case of the impulse radio. The transmitted symbols arerepresented by ternary spreading codes of one frame length, composed of aseries of 1, 0 or −1. According to the specifications proposed by the UWBforum, all the DS-UWB systems will be able to provide these codes using aBPSK baseband modulation. Optionally, a more efficient modulation, namedM-BOK, is defined in order to ensure a more robust transmission. The lengthof the spreading code varies from 1–24 chips according to the considereddata rate. The transmission data rate proposed for the DS-UWB systems


range from 28–1,320 Mbps. The management of multiple users, clustered insub-networks called piconets, is performed by the use of orthogonal codes.In this prospect, the DS-UWB modulation is similar to the CDMA systemused in UMTS. Finally, we can note that the isolation of users belonging todifferent piconets is improved by the use of slightly different chip frequenciesinto each piconet. More details on this technology can be found in [WEL 03].

Compared to impulse radio, the DS-UWB systems seem easier toimplement, because the considered frequency bands are narrower, whichimposes less constraints on RF components. The used modulation still beingbased on impulses, this radio access technique is robust against the multipatheffects of the channel. In terms of regulation, the separation into two dualbands makes it possible to protect the sensitive frequency bands, but thetransmitted spectrum is not very flexible. In terms of standardization, we maynotice that following the disbanding of the IEEE 802.15.3a working group,no official norm is currently based on the DS-UWB modulation. However,some industrial companies are developing this technical solution, startingfrom the specifications proposed by the UWB Forum group. As an example,the company Freescale Semiconductor, founder of the UWB Forum group,implemented the DS-UWB modulation in the component Freescale XS110.

1.6.3. Multiband OFDM

Multiband orthogonal frequency division multiplexing (MB-OFDM) is asolution based upon the UWB spectrum proposed in standardization and usedby the industrial groups MBOA and WiMedia Alliance [BAT 04b]. It is amultiband approach, where the FCC spectrum is subdivided into 14 subbandsof 528 MHz. Figure 1.8 shows these subbands which are divided into differentgroups. First of all, the industrial companies focussed their development effortson group 1 (3.1–4.9 GHz). The other groups should be quickly exploited in orderto produce systems in conformity with the European and Asian regulation.

In each subband, an OFDM modulation is applied, the signal beingdistributed over 100 carriers with narrow bandwidth. For each carrier, thebaseband modulation is either BPSK or QPSK. This configuration facilitates avery flexible management of the radio spectrum. Indeed, to avoid the jammingof any frequency band, we can forbid a series of carriers or the totality ofa subband. This management can possibly be performed according to thelegislation of the country of use or in a dynamic way according to the potentialjammers. The management of the multi-users of the same group of subbandsis performed using time-frequency code techniques. In a group of subbands,the communication of a given user regularly hops from one band to another,according to a cycle of approximately 1 μs duration. The hopping pattern


from one band to another corresponds to the considered time-frequency code,which is unique to each user. The data rates offered by this technology extendfrom 53.3–480 Mbps. References [BAT 04a, BAT 04b] give all the necessarydetails for the implementation of this system.

0 2 4 6 8 10 12-80

-70

-60

-50

-40

Frequency (GHz)

Pow

er s

pect

ral

dens

ity (

dBm

.MH

z-1)

← ← ←→ → →← ←→ →← ← ←

Group 1 Gr. 5Gr. 3Gr. 2 Gr. 4

Figure 1.8. Subbands for the MB-OFDM solution

The advantages of the MB-OFDM radio access technique are mainly relatedto its low complexity of implementation, as the OFDM modulation shows a highdegree of maturity. Moreover, it is currently the only UWB communicationtechnique developed as an international standard, ECMA – 368, available sinceDecember 2005. The restriction on the used frequency band to the first groupof subbands allows it to use existing systems and RF components. However,in order to achieve an international deployment of the MB-OFDM solution,it will be necessary to develop systems operating under the European andAsian frequency regulations. In technical terms, it should be noted that signalsare no longer impulsional, and the technology no longer benefits from theadvantages related to a very wide frequency band, such as the robustnessto the radio channel effects or the possibilities of localization. The integratedcircuit UBLink proposed by the company Wisair is an example of commerciallyavailable MB-OFDM design.

1.7. Conclusion

Initially used for radar localization applications, UWB technology hasbeen studied for the last 15 years in the field of wireless communications.The main characteristics of this technology, like the width of the spectrum


and its strong temporal resolution, made it possible for the scientific andindustrial communities to propose a certain number of interesting applications:high data rate WLAN networks, home automation applications, etc. Asdeveloped in this chapter, various types of UWB modulations were proposedin standardization, in particular DS-UWB and MB-OFDM. UWB regulationhas been effective in the USA since 2002. In Europe, a mask of emission forUWB signals was established in 2006, but the coexistence of UWB systemswith other applications is still under study.

As for any radio access technique, an accurate knowledge of the propagationchannel as well as the antennas is predominant for the development ofUWB communication systems. Thus, the following section presents the radiowaves propagation phenomena inside buildings, and describes the principalparameters for UWB radio channel characterization. In this book, we addressantennas by including them in the channel. A thorough study of the antennasin the specific case of UWB could be the subject of a specific book. Indeed,the realization of an antenna presenting good characteristics in terms ofadaptation and radiation on such a broad band is still a challenging task[SCH 03c, SCH 03b, OSS 03].

Chapter 2

Radio Wave Propagation

2.1. Introduction

The existence of electromagnetic waves was theoretically predicted byJ.C. Maxwell as early as 1855 [MAX 55]. The German physicist Hertz tried todemonstrate that electromagnetic waves travel at a finite speed, and in 1886he performed the very first radio propagation experiments. The oscillatingcircuit designed by Hertz consisted of two discharging metallic spheres, whichproduced an observable spark on an open wire loop [SCH 86]. Interestingly,the signal used by Hertz consisted of a short duration pulse, which couldhence be regarded as an ultra-wideband signal [AIE 03a].

In order to facilitate the industrial use of radio transmission, a largeamount of research has been conducted to characterize the electromagneticwave propagation mechanisms. This research first focused on signals confinedin narrow frequency bands and then extended to wideband signals. Thischapter details the definition of the propagation channel and its mathematicalrepresentation. The characteristic parameters of the radio-mobile channel arethen presented.

2.2. Definition of the propagation channel

By definition, a radio transmission system transforms an emitted electricalsignal e(t) into a received electrical signal s(t) by means of electromagneticwaves. The propagation channel corresponds to the system converting thesignal e(t) into the signal s(t) and thus accounts for the interactions betweenthe electromagnetic waves and their environment. At this point, a distinctionshould be made between the propagation channel and the transmission


channel. The propagation channel represents the transformation of theelectromagnetic waves throughout their propagation, while the transmissionchannel also includes antenna radiation patterns (cf. Figure 2.1). In theliterature, some authors assimilate these two concepts, but the distinctioncomes fully into play when considering multiple-input multiple-output(MIMO) channels [COS 04]. The full study of antennas in the specificUWB context would require a dedicated book. Indeed, the development ofa UWB antenna presenting adequate characteristics in terms of adaptationand radiation over such a wide frequency band is still a challenging issue[SCH 03c, SCH 03b, OSS 03].

Emittedsignal

e(t)

Receivedsignal

s(t)

Propagation channel

Transmission channel

Figure 2.1. Propagation channel and transmission channel

2.2.1. Free space propagation

Let us first consider an ideal case where the transmission system is placedin free space, i.e. in an environment where no obstruction is present. Denotingby GE the emission antenna gain and PE the emitted signal power, the powerdensity observed at a distance d is given by [PAR 00]:

W =PEGE

4πd2[2.1]

The power PR collected at the output of a receiving antenna with gain GR

relates to the power density W as follows:

PR = WAR = Wλ2GR

4π[2.2]

where AR represents the effective area of the receiving antenna, and λ representsthe wavelength at the working frequency.

Radio Wave Propagation 45

Equations [2.1] and [2.2] yield the Friis formula, giving the signal attenuationin free space:

PR

PT= GT GR

(c

4πfd

)2

[2.3]

where we used the relation c = fλ existing between the wavelength λ, thefrequency f and the propagation speed c.

It should be noted that this relation holds for a distance d large enough forthe receiving antenna to be considered in the far field region with respect tothe transmitting antenna [AFF 00]. A receiver is situated in the far field if thedistance d is larger than the Fraunhofer distance dF , which is related to thelargest dimension of the transmitting antenna D and to the wavelength λ asfollows:1

dF =2D2

λ[2.4]

Free space propagation is a theoretical or reference situation. In realisticpropagation conditions, the transmitted wave is affected by the systemenvironment through different mechanisms, which are presented in thefollowing section.

2.2.2. Multipath propagation

In a realistic environment, signal transmission follows not only the directpath, but also a number of distinct propagation paths. These paths undergovarious effects depending on the type of interaction between the wave and thesurrounding objects. At the output port of the receiving antenna, the observedsignal corresponds to a combination of different waves, each of them presentinga different attenuation and a different phase rotation. Moreover, each wavereaches the receiver with a distinct delay, linked to the length of the propagationpath. Multipath propagation mechanisms may lead to a significant distortionof the received signal. On the other hand, a direct path, known as the lineof sight (LOS) path, is not always available, which is particularly frequent inindoor configurations. In this case, so called non-line of sight (NLOS) pathsare necessary to enable efficient radio communication. Figure 2.2 illustrates theconcept of multipath propagation, as well as the main propagation phenomena.

1. It should be noted, though, that for systems operating at different frequencies, theantenna dimension D is generally adapted to the wavelength. For a wire antenna, theantenna length is for instance defined as D = λ

2, and hence the Fraunhofer distance

follows dF = λ2.


Receiver

Transmitter

Diffuse reflection

Specularreflection

Diffraction

Diffuse scattering

Transmission

Waveguide effect

Figure 2.2. Main propagation mechanisms

• Reflection: reflection takes place on obstacles of large dimensions withrespect to wavelength. When two different materials are separated by a planesurface (i.e. a surface where possible rough spots are small with respect to thewavelength), the reflection is said to be specular. In this case, the directionand the amplitude of the reflected ray are governed by the Snell-Descartesand Fresnel laws. When the surface separating the two materials presentsnon-negligible random rough spots, the reflection is called diffuse reflection.Most of the energy is then directed along the reflected ray, but part of theenergy is diffused in neighbor directions.


• Transmission: when the medium where a reflection takes place is notperfectly radio-opaque, part of the incident wave travels through the materialfollowing a so-called transmission mechanism. Most of the building materialsused in indoor environments significantly attenuate the transmitted wave. Fora given material, the attenuation and the direction of the transmitted signalare related to the wavelength, since the refractive index of the material varieswith the frequency. Finally, for layered materials such as plasterboard, multiplereflection may occur within the material.

• Diffraction: diffraction takes place on the edges of large sizedobstacles with respect to the wavelength. This mechanism accounts for theelectromagnetic field continuum on either side of the optical line of sight. Thecalculation of a diffracted field uses Huygens’ principle, which considers everypoint of a wavefront as a secondary spherical source. Hence, diffracted wavesare distributed along a geometrical cone, with an angle corresponding to theincident angle.

• Diffusion: when an electromagnetic wave travels towards a group ofobstacles of small dimensions with respect to the wavelength, the observedphenomenon corresponds to the superimposition of a large number of randomdiffractions. In this case, the behavior of the incident wave is handled in astatistical way and the resulting phenomenon is called diffusion. In general, theelectromagnetic wave is directed in all directions with a variable attenuation.This phenomenon is generally observed in outdoor environments, for instancein the presence of tree foliage. In indoor environments, diffusion may occur ona group of small objects.

• Waveguide effect: the waveguide effect occurs in indoor environments,between two corridor walls for instance. Successive reflections on two parallelobstacles lead to a global wave motion along the guiding direction. Thisphenomenon also occurs in urban environments, for instance between twobuildings lining a narrow street.

2.2.3. Propagation channel variations

Owing to the different interactions between the radio waves and theirpropagation medium, significant variations of the channel characteristics areobservable at different scales. When isotropic antennas are used in free space,the resulting power attenuation is proportional to the square of the distanced between the antennas (cf. section 2.2.1). However, actual observationspresent large scale power variations linked to the propagation environment.In practice, the obstacles within the environment as well as the combinationof multiple propagation paths lead to an additional attenuation of the


transmitted waves. In general, this attenuation is a function of the distance dbetween the transmitter and the receiver. It is characterized by the path lossexponent Nd, the received signal power decreasing proportionally to d−Nd .The parameter Nd is equal to 2 in free space, and varies between 2 and 5 inNLOS configurations. In LOS configurations, waveguide effects may lead to avalue of Nd lower than 2. Finally, we may note differences in the order from1 to several dB between the received power and the mean trend following ad−Nd law. This is due to occasional obstructions known as shadowing or slowfading.

Small scale fluctuations are directly linked to multipath propagationmechanisms. Multiple versions of a single signal presenting differentattenuations and different phase delays may eventually combine at thereceiver, which produces significant fast fluctuations in the order of 10 to20 dB.

2.2.3.1. Spatial selectivity

Let us consider a signal composed of a single carrier frequency propagatingalong two paths, the direct path and a reflected path. If the reflection occurs inthe vicinity of the LOS path, we may consider that these two paths will cause asimilar attenuation. However, depending on the wavelength of the transmittedsignal and on the length difference between the two paths, the two versionsof the signal may arrive in phase or antiphase. This concept is illustrated inFigure 2.3. In the first case, the signals are adding constructively and somepower gain is observed. In the second case, the signals are adding destructivelyand the total received power is strongly attenuated. When the mobile device isdisplaced, the phase rotation linked to each path leads to a series of signal peaksand signal fades, which is called a fast fading signal. When this phenomenonoccurs with a large amount of paths, the received signal may be considered asa random process.

2.2.3.2. Frequency selectivity

Let us now consider a more realistic signal, spreading over a givenfrequency bandwidth. As explained in the previous section, the spatialselectivity phenomenon depends on the phase difference between multiplepaths. Thus, spatial selectivity also depends on signal frequency. When thefrequency band is narrow, all frequencies forming the transmitted signalundergo similar phase variations. Hence, the possible power fades are constantover the whole considered frequency band. This phenomenon is known as flatfading.

For signals occupying wider frequency bands, the various frequenciesmay be affected in a different way, and thus the received signal is somehow


t

Vglobal signal

t

V

t

V

t2

t2 + t

reflected path(case 1)

t

V t1direct path

reflected path(case 2)

case 1

case 2

Figure 2.3. Constructive and destructive addition of two propagation paths

distorted with respect to the transmitted signal. In this case, we mayobserve frequency selective fading, which consists of a variation in the powerreceived with increasing frequency. The bandwidth over which the frequencycomponents are affected in a similar way is called the coherence bandwidth orcorrelation bandwidth.

In the delay domain, frequency selectivity corresponds to a delay betweenthe various versions of the signal propagating along different paths. This delay isin the order of a few nanoseconds in indoor environments, and in the order of afew microseconds in outdoor environments. Depending on the signal bandwidth,these echoes may superimpose on each other, which results in significant fades.For signals presenting a very wide frequency band, and particularly for UWBsignals, the time domain resolution is very high, which limits the possibleinterference between different delayed versions of the transmitted signal. Inthis case, signal fading is less pronounced. It is then possible to apply advancedreception techniques, such as channel equalization or RAKE reception,2 in orderto collect as much energy as possible from the multiple propagation paths[CRA 98, FOE 01b, GAU 03].

2. A RAKE receiver combines the signals from different multipaths, by using severalreception branches in parallel [HAY 01].


Finally, it should be noted that in the case of wideband signals, frequencyselectivity leads to a time domain spreading of the transmitted signal.Characterizing this spreading is essential to calibrate communication systemsand mitigate intersymbol interference.3

2.2.3.3. Doppler effectThe spatial selectivity phenomenon demonstrates that the properties of

the radio propagation channel may vary significantly when the receivingantenna is positioned at different locations. It is thus questionable how thepropagation channel is affected when the transmitting antenna, the receivingantenna or even the environment are moving. The Doppler effect correspondsto an observed shift in the frequency of an electromagnetic signal due to thevariation of its propagation path. As a simple example, let us consider amobile receiver moving at a speed v and receiving a radio signal as a planewave arriving with an angle α with respect to the mobile direction. In thiscase, the observed Doppler shift is [PAR 00]:

ν = fvc

cos(α) [2.5]

where f is the signal frequency and c is the wave propagation speed.

The statistical case where the ray distribution is represented by theprobability density function (PDF) of their angle of arrival pα(α) wasdeveloped in [CLA 68]. For a simple case where the handset moves at aconstant speed, the PDF of the Doppler shift pν(ν) is given by:

pν(ν) =1√

1−( ννmax

)2 ·[pα

(− arccos

(ν

νmax

))+pα

(arccos

(ν

νmax

))][2.6]

where νmax is the maximum Doppler shift given by:

νmax = fvc

[2.7]

This theoretical PDF of the Doppler shift may be linked to the Dopplerspectrum of a measured signal. In particular, for a uniform distribution of thearrival angles, the PDF of the Doppler shift is proportional to the Jakes Dopplerspectrum [JAK 93]:

pν(ν) =1

π√

1− ( ννmax

)2 [2.8]

3. Intersymbol interference consists of the corruption of a transmitted symbol by theprevious symbols due to the time domain spreading generated by the propagationchannel. It is one of the main sources for the degradation of the transmission quality.


In what follows, a distinction will be made between the concepts of temporaland spatial variations. Spatial channel variations are due to the displacementof at least one of the antennas in an otherwise static environment. Temporalvariations are linked to a change in the close environment of a fixed radio link[HAS 94a]. In the radio-mobile context, both types of variation are generallyobserved, but one or the other may be considered as predominant, dependingon the situation. In the indoor environment, temporal variations are mainlydue to moving people.

In both cases of spatial and temporal variations, propagation paths betweenthe transmitter and the receiver may appear, disappear or undergo successivetransformations. In the case of a stationary channel, only the existing pathsare considered, and the channel variations consist of an evolution of the pathlength, which may be positive or negative. Hence, both spatial and temporalchannel variations lead to an observed Doppler effect.

2.3. Propagation channel representation

2.3.1. Mathematical formulation

Owing to the multipath propagation phenomena, the received signal s(t)is composed of a number of superimposed replicas of the transmitted signale(t), each of them presenting a different delay and a different attenuation. Thepropagation channel thus behaves like a linear filter. Hence, the propagationchannel may be represented by its impulse response (IR) h(τ), correspondingto the output of this filter when the excitation is a Dirac function. The receivedsignal may thus be written as:

s(t) =∫ ∞−∞

e(t− τ)h(τ)dτ [2.9]

In most radio systems, the transmitted signal spreads over a frequency bandwhich is not centered around zero. A given signal x(t) may thus be representedby its complex envelope γx(t) defined as:

x(t) = �{γx(t)ej2πf0t}

[2.10]

where �{·} represents the real part of a complex number and f0 representsa given frequency in the considered band. The complex envelope γx(t) is alsonamed the equivalent baseband term of x(t).


It can be shown that there are two ways of defining the baseband filterheq(τ) equivalent to the passband filter h(τ) (cf. Appendix A):

heq1(τ) =12γh(τ)

heq2(τ) = h(τ)e−j2πf0τ

[2.11]

The three representations in Figure 2.4 are thus equivalent to observingthe channel effect on the transmitted signal. In the remainder of this book, wewill use, unless otherwise stated, the channel impulse response in its complexenvelope form γh(τ), which will be denoted h(τ) for the sake of simplicity.

h(τ)

heq1(τ) = 12γh(τ)

heq2(τ) = h(τ)e−j2πf0τ

�

�

�

�

�

�

e(t)

γe(t)

γe(t)

s(t)

γs(t)

γs(t)

Figure 2.4. Equivalent representations of a static radio-mobile channel

2.3.2. Characterization of deterministic channels

The representation of the radio channel in the form of an IR h(τ) is valid forstatic channels only. In practice, the environment or the antenna position maybe modified, and hence the radio channel may vary with time. The IR h(t, τ)is thus dependent on both time and delay. The inputs and outputs of a linearfilter may be described in the time domain or in the frequency domain. Thisleads to a set of four transfer functions that may be used to describe the radiochannel [BEL 63]. Figure 2.5 illustrates the relations between these functions.


h(t, τ)

T (f, t)

H(f, ν)

S(τ, ν)

time-delay

frequency-time

frequency-Doppler

delay-Doppler�

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

F−1 F−1

F F

F F

F−1 F−1

Figure 2.5. Characteristic functions for a deterministic channel. Arrows represent aFourier transform (F) or an inverse Fourier transform (F−1)

2.3.2.1. The time varying impulse response

The function h(t, τ) is called the time-variant impulse response. It relatesthe received signal s(t) to the transmitted signal e(t) according to the followingfiltering operation:

s(t) =∫ ∞−∞

e(t− τ)h(t, τ)dτ [2.12]

The magnitude of this impulse response may be observed to distinguishbetween different signal echoes according to their propagation delay. Equation[2.12] thus provides a physical representation of the channel as a continuumof scatterers that are fixed – since their delay is constant – and scintillating –which corresponds to the channel’s temporal evolution.

2.3.2.2. The frequency domain function

The function H(f, ν) is also called the output Doppler-spread function andreflects the Doppler shift phenomenon caused by the channel. It is the dualfunction of the function h(t, τ) in the frequency-Doppler shift space. It thus


relates the received signal spectrum S(f) to the transmitted signal spectrumE(f) as follows:

S(f) =∫ ∞−∞

E(f − ν)H(f − ν, ν)dν [2.13]

Using this representation, the output signal spectrum S(f) is consideredas the sum of superimposed input signal spectrum replicas E(f), each replicabeing Doppler shifted and filtered.

2.3.2.3. The time varying transfer function

Another approach to characterizing the radio channel consists of describingthe relation between the time domain output signal s(t) to the input signalspectrum E(f), using the time varying transfer function T (f, t):

s(t) =∫ ∞−∞

E(f)T (f, t)ej2πftdf [2.14]

The function T (f, t) is related to the functions h(t, τ) and H(f, ν) through asimple Fourier transform. If the bandwidth of the considered channel is narrowenough, the time-variant transfer function may be directly measured using anetwork analyzer.

2.3.2.4. The delay-Doppler spread function

A final approach consists of representing the radio channel in thedelay-Doppler shift space. The corresponding function allows us tosimultaneously observe the channel dispersion in both the time domain andthe frequency domain. For this reason it is referred to as the delay-Dopplerspread function. The function S(τ, ν) relates the output signal s(t) to theinput signal e(t) through the following relation:

s(t) =∫ ∞−∞

∫ ∞−∞

e(t− τ)S(τ, ν)ej2πνtdνdτ [2.15]

Equation [2.15] represents the output signal s(t) as a sum of superimposedreplicas the input signal e(t), each replica being delayed and Doppler-shifted.The function S(τ, ν) is related to the functions h(t, τ) and H(f, ν) through asimple Fourier transform.

2.3.3. Characterization of linear random channels

In practical situations, the propagation channel fluctuations are due to anumber of superimposed phenomena, which cannot be measured individually.


The radio channel variations may thus be regarded as a random process and itis no longer valid to describe them deterministically. The propagation channel isthus characterized in a statistical way. In practice, the statistical description ofthe channel is limited to the second order, and we consider the autocorrelationfunctions of the channel system functions only. These functions are defined asfollows:

Rh(t, u; τ, η) = E[h(t, τ)h∗(u, η)

]RH(f,m; ν, μ) = E

[H(f, ν)H∗(m,μ)

]RT (f,m; t, u) = E

[T (f, t)T ∗(m,u)

]RS(τ, η; ν, μ) = E

[S(τ, ν)S∗(η, μ)

][2.16]

where E[·] represents the mathematical expectation and (·)∗ represents thecomplex conjugation operation.

These four autocorrelation functions are linked through double Fouriertransforms in a similar scheme to the one linking the channel system functions(cf. Figure 2.5). The second order moments of the input and output signalsare then given by:

Rs(t, u) =∫ ∞−∞

∫ ∞−∞

e(t− τ)e∗(u− η)Rh(t, u; τ, η)dτdη

Res(t, u) =∫ ∞−∞

Re(t, u− η)h(u, η)dη

[2.17]

The first and second order moments are sufficient to completely describethe output signal s(t) in the case of a Gaussian signal.

2.3.4. Channel classification

The representation of the random radio channel may be simplified byconsidering different assumptions about the channel characteristics.

2.3.4.1. Wide sense stationary channels

A channel is considered as wide sense stationary (WSS) if its temporal (orspatial) variation meets the statistical conditions of second order stationarity.In other words, the expectation of the channel impulse response needs to beinvariant with time, and its autocorrelation Rh(t, u; τ, η) will depend on the


variables t and u through the difference ξ = t − u only. In practice, theseconditions mean that the channel fluctuation statistics are constant over ashort time interval ξ, which is a reasonable assumption for traditional channels(e.g. indoor or urban environment). Under these conditions, the autocorrelationfunctions of the time-variant impulse response and the time-variant transferfunction may be written as:

Rh(t, t + ξ; τ, η) = Rh(ξ; τ, η)

RT (f,m; t, t + ξ) = RT (f,m; ξ)[2.18]

Considering the double Fourier transform relationship between Rh(t, u; τ, η)and RS(τ, η; ν, μ), and using ξ = t− u, this yields:

RS(τ, η; ν, μ) =∫ ∞−∞

∫ ∞−∞

Rh(t, u; τ, η)ej2π(uμ−tν)dtdu

= δ(ν − μ)∫ ∞−∞

Rh(ξ; τ, η)e−j2π(ξν)dξ

= δ(ν − μ)PS(τ, η; ν)

[2.19]

where the term PS(τ, η; ν) may be identified as a power spectral densityobtained from Rh(ξ; τ, η) by applying the Wiener-Kinchine theorem.

This last relation indicates that the spectral content of the signal isuncorrelated for different Doppler shifts. Physically, this means that echoesgenerating different Doppler shifts are uncorrelated. Similarly, we may writethe autocorrelation of the frequency domain function as:

RH(f,m; ν, μ) = δ(ν − μ)PH(f,m; ν) [2.20]

2.3.4.2. Uncorrelated scattering channels

Under the uncorrelated scattering (US) assumption, we consider that thecontributions from elemental scatterers corresponding to different delays areuncorrelated. This condition is equivalent to an assumption of second orderstationarity in the frequency domain. As in the WSS case, we may simplify theautocorrelation functions of the frequency domain function and the time-varianttransfer function as follows (and noting by Ω the frequency difference m− f):

RH(f, f + Ω; ν, μ) = RH(Ω; ν, μ)

RT (f, f + Ω; t, u) = RT (Ω; t, u)[2.21]


The time-variant impulse response and the delay-Doppler spread functionmay be re-written in the form of power spectral densities:

Rh(t, u; τ, η) = δ(η − τ)Ph(t, u; τ)

RS(τ, η; ν, μ) = δ(η − τ)PS(τ ; ν, μ)[2.22]

2.3.4.3. Wide sense stationary uncorrelated scattering channels

A wide sense stationary uncorrelated scattering (WSSUS) channel followsboth the WSS and US assumptions. It corresponds to the simplest class ofchannels, which presents an uncorrelated spread in both the delay domain andthe Doppler shift domain. In this case, the autocorrelation functions of the fourchannel system functions may be simplified as follows:

Rh(t, t + ξ; τ, η) = δ(η − τ)Ph(ξ; τ)

RH(f, f + Ω; ν, μ) = δ(ν − μ)PH(Ω; ν)

RT (f, f + Ω; t, t + ξ) = RT (Ω; ξ)

RS(τ, η; ν, μ) = δ(η − τ)δ(ν − μ)PS(τ ; ν)

[2.23]

Figure 2.6 illustrates the simple Fourier transform relationships linking thefour autocorrelation functions for a WSSUS channel.

Two of the obtained functions are of particular interest. The functionPS(τ ; ν) is called a scattering function. It physically represents the Dopplerspectrum of radio wave paths as a function of their propagation delay.

For ergodic signals, the function Ph(ξ; τ) may be written as:

Ph(ξ; τ) = E[h(t + ξ, τ)h∗(t, τ)

]= lim

T→∞1T

∫ T2

−T2

h(t + ξ, τ)h∗(t, τ)dt[2.24]

Hence, the term Ph(0, τ) corresponds to the temporal average of the impulseresponse power. This function is called the power delay profile (PDP).

In practice, it is generally assumed that observed channels fall under theWSSUS assumption. For measured channels, it is sometimes necessary to


Ph(ξ, τ)

RT (Ω, ξ)

PH(Ω, ν)

PS(τ, ν)

time-delay

frequency-time

Doppler-frequency

delay-Doppler�

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

F−1 F−1

F F

F F

F−1 F−1

Figure 2.6. Autocorrelation functions of a WSSUS random channel

confirm this postulation. A thorough discussion about the validation of theWSSUS assumption for experimental measurements has been published in[BUL 02]. In particular, the RUN method is based on assessments of theprocess variance over successive sub-intervals [BEN 66].

2.4. Channel characteristic parameters

In order to evaluate the characteristics of a propagation channel, a setof measured impulse responses need to be analyzed. This section presentsa number of parameters describing different aspects of the radio channel.In general, their computation requires the WSSUS assumption. As it is notpractically feasible to collect a set of statistical channel realizations, wegenerally assume that the channel system functions are ergodic. Hence, itis for instance possible to approximate the statistical expectation using atemporal (or spatial) average over a set of successive measurements.

2.4.1. Frequency selectivity

Frequency selectivity is characterized by the presence of multiple paths,particularly observable on the channel’s impulse response. The powerrepartition as a function of the delay is given by the PDP, defined by equation


[2.24]. In order to mitigate the local effects of fast channel fading, the PDP iscalculated from a set of M impulse responses, successively measured over apath length in the order of 20–40 wavelengths [LEE 85]. This calculation isvalid under the stationarity assumption. The following equation presents thePDP calculation:

Ph(0, τ) =1M

M∑m=1

∣∣h(tm, τ)∣∣2 [2.25]

2.4.1.1. RMS delay spread

The root mean squared (RMS) delay spread τRMS, sometimes simplyreferred to as delay spread, represents the standard deviation of the PDP. It iscalculated as follows:

τRMS =

√√√√∫∞−∞ (τ − τm

)2Ph(0, τ)dτ∫∞

−∞ Ph(0, τ)dτ[2.26]

where τm is the mean delay given by:

τm =

∫∞−∞ τPh(0, τ)dτ∫∞−∞ Ph(0, τ)dτ

[2.27]

2.4.1.2. Coherence bandwidth

The RMS delay spread is a significant parameter for the analysis of theintersymbol interference. It is also closely linked to the correlation between thedifferent frequencies of the signal spectrum. In order to quantify this frequencydependence, the n% coherence bandwidth is defined from the autocorrelationof the channel transfer function RT (Ω, ξ):

Bc,n% = min{

Ω :∣∣∣∣RT (Ω, 0)RT (0, 0)

∣∣∣∣ = n

100

}[2.28]

The function RT (Ω, 0) is referred to as the frequency correlation functionand is obtained from the PDP Ph(0, τ) by a simple Fourier transform. Thecoherence bandwidth is thus the frequency lag above which the frequencyautocorrelation function crosses a given threshold. Thresholds generally givenin the literature are 90% and 50% [BAR 95].


0 2 3

Rel

ativ

e m

agni

tude

(dB

)

Noise level

Delay (ns)1

q% of the total energy

Figure 2.7. Power delay profile defining the delay window

2.4.1.3. Delay window and delay interval

Two other parameters are also used to give a more precise idea of the PDPspread [COS 89]. The q% delay window is the duration of the central part ofthe PDP containing q% of the total energy. Referring to the delays representedin Figure 2.7, the delay window is given by:

Wq% =(τ2 − τ1

)q%

[2.29]

The delays τ1 and τ2 are defined by:∫ τ2

τ1

Ph(0, τ)dτ =q

100

∫ τ3

τ0

Ph(0, τ)dτ [2.30]

and the energy which is outside the window is split into two equal parts. Thedelays τ0 and τ3 are the delays at which the PDP first rises and finally fallsthrough the signal noise level.

The p dB delay interval refers to a threshold positioned at p dB below themaximum of the PDP. It simply corresponds to the interval from the first delayat which the PDP exceeds this threshold to the last delay at which it falls belowthis threshold.


2.4.1.4. Exponential decay constants

A number of analyses of the UWB radio propagation channel agree ona representation of the impulse response in the form of a discrete sum ofindividual contributions. Each contribution, known as ray, corresponds to apropagation path and is characterized by its distinct delay and amplitude.This representation is widely used for wideband channels [HAS 93]. In order toaccount for the possible presence of ray clusters, this discrete impulse responseis represented using the formalism proposed by Saleh and Valenzuela [SAL 87]:

h(t, τ) =L(t)∑l=1

Kl(t)∑k=1

βk,l(t)ejθk,l(t)δ(τ − Tl(t)− τk,l(t)

)[2.31]

where L(t) is the number of clusters, Kl(t) is the number of rays in the lth

cluster, and Tl(t) is the arrival time of the lth cluster. Parameters βk,l(t),θk,l(t) and τk,l(t) respectively represent the magnitude, the phase and thearrival time associated with the kth ray within the lth cluster. Theoretically,all these parameters vary with time. Defining the PDP from a set ofmeasurements according to equation [2.25], and assuming that the delay ofeach ray is approximately constant during the measurements, the Saleh andValenzuela formalism yields the following formula:

Ph(0, τ) =L∑

l=1

Kl∑k=1

β2k,lδ(τ − Tl − τk,l

)[2.32]

As shown in Figure 2.8, the magnitude of the PDP rays generally followsa decay which is close to an exponential function. This exponential decay maybe observed at both the cluster level and the ray level within a single cluster.The inter- and intra-cluster exponential decay constants, respectively denotedΓ and γ, are thus defined so that the magnitude of the rays obeys the followingrule:

β2k,l = β2

1.1e−Tl−T1

Γ e−τk,l

γ [2.33]

These constants may be retrieved from measurements by applying a linearleast squares fitting procedure on the PDP represented in dB.

2.4.1.5. Cluster and ray arrival rates

Without more accurate knowledge about the environment, it is generallyassumed that ray arrivals correspond to independent events, and that thenumber of these events is dependent on the observation duration only. By


T1 T2 T3

k1

k2

k3

Delay (ns)

Pow

er (

mW

)

e- /

e- /

e- /

Cluster

e- /

Figure 2.8. Power delay profile following the Saleh and Valenzuela formalism

definition, the ray – or cluster – arrivals may reasonably be regarded as aPoisson process. In the Saleh and Valenzuela formalism, it is thus proposed thatthe arrival probability for a new cluster or a new ray follows an exponentiallaw, with respective parameters Λ and λ. Parameters Λ and λ are respectivelycalled cluster and ray arrival rates, and the numbers 1

Λ and 1λ represent the

mean duration between two successive clusters or rays. These parameters areassessed by studying the inter-cluster and inter-ray duration distributions.

2.4.2. Propagation loss

When expressed in dB, equation [2.3] corresponding to the Friis formula forfree space propagation is written:

PL(f, d) = 20 log(

4πfd

c

)−GT (f)−GR(f) [2.34]

where PL(f, d) represents the ratio between the transmitted power and thereceived power.

The slow variations of the propagation channel are mainly due topropagation loss and shadowing effect. For a practical channel, in order to


characterize the double frequency and distance dependence of the path loss,the parameter PL(f, d) is approximated by the following formula:

PL(f, d) = PL(f0, d0

)+ 10Nf log

(f

f0

)+ 10Nd log

(d

d0

)+ S(f, d) [2.35]

where f0 and d0 correspond to an arbitrary frequency and an arbitrarydistance.4 Nf and Nd are called frequency and distance dependent path lossexponents. Parameter Nd accounts for the interactions between the radio waveand the environment, such as the transmission phenomenon or the waveguideeffect, and can significantly differ from the theoretical value Nd = 2. ParameterNf accounts for the frequency dependence of the propagation phenomena,and also includes the variations of the effective area for an ideal isotropicantenna. By considering the propagation channel without antennas in a LOSsituation, this parameter should be close to its theoretical value Nf = 2. Someauthors consider antennas as a part of the propagation channel; in this case,additional variations of the parameter Nf may be observed, which is linked tothe measurement antenna gain. Finally, the term S(f, d) corresponds to theslow variations of the propagation channel. As the parameters Nf and Nd arecalculated by linear regression, the parameter S(f, d) presents a zero average.When expressed in dB, this variable is generally considered as Gaussian, andit is characterized by its standard deviation σS .

In order to calculate the parameter Nf from measurements, we introduce thepower transfer function PT (f), equivalent to the PDP Ph(0, τ) in the frequencydomain. This takes the average received power as a function of frequency for anumber of locally measured transfer functions:

PT (f) =1M

M∑m=1

∣∣T (f, tm)∣∣2 [2.36]

2.4.3. Fast fading

The fast fading of the propagation channel corresponds to the magnitudefluctuations in the received signal. It may be assessed for a narrowband signalor for a given delay in the case of a wideband signal. Mathematically, it ischaracterized by the statistical law of the random variable |h(t, τ)| for agiven τ . In practice, we study a set of samples |h(tm, τ)| corresponding to Mmeasurements taken at close locations (or in a time-variant environment),

4. We may use the central frequency in the considered band for f0, and the distanced0 is generally 1 m.


while verifying that the channel stationarity condition holds. The distributionsgenerally used to assess fast fading include Rayleigh, Rice, Nakagami,Weibull, and log-normal laws (cf. Appendix B). In order to select a specifictheoretical distribution, a goodness-of-fit test is employed, such as theKolmogorov-Smirnov test (cf. Appendix B.2).

Some useful tools also exist to characterize the temporal behavior of a signal.The level crossing rate consists of determining the frequency at which the signalmagnitude decreases below a given threshold. The average fade duration is anestimate of the time during which the signal magnitude stays below a giventhreshold [PAR 00].

2.4.4. Spectral analysis

Another way to characterize temporal variations in the channel consists ofstudying the Doppler spectrum for the main impulse response paths. Thesespectra may be observed on the scattering function PS(τ, ν). In order tocharacterize the channel variations independently of the delay, we use themean Doppler spectrum defined as:

PH(0, ν) =∫ ∞−∞

PS(τ, ν)dτ [2.37]

As in the PDP case, we may define the Doppler spread as:

νRMS =

√√√√∫∞−∞ (ν − νm

)2PH(0, ν)dν∫∞

−∞ PH(0, ν)dν[2.38]

where νm is the mean Doppler shift defined by:

νm =

∫∞−∞ νPH(0, ν)dν∫∞−∞ PH(0, ν)dν

[2.39]

As explained earlier (section 2.2.3.3), the Doppler spectrum is closely linkedto the arrival direction of the multiple propagation paths. Parameters such asthe angular spectrum may be used to characterize the signal’s departure andarrival directions. This is of particular interest for MIMO applications [COS 04].

2.5. Conclusion

In order to design and optimize wireless communication systems, an accurateknowledge of the radio propagation channel is required. The performance of a


wireless transmission system is indeed dictated by the propagation conditionsbetween the transmitter and the receiver. These devices need to be designed inorder to benefit from the channel characteristics and to mitigate its negativeeffects.

In this chapter, the propagation channel characteristics have been presentedin terms of power attenuation and multipath propagation. The spatial andfrequency selectivity concepts as well as the Doppler effect were introduced.Multipath propagation may be regarded as a filter causing a distortion and atemporal variation to the transmitted signal. A mathematical framework waspresented in order to describe both deterministic and random channels. Forthis, the particular case of WSSUS channels has been thoroughly discussed.

A number of parameters are available to characterize the propagationphenomena. We generally model the propagation loss with respect tofrequency and distance, the channel impulse response’s general shape and itsvariations in terms of fast fading. The physical concepts and mathematicaltools presented in this chapter will serve as a basis to describe the simulationand modeling techniques detailed in Chapters 4 and 5.


Chapter 3

UWB Propagation Channel Sounding

3.1. Introduction

Experimental characterization of the radio channel requires the analysisof a large number of propagation measurements. In order to set up ameasurement campaign, a large number of sounding techniques are available[GUI 99]. Selecting one method or the other depends on the measurementenvironment, on the observed frequency band, and on the acquisition speedconstraints.

Sounding UWB channels raises some particular issues, which are developedin this chapter. The different sounding methods for wideband channels arethen exposed, by distinguishing between frequency domain and time domaintechniques. In order to observe the UWB channel fluctuations in more detail,it is necessary to employ a real time measurement technique. For this purpose,we present an advanced sounding technique, exploiting the performances of awideband, single-input multiple-output (SIMO) sounder.

The end of the chapter illustrates the different channel sounding techniquesby presenting a few measurement campaigns. First, the most significant UWBchannel measurement campaigns are listed. For each experiment, the equipmentand the measurement conditions are described. We then present the setting upof a sounding campaign through a few examples.

3.2. Specificity of UWB channel sounding

The purpose of channel sounding is to measure the impulse responseh(t, τ) linking the received signal s(t) to the transmitted signal e(t) through


a filtering operation (see equation [2.9]). Such measurements characterizeboth the frequency selectivity and the time variability of the channel. Inpractice, there is no inverse convolution operation available, that would allowfor the extraction of the impulse response from arbitrary signals e(t) and s(t).However, a number of techniques using specific exciting signals e(t) may beused, where the impulse response is obtained by processing the signals e(t)and s(t). The transmitted signal needs to fulfill some properties depending onthe method used for calculating the impulse response.

Rel

ativ

e m

agni

tude

(dB

)

Delay (ns) Delay (ns)

Delay (ns)

Convolution

Sounder impulse response

Channel impulse response over an infinite

bandwidth

Measured impulse responseUnresolved

path

Rel

ativ

e m

agni

tude

(dB

)

Rel

ativ

e m

agni

tude

(dB

)

Figure 3.1. Time resolution of a wideband sounder

The main characteristics of a wideband sounder are the following:

• Analyzed bandwidth: the analyzed bandwidth corresponds to thefrequency band over which the impulse response is estimated. It generallycorresponds to the bandwidth of the transmitted probe signal. Propagationchannel measurements over bandwidths in the order of 100 MHz is wellsupported by the currently available sounders [GUI 99]. In the case of UWBsignals, the bandwidth of several GHz may represent a challenge for channelmeasurements.

• Time resolution: the time resolution characterizes the sounder’scapability to distinguish between two paths with very close delays. Theimpulse response estimated by the sounder corresponds to a convolution

UWB Propagation Channel Sounding 69

between the channel impulse response over an infinite bandwidth and thesounder’s impulse response over the analyzed band (see Figure 3.1). Thelatter may be obtained by directly cable-connecting the transmitter and thereceiver. The time resolution is generally defined as half the width of thesounder impulse response peak. As an approximation, it may also be definedas the inverse of the analyzed bandwidth. In order to avoid the shadowing ofsome paths by the side lobes of the sounder impulse response, a weightingwindow may be applied [HAR 78]. Such a window is selected as a compromisebetween the level of the side lobes and the width of the main lobe.

• Maximum Doppler shift: when the propagation channel varies with time,we can measure its frequency dispersion by studying its Doppler spectrum (seesection 2.4.4). For this purpose, the sounder needs to be able to quickly measuresuccessive impulse responses. The measurement repetition duration ΔT (meas)

is defined as the duration separating two successive channel measurements. Itencompasses the measurement acquisition duration t(meas) and some time fordata processing and storage. It is then possible to measure a maximum absoluteDoppler shift ν

(meas)max = 1

2ΔT (meas) . However, it should be noted that during themeasurement of a single impulse response, the channel should be considered asstatic. Thus, a sounder capable of measuring the time varying channel needsto present a very low acquisition duration t(meas).

• Dynamic and length of the channel impulse response: the impulseresponse dynamic corresponds to the power ratio between the maximumimpulse response and the noise level. A high dynamic allows the sounder todetect strongly attenuated paths. The length of the channel’s impulse responsecorresponds to the maximum delay that can be measured.

In the case of the UWB propagation channel, the time resolution is generallyhigh, due to the wide analyzed bandwidth. Consequently, developing UWBsounders with a low measurement duration is a challenging task.

Some constraints are common in UWB channels, because of the widemeasured frequency band. Over an analyzed bandwidth of several GHz, thebehavior of the sounding equipment may vary strongly, and this needs tobe accounted for in the measurement process. In particular, the antennascharacteristics need to be stable across the measured frequency band.Narrowband antennas (dipoles, horns, etc.) and dispersive wideband antennas(spiral and log-periodical antennas, etc.) may thus not be used for this purpose[SCH 03a]. In practice, biconical, monoconical or planar UWB antennas are


used. Some examples of these antennas are given in Figure 3.2. In any case, itis necessary to properly characterize the antennas used for the measurement[SIB 04]. The properties of some other pieces of equipment, such as cables oramplifiers, may also vary in frequency, and it is important to characterize eachitem accurately before the measurement.

Ideal biconicalantenna

Biconicalantenna

Bowtie planarantenna

Monoconicalantenna

Figure 3.2. UWB measurement antennas

Finally, a UWB receiver is sensitive to any radio emission at frequenciesnear or within the analyzed frequency band. Before the measurement starts,we need to make sure that the analyzed radio spectrum is free of any jammingfrom external systems. Out-of-band emissions, such as the GSM and WiFisignals, should also be filtered. This can be done using a high-pass filter. Thisfilter should be taken into account during the calibration phase in order not toaffect the measured signal.

3.3. Measurement techniques for UWB channel sounding

This section presents the main UWB radio channel measurement methods:frequency domain methods and time domain methods. For each method, thebasic principles are presented, and the advantages and drawbacks of thismethod are detailed. We finally present an innovative hybrid method for thereal time measurement of UWB channels.


3.3.1. Frequency domain techniques

The frequency domain method is the most commonly used UWB channelsounding technique, on account of its ease of implementation. It consists ofsampling the channel transfer function T (f, t). This is done by transmitting anarrowband signal at a fixed frequency, and by measuring the attenuation andthe relative phase of the received signal [GUI 99]. In practice, the analyzed bandis divided into N samples separated by a frequency step Δf (meas). The impulseresponse is obtained using an inverse Fourier transform along the frequencyaxis.

The obtained time resolution1 is:

R(meas)t =

1NΔf (meas)

[3.1]

and the length of the channel impulse response is:

τ (meas)max =

N − 1NΔf (meas)

[3.2]

3.3.1.1. Vector network analyzer

The tool best suited to characterizing the channel using a frequencysweeping method is the vector network analyzer (VNA). This device isgenerally used to characterize high frequency quadripoles through themeasurement of S-parameters. For the purpose of channel sounding, port 1 isconnected to the transmitting antenna and port 2 is connected to the receivingantenna. The channel transfer function is derived from parameter S21(f).

In general, a sine signal is used to sweep the analyzed band. The receivedsignal is down-converted towards an intermediate frequency (IF), where itis pass-band filtered around a fixed frequency and analyzed. Hence, thisdevice is capable of sweeping a very wide frequency band. Using narrowbandfilters at the receiver leads to a very good measurement dynamic, but alsoincreases the overall measurement duration. In addition, the measurement ofthe transfer function phase requires a very good synchronization between thelocal oscillators (LO) at the transmitter and at the receiver. Figure 3.3 gives aschematic view of this device.

1. This time resolution is calculated without applying any frequency domainwindowing.


LO

S21 measurementat IF

LO

Propagation channel

Referencesignal

Analysisand storage

Figure 3.3. Propagation measurement using a frequency domain sounder

This technique offers advantages in terms of bandwidth and dynamic.As a result, it has been frequently used for the purpose of UWB channelsounding [GUN 00, OPS 01, GHA 02a, CHE 02, KEI 02, HOV 02, KUN 02a,GHA 03b, BUE 03, DAB 03, ALV 03, CHA 04, SCH 04, BAL 04a, KAR 04b,JAM 04, CHO 04b, CAS 04a, HAN 05]. However, the measurement durationis proportional to the number of measured frequency tones. For an analyzedbandwidth of several GHz, the measurement duration is in the order of 10seconds. Hence, this technique cannot be used for time varying channels.When conducting VNA-based measurements, we should thus ensure that theenvironment remains static for the measurement duration. In addition, thedistance from transmitter to receiver is limited to approximately 20 m, due topower attenuation in the feeding cables.

3.3.1.2. Chirp sounder

A chirp sounder is a frequency domain method providing a solution to theissue of acquisition duration. Indeed, the sounding signal is no longer a pure sinewave, but a frequency chirp. Such a signal is generated using digital frequencysynthesis components [COS 04].


This frequency chirp may be characterized by the sequence duration Tc andthe covered frequency range Bc, as illustrated in Figure 3.4. For a BcTc productlarger than 100, over 98% of the energy is confined in the analyzed bandwidthBc.

The channel impulse response may be calculated either by matchedfiltering or using a heterodyne receiver and a low-pass filter. In the first case,the impulse response of the matched filter corresponds to a time reversedversion of the emitted chirp signal [ART 95]. The channel impulse responseis directly obtained at the output of the matched filter. In the case of aheterodyne reception, the output of the low-pass filter provides the channeltransfer function, represented on a compact frequency band. Its bandwidthdepends on the parameters Bc and Tc [COS 04]. The signal acquisition maythus be performed at a reduced sampling frequency. However, generatinga chirp signal with a bandwidth larger than a few hundred MHz is still achallenging task. For this reason, chirp sounders have not yet been used forUWB channel sounding.

TimeTime

Freq

uenc

y

Tc

Bc

Frequency

Mag

nitu

deBcTc

> 98% energyM

agni

tude

Figure 3.4. Chirp signal

3.3.2. Time domain techniques

The common characteristic of all time domain techniques is the use of awideband excitation signal at the emitter. This way, the receiver processesthe whole frequency band simultaneously, which drastically reduces themeasurement duration. This section presents the most common time domainmethods, and in particular those that have been used for UWB channelsounding.

3.3.2.1. Pulsed techniques

The pulsed technique is mathematically the most straightforwardtime domain measurement method. Indeed, if the transmitted signal e(t)corresponds to a Dirac pulse, the received signal s(t) is directly proportionalto the channel impulse response h(t, τ). However, such a Dirac pulse wouldpresent an infinite flat spectrum and is not physically implementable. In


practice, we use pulse generators enabling the emission of short signals with aduration Δt in the order of 100 picoseconds. Denoting by ΠΔt(t) the emittedpulse, the received signal is given by:

s(t) = h(t, τ)⊗ΠΔt(t) [3.3]

and represents a close approximation of the channel impulse response.

At the receiver, a very fast acquisition of the signal is necessary. A digitalsampling oscilloscope (DSO) is generally used, with sampling rates up to20 Gsamples.s-1. Other types of receivers are also implemented: for instance,a correlation receiver has been developed by the company Time Domain[YAN 02].

This technique is particularly interesting for the measurement of UWBchannels. Indeed, pulse generators capable of emitting directly in the FCCfrequency band (3.1–10.6 GHz) are now available. Generally, UWB soundersbased on this principle do not require an up-converter stage, which simplifies theexperimental setup. It should be noted, though, that the signals synthesized bythe current pulse generators are limited to a maximum bandwidth of 1–2 GHz,with an upper frequency limited to 5 GHz. Hence, only parts of the FCC bandmay be measured using a direct pulse generator technique. In order to soundthe upper part of the FCC spectrum, it is possible to add an up-converter stage,composed of an LO and a mixer at both the transmitter and the receiver. Thissolution is presented as a dashed line in Figure 3.5.

The main advantage of the pulsed sounding technique is its low acquisitionduration, the channel impulse response being recorded in real time. Thistechnique should thus be selected for the measurement of space or timechannel variations. However, this method also presents a number of drawbacks.Firstly, generating short duration pulses requires the amplifiers to delivera high power directly followed by idle periods. The resulting low averagepower leads to a poor signal to noise ratio, and this method is not suitedto large distances in NLOS configurations. Secondly, the power dynamic atthe amplifier stage does not allow for an accurate control of the pulse shape.Finally, this technique requires a perfect synchronization between the emitterand the receiver, which may be solved by connecting the terminals using acable.

The attractive simplicity of this solution led a number of scientists to usethis method for UWB channel sounding, but with a sounded frequency bandgenerally below the FCC band [WIN 97a, WIN 97b, GUN 00, OPS 01, CHE 02,YAN 02, TER 03, LI 03]. Two measurement programs have been establishedusing this technique within the 3.1–10.6 GHz band [PEN 02, BUE 03].


LO

DSO

LO

Propagation channel

Referencesignal

Analysisand storage

Pulse generator

0°

90°

QI

Synchronization

Figure 3.5. Propagation measurement using a pulsed technique

3.3.2.2. Correlation measurements

A possible way to increase the signal to noise ratio at the receiver is to usethe autocorrelation properties of pseudo-noise (PN) sequences. Let Ree(t) andRes(t) respectively denote the input signal autocorrelation and the correlationfunction of the input signal e(t) with the output signal s(t). According to theconvolution and correlation function properties, these functions are also linkedby a convolution equation:

Res(t) = h(t, τ)⊗Ree(t) [3.4]

If the input signal is close to a white noise, its autocorrelation function isclose to a Dirac pulse. In this case, the identification problem is similar to theone occurring in the pulsed technique. In practice, we use maximum length PNsequences, also called m-sequences. This corresponds to a good approximationof a colored noise with zero mean and limited bandwidth. An m-sequence may


be generated using a shift register with m bits and an adder, which results ina sequence of length 2m− 1. Its autocorrelation function presents a theoreticaldynamic of 20 log(2m − 1) dB. In the frequency domain, the −3 dB analyzedbandwidth is equal to the clock frequency fc used at the PN sequence generator.

At the transmitter, a correlation sounder is thus composed of a PN sequencegenerator and an up-converter stage towards the working frequency. Typically,wideband correlation sounders transmit signals in the order of 100 MHz. ForUWB channel sounding, the frequency band may be widened by increasing theclock frequency, but the sounder implementation becomes more complex. TheUniversity of Ilmenau, Germany, presented a MIMO UWB sounder working inthe 0.8–5 GHz frequency band [SAC 02]. For this purpose, an integrated circuitshift register has been specifically developed.

At the receiver, once the received signal has been down-converted inbaseband, several acquisition techniques may be used. The first consists ofusing an analog filter matching the transmitted PN sequence. This principleenables the measurement of the impulse response in real time. However,the analyzed bandwidth is limited by the passband of the filter, and themeasurement dynamic is low. Another technique consists of sampling thereceived signal and computing the convolution function using digital filters.The maximum analyzed bandwidth is then limited by the speed of theanalog-to-digital converters. This solution is presented in Figure 3.6. It hasbeen used by the University of Rome “Tor Vergata”, Italy, to sound the3.6–6 GHz band [DUR 04]. The receiver was simply composed of a DSO.

Time domain correlation sounders present the advantages of a highimpulse response dynamic, and a possible functioning in real time. Theirimplementation is however complex, and the quality of the measured impulseresponse largely depends on the performance of the sounder components.In particular, an accurate synchronization between the transmitter and thereceiver is necessary. This may be achieved using a stable reference (e.g. arubidium oscillator) or a direct cable connection between the two terminals.

Sliding correlation technique

The sliding correlation sounder is a similar technique that proceeds theconvolution operation in the analog domain while increasing the measurementdynamic. The convolution is performed using a replica of the original PNsequence with a clock frequency fc2 slightly different from the initial clockfrequency fc1. This leads to a time domain sliding of the PN sequences withrespect to each other. Hence, using an integrator, one point of the correlation


OL

Fast acquisition

OL

Propagationchannel

Referencesignal

Analysisand storage

Arbitrarysequencegenerator(e.g. shiftregister)

0°

90°

QI

Synchronization

Correlationor inversion

Figure 3.6. Propagation measurement using a PN sequence. The illustratedacquisition technique consists of digitizing the received signal

prior to convolution processing

function between the transmitted signal and the received signal is calculatedat each instant.

The obtained impulse response is expanded by a ratio k = fc1fc2−fc1

inthe time domain and compressed by a ratio k in the frequency domain.This compression enables the use of narrower filters at the receiver, whichimproves the dynamic. In addition, a lower sampling rate may be used for theanalog-to-digital conversion.

This technique has been used by the University of Kyoto Sangyo (Japan)to develop a UWB sounder operating in the 5.5–8.5 GHz frequency band[TAK 01]. The main drawback of this technique is the duration of the impulseresponse calculation, which precludes any Doppler analysis of fast time varyingchannels.


3.3.2.3. Inversion techniques

Inversion techniques are based on the transmission of an arbitrary sequenceand are thus similar to correlation sounding techniques (see Figure 3.6). Themain difference lies in the impulse response estimation, which is performedusing an estimation filter. Filtering is generally applied in the digital domainafter the acquisition of the analog signal. The used filter minimizes the squarederror between the impulse response and the estimated response. In particular,such a filter accounts for the imperfections of the measurement device.

The inversion technique is notably used in the sounder developed at FranceTelecom Research and Development [CON 03]. It uses a Wiener filter, with afrequency spectrum given by:

GWiener(f) =E∗(f)I∗(f)

|E(f)I(f)|2 + α[3.5]

where E(f) represents the transmitted signal spectrum, I(f) represents thesounder response spectrum, and α is a non-zero constant linked to the signalto noise ratio [BAR 95].

As a main advantage, the inversion technique improves the impulseresponse calculation by accounting for the imperfections of the soundercomponents. The used PN sequence is optimized in order to spread overa wide band with a relatively constant envelope. The limitations of thistechnique are directly linked to the performances of the digital-to-analog andanalog-to-digital converters. In particular, the analyzed bandwidth is in theorder of a few hundred MHz.

For the sake of comparison, Table 3.1 presents the main advantages anddrawbacks of the presented frequency domain and time domain techniques.

3.3.3. Multiple-band time domain sounder for dynamic channels

Classical frequency or time domain sounding techniques are not intrinsicallywell adapted to the measurement of time varying UWB channels. On theone hand, frequency domain techniques lead to a long measurement duration.On the other hand, time domain techniques are fast enough to enable themeasurement of time varying channels, but their implementation within theFCC band is challenging. This section presents a hybrid solution consistingof using a wideband time domain sounder and successively measuring severaladjacent partial bands. This principle was initially exploited by the Universityof Kassel (Germany). They developed a sounder capable of measuring a channelof 600 MHz divided into 10 partial bands of 60 MHz, with a measurement


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repetition duration of 300 μs [KAT 00]. In the following, we present the differentissues linked to the development of such a sounder, and we illustrate how it canbe implemented on the basis of a wideband SIMO sounder [PAJ 03].

3.3.3.1. Principle of multiple-band time domain sounding

The technique of multiple-band time domain sounding exploits theperformance of a time domain sounder, such as the sounder developed byFrance Telecom Research & Development. In its standard version, this sounderallows for the measurement of 250 MHz frequency bands. At the up-converterstage, an LO signal is responsible for the up-conversion of the transmittedsequence towards the analyzed band. By appropriately driving this LO signal,it is possible to sound several adjacent bands. The different challenges are thefollowing:

• Analyzed band: the number of measured partial bands determines thewidth of the global analyzed band. At both the transmitter the receiver, theglobal analyzed band needs to be filtered and cleared from any interferingsignal, such as the LO signal and its harmonics.

• Measurement repetition duration: in an indoor configuration, themaximum speed of mobile terminals is about 2 m.s−1. Considering an extremecase, i.e. a mobile terminal and a maximum frequency of 10.6 GHz, themaximum Doppler shift is v

λ = 70 Hz. This maximum Doppler shift increasesto 2v

λ = 140 Hz if we consider mobile scatterers, taking into account the pathswith one reflection as significant paths. Thus, to characterize time varyingchannels, the equipment has to sample the channel every 3.5 ms. This timeincludes the necessary switching from one band to another, which needs to besynchronized with the transmitted sequence.

• Calibration: when measuring adjacent bands, a simple process needs to beset up for an accurate calibration of the sounder in terms of phase, magnitudeand absolute delay, for each of the adjacent bands.

• Measurement dynamic: when working as a multiple-band sounder, thedynamic performance of the original wideband sounder needs to be preserved,in order to obtain a reliable result.

These different issues are similar to those occurring when characterizingthe wideband channel with multiple antennas at the receiver, in a SIMOconfiguration. A SIMO sounder may thus be easily adapted to performmultiple-band time domain sounding. For a better understanding, the nextsection reviews the general structure of the SIMO sounder available at FranceTelecom. A further description of this sounder is available in [CON 03].


3.3.3.2. Description of the SIMO channel sounder

The sounder developed at France Telecom Research & Development is atime domain sounder allowing for radio channel measurement over differentfrequency bands between 2 GHz and 60 GHz. The sounding method is theWiener inversion technique, applied on a PN sequence exhibiting a flatspectrum over the analyzed bandwidth. For frequency bands below 17 GHz,a multiple sensor mode enables the simultaneous measurement of the radiochannel over 10 receiving antennas.

In terms of performance, the sensitivity of this sounder is about −85 dBm.The impulse response dynamic depends on the length of the PN sequence, thesignal to noise ratio at the sounder input, and the oscillator phase noise. For areceived signal of about −60 dBm over a band of 250 MHz around 5 GHz anda sequence of 8192 samples, the measurement dynamic is larger than 40 dB.

Figure 3.7 presents a simplified block diagram of the receiver. To repeat themeasurement as quickly as possible, a fast switch selects the following antennaevery other sequence. The first PN sequence is used for the measurement,while the antennas switch during the next PN sequence. The signal is thenamplified using a wideband (3–18 GHz) low noise amplifier (LNA). It is thenpass-band filtered around the RF carrier frequency. A first down-converterstage driven by an external frequency synthesizer displaces the signal aroundan IF at 1.5 GHz. Automatic gain control (AGC) is then applied using variableattenuators to compensate for the power variations in the received signal.AGC is regularly performed, before the measurement of the signal receivedby the different sensors. Thus, the AGC duration limits the measurementrepetition duration. In a traditional configuration with 10 antennas, theminimum repetition duration is about 1.2 ms. A second down-converter stagedisplaces the signal around a second IF at 250 MHz. The received signal isthen sampled using an analog-to-digital converter (ADC) at a sampling rateof 1 Gsample.s−1. We may note that the transmitter and the receiver use thesame IF at 1.5 GHz. Thus, the LO frequency is the same for the externalsynthesizers at the transmitter and the receiver. All LO are synchronizedusing a reference rubidium at 10 MHz.

3.3.3.3. Extension towards UWB

In order to perform measurements over adjacent frequency bands, it isnecessary to modify the LO frequency at the transmitter and at the receiver.Traditional oscillators present a locking time in the order of 10–50 ms. Thistransition duration is mainly due to the positioning duration of the internalphase locked loop, and cannot be reduced. Directly driving a single externalsynthesizer thus leads to a total measurement duration in the order of40–200 ms for an analyzed band of 1 GHz. Taking into account the constraints


LNA

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101

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AD

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LO

RF

Figure 3.7. Receiver block diagram

linked to real time measurements (see section 3.3.3.1), this solution cannot beused.

The extension of the SIMO sounder towards a real time UWB sounderexploits the duality between multiple-input measurements and multiple-bandmeasurements. The main idea is to reuse the fast antenna switching module,in order to switch between the carrier frequencies of each partial band to bemeasured.

A practical implementation of this concept is presented in Figure 3.8. Ascan be seen, the input connector is now directly connected with the LNA,and a single antenna is available. The sounder is thus in a single-inputsingle-output (SISO) measurement configuration. The fast switching moduleis used to sequentially feed the mixer of the first down-converter stage withone of the 10 LO signals (f1 to f10) in turn. These signals are generatedby external synthesizers and tuned so that the receiver actually sweeps theselected partial bands. As each synthesizer is locked at a fixed frequency, nodelay is experienced for the locking of the LO frequency. In this configuration,the sounder is capable of sweeping up to 10 partial bands of 250 MHz each.Hence, UWB measurements are theoretically possible up to a bandwidth of2.5 GHz.

On account of its development concept, this sounder fulfills most ofthe required criteria for real time UWB channel measurement. Indeed, themultiple-input architecture is directly used for the measurement over multiplebands. For the calibration of each partial band in terms of phase, magnitude


LNA

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synthesizers

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Figure 3.8. Block diagram of the modified receiver with UWB extension

and delay, the procedure used in the SIMO configuration is still valid. Inaddition, regarding the fast switching of partial bands, the overall switchingtime through all partial bands may be as low as 1.2 ms, which allows for themeasurement of channel variations with a maximum Doppler shift of 416 Hz.

In the original version of the SIMO sounder, the filter preceding the firstdown-converter stage was only a few hundred MHz wide to reject undesirablesignals and reduce the noise level. The same type of filtering was performed atthe emitter. In the UWB configuration, however, the sounded frequency bandneeds to be filtered by one single pass-band filter, in order to avoid unnecessaryfilter switching. In its current version, the UWB sounder is equipped with filtersof 1 GHz bandwidth.

Unlike the SIMO channel sounding case, UWB measurements usingthe sweeping method necessitates a periodical modification of the emittedsignal central frequency. For this reason, the frequency switch performedat the receiver and at the transmitter need to be perfectly synchronized.To solve this problem, the same LO signal may be used to feed both thereceiver down-converter and the transmitter up-converter stages. The maindrawback of this solution is that the transmitter and the receiver need to becable connected. However, in most indoor configurations, this connection isrealizable using a cable of acceptable length. Advantageously, this solutionallows us to use only one set of external synthesizer, which considerablyreduces the global cost of the equipment.


3.3.3.4. Experimental validation

The modifications presented above have been applied to the sounderdeveloped by France Telecom for its extension to real time UWBmeasurements. To sweep the 5–6 GHz frequency band, 5 external synthesizershave been connected to the fast switching module. In this configuration, theimpulse response dynamic was measured at 40 dB. Using 5 partial bands,the minimum measurement repetition duration is about 1 ms and the actualmeasurement duration is 20.5 μs. With its 256 MB memory, the acquisitioncard is able to sound the time varying UWB channel for a duration of 80 s instandard conditions (bandwidth of 1 GHz and observable Doppler spread of150 Hz).

Figure 3.9 presents the results obtained during a real time radio channelmeasurement in a dynamic environment. During this experiment, thetransmitting antenna was fixed and the receiving antenna was held by amoving person. This configuration corresponds to the practical situation wherea user with a mobile terminal walks in the proximity of a fixed access point.

Dis

tanc

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Time (s)0 2 4 6 8 10 12

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(c)

(d)

(e)

Figure 3.9. Time varying impulse response in a dynamic environment

The impulse response represented in Figure 3.9 corresponds to a 12.5 srecord of the signal obtained at the receiving antenna moving duringthe experiment. Acquisitions were performed every 10 ms. For ease of


interpretation, the path delay on the y-axis has been converted to path lengthin meters. In the first part of the trajectory (between t = 0 s and t = 7 s), theperson is moving towards the emitter antenna, reducing its relative distancefrom 6 m to 2 m. Hence, we can observe a main path with increasing power(a). In the second part of the trajectory (between t = 7 s and t = 11 s), theperson is moving away from the transmitter antenna, partially obstructingthe line of sight. This explains the shadowing experienced by the shortestpath (b). In this part of the curve, three other main paths are observable, onewith increasing length (c) and two with decreasing lengths (d, e). These twolast paths might correspond to echoes transmitted via a reflection on a wallopposite the transmitter location.

This feasibility study shows that it is possible to develop the UWB channelsounder by applying minor modifications to a wideband SIMO sounder. Byexploiting the duality between multiple inputs and multiple bands, most of theSIMO-capable sounders could be extended towards UWB channel sounding.The prototype presented here allows for the measurement of UWB channelsover a band of 1 GHz with a dynamic of 40 dB.

3.4. UWB measurement campaigns

3.4.1. Overview of UWB measurement campaigns

A number of UWB radio channel measurement campaigns were cited inthis chapter. These diverse campaigns used different sounding techniques,but also differ in the measured frequency band, the type of environment, theantennas used and the measurement set-up. In order to compare the analysisresults from these experiments, it is necessary to recall the conditions ofeach campaign. Table 3.2 summarizes the inventoried UWB measurementcampaigns and provides some useful information for each of them.

Among the first UWB studies, the UltRaLab laboratory from the Universityof South California undertook two measurement programs in 1997, but mostUWB experiments started from the year 2000 onwards. Most measurementprograms used the VNA frequency domain method. Other experimental set-upsare based on a time domain method, using pulses or PN sequences. Differentindoor environments, such as the office or residential environments, and someoutdoor environments (forest, urban) were sounded. We may also note someoriginal experiments, on a metal ship or in an industrial environment. Finally,regarding the analyzed band, only seven measurement campaigns cover theentire FCC band [KUN 02a, BUE 03, ALV 03, CAS 04c, KAR 04b, HAN 05,PAG 06b]. Within the FCC band, three experiments only permitted real timeUWB measurements [PEN 02, CAS 03, PAG 06a].


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mnid

irec

tional

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ante

nnas

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–10.6

GH

z,w

ith

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rial

LO

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wo

x-p

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tioner

s(t

ransm

itte

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er)

wit

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ng

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cm


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men

tca

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nnas

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ty2004

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VN

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mnid

irec

tional

monoco

nic

al

ante

nnas

(CM

A118/A

)

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–10

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z,w

ith

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5M

Hz

step

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ceLO

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-N

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tioner

wit

h7.9

mm

step

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sung

2004

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O04b]

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lanar

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ole

s3–10

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MH

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ep

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iden

tial

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NLO

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tions

on

a60

cm×

60

cmgri

d

Tokyo

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it.

ofTec

h.

2004

[TSU

04,

HA

N05]

VN

AM

onopole

sand

bic

onic

al

ante

nnas

3.1

–10.6

GH

z,w

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10

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iden

tial;

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ceLO

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pto

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×7

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rece

iver

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nce

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ecom

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D

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G06b]

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tional

monoco

nic

al

ante

nnas

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–11.1

GH

z,w

ith

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Hz

step

Offi

ceLO

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NLO

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tions

on

aro

tati

ng

arm

(20

cmra

diu

s)

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nce

Tel

ecom

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D

2005

[PA

G06a]

Mult

iple

-band

tim

edom

ain

sounder

Om

nid

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tional

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nic

al

ante

nnas

4–5

GH

z,w

ith

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step

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ceco

rrid

or

LO

S—

Tab

le3.

2.U

WB

pro

paga

tion

channel

mea

sure

men

tca

mpa

igns


3.4.2. Illustration of channel sounding experiments

The previous study of the different UWB channel sounding techniquesshows that the frequency domain technique using a VNA is the only availablemethod that enables a full characterization over the whole FCC band. In thefollowing, two measurement campaigns using this method are presented. Thefirst campaign covers the 3.1–10.6 GHz band [PAG 06b], and the second onecovers the 2–6 GHz band. A third campaign is then described, presenting realtime measurements in the 4–5 GHz band.

3.4.2.1. Static measurement campaign over the 3.1–10.6 GHz band

The measurement system used for the static measurement campaign overthe 3.1–10.6 GHz band is presented in Figure 3.10.

VNAHP8510C

Port1

Driving and storage

Rotatingarm driver

Webcam

RS 232

Port2USB

GPIB

Propagation channel

Rotating arm

Figure 3.10. Equipment setup for the static UWB soundingover the 3.1–10.6 GHz band

Measurements were taken using a VNA (see Figure 3.11(a)) in thefrequency band 3.1–11.1 GHz with a frequency step Δf (meas) of 2 MHz.The full acquisition process consists of measuring 4005 frequency tones in aduration of about 15 seconds. Using a Hanning window, side lobes may bereduced to −32 dB. This compromise corresponds to an impulse responseresolution R

(meas)t of 0.25 ns.


(a) (b)

Figure 3.11. Measurement equipment: (a) HP8510C sounder and (b) rotating arm

In order to estimate the local PDP and assess the signal spatial fluctuations,a rotating arm with radius 20 cm was used to measure the radio channel at 90different locations (see Figure 3.11(b)). This configuration corresponds to acircular path of 45λ and to a distance between two successive sensors below λ

2at the maximum frequency of 10.6 GHz.

Measurements were performed using two CMA118/A antennas from thecompany Antenna Research Associates. These antennas are monoconicalantennas with a metallic ground plane. Their radiation pattern isomnidirectional in the azimuth plane and a standing wave ratio (SWR) lowerthan 2 in the 1–18 GHz frequency band. It should be noted that the radiationpattern of these antennas strongly varies, especially in the elevation plane, asthe frequency increases several octaves. Their complex gain has thus beencharacterized in 3D in the 1–10 GHz band with a 1 GHz step. Figure 3.12illustrates the antenna characterization process.


Figure 3.12. Measurement antennas. CMA 118/A antennas(from the ARA company) during their characterization

This sounding equipment was complemented with up to three widebandpower amplifiers. The sounder calibration consists of a measurement sampletaken while the receiver and the transmitter are directly cable connected.In order to achieve an accurate time reference, all cables involved in themeasurement process need to be taken into account at the calibration stage.As active components, the amplifiers are not included in this measurement.Instead, they are characterized separately and their transfer function issubtracted from the measurements at the digital post-processing stage.

Measurements were taken in an indoor office environment. Externalwalls are made of brick and concrete, and internal walls consist of thinnerplaster and plastic boards. Two typical radio access configurations have beenstudied. In both cases, the transmitter was situated at a height of 1.40 m andwas considered as the mobile terminal. The receiver was considered as theaccess point and was first placed in a meeting room at a height of 2.19 m,and then in a corridor at a height of 2.45 m. Figure 3.13 presents these twoconfigurations. In both cases, LOS and NLOS configurations were assessed.The transmitter-receiver distance varied between 1 m and 20 m. Over thewhole measurement campaign, the rotating arm was placed at more than 120different locations, which corresponds to a set of over 10,000 UWB impulseresponses available for statistical characterization. The analysis of thesemeasurements is presented in Chapter 5.


4 m

Cor

ridor

con

figur

atio

nM

eetin

g ro

om c

onfig

urat

ion

Fig

ure

3.13

.M

easu

rem

entlo

cations

duri

ng

the

UW

Bso

undin

gca

mpa

ign

ove

rth

e3.1

–10.6

GH

zba

nd.Bla

cksq

uare

sre

pre

sentfixe

dlo

cations

(rec

eive

r)and

white

circ

les

corr

espo

nd

toth

ero

tating

arm

loca

tions

(tra

nsm

itte

r)


3.4.2.2. Static measurement campaign over the 2–6 GHz band

The schematic description of the equipment used for the static measurementcampaign over the 2–6 GHz band is presented in Figure 3.14. Measurementswere performed using the VNA HP8753 D over the frequency band 2–6 GHzwith a frequency step Δfmes of 2.5 MHz. The acquisition process for afull measurement consists of the measurement of 1601 frequency tones in aduration of 4 seconds. The CMA 118/A antennas have also been used for thismeasurement. The measurement did not require the use of power amplifiersat the transmitter or at the receiver. Indeed, the link budget without theamplifiers was high enough to support transmitter-receiver distances up to12 m.

MATLAB/SCILABPost processing

Analysis

PCLabview

Tx (Port 1)

VectorNetworkAnalyzer

HP 8753 D

Rx (Port 2)

Tx Ant

Rx Ant

Propagation channel

CMA – 118/A

Cable 20 m

Cable 20 mGPIB

CMA – 118/A

Figure 3.14. Equipment setup for the static UWBsounding over the 2–6 GHz band

The environments sounded during these measurements are residentialhouses: the first house is a modern building and the second one is an olderbuilding. The external walls of the first house consist of concrete blocks,bricks and insulation material made of glass wool. The external walls of theolder house do not incorporate any insulating material. Internal walls of bothhouses are made of brick and plasterboards. Both dwellings are two-floorhouses. However, measurements have been performed at the ground level only.The transmitter and the receiver are placed at the same height of 1.40 m.Figure 3.15(a) represents the first house with LOS measurement locations.Figures 3.15(b) and 3.15(c) represent the second house with both LOS andNLOS measurement locations. In these two environments, the number ofmeasurements is respectively 89 and 230.

3.4.2.3. Dynamic measurement campaign over the 4–5 GHz band

Finally, in order to study the effect that mobile people have on the UWBchannel, we present a real time measurement campaign performed over abandwidth of 1 GHz [PAG 06a].


(a)

(b)

(c)

Figure 3.15. Measurement locations during the UWB sounding campaign overthe 2–6 GHz band. Squares represent fixed locations (Tx: transceiver)and circles represent mobile locations (receiver): (a) modern house;

(b) old house in LOS; and (c) NLOS


A few channel sounders only are currently capable of measuring the UWBchannel in real time. This experimental study has been performed using theUWB sounder presented in section 3.3.3. The channel impulse response wasmeasured every 10 ms, which enables the measurement of Doppler shiftsup to 50 MHz. The analyzed band extends from 4 GHz to 5 GHz, with aresolution of 2 MHz, which corresponds to a maximum delay of 500 ns. At thetransmitter and the receiver, CMA118/A antennas were used, as presented insection 3.4.2.1.

Tx antenna

Rx antenna

Peoplemotion

B

F

Rx

Tx

B

F

Figure 3.16. Environment of the real time experiment. F: forward movement,B: backward movement, Tx: transmitter, Rx: receiver

The experiment took place in a typical indoor office environment. Allmeasurements were taken near a bend of the building’s main hallway, asdepicted in Figure 3.16. The receiving antennas was fixed on a wall at a heightof 2.10 m. The transmitting antenna was placed in the middle of the corridorat a distance of 11 m from the receiving antenna and at a height of 1.35 m.In order to assess the time variations of the UWB channel, measurementswere taken over the fixed radio link as groups of people walked towards theend of the hallway and back. During this displacement, people occasionallyobstructed the LOS path and other main paths of the channel impulseresponse. The number of people within each group varied from 1 to 12. Thisexperiment corresponds to a practical situation where the user of a WLANis standing in a crowd of people, in a subway corridor for instance. Themeasurement campaign consisted of a collection of 27 records of the timevarying UWB radio channel, containing about 3,000 impulse responses each.Chapter 5 presents a statistical analysis of this experimental data.


3.5. Conclusion

In this chapter, the different channel sounding techniques adapted to UWBmeasurements have been presented. Frequency domain methods use either avector network analyzer or a chirp sounder. Time domain methods includepulsed techniques, correlation measurements and inversion techniques. Due tothe wide analyzed bandwidth, the vector network analyzer method seems tobe the most appropriate technique for static UWB channel sounding. However,its main limitation lies in its long measurement duration. Several seconds areindeed required to measure the 3.1–10.6 GHz band. For the acquisition of realtime UWB channel measurements, an innovative sounding technique based onthe extension of a wideband SIMO sounder has been presented. This adaptationcorresponds to minor modifications of the original equipment and allows for realtime measurements over a 1 GHz band.

A literature survey made it possible to inventory about 20 UWBmeasurement campaigns since 1997. Most of these campaigns used aVNA-based frequency domain method. The reported campaigns coverthe indoor residential and office environment, as well as some outdoorenvironments. Finally, the experimental setup of a typical sounding campaignhas been illustrated through three examples: two measurement campaignsusing a VNA over the 3–10.6 GHz and 2–6 GHz frequency bands respectively,and a series of real time measurements performed over the 4–5 GHz bandusing a multiple-band time domain sounder.

Chapter 4

Deterministic Modeling of the UWB Channel

4.1. Introduction

Deterministic models are often used as site specific models allowing us torealistically predict signal propagation in a given environment using simulationsoftware. Currently, little simulation software of this type is proposed for UWBin comparison to narrowband systems, where they are widely used to determineradio system deployment.

The use of classical deterministic modeling software for UWB needs aparticular adjustment in order to cover the entire frequency band of impulsesignals. Concerning the total calculation field, it is mandatory to considernot only the power loss amplitude but also the phase information in order toeasily reconstruct in the time domain the received signal corresponding to themodeled UWB link.

This chapter describes the UWB deterministic modeling. After thepresentation of classical techniques used for deterministic modeling,the specificities of UWB applications are described. Then, the differentdeterministic models proposed in the literature for UWB signal propagationare presented. Finally, theoretical formalisms are detailed and compared tomeasurement results in order to illustrate the deterministic modeling in theUWB context.

4.2. Overview of deterministic modeling

Propagation models considered to be deterministic are obtained fromsimulations made in simplified propagation environments. They are based on


electromagnetic wave propagation theory. Their use requires a good knowledgeon the propagation environment and allows us to obtain precise as well asaccurate predictions of signal propagation in the channel corresponding to theconsidered environment.

For a theoretical point of view, the wave propagation characteristics canbe calculated by solving Maxwell equations. However, this requires us to makecomplex mathematical operations and to use powerful numerical calculations.The most frequently used approaches are based on frequency difference in timedomain (FDTD) techniques, methods of moments (MoM) or ray techniques.

4.2.1. FDTD based approach

The FDTD based approach allows us to obtain a complete cartography ofthe field on all points of a given map. It is typically used for electromagneticfield coverage in a given environment [LAU 95, SCH 97b, KON 99].

The FDTD used for modeling consists of solving Maxwell equations usingregular spatial discretization in time. All derivations are simplified by algebraicsystems of equation. The studied volume is discretized in various elementarycells, the size of which is related to wavelength of typically λ/10 or λ/15. Thesolving method fixes some restrictions in term of the considered cells sizes andtime grid in order to ensure computation stability. The studied environment islimited by absorbing walls limiting the reflection phenomena on the boundaries[IBA 00].

These approaches demand huge memory spaces to obtain the solutionsin all points of the considered environment and to update all iterative fieldcalculations for the different instants. This approach is often used for smallenvironments with respect to the wavelength or complementary to otherapproaches [YIN 00].

4.2.2. MoM based approach

Similarly to the FDTD approach, the MoM based approach is a numericalmethod which requires a large numerical memory for field calculation and radiocoverage in a given environment [DEB 96, YAN 99].

The MoM is based on the use of an integral form of Maxwell equations. Theintegral system is transformed by an impedance matrix discretization whichrepresents the interactions between elementary cells of the environment. Theaccuracy of the solutions obtained with this approach depends on the size ofthe considered cells.

Deterministic Modeling of the UWB Channel 101

This approach is used when the structure size is roughly a few wavelengths.It can also be considered complementary to other approaches like the ray basedapproaches in order to obtain hybrid models. Nevertheless, the MoM basedapproach is mainly used to validate results obtained with other approaches likethe ray based approach [YAN 98].

4.2.3. Ray based approach

Based on geometric optic (GO) combined with uniform theory of diffraction(UTD) (see Appendix C), the ray based approach is well suited for the studyof radio wave propagation. The GO considers that the energy is radiatedalong infinite tubes called rays. These rays define the propagation directionsand can reflect or refract on all the surfaces they encounter. The use of UTDcomplements the GO as it introduces the diffracted rays and ensures thecontinuity of the field on regions where the GO predicts a non-existence of afield.

Before the determination of the propagated field, we need to find the raysfrom which the GO and the UTD will be applied. This step of ray finding canuse various techniques. There are two main techniques of ray determination: raylaunching is considered to be a forward technique and ray tracing is consideredto be a backward technique [SAR 03] (see Appendix D). When the rays areobtained, the propagated field can thus be calculated from the transmission toreception side.

The ray based approach needs less numerical resources than the FDTD andMoM approaches for wave propagation prediction. Consequently, it is mostlyused for deterministic propagation modeling [IKE 91, MCK 91, TAM 95,TAN 95, SAN 96, CHE 96, RIZ 97, VIL 99, ZHA 00]. Such approaches arenot valid for low frequencies (typically lower than 100 MHz), when the sizeof objects interacting with rays become small or have the same order as thewavelength.

An improvement of the propagation prediction with the ray based approachcan be made by combining it with exact approaches such as those using FDTDor MoM.

4.3. Specificity of deterministic modeling in UWB

When studying narrowband transmission techniques using deterministicsoftware, much is made of the power loss of the transmitted signal. So, modelingallows the establishment of radio coverage maps on any considered environmentat a given central frequency corresponding to the transmitted narrowband


signal. Indeed, we consider that the bandwidth is narrow enough to only focusthe propagation study on the central frequency.

In UWB, the frequency components of the transmitted signal cover avast bandwidth which can reach 7.5 GHz. So, the performed simulation willnecessarily address all the phenomena appearing on the entire bandwidth.Thus, we cannot simply focus on the propagation around the central frequency.This implies that we have to consider in the synthesized link both antennasand material properties of the considered environment on the whole coveredfrequency band.

Another particularity of the UWB deterministic modeling is the need toconsider the phase information related to the propagation as well as combiningthe effects of antennas and material properties. This phase information isimportant as it allows the identification of potential deformations (suchas attenuation, dispersion, etc.) appearing on the received signal duringthe transmission. Deterministic modeling can thus be used in specificenvironmental configuration in order to better understand the effects ofphysical phenomena observed on results of channel propagation measurementcampaigns.

So, the use of site specific tool for deterministic modeling allows us on theone hand to study the waves propagation in various types of environments andin specific configurations, and on the other hand to physically understand theeffects observed on measurements.

4.4. Overview of UWB deterministic modeling

In this section, the four principal deterministic models which appear in theliterature are described, with a main focus on their respective specificities.

4.4.1. Qiu model

Some authors consider the study proposed by Qiu [QIU 02] on the diffractionundergone by an UWB signal as a UWB deterministic model. In the study madeby Qiu, he mainly focuses on the distortions and dispersions introduced in alink and on system performances by single and multiple diffractions.

4.4.2. Yao model

The particularity of the model proposed by Yao is that it takes intoaccount the GO and UTD coefficients in the time domain in order to account


for the effects of the propagation channel interactions [YAO 03a, YAO 03b].These time domain coefficients allow us to directly express the impulseresponse of each interaction [VER 90, BAR 91, ROU 95, YAO 97]. Thisapproach can appear appropriate for the UWB channel propagation modelingas the reconstructed signal is a sum of each ray contribution. The contributionof each ray at the receiver side is a successive convolution of the impulseresponses of each interaction of the considered ray with the transmitted signal.

Nevertheless, a deterministic modeling tool using this approach will needsignificant numerical resources. In fact, a numerical operation consisting ofa convolution needs great memory resources. So, although this model givesacceptable results, its use can become very restrictive in term of calculationtime.

4.4.3. Attiya model

The deterministic model proposed by Attiya [ATT 04] considers the GOand the UTD interactions coefficients expressed in the frequency domain (seeAppendix C). The received signal is obtained in the time domain thanks tothe use of an inverse Fourier transform. This allows us to directly use allthe classical formulations corresponding to the frequency behavior of thepropagation phenomena.

Another difference between Yao and Attiya’s deterministic model lies in theconsideration of antennas, something Yao neglected entirely. Attiya’s proposedmodel takes into account the antennas by inserting analytical formulations ofantenna radiation in the expression of the reconstructed signal. In his model,he focuses on the case of horn antennas for which he proposes a time domaincharacterization technique [ATT 03].

The same impulse response obtained from measurement in an anechoicchamber between a transmitting antenna and a receiving antenna isdirectly applied in the time domain on each ray. For each ray, the relationcorresponding to the effect of ray interactions is obtained after inverseFourier transformation. So, the determination of the received signals afterantennas are made by adding all the contributions of each ray. Each of thesecontributions is obtained by convolution of the impulse response betweenantennas with the relation corresponding to effect of a channel withoutantenna. So, it appears that this method shows two limits. The first limit isthe consideration of the impulse response of antennas in order to insert theirbehavior in the model. The second limit is the application of the same impulseresponse for all rays, although they do not go and reach transmitting andreceiving antennas respectively from the same direction.


4.4.4. Uguen and Tchoffo Talom model

The other deterministic model proposed in the literature is that of Uguenand Tchoffo Talom [TCH 04, UGU 05]. The first contribution of this modelmainly presents the synthesis of a received signal which adopts a formalismconsidering the channel ray by ray [UGU 02]. In this first contribution,some important elements of the transmission channel were not considered,such as the indoor multi-layered materials and antennas. Eventually, a morecomplete description was made [TCH 04, UGU 05]. In comparison to the firstproposition, the introduced improvement concerns a better description of theconsideration of each channel element in the model.

This model is quite similar to the one proposed by Attiya [ATT 04].However, unlike the Attiya model, the antennas are better taken intoaccount in the model proposed by Uguen and Tchoffo Talom. Moreover,the construction of each ray contribution is made separately, which allowsus to naturally access to the direction of departure (DoD) and direction ofarrival (DoA) information. So, each ray is affected by the antenna functionscorresponding to the actual DoD and DoA of the ray, defined in the frequencydomain.

4.5. Illustration of a deterministic model formalism

In this section, we illustrate the UWB deterministic modeling by presentingthe theoretical formalism of the model proposed by Uguen and Tchoffo Talom[TCH 04, UGU 05]. This model allows us to synthesize a received signal for anindoor UWB link.

We consider the application of an impulse signal p(τ) on the transmittingantenna feeding port. As explained previously, it is not helpful to sum all the raycontributions before the transformation from the frequency domain to the timedomain (see Appendix E). It is better to apply the transformation separatelyon each ray and then to sum each ray contribution directly in the time domain.This approach allows us to reduce the number of frequency points to considerand avoids unneeded frequency domain truncation of the complex exponentialcorresponding to the phase shift introduced by the propagation.

The signal after the receiving antenna is obtained by summing all thevectorial and complex component of the field coming from the rays arrivingon the receiving antenna. After the frequency sweep on the band of interest,the signal is expressed in the time domain using an inverse discrete Fouriertransformation. So, this signal can be considered as the convolution of thesignal p(τ) with the SISO impulse response of the propagation channel.


The presentation of the theoretical formalism of the deterministic model ismade by the detailed synthesis of the received signal. This detail mainly focuseson the ray by ray treatment of the propagation and antenna information as wellas the proper consideration of antennas in the modeling.

4.5.1. Received signal synthesis

The received signal r(τ) is constructed as the sum of the appropriatelyshifted contribution rk(τ) of the Nray rays obtained from the ray tracing step(see Figure 4.1) by:

r(τ) =Nray∑k=1

rk

(τ − τk

)[4.1]

The parameter τk is the delay corresponding to the free space propagationof the kth ray.

The non-delayed signal rk(τ) (see relation [4.2]) corresponds to theconvolution of the transmitted signal p(τ) applied at the transmitting antennaport with the non-delayed ray impulse response (RIR) hk(τ).

rk(τ) = hk(τ) ∗ p(τ) [4.2]

In relation [4.1], Nray is one of the important parameters for thereconstruction of the received signal. It determines the realism of the obtainedsynthesized signal r(τ).

Deterministic models using rays are strongly dependent on the number ofsignificant rays contributing to the total field. So, it is important to use rapidand appropriate techniques allowing us to obtain the main contributors in LOSor NLOS situations. Most of the time, this last situation requires us to considera great number of rays in order to improve the realism of the synthesized signal.

4.5.2. Ray impulse response without delay

The non-delayed ray impulse response (RIR) is noted hk(τ) and defined inthe time domain by:

hk(τ) = fr(− τ, sr

k

)� ck(τ) � f t

(τ, st

k

)[4.3]


r 1(τ

)r 1

(τ−τ

1)τ

τ 1

r 2(τ

)r 2

(τ−τ

2)τ

τ 2r k

(τ)

r k(τ−τ

k)τ

τ kT

FFT

=

r(τ)

τ

Fig

ure

4.1

.Buildin

gofre

ceiv

edsi

gnalr(

τ)

byth

esu

mofsh

ifte

dr k

(τ)


fr(τ, srk) is a line vector corresponding to the impulse response of the

received antenna in the arrival direction srk of the kth ray.

f t(τ, stk) is a column vector corresponding to the impulse response of the

transmitted antenna in the departure direction stk of the kth ray.

ck(τ) is a 2×2 matrix corresponding to the consideration of attenuations anddistortions introduced by the reflection, transmission or diffraction interactionsappearing on the kth ray when propagating through the channel. This term doesnot consider the delay introduced by propagation τk. This delay is directly usedwhen adding all the rk(τ) at the appropriated time position (see Figure 4.1).

stk and sr

k are the directions of departure (t) and arrival (r) of the kth ray.They are respectively the couples of polar coordinates (θt

k, φtk) and (θr

k, φrk) in

the entire spherical base.

Nevertheless, as reflection, transmission and diffraction phenomena have asimple analytical expression in the frequency domain, rk(τ) is obtained froman inverse Fourier transform applied on its frequency expression Rk(f):

Rk(f) = Fr∗(f, srk

)Ck(f)Ft

(f, st

k

)P (f) [4.4]

P (f) corresponds to the Fourier transform of the transmitted signal.

Ft,r are the complex vectors corresponding respectively to the transmittingand receiving antenna frequency behavior. They allow us to consider thedirectivity Dt,r, the return loss Γt,r, the radiation efficiency ηt,r and theantenna polarization state Ut,r [LO 88]:

Ft(f, st

k

)=√

Gt1

(f, st

k

)Ut(f, st

k

)[4.5]

Fr(f, sr

k

)= −j

λ

4π

√Gr

2

(f, sr

k

)Ur(f, sr

k

)[4.6]

Gt1

(f, st

k

)= ηt(f)

(1− ∣∣Γt(f)

∣∣2)Dt(f, st

k

)[4.7]

Gr2

(f, sr

k

)= ηr(f) Dr

(f, sr

k

)[4.8]

Ut,r(f, st,r

k

)= U t,r

θ θt,r + U t,rφ φt,r [4.9]


The terms Ut,r are unitary vectors defined in the basis corresponding to thedirections of departure st

k and arrival srk for a given ray. These terms follow the

relation:

U∗U = 1 [4.10]

The term −j λ4π in the expression of Fr corresponds to the integration

operation made at the receiver side.

Ck is the 2×2 matrix corresponding to the frequency filter presented by thepropagation channel on the kth ray. This matrix is defined from the GO/UTDfield and is expressed in a vectorial form:

Ck(f) =Ek

Einck

=

⎡⎣Cθ,θ

Cθ,φ

Cφ,θ

Cφ,φ

⎤⎦ [4.11]

with Ek the field at the receiving antenna and Einck the field coming from the

transmitting antenna in the direction stk by:

Einck = Ft

(f, st

k

)P (f) [4.12]

Ek = Ek e+j2πfτk [4.13]

4.5.3. Ray channel matrix without delay

The ray channel matrix without delay is expressed in a vectorial way byCk. It depends on the expression of the GO and the UTD field by the useof the field Ek (see relation [4.14]). The superscript tilde corresponds to theextraction of the delay related to the propagation in Ek expression.

Ek = Ck Einck e−j2πfτk [4.14]

Typically, there can appear on a kth ray approximately Nk interactions ofreflection, transmission or diffraction nature. So, Ek is expressed by the relation:

Ek =1s0

k

AkGke−j2πfτk Einck [4.15]

1s0

kcorresponds to the spherical nature of the wave coming from the

transmitting antenna.


τk is the delay related to the propagation of the kth ray. It is the sum ofdelays associated with the distances between the interactions appearing on theconsidered ray.

τk =Nk∑i=0

τ ik [4.16]

Ak corresponds to the product of all the divergence factors of eachinteraction appearing on the ray. The expression of each divergence Ai

k isrelated to the considered interaction’s nature:

Ak =Nk∏i=1

Aik [4.17]

Gk is the interaction matrix representing the consecutive reflections,transmissions or diffractions appearing on the kth ray. The term Gi

k ofeach interactions is related to the frequency, the polarization ‖ or ⊥ andthe reflection, transmission and diffraction incidence angles. These termscorrespond to 2 × 2 matrices and are defined according to the incidence basisof reflection, transmission and diffraction interaction considered by:

Gik =

⎡⎣G‖,‖

G‖,⊥

G⊥,‖

G⊥,⊥

⎤⎦ [4.18]

In other terms, the matrix Gik corresponds to the R, T or D matrix

according to the interaction nature (see Appendix C).

So, it is necessary to insert, in the global expression of Gk [4.19], the matrixused to change the basis related to the possible existence of an angle between theincidence plane of an interaction and the reflection, transmission or diffractionplane of the previous interaction.

Gk = MBout,Nkk →Br

k

[Nk∏i=2

Gik MBout,i−1

k →Bin,ik

]G1

kMBt

k→Bin,1k [4.19]

MBtk→Bin,1

k is a matrix used to change the description of a field from a basisBt

k related to a given departure direction of a kth ray to the incoming basisBin,1

k of the first ray interaction.


MBout,Nkk →Br

k is a matrix used to change the field from the outgoing basisBout,Nk

k of the last interaction to the incoming basis Brk of the arrival direction

of the kth ray.

MBout,i−1k →Bin,i

k is a matrix allowing for a kth ray to express the field,initially in an outgoing basis Bout,i−1

k of the (i−1)th interaction in the incomingbasis Bin,i

k of the ith interaction.

4.5.4. Described model results

4.5.4.1. Emitted waveform and considered scenario

We consider the impulse waveform transmission p(τ), which is obtainedusing the relation:

p(τ) =√

Epp(τ) [4.20]

with Ep the energy of the impulse signal p(τ) and p(τ) a Gaussian impulsenormalized in energy.

p(τ) can be expressed using relation [4.21]:

p(τ) =

√2√

2β√

πsin(2πfcτ

)e−( τ

β )2 [4.21]

Bα,β =2

πβ

√α

ln 1020

≈ 0.216√

α

β[4.22]

where Bα,β is the band of p(τ) given at −α dB, β is a scaling factor allowingus to adjust the time domain support of p(τ) and fc is the central frequency ofp(τ).

In the frequency domain, the applied impulse signal is given by:

P (f) =√

Ep P (f) [4.23]

P (f) =

√β√

π√2

(e−[π β (f+fc)]

2 − e−[π β (f−fc)]2)

[4.24]

So, |P (f)|2 is the energy spectral density (ESD) of the impulse signal. Theimpulse energy Ep is then obtained by integrating either the square of the


signal p(τ) or |P (f)|2, according to the following Parseval-Plancherel relation[PRO 83]:

Ep =∫

R

p2(τ) dτ =∫

R

∣∣P (f)∣∣2 df [4.25]

To specify Ep, relation [4.26] proposed by [UGU 04] can be used:

Ep =Tr P 1MHz

max

σ2 γ1MHzmax

[4.26]

So, the impulse energy can be determined with respect to the emissionlimits specified by regulation using P 1 MHz

max , the pulse repetition period Tr,the considered modulation given by σ, and γ1 MHz

max the capability of thetransmitting antenna to emit an amplified signal in the channel over a 1 MHzband.

According to the FCC specifications concerning the transmitted UWBsignal, the authorized maximum PSD is P 1 MHz

max = −41.3 dBm/MHz. In thiscase, Ep is directly expressed by:

Ep =Tr 10−4.13

σ2γ1 MHzmax

[4.27]

Figure 4.2 shows two impulses obtained for a central frequency fc = 4 GHzand an ideal1 transmitting antenna. We can note that the signal time spreadingconversely increases with the band as well as the maximum level.

The previously described model is applied for an indoor link of a LOSconfiguration in the environment represented in Figure 4.3. The rays reported inthe figure are obtained using a 3D ray determination technique which combinesray launching and ray tracing [TCH 05a].

The material properties of the environment shown in Figure 4.3 are reportedin Table 4.1. These properties are obtained from material characterizations[TCH 05a]. The frequency dependence of the materials is introduced by thepermittivity expression in the interactions coefficients (see Appendix C). Inthis table, we can note that the floor and the ceiling are in reinforced concretebecause the environment is the ground floor of a house with two levels.

1. An ideal antenna is an omnidirectional isotropic antenna with a unitary gain in alldirections.


(a)

(b)

Figure 4.2. Impulses applied on an ideal transmitting antenna with fc = 4 GHz:B

10 dB,β= 0.5 GHz (a) and B

10 dB,β= 2 GHz (b)


Figure 4.3. 3D rays obtained for an indoor link in LOS configuration

Elements Materials Material properties

ε′r ε′′r μ′r μ′′r σ (S/m) Δδ (m) e (cm)

Wall brick 3.8 0 1 0 0.05 0 10

Windows glass 3.1 0 1 0 0 0 1.5

Doors wood 2.84 −0.02 1 0 0 0 3

Ceiling reinforced concrete 7.7 0 1 0 1 0 10

Floor reinforced concrete 7.7 0 1 0 1 0 —

Table 4.1. Properties and structure of various elements of the considered environment

4.5.4.2. Channel matrix of each emitted waveform in the LOS case

Considering the two waveforms (see Figure 4.2) for p(τ) and the LOSconfiguration (see Figure 4.3), Figures 4.4 and 4.5 represent the fourcomponents of the channel matrix c(τ):

c(τ) =[cθ,θ(τ) cθ,φ(τ)cφ,θ(τ) cφ,φ(τ)

][4.28]

These illustrations are an artifice of representation which allows us to reporton the same time axis all the contributions of the rays associated with eachcomponent of the matrix c. Each component of c(τ) is obtained by adding theelectric field contribution of each of the Nray for the considered component.


This representation allows us to underline the time domain behavior of theNray ray fields arriving at the receiver without considering any transmitting orreceiving antenna.

We can note in these figures that the field level is weak on the crosscomponents (cθ,φ and cφ,θ). So, in order to obtain the received signal, theantennas considered at the transmitting and receiving sides will project thesec(τ) matrix components according to their characteristics [TCH 05b]. Theshape of the final obtained signal will strongly depend on the components ofc(τ) modified by the chosen couple of antennas.

Moreover, when the frequency band of the impulse p(τ) decreases,each contribution of all rays can no longer be clearly isolated. For a bandB10 dB,β = 500 MHz and for each component of c(τ), the obtained signalcorresponds to a compact grouping of the ray contributions arriving at atime lap with approximately the same width as the transmitted signal. Thisdoes not allow us to isolate the contribution of each ray but underlines theprogressive rise of shadowing as the transmitted signal bandwidth decreases.

4.5.4.3. Received signal with ideal antennas

In this part, from the components of channel matrix c (see Figure 4.5) andfor the LOS case as well as the transmitted pulse p(τ) of Figure 4.2(b), wefocus on the reconstructed waveform obtained in the case where the antennasat transmission (Tx) and reception (Rx) sides are ideal omnidirectional, withunitary gain.

Figures 4.6(a) and 4.6(b) show the reconstructed signal r(τ) obtainedrespectively for a couple of antennas polarized along θ and φ.

In the considered configurations, the transmitting and receiving antennasshow a good accordance in term of polarization. So, the reconstructed signals(see Figures 4.6(a) and 4.6(b)) are respectively a projection of the channelmatrix c(τ) components cθ,θ (see Figure 4.5(a)) and cφ,φ (see Figure 4.5(d)).

In the case of a real antenna, the received signal r(τ) will probably be aless simple projection of different matrix c components. So, it will no longer beeasily identified to one of the matrix c(τ) components.

One of the interests of the deterministic model detailed in section 4.5 is theease of identifying DOA and DOD information. This is because the signal r(τ)is reconstructed thanks to the rays obtained after ray tracing which directlygives the information corresponding to the direction of the rays. The otherinterest is that no sum is beforehand applied on the contributions of each ray.So, it is easy to extract the contribution associated with each ray.


(a)

(b)

(c)

(d)

Fig

ure

4.4

.C

hannel

matr

ixco

mpo

nen

tc(τ

)fo

rth

esc

enari

oofFig

ure

4.3

with

the

impulse

p(τ

)ofFig

ure

4.2

(a):

cθ,θ

(τ)

(a),

cθ,φ

(τ)

(b),

cφ,θ

(τ)

(c)

and

cφ,φ

(τ)

(d)


(a)

(b)

(c)

(d)

Fig

ure

4.5

.C

hannel

matr

ixco

mpo

nen

tc(τ

)fo

rth

esc

enari

oofFig

ure

4.3

with

the

impulse

p(τ

)ofFig

ure

4.2

(b):

cθ,θ

(τ)

(a),

cθ,φ

(τ)

(b),

cφ,θ

(τ)

(c)

and

cφ,φ

(τ)

(d)


(a)

(b)

Figure 4.6. Received signal r(τ) for the LOS scenario of Figure 4.3, the pulse p(τ)of Figure 4.2(b) and the ideal omnidirectional antennas at Tx and Rx sides:

Tx-Rx antennas polarized along θ (a) and Tx-Rx polarized antennas along φ (b)


Figure 4.7 illustrates the extraction of DOA information corresponding tothe signal reported in Figure 4.6(a). We can note that the obtained rays arewell described in 3D. The direct path is clearly identified. It arrives at thereceiving antenna side in the direction corresponding to the angles θ ≈ 95◦ andφ ≈ 245◦. Here, the θ direction is not 90◦ because the transmitter and receiverantennas are not placed at the same height.

4.6. Consideration of real antenna characteristics in deterministic modeling

Previously when ideal antennas were considered, we could easily identifythe matrix c(τ) component corresponding to the signal received after the Rxantenna. Here, real couple of antenna radiation characteristics are considered.In Figure 3.12, the used antennas which are called the CMA (Conical MonopoleAntenna) are represented. The characteristic of these antennas are obtainedfrom measurements performed on 4 π steradian in the Stargate 32 near-fieldantenna measurement engine of Satimo (see Figure 4.8) [TCH 05b].

The considered modeling configuration is the case illustrated in Figure 4.3.The received signal is illustrated in Figure 4.9(a). We can note that theomnidirectional characteristic of the CMA allows us to obtain a signal differentfrom those obtained previously with ideal antennas. So, the obtained signal isno longer easily identified to one component of the channel matrix c(τ) (seeFigure 4.5).

Figure 4.9(b) illustrates the amplitude and phase contribution applied bythe antennas on each ray. The rays corresponding to the main contribution onthe received signal are represented by a dark line. The contribution of a rayis thus proportional to the gray intensity used for its drawing. The darkestrays are those for which the combined directivity of transmitting and receivingantennas are important. If a rotation is applied along θ in order to fit bothantenna directions of maximum radiation in elevation, the received signal willhave a higher level than in the previous case (see Figure 4.10) and the otherdirections will contribute less to the obtained signal.2

We can note that the consideration of real antennas characteristics in thedeterministic model is crucial and contributes to the validation and realism ofthe received signal synthesized with the modeling.

2. By comparing the two figures, it seems that the second RI is less dense. In fact, itis the first and main ray which has more energy in this case.


Fig

ure

4.7

.Illu

stra

tion

of

r(τ)

DO

A(s

eeFig

ure

4.3

)and

the

Tx-

Rx

idea

lante

nnas

pola

rize

dalo

ng

θ


Figure 4.8. Satimo Stargate 32 near-field antenna measurement engine

4.7. Building material effects on channel properties

The previously described studies were made for materials whose propertiesare reported in Table 4.1. So, the received signal reported in Figure 4.11(a)is obtained for a LOS link (see Figure 4.3), the waveform transmission inFigure 4.2(b) and the use of a couple of CMA antennas. This signal is thesame as that reported in Figure 4.9(a).

Considering the properties reported in Table 4.2, the effect of buildingmaterial properties on the received signal synthesized by deterministic modelingis underlined. The new adopted properties correspond to a reduction of theprevious wall thickness values (see Table 4.1), to a change of window structureand especially to an increase of floor and ceiling conductivity. In fact, thereinforced concrete used for constructing floors and ceilings at various stages ofhouse building are made with metallic rods which can contribute to the increasein conductivity.

The signal received with these new material properties shows importantdifferences in comparison to the previous signals (see Figure 4.11). There arerays arriving after the direct path which show a higher level. These rays arethose which connected the transmitter and receiver and reflected on the floor orthe ceiling. So, the conductivity increase σ of the reinforced concrete introducesa high level contribution on the received signal for the rays which interact withthe ceiling or the floor.


(a)

(b)

Figure 4.9. Received signal and ray contributions corresponding to the CMAantennas: received signal after the receiving antenna (a) and 3D rays

with their corresponding contribution (b)


(a)

(b)

Figure 4.10. Received signal and ray contributions corresponding to the CMAantennas (rotation of 35◦ in θ for both Tx and Rx antennas): received signal after

receiving antenna (a) and 3D rays with their corresponding contributions (b)


(a)

(b)

Figure 4.11. Received signal obtained with CMA antennas for two configurationsof building material properties: case of materials in Table 4.1 and

case of materials in Table 4.2


Elements Materials Material properties

ε′r ε′′r μ′r μ′′r σ (S/m) Δδ (m) e (cm)

Walls brick 3.8 0 1 0 0.05 0 7

Windows glass 3.1 0 1 0 0 0 0.5

air 1 0 1 0 0 0 0.5

glass 3.1 0 1 0 0 0 0.5

Doors wood 2.84 −0.02 1 0 0 0 3

Ceiling reinforced concrete 7.7 0 1 0 10 0 10

Floor reinforced concrete 7.7 0 1 0 10 0 —

Table 4.2. Properties and structure of various building environmentconsidered for the study of material influence

In addition to the antennas, the change of material properties stronglyaffects the received signal shape. In order to increase the realism of thewaveforms obtained with a deterministic modeling tool, the characterizationof building materials is needed to insert into the modeling the goodmaterial properties for the environment considered in link modeling[KRA 93, SAT 95, HUA 96, COU 98, MUQ 03a].

4.8. Simulation and measurement comparisons

In this section, comparisons are made between the results of the realizedmeasurements (see section 3.4.2.2) and the performed simulations using thedeterministic model described in section 4.5. These comparisons allow us toevaluate the impact of the antenna characteristics in the described model andthe received signal building for various LOS links.

These comparisons consider a transmitted signal covering a band of2–6 GHz. As the measurements were made in the frequency domain, noimpulse signal is applied. Nevertheless, the transmitted signal corresponds toa sinc function in the time domain.

4.8.1. Evaluation of real antenna consideration

To evaluate the consideration of antenna radiation characteristics inthe deterministic model described in section 4.5, direct link measurementswere made in an anechoic chamber. This configuration allows us to be freefrom multipath and to obtain a direct link with only one ray [TCH 06]. For


this evaluation, two antenna couples are used: directive horn antennas andomnidirectional CMA antennas.

In the anechoic chamber, the antennas are placed at the same height anddirected, in the case of horn antennas, so that both antenna directions ofmaximum gain face each other. This configuration is reproduced in simulationfor the same departure and arrival directions as in the measurement.The simulation uses antenna characteristics data obtained from widebandmeasurement made in the Stargate 32 engine [TCH 05b].

Figure 4.12 illustrates the impulse response and transfers functions obtainedwith measurement and simulation in the case of the couple of horn antennas.

We can observe a good matching between measurements and simulationresults. Although there is only one ray, the obtained transfer functions arenot constant. This can be explained by the frequency dependencies of antennacharacteristics which affect the channel transfer function.

Figure 4.13 illustrates the impulse responses and transfers functionsobtained with measurement and simulation in the case of the couple ofCMA antennas. We can also notice in this case a good matching betweenmeasurements and simulation results.

The comparison of these two configurations testify to the relevance ofantenna characteristics in deterministic link modeling. Indeed, according totheir characteristics, antennas will affect the shape of the received impulseresponses. Moreover, the comparison between measurement and simulationvalidates the adopted vectorial insertion of antenna characteristics in thedescribed deterministic model.

4.8.2. Evaluation of impulse response reconstruction

To evaluate the impulse response reconstruction, the focus here is on LOSlinks for which the measurement configurations are described in section 3.4.2.2.In each of the shown figures, the measured and simulated impulse responses aswell as transfer functions are superimposed. The measurement and simulationresults are respectively represented in gray and black.

These illustrations concern four typical LOS situations extracted from 126measurements points made in the environment described in section 3.4.2.2.Figures 4.14 and 4.15 represent the results obtained considering the fourfollowing positions corresponding to 1.14 m, 4.38 m, 6.78 m and 8.94 mdistances.


The measured and simulated transfer functions show a great similarityin terms of level and fluctuations in form (see Figure 4.14). The samehigh frequency decrease is observed in measurement and simulation.Nevertheless, some differences are presented on the transfer function reportedin Figure 4.14(a). These differences can be explained by the fact that for thepresented results the transmitter was placed near a stone made fireplace. Insimulation, a normal wall made with concrete was considered. Moreover, somedifferences can also be observed in phase information. This can be explainedby the rays considered for the modeling, which are insufficient to provideaccess to the degree of measurement detail.

Although the transfer functions seem different, we can note a greataccordance between measured and simulated impulse responses (seeFigure 4.15). Moreover, the simulated impulse responses are less consistentin term of rays compared to the measurement impulse responses. This canbe explained by the simplified description of the environment used in themodeling. This simple description of the environment leads us to discardfurniture and the inappropriate material properties for the consideredenvironment walls.

We may keep in mind that in such situations of very good concordancebetween simulation and measurement results, the simulation represents thebenefit of giving additional information like departure and arrival angles. Thechannel is here known on various dimensions and with less cost than using asounder with a single sensor.

4.9. Conclusion

For a long time, the deployment of narrowband technologies has used thedeterministic modeling of the radio propagation channel to establish coveragemaps. With the use of UWB technology, some deterministic models havebeen proposed for signal prediction in new context. These models allow signalprediction and the rapid study of various environments with low costs interms of channel transmission effects on the UWB link.

From all the deterministic models presented, those which use frequencydomain formalisms clearly seem better suited for the study of UWB wavepropagation. More especially, the detailed Uguen and Tchoffo Talom modelallows us to easily insert the antenna radiation information in the model.Moreover, this model naturally enables the access to DoD and DoA informationas the electromagnetic calculations are performed ray by ray. The contributionsof all the rays are then summed to obtain the overall received signal.


When deterministic modeling is used in UWB, it is important to take intoaccount antenna characteristics and to use appropriate material properties forthe considered environment. The reconstructed signal is strongly dependent onthe number and relevance of the rays used in modeling. This firstly dependson the techniques used for ray determination and secondly on the details withwhich the environment is described.


(V)

delay (ns)

(a)

(level)

(radian)

Magnitude

Phase

Freq (GHz)

Freq (GHz)

(b)

Figure 4.12. Measurement (gray) and simulation (black) received signals forthe couple of horn antennas: (a) impulse response and (b) transfer function:

magnitude and phase


(V)

delay (ns)

(a)

(level)

(radian)

Magnitude

Phase

Freq (GHz)

Freq (GHz)

(b)

Figure 4.13. Measurement (gray) and simulation (black) received signals forthe couple of CMA antennas: (a) impulse response and (b) transfer function:

magnitude and phase


(level) (radian)

Mag

nitu

de

Phas

eFr

eq(G

Hz)

Freq

(GH

z)

(a)

(level) (radian)

Mag

nitu

de

Phas

eFr

eq(G

Hz)

Freq

(GH

z)

(b)

(level) (radian)

Mag

nitu

de

Phas

eFr

eq(G

Hz)

Freq

(GH

z)

(c)

(level) (radian)

Mag

nitu

de

Phas

eFr

eq(G

Hz)

Freq

(GH

z)

(d)

Fig

ure

4.14

.M

easu

red

(gra

y)and

sim

ula

ted

(bla

ck)

transf

erfu

nct

ions

for

4dis

tance

sbe

twee

nT

xand

Rx:

(a)

d=

1.1

4m

,(b

)d

=4.3

8m

,(c

)d

=6.7

8m

and

(d)

d=

8.9

4m


(V)

delay

(ns)

(a)

(V)

delay

(ns)

(b)

(V)

delay

(ns)

(c)

(V)

delay

(ns)

(d)

Fig

ure

4.15

.M

easu

red

(gra

y)and

sim

ula

ted

(bla

ck)

norm

alize

dim

pulse

resp

onse

sfo

r4

dis

tance

sbe

twee

nT

xand

Rx:

(a)

d=

1.1

4m

,(b

)d

=4.3

8m

,(c

)d

=6.7

8m

and

(d)

d=

8.9

4m


Chapter 5

Statistical Modeling of the UWB Channel

Deterministic modeling makes a relatively accurate reproduction of theUWB channel properties possible for a given configuration in a knownenvironment. Assuming that the elementary propagation phenomena are wellmodeled, the obtained impulse responses can be very realistic. The mainconstraints linked to this type of model lie in their long calculation time andthe necessity of describing the considered environment in detail.

Statistical models represent an interesting alternative for the simulation ofUWB communication systems. They consist of reproducing a possible behaviorof the propagation channel in a given type of environment. They are based ona large number of measurements, from which each parameter of the model isdefined using a statistical law. These models enable the random generation ofdifferent impulse responses.

This chapter presents the statistical modeling of the UWB channelthrough a practical approach. The principles of UWB propagation channelcharacterization is first illustrated from a series of measurements performed inan indoor office environment. For each step of the characterization process,experimental results are compared to the main anaylses published in theliterature. Following a description of the different statistical models of theUWB channel, a full channel model is detailed. Its practical conceptionis based on a set of experimental characteristics. In particular, advancedtechniques are presented for the modeling of spatial and temporal variationsof the UWB channel.


5.1. Experimental characterization of channel parameters

In this section, the characterization process of the UWB propagationchannel is illustrated from a measurement campaign covering the whole FCCfrequency band. The description of this measurement campaign is givenin section 3.4.2.1. This study also compares the experimental results fromdifferent analyses of the UWB channel.

5.1.1. Propagation loss

5.1.1.1. Frequency propagation loss

One of the channel properties characteristic to UWB signals is thepower decay observed with increasing frequency. In an ideal free spaceconfiguration, the propagation loss is given by the Friis formula, asrecalled in equation [2.34]. This formula implies that for a given distanced, the channel power transfer function (see equation [2.36]), expressedin dB, should follow a frequency variation in the form of −20 log(f). Itshould be noted that this frequency dependence is linked to the effectivearea of an isotropic antenna and is not strictly speaking a characteristicof the propagation channel. In the literature, the attenuation of thereceived power as the frequency increases has been observed in differentstudies dedicated to antennas [KOV 03, HOF 03], or to the UWB channel[CHE 02, KUN 02a, ALV 03, BAL 04b, HAN 04, CHO 05, PAG 05]. As anexample, Table 5.1 presents different estimates of the frequency dependentpath loss exponent Nf . We may observe a relative diversity in the obtainedvalues, as some of the authors even reported an increase in the received powerwith increasing frequency [KOV 03]. This may be explained by the highdependence between the parameter Nf and the measurement antenna.

Measurementcampaign

Whyless.com[KUN 02a]

Aalborg University[KOV 03]

Instit. forInfocommResearch[BAL 04b]

Samsung[CHO 05]

Nf 1.6 to 2.8 −0.3 to 5.5 1.0 to 3.7 2.0 to 3.1

Table 5.1. Estimation of the frequency dependent path loss exponent for differentanalyses of the UWB channel. The published values have been adapted to the

definition of the parameter Nf used in this book

In order to estimate the frequency dependent path loss, we studied thechannel attenuation at different frequencies regularly spaced between 4 GHzand 10 GHz. For each measurement location, the path loss PL(f, d) was

Statistical Modeling of the UWB Channel 135

extracted from the power transfer function at the selected frequencies. In orderto remove the distance dependency, each power transfer function was initiallynormalized by arbitrarily setting the attenuation of the total received powerover the whole measurement bandwidth to 0 dB. The resulting normalizedpath loss PLnorm(f) can be compared to a model in the form:

PLnorm(f) = PLnorm

(f0

)+ 10Nf log

(f

f0

)+ S(f) [5.1]

where S(f) represents a residual term with zero mean expressing the differencein dB between the measurement and the model.

3 4 5 6 7 8 9 10 11

-4

-2

0

2

4

6

8

10

Frequency (GHz)

PL no

rm(f

) (d

B)

Figure 5.1. Average normalized path loss vs. frequency

The normalized path loss averaged over all measurement locations isrepresented as a function of frequency in Figure 5.1. It should be noted thatthe antenna gains GT (f) and GR(f), measured in an anechoic chamber, weresubtracted from each power transfer function at the selected frequencies, priorto path loss calculation. For each antenna, the antenna gain was selected bytaking the direction of the direct transmitter-receiver path into account. Thisapproach may seem simplistic a priori, as the total power is not only receivedvia the direct path, but also via numerous multipaths arriving from otherdirections. However, with no further knowledge of the departure and arrivaldirection of these secondary paths, this method makes a sensible compensationof the antenna effect possible. We may observe that the dispersion of themeasured plots around the linear approximation is reduced to a standarddeviation of σS = 0.6 dB. The frequency dependent path loss exponent isNf = 2.28. With respect to the error level inherent to the measurement


and calculation methods, this value may be considered close to the theory(Nf = 2). Hence, we recommend using the theoretical frequency loss of20 log(f) in the modeling of UWB propagation channels, as suggested in[BUE 03].

5.1.1.2. Distance propagation loss

In the previous section, we observed that the used antennas may have anon-negligible impact on the radio parameters. In the following analyses, inorder to minimize this effect, the collected data were corrected by accounting forthe gain of both antennas, measured in the direction of the transmitter-receiverpath. The antenna radiation patterns, measured every GHz, were interpolatedin frequency.

According to the previous analysis on the frequency path loss, allmeasurements were fitted to a general formula as follows:


)+ 20 log

(f

f0

)+ 10Nd log

(d

d0

)+ S(f, d) [5.2]

where f0 represents the central frequency of 6.85 GHz and d0 is an arbitrarydistance of 1 m.

0.6 0.8 1 2 3 4 5 6 8 10 20 30 40110

100

90

80

70

60

50

40

Distance (m)

Atte

nuta

tion

(dB

)

LOSNLOS

Figure 5.2. Path loss vs. distance. Each point representsthe median attenuation in the FCC band

For each measurement location, the accounted path loss is the medianattenuation in the FCC band, after shifting each measurement to the referencefrequency f0. Path loss exponents were obtained by linear fit in each LOS andNLOS situation. Figure 5.2 presents the obtained results. The measurementplots mainly follow a linear decay in log-scale, which corresponds to an


exponential decay of the received power with respect to the distance. In theLOS situation, a path loss exponent Nd = 1.62 was recorded, with a standarddeviation σS = 1.7 dB.1 In the NLOS case, the measurement plots aresomewhat more dispersed, with a distance dependent path loss exponent Nd

= 3.22, and a standard deviation σS = 5.7 dB.2 The values of the parameterPL(f0, d0) were respectively evaluated at 53.7 dB and 59.4 dB. Table 5.2shows that these values are in line with other analyses of the UWB channelpublished in the literature. For comparison purposes, the UWB path lossparameters proposed by the standardization organization ITU [ITU 04] arealso reported.

More details regarding the influence of frequency on the path losscoefficients are given in [PAJ 07]. In general, these parameters undergo anegligible variation when they are observed on partial frequency bands withinthe 3.1–10.6 GHz band.

5.1.2. Impulse response characterization

Figure 5.3 presents typical PDP measured in LOS and NLOS configurations,as well as one of the 90 impulse responses. The delay on the x-axis has beenconverted in path length in meters, to ease the interpretation of the main paths.In both LOS and NLOS situations, we may observe one or several clusters,corresponding to a main echo followed by an exponential decay of diffuse power.In the LOS case, walls or pieces of furniture in the vicinity of the radio linkgenerate significant reflected or diffracted echoes, which explains the presenceof peaks in the PDP. An attenuation of 10 dB to 20 dB has thus been observedbetween the power of the main path of each cluster and the power of thesecondary paths. The general shape of the PDP is globally smoother in theNLOS case.

5.1.2.1. Delay spread

The RMS delay spread τRMS was calculated for each measured PDP,over the whole 3.1–10.6 GHz band. In order to minimize the effect of noise,a threshold placed 20 dB below the maximum value of the PDP was used.

1. In the LOS case, the value of Nd may be lower than in the theoretical case of freespace (Nd = 2). This is due to the waveguide effect, frequently observed in indoorconfigurations (see section 2.2.2).

2. This significant value of the standard deviation in the NLOS case may be explainedby the diversity of NLOS configurations, as the obstruction between the transmitterand the receiver may result from a single plasterboard or several concrete walls.


Measurement Nd σS (dB) PL(f0, d0) (dB)

campaign LOS NLOS LOS NLOS LOS NLOS

UltRaLab [CAS 01] 2.4 5.9

AT&T Labs - MIT [GHA 02a] 1.7 3.5 1.6 2.7 47 51

Time Domain Corporation[YAN 02]

2.1 3.55

Intel Labs [CHE 02] 1.72 4.09 1.48 3.63

Whyless.com [KUN 02a] 1.58 1.96

UCAN - CEA LETI [KEI 03] 1.6 to1.7

3.7 to7.2

Ultrawaves - Oulu University[HOV 03]

1.04 to1.80

3.18 to3.85

UCAN - Cantabria University[ALV 03]

1.4 3.2 to4.1

New Jersey Instit. of Tech.[DAB 03]

1.55 to1.72

0.77 to1.98

NETEX - Virginia Tech[MUQ 03b]

1.58 to1.60

2.41 to2.60

1.6 to1.9

3.3 to6.1

NETEX - Virginia Tech[BUE 03]

1.3 2.3 to2.4

2.8 to3.6

2.8 to5.4

AT&T - WINLAB [GHA 03b] 2.01 to2.07

2.95 to3.12

2.3 to3.2

3.8 to4.1

43.7 to45.9

47.3 to50.3

Hong Kong University [LI 03] 1.8 3.4 0.6 3.2

Ultrawaves - University ofRome “Tor Vergata”

[CAS 04a]

1.92 3.66 1.42 2.18 48.68 47.24

Instit. for Infocomm Research[BAL 04b]

1.8 1.8 to2.1

1.5 2.4 to4.2

36.6 46.4 to52

ETH Zurich [SCH 04] 1.2 to1.6

2.2 49 to51

45

Samsung [CHO 05] 1.18 to2.48

2.18 to2.69

0.93 to1.50

1.43 to4.69

46.5 to50.1

41.3 to47.3

France Telecom - INSA[PAG 06b]

1.62 3.22 1.7 5.7 53.7 59.4

ITU Recommendation[ITU 04]

1.7 3.5 to 7 1.5 2.7 to 4

Table 5.2. Estimate of the distance dependent path loss for different analysesof the UWB channel


(a)

0 20 40 60 80-50

-40

-30

-20

-10

0

Distance-delay (m)

Rel

ativ

e po

wer

(dB

)

IRPDP

(b)

0 20 40 60 80-50

-40

-30

-20

-10

0

Distance-delay (m)

Rel

ativ

e po

wer

(dB

)

IRPDP

Figure 5.3. Typical PDP and impulse response.(a) LOS and (b) NLOS configurations

Over the whole set of measurements performed in LOS configuration, themean delay spread is τRMS = 4.1 ns, with a standard deviation στ = 2.7 ns.In the NLOS configuration, the mean delay spread is τRMS = 9.9 ns, witha standard deviation στ = 5.0 ns. Table 5.3 presents the results publishedin other analyses of the UWB radio channel. Values obtained for τRMS

are in accordance with some of the previous experiments, although thisparameter may vary from one experiment to the other. This is due to thehigh sensitivity of this parameter to the measurement environment and to theused experimental setup. The large scope of values in the published resultsmay also be explained by the different thresholds used when calculating τRMS

[CAS 04a].


Mea

sure

men

tτ R

MS

(ns)

στ

(ns)

cam

pai

gnLO

SN

LO

SLO

SN

LO

S

UC

AN

-C

EA

LE

TI

[KE

I03]

10.9

to12.2

9.9

to22.4

1.9

to2.1

1.4

to9.5

Tim

eD

om

ain

Corp

ora

tion

(DSO

)[P

EN

02]

5.2

78.7

8to

14.5

9

Tim

eD

om

ain

Corp

ora

tion

(corr

elato

r)[Y

AN

02]

5.7

25.2

2

AT

&T

Labs

-M

IT[G

HA

02a]

4.7

8.2

2.3

3.3

New

Jer

sey

Inst

it.ofTec

h.[D

AB

03]

7.7

1to

17.3

4

NE

TE

X-V

irgin

iaTec

h[B

UE

03]

0.5

3to

4.5

52.3

0to

18.5

0

AT

&T

-W

INLA

B[G

HA

03a]

3.3

8to

5.4

97.3

1to

8.1

51.5

8to

1.6

32.4

5to

3.4

7

Hong

Kong

Univ

ersi

ty[L

I03]

19.9

14.3

1.8

2.8

Lund

Univ

ersi

ty[K

AR

04b]

28

to31

34

to40

Inst

it.ofIn

foco

mm

Res

earc

h[B

AL

04b]

15.6

18.7

to23.6

ET

HZuri

ch[S

CH

04]

21.0

8to

53.6

231.1

1to

74.0

81.6

3to

3.3

71.8

7to

7.0

4

Sam

sung

[CH

O05]

12.4

8to

14

26.5

1to

38.6

11.5

3to

1.8

75.2

2to

8.0

3

Fra

nce

Tel

ecom

-IN

SA

[PA

G06b]

4.1

9.9

2.7

5

Tab

le5.

3.Est

imate

ofth

edel

ay

spre

ad

for

diff

eren

tanaly

ses

ofth

eU

WB

channel


In order to observe the evolution of these parameters with frequency, themean values of τRMS calculated for seven partial bands of 528 MHz each arerepresented in Figure 5.4 as a function of the central frequency of each band.For each band, the value of στ is represented by the length of the vertical line.The values of τRMS and στ obtained in each partial band are relatively closeto the values calculated from the global UWB frequency band. As can be seen,the delay spread is not affected by the frequency. This was also observed bythe University of Oulu from measurements performed in the 1–11 GHz band[JAM 04].

3 4 5 6 7 8 9 10 110

5

10

15

Central frequency (GHz)

RM

S d

elay

spr

ead

(ns)

LOS NLOS

Figure 5.4. Mean delay spread for different partial bands. The length of the verticalline represents the corresponding standard deviation

5.1.2.2. Power delay profile decay

Exponential decay constants

The typical PDP presented in Figure 5.3 shows that the received poweris grouped in different clusters, corresponding to the main propagationechoes. The decay of the received power with increasing delay is generallycharacterized with the inter- and intra-cluster exponential decay constants,respectively denoted Γ and γ (see section 2.4.1.4).

To evaluate these parameters, the time intervals corresponding to theclusters of each measured PDP are identified by visual inspection. Thistechnique was also used in [KAR 04a]. In each of the identified interval, alinear fit is performed at the delays included between the maximum and theminimum values of the PDP (expressed in dB). This enables the extractionof the intra-cluster exponential decay constant γ. The inter-cluster decay


constant Γ is obtained using a linear fit on the maximum of each cluster.In all cases, only the parts of the PDP presenting a power larger than 5 dBabove the noise level were considered. Figure 5.5 illustrates this parameterextraction.

0 30 60 90 120-60

-50

-40

-30

-20

-10

0

Delay (ns)

Rel

ativ

e po

wer

(dB

)

Inter-cluster decayIntra-cluster decay

Figure 5.5. Extraction of the inter- and intra-cluster exponential decay constants

Among all PDP measured in a LOS situation, between 3 and 8 clusters (5.6on average) were identified. The mean exponential decay constants have beenevaluated as Γ = 15.7 ns and γ = 7.5 ns. In NLOS configuration, the PDPencompass between 1 and 4 clusters (2.4 on average). The mean exponentialdecay constants have been assessed as Γ = 16.5 ns and γ = 12.0 ns.

Table 5.4 compares these experimental values with results published fromsimilar experiments. In some analyses [CAS 02, ALV 03], the whole PDP wasconsidered as a single cluster, which explains the lack of results regarding Γ.The value of the parameters Γ and γ is generally between 7 ns and 30 ns,even if some higher values have occasionally been reported [CRA 02, ALV 03,CHO 04a]. The inter-cluster decay is generally stronger than the intra-clusterdecay. Results published in [KAR 04b] are a particular case where this tendencyis inversed, and where the values of Γ and γ are quite low. This may arise fromthe measurement environment, as the experiment took place in a factory. Forthis experiment, a dependency of the parameter γ with the delay has beenobserved. In [CRA 02], the authors suggest that the constant Γ is linked tothe building architecture, while γ is determined by the objects in the vicinityof the receiving antenna. The diversity of the sounded environments may thusexplain the variety of the obtained results.


Mea

sure

men

tΓ

(ns)

γ(n

s)

cam

pai

gnLO

SN

LO

SLO

SN

LO

S

Whyle

ss.c

om

[KU

N02a]

13.6

Ult

RaLab

[CA

S02]

16.1

Ult

RaLab

[CR

A02]

27.9

84.1

UC

AN

-C

EA

LE

TI

[KE

I03]

14.5

to21

9to

20

6to

85

to15

UC

AN

-C

anta

bri

aU

niv

ersi

ty[A

LV

03]

100

125

to167

NE

TE

X-

Vir

gin

iaTec

h[B

UE

03,M

CK

03]

7.1

21

28

Inte

lLabs

[FO

E03b]

7.6

16

1.6

8.5

Ult

raw

aves

-U

niv

ersi

tyofR

om

e“Tor

Ver

gata

”[C

AS

04b]

13

10.8

3to

13.9

77

to58

Lund

Univ

ersi

ty[K

AR

04b]

2.6

34.9

44.5

85.5

8

Sam

sung

[CH

O04a]

22.1

to24.0

36.9

to51.5

14.3

to30.8

27.4

to38.6

Inst

it.ofIn

foco

mm

Res

earc

h[B

AL

04b]

27.8

24.6

to30.4

14.1

25.3

to33.8

Fra

nce

Tel

ecom

-IN

SA

[PA

G06b]

15.7

16.5

7.5

12.0

Tab

le5.

4.Est

imate

ofth

ePD

Pex

ponen

tialdec

ay

const

ants

for

diff

eren

tanaly

ses

ofth

eU

WB

channel

.T

he

publ

ished

valu

eshave

been

adapte

dto

the

defi

nitio

nofth

epa

ram

eter

sΓ

and

γuse

din

this

book


Power decay constants

The assumption of an exponential decay for the cluster and ray amplitudeswas first introduced by Saleh and Valenzuela from their observation ofthe indoor wideband radio channel [SAL 87]. However, the analysis of theresults from the measurement campaign shows that exponential decay is notcompletely satisfactory to model the slope of the PDP. Indeed, followingthis assumption, the PDP expressed in log-scale should present a lineardecrease with increasing delay. The whole PDP as well as each constitutivecluster should hence fit into a triangular shape. This general shape is notrepresentative of the experimental observations (see Figure 5.5).

By considering successive echoes of the main path, we may identify two mainsources of attenuation. On the one hand the propagation of the wavefront overa longer path induces a stronger power loss. On the other hand, delayed echoesundergo more propagation phenomena, which can be of a different nature, suchas reflection or diffraction. This physical interpretation leads us to model themultipath attenuation following a similar approach to that used for distancepath loss. We may recall that in this case, the observed attenuation at atransmitter-receiver distance d is proportional to d−Nd , where Nd representsthe distance dependent path loss exponent. Regarding the different rays of theimpulse response, the length of a propagation path is proportional to its delay.Hence, we suggest an adaptation of the Saleh and Valenzuela model, wherethe cluster and ray amplitudes decrease according to a power function. In theclassical formalism presented in section 2.4.1.4, the amplitude βk,l of the kth

ray in the lth cluster (see equation [2.33]) is replaced by the following formula:

β2kl = β2

11

(Tl

T1

)−Ω(τk,l + Tl

Tl

)−ω

[5.3]

where Tl represents the delay associated with the lth cluster and τk,l is the delayof the kth ray within the lth cluster. The parameters Ω and ω are respectivelycalled inter-cluster and intra-cluster power decay constants.

As for the case of exponential decay, the values of the parameters Ω and ωhave been assessed by linear fit on the PDP clusters. In each case, the standarddeviation σε of the error in dB between the model and the measurementhas been calculated, in order to validate the proposed approach. Figure 5.6illustrates the extraction of the parameters Ω and ω. It can be compared to theresults reported in Figure 5.5.

Regarding inter-cluster decay, using a power function instead of anexponential function leads to a decrease in the average standard deviationσε from 4.8 dB to 2.9 dB in the LOS case, and from 2.4 dB to 1.7 dB in the


0 30 60 90 120-60

-50

-40

-30

-20

-10

0

Delay (ns)

Rel

ativ

e po

wer

(dB

)

Inter-cluster decayIntra-cluster decay

Figure 5.6. Extraction of the inter- and intra-cluster power decay constants

NLOS case. Regarding the intra-cluster decay, the average modeling error σε

decreases from 1.9 dB to 1.8 dB in the LOS case, and from 1.7 dB to 1.6 dBin the NLOS case. This validates the proposed model, which is closer to ourexperimental measurements. Finally, in the LOS configuration, we observed asignificant power attenuation G between the main path of each cluster and thefollowing rays, as may be seen in the example of Figure 5.6. This phenomenonwas already observed for UWB channels in [CAS 02] and [KUN 03].

Over the whole set of experimental measurements, we observed the averagevalues Ω = 4.4 and ω = 11.1 in the LOS case, and Ω = 3.9 and ω = 10.2 in theNLOS case. In the LOS configuration, the average attenuation G was measuredat 12 dB.

5.1.2.3. Ray and cluster arrival rate

Study of the clusters

In order to estimate the arrival time statistics for a new cluster, we considerthe arrival time of the lth cluster, noted Tl, over the whole set of measuredPDP presenting more than one cluster. This corresponds to the delay of themaximum value of the PDP in each time interval representing a cluster. Thestatistical distribution of the inter-cluster durations ΔT is then studied. ΔT iscalculated as follows:

ΔT = Tl+1 − Tl, l ∈ [1;L− 1] [5.4]

where L represents the number of clusters in the PDP.

Over the whole set of PDP presenting more than one cluster, the averageinter-cluster duration was ΔT = 27.4 ns in the LOS case and ΔT = 40.1 ns in


the NLOS case. The graphs in Figure 5.7 are percentile-percentile diagrams,representing the experimental distribution percentiles of ΔT on the x-axis, andthe theoretical percentiles of an exponential distribution with parameter Λ onthe y-axis. The best fit leads to a value Λ = 1

27.4 ns = 36.5MHz in the LOS case,and Λ = 1

40.1 ns = 24.9 MHz in the NLOS case. In both cases, the alignment ofthe plots on the diagram diagonal shows that the exponential distribution is areasonable approximation to modeling inter-cluster duration.

(a) (b)

0 20 40 60 80 100 1200

20

40

60

80

100

120

Experimental ΔT (ns)

The

oret

ical

ΔT

(ns

)

LOS

0 30 60 90 120 150 1800

30

60

90

120

150

180


The

oret

ical

ΔT

(ns

)

NLOS

Figure 5.7. Percentile-percentile diagrams for the inter-cluster duration.Experimental percentiles vs. theoretical percentiles corresponding toan exponential distribution with parameter Λ = 36.5 MHz in the

LOS case (a) and Λ = 24.9 MHz in the NLOS case (b)

Study of the rays

Individual echoes due to the different multiple paths are not directlyobservable on the measured PDP. Because of the limited frequency bandof the measurement, each echo is received in the form of an impulse withnon-zero duration. The impulse response is a continuous waveform composedof the sum of all individual contributions, each one presenting a differentattenuation and a different phase rotation.

Different methods are available to extract the delay and amplitudeinformation of the main paths constituting an impulse response. TheCLEAN method, initially used in radio astronomy [HOG 74], was adoptedby different researchers for the characterization of the UWB radio channel[YAN 02, PEN 02]. This method was modified by the University of SouthCalifornia for the study of the arrival direction [CRA 02]. The Tokyo Instituteof Technology used an algorithm based on the high-resolution method calledspace alternating generalized expectation (SAGE), also allowing the analysis


of the arrival direction [HAN 03]. It should be noted that these two studieswere based on measurements performed with a large number of co-locatedsensors.

In order to illustrate the process of ray identification we presenthere the frequency domain maximum likelihood (FDML) algorithm[DEN 03a, LEE 02]. The search of ray locations is performed in an iterativeway, from the representation of the impulse response in its real form h(τ).As an assumption, the channel is thus described in the form:

h(τ) =K∑

k=1

βkδ(τ − τk

)[5.5]

where K represents the number of rays, and βk and τk are the real amplitudeand delay linked to the kth ray. The parameter βk may take negative values,in order to account for the phase inversion linked to some interactions, such asthe reflections.

At each iteration of the process, a new ray is detected by finding thecorrelation peak between the measured impulse response and a templatesignal, corresponding to the sounding waveform. Contrarily to the CLEANalgorithm, the FDML method proposes to optimize the whole set of detectedrays. This requires a minimization of the squared error between the measuredfrequency spectrum and the synthetic spectrum, built from the identifiedrays. This optimization presents two main advantages. First, it enables thedetection of superimposed rays, which does not always lead to a correlationpeak. Second, the processing is performed in the frequency domain, whichavoids the resolution limitations linked to the sampling rate in the timedomain. More details on adapting the FDML algorithm to accelerate thecalculation time are available in [PAG 05]. The results of the FDML algorithmallow us to study the arrival time of the kth ray, over the whole set of selectedimpulse responses. As with the clusters case, we study the distribution of theinter-ray durations, defined as follows:

Δτ = τk+1 − τk, k ∈ [1;K − 1] [5.6]

where K represents the number of rays in the impulse response.

Over the whole set of measurements performed in both LOS and NLOSconfigurations, the average inter-ray duration was respectively evaluated atΔτ = 0.168 ns and Δτ = 0.161 ns. Figure 5.8 presents a percentile-percentilediagram used to compare the experimental distribution of Δτ to an exponentialdistribution with parameter λ = 1

0.168 ns = 5.95 GHz in the LOS case andλ = 1

0.161 ns = 6.19 GHz in the NLOS case. In this case, some differences may


be noted between the theoretical and experimental data, but the exponentialapproximation still provides an acceptable fit to the measurements.

(a) (b)

0 0.2 0.4 0.6 0.80

0.2

0.4

0.6

0.8


The

oret

ical

ΔT

(ns

)

0 0.2 0.4 0.6 0.80

0.2

0.4

0.6

0.8


The

oret

ical

ΔT

(ns

)

LOS NLOS

Figure 5.8. Percentile-percentile diagrams for the inter-ray duration. Experimentalpercentiles vs. theoretical percentiles corresponding to an exponential distribution

with (a) parameter λ = 5.95 GHz in the LOS case and (b) λ = 6.19 GHzin the NLOS case

The experimental values obtained for the cluster arrival rate Λ and the rayarrival rate λ are compared with the results available in the literature, shown inTable 5.5. Regarding the cluster arrival rate, the observed values are generallyin the order of 10 to several hundreds of MHz. The average duration betweentwo clusters is thus in the order of 10 ns to 100 ns. It should be recalled that acluster within the PDP corresponds to a main path, arising from transmissionsor reflections on walls, on the ceiling or on the building ground. The parameterΛ is thus dependent on the structure of the building where the measurementtook place. The ray arrival rate λ presents variable values depending on theexperiment. Indeed, values obtained depend highly on the ray identificationtechnique that was used in the analysis. For this reason, researchers from theGerman institute IMST advise to arbitrarily setting the inter-ray duration atthe temporal resolution value obtained [KUN 02a]. In this case, the ray arrivalrate would be equal to the width Bw of the analyzed band.

5.1.3. Study of small-scale channel variations

The last characteristic of the UWB radio channel studied from theexperimental campaign (see section 5.1) is related to the fast fading of theimpulse response. During the campaign, a rotating arm was used, whichenabled the measurement of the channel impulse response at 90 locations


Mea

sure

men

tΛ

(MH

z)λ

(MH

z)

cam

pai

gnLO

SN

LO

SLO

SN

LO

S

Whyle

ss.c

om

[KU

N02a]

100

to1000

Bw

Ult

RaLab

[CR

A02]

21.9

8434.7

8

UC

AN

-CE

ALE

TI

[KE

I03]

10

to25

10

to800

45

to180

1500

to5500

NE

TE

X-

Vir

gin

iaTec

h[B

UE

03,M

CK

03]

200

100

1429

714

Inte

lLabs

[FO

E03b]

16.7

90.9

2000

2857

Ult

raw

aves

-U

niv

ersi

tyofR

om

e“Tor

Ver

gata

”[C

AS

04b]

26

59

Lund

Univ

ersi

ty[K

AR

04b]

70.9

89.1

Sam

sung

[CH

O04a]

85

to115

47

to64

1160

to1960

1390

to1790

Inst

it.ofIn

foco

mm

Res

earc

h[B

AL

04b]

18.6

2.4

to13.4

280

270

to360

Fra

nce

Tel

ecom

-IN

SA

[PA

G06b]

36.5

24.9

5946

6194

Tab

le5.

5.Est

imate

ofth

eave

rage

clust

erand

ray

arr

ivalra

tes

for

diff

eren

tanaly

ses

ofth

eU

WB

channel

.T

he

publ

ished

valu

eshave

been

adapte

dto

the

defi

nitio

nofth

epa

ram

eter

sΛ

and

λuse

din

this

book


situated around a circle of 20 cm in radius. For each measurement, the spacefluctuation statistics were studied by comparing the 90 impulse responsescollected locally. The study consisted of analyzing the statistical distributionof the amplitude of the received signal at each delay. In the literature,previous studies showed that this distribution was well represented using aNakagami function [CAS 02]. The Nakagami m parameter was thus estimatedfor each measured PDP, at delays separated by 0.5 ns on the time scale (seeAppendix B.1.3).

An example of values for the parameter m is given for a specific measurementin Figure 5.9. As can be noted, the best fitted Nakagami distribution presentsa parameter m close to 1 for the vast majority of the delays within the PDP.Thus, the amplitude distribution of the impulse response for a given delay maybe correctly described using a Rayleigh distribution. This was observed for mostof the measured PDP. In addition, we may observe that the cases where theparameter m takes higher values correspond to the main paths of the PDP. Inthis case, the value of the parameter m may increase to m = 4 or m = 5, andup to m = 8 in the extreme cases.

The characterization of amplitude distribution in the UWB impulseresponse is a controversial issue in the literature. The Rayleigh distributionhas frequently been observed in the study of UWB radio channel fastfading statistics [CRA 02, KUN 02a, SCH 04, KAR 04b]. Researchersfrom ETH Zurich [SCH 04] and from the Lund University [KAR 04b] alsonoted a modification of this distribution for the main path. Other studiesshow that the fast fading is well represented by a Nakagami distribution[CAS 02, CAS 04b, BAL 04b]. In this case, the parameter m may vary withthe delay. However, it has been demonstrated that a theoretical impulseresponse presenting a Rayleigh fast fading may be observed as following aNakagami distribution, depending on the duration over which the receivedpower is integrated in the time domain [KUN 03]. Finally, it should benoted that some analyses recommend that we use a log-normal distribution[KEI 03, FOE 03b, LI 03, BUE 03, MCK 03] or a Rice distribution [HOV 02].

In practice, we may distinguish between two sources of channel fluctuations[HAS 94a]. Spatial variations arise when at least one of the antennas is moved inan otherwise static environment. Temporal variations are due to environmentalmodifications and may be observed in fixed radio links. A study of the channelvariations when the transmitting antenna is moved on a 1 m2 grid was presentedin [PAG 04]. Results show that in the case of the UWB channel, the delaylinked to the main paths of the impulse response significantly varies while theantenna is moved. This shift of the main paths in the time domain is due tothe high resolution of UWB signals and needs to be taken into account whenmodeling the channel spatial variations. More details on these observations are


0 20 40 60 80 100 120 140-50

-40

-30

-20

-10

0

Rel

ativ

e po

wer

(dB

)

Delay (ns)

0 20 40 60 80 100 120 1400

1

2

3

4

Nak

agam

i m

Delay (ns)

PDP

Figure 5.9. Nakagami m parameter analysis. PDP measured in an NLOS situationand parameter value m for each delay

available in [PAG 05]. In indoor environments, the temporal variations of thepropagation channel are mainly due to moving people. This phenomenon isstudied more particularly in the following section.

5.1.4. Effect of moving people

The study of the effect of moving people on the UWB channel is based on theanalysis of a measurement campaign performed in an indoor office environment.For this campaign, a UWB sounder enabling real time measurements over the4–5 GHz frequency band was used. During the measurement process, a groupof 1 to 12 people was walking in a corridor in the vicinity of a fixed radio link.A complete description of this campaign is given in section 3.4.2.3.

5.1.4.1. Observation of temporal variations

A typical impulse response collected during the experiment is given inFigure 5.10. In this graph, the delay has been converted to path length in metersto ease the interpretation of multipaths. After the direct path (a), whose lengthcorresponds to the transmitter-receiver distance (11 m), we may distinguish twoechoes (b) and (c) corresponding to reflections on the corridor walls.


0 10 20 30 40 50 60

110

100

90

80

70

Distance-delay (m)

Pow

er a

ttenu

atio

n (d

B)

(a)

(b)

(c)

Figure 5.10. Typical impulse response

A first observation of the effect that moving people have on the UWBchannel is given in Figure 5.11. The time varying impulse response isrepresented in the case of 12 people walking back and forth through the radiolink. Successive measurements are represented from left to right, while thevertical axis represents the excess delay converted in path length (m). Theinfluence that moving people have on the CIR appears clearly on this graph.The main paths (a) and (b) are regularly obstructed by moving people, duringboth forward (t = 15 s to t = 27 s) and backward (t = 63 s to t = 74 s)displacements along the corridor. At other values of the excess path, we canobserve strong signal fluctuations, with respect to the stationary part of thediagram.

5.1.4.2. Slow fading

As a first step in the analysis, we observed the slow fading generated byhuman beings in the vicinity of the radio link. For this purpose, we studied theslow temporal evolution of the mean power received in the LOS path in thepresence of people. Fast fading fluctuations were eliminated by averaging thereceived power using a sliding window.

Figure 5.12 presents the aggregate effect of several people passing throughthe main signal path. In general, the progression of one person through theLOS path yields a maximum attenuation of about 8 dB, the shadowing effectlasting for about 4 s. The obstruction duration increases with the number ofpeople, up to about 15 s for a group of 12 people. In this case, the maximumattenuation of the mean power is about 15 dB. We clearly see that theshadowing pattern obtained for groups of people is composed of superimposed


Time (s)

Dis

tanc

e-de

lay

(m)

0 20 40 60 80

0

5

10

15

20

25

30

35

40

45

Rel

ativ

e at

tenu

atio

n (d

B)

40

35

30

25

20

15

10

5

0

(a)

(b)

(c)

← Backward mov. →← Forward mov. →

Figure 5.11. Time varying impulse response in the case of 12 moving people

individual contributions. However, the particular effect that each person hason the received signal is not always observable, as, for example, in the caseinvolving 4 people.

5.1.4.3. Fast fading

In addition to the large-scale fading generated by moving people,small-scale fading is observed while people are walking in the vicinity of theradio link. The signal received at a delay corresponding to the main pathsof the impulse response may be thought of as a vector summation of severalmultipath components, as would be the case in a typical situation exhibitingRician fading. As depicted in Figure 5.13, we may distinguish between twocomponents of the received signal. The dominant component accounts for thesignal normally received in a static environment. The random componentrepresents the summation of all waves scattered by moving people.

In order to accurately analyze the fast fading observed duringexperimentation, the random component was isolated by filtering. Figure 5.14represents both magnitude and phase fluctuations of the random componentextracted from the signal received via the main path, when obstructed by


04

812

16

-30

-25

-20

-15

-10-505

Relative power (dB)1

peop

le

Tim

e (s

)0

48

1216

2024

2832

36

-30

-25

-20

-15

-10-505

4 pe

ople

Tim

e (s

)0

48

1216

2024

2832

36

-30

-25

-20

-15

-10-505

12 p

eopl

e

Tim

e (s

)

Rec

eive

d po

wer

Slo

w fa

ding

Fig

ure

5.12

.Typ

icalla

rge-

scale

fadin

gpa

tter

ns

for

the

LO

Sco

mpo

nen

t.Effec

tof1,4

and

12

people


Q

I

time

Dominantcomponent

Randomcomponent

Figure 5.13. Vector decomposition of the received signal

12 moving people. This situation corresponds to the measurement depictedin Figure 5.12 (graph on the right). We may notice that the magnitude ofthe small-scale fading presents a high degree of regularity, compared to thenon-stationary large-scale fading pattern.

Using a Kolmogorov-Smirnov testing procedure (see Appendix B.2), theamplitude distribution of the random component is well suited to a Rayleighdistribution. This observation could be made for most of the availablemeasurements, independently of the number of moving people. The signalreceived via the main paths of the impulse response, composed of a Rayleighrandom component and a dominant component of greater amplitude, theresulting signal hence follows a Rician distribution (see Appendix B.1.2).

The Rician K parameter is defined as the power ratio between the dominantcomponent and the random fluctuations. As the dominant component presentsa slowly time-variant amplitude, the parameter K varies over time accordingly,depending on the obstruction of the main path. We may notice in this examplethat the mean signal power of the random component is about 12 dB below theunobstructed signal level. Depending on the attenuation level of the dominantsignal, the parameter K varies from about 12 dB down to less than −20 dB.In this case, the total received signal follows a Rayleigh distribution. Theseresults were observed on other measurement records, with maximum values ofthe parameter K varying between 8 dB and 13 dB.

In addition, the phase of the random component depicted in Figure 5.14presents a rather unstable behavior while people are interfering with the mainpath of the impulse response, with distinct periods of linear progress. However,


14 16 18 20 22 24-50

-40

-30

-20

-10

0

Time (s)

Rel

ativ

e po

wer

(dB

)

↑↑

14 16 18 20 22 24

-2

0

2

Time (s)

Pha

se (

rad)

↓↓

Figure 5.14. Fast fading of the random component. LOS path, 12 people

we may note rapid and significant phase shifts at instants corresponding tofading nulls (indicated by arrows on the figure), due to the rapidly decreasingpower.

5.1.4.4. Spectral analysis

This section presents a spectral analysis the analysis of the temporal signalvariations received via the main paths of the impulse response. Figure 5.15represents the average scattering function PS(τ, ν) of the random component,for the delay τ corresponding to the LOS path. Measurements involving 1to 12 moving people are taken into account, and the collected records weredistinguished according to the direction of the movement. The general shapeof the scattering function is triangular, with an average Doppler shift centeredaround 0 Hz. The spectrum width was calculated in terms of Doppler spreadνRMS , defined in equation [2.38]. The calculated Doppler spread variedbetween 0.6 and 3.3 Hz, with no marked influence from the number of movingpeople. Similar 0 Hz-centered, triangular shapes of the Doppler spectrumare reported from continuous wave measurements of the channel temporalvariations performed at frequencies around 1 GHz [HAS 94b, BUL 87].


-15 -10 -5 0 5 10 15-25

-20

-15

-10

-5

0

Doppler shift (Hz)

Rel

ativ

e po

wer

(dB

)ForwardBackward

Figure 5.15. Average scattering function of the random component.LOS path, forward and backward motions

Some asymmetry can be observed in Figure 5.15 between measurementsperformed during forward and backward movements. This can be explainedby the location of the antennas, which emphasize either the lengthening orthe shortening of propagation paths, depending on the direction of the humanmotion. More details on the interpretation of these results can be found in[PAG 06a].

5.2. Statistical channel modeling

In section 5.1, the characterization of the radio channel parameterswas presented from a series of experimental measurements. The frequencydependent and distance dependent attenuation linked to the radio signalpropagation was evaluated, as well as a number of parameters regarding theimpulse response. The RMS delay spread, the PDP magnitude decay and therays arrival rate are a few examples. Statistical models use these experimentalparameters to realistically reproduce the channel effects. This section presentsa few statistical models for the UWB propagation channel available in theliterature. The analyses presented in section 5.1 are then exploited to illustratein more detail the design of a statistical model based on experimental data.


5.2.1. Examples of statistical models

In order to provide a unique channel model for the evaluation of differentUWB systems proposals during standardization meetings, the IEEE 802.15work group made several calls for contributions. Two statistical models weredefined, the first one for short range, high rate, indoor applications (IEEE802.15.3a model), and the second one for applications with longer range inboth indoor and outdoor environments (IEEE 802.15.4a model). These modelsare briefly presented in the following sections.

5.2.1.1. IEEE 802.15.3a model

The IEEE 802.15.3a model [FOE 03a, MOL 03] was developed fromaround 10 contributions, all referring to distinct experimental measurements,performed in indoor residential or office environments [GHA 02a, PEN 02,FOE 03b, HOV 03, KUN 02b, GHA 02b, CAS 02, CRA 02, SIW 02].

In order to reflect the phenomenon of ray clustering that was observedin several measurement campaigns, the model is based on the Saleh andValenzuela formalism (see equation [2.31]). Parameters are provided tocharacterize the clusters and ray arrival rates (Λ and λ), as well as the inter- andintra-cluster exponential decay constants (Γ and γ). Four sets of parametersare provided to model the four following channel types:• the channel model CM 1 corresponds to a distance of 0–4 m in a LOS

situation;• the channel model CM 2 corresponds to a distance of 0–4 m in an NLOS

situation;• the channel model CM 3 corresponds to a distance of 4–10 m in an NLOS

situation;• the channel model CM 4 corresponds to an NLOS situation with a large

delay spread τRMS = 25 ns.

Regarding channel attenuation, the IEEE 802.15.3a model proposes atheoretical approach using a path loss exponent Nd = 2 for the LOS situation,which is equivalent to a free space propagation. The NLOS case was notaddressed.

Finally, the fluctuations of ray amplitude modeled using a log-normallaw (see Appendix B.1.6), and a random inversion coefficient is introducedto simulate the phase inversion observed in the impulse response due toreflections.

This comprehensive model is a reference for the study of UWB systems. Itcan be applied in indoor environments and short range conditions. However,


modeling of the path loss is not practically addressed. It can also be noted thatthe measurements used for the model calibration [PEN 02, CHE 02] are limitedto at most 6 GHz bandwidth (2 GHz for the models CM 1 and CM 2).

5.2.1.2. IEEE 802.15.4a model

In order to be representative of a larger number of potential applications,the IEEE 802.15.4a working group proposed a model with a wider scopein terms of both frequency and environments [MOL 04]. The targetedapplications are low rate communications (from 1 kbps to a few Mbps), inthe following environments: indoor (residential and office), outdoor, industrial(factory, etc.) and on-body (for WBAN applications). Two UWB frequencybands are considered: 2–10 GHz and 0.1–1 GHz. We present here the modelcorresponding to the first frequency band.

The general structure of this statistical model is similar to the IEEE802.15.3a model (see equation [2.31]). Some differences are however noteworthyregarding the shape of the impulse response:

• The phase θk,l of each ray is no longer limited to the values 0 or π, butis uniformly distributed between 0 and 2π. Thus, this model reproduces thecomplex envelope of the baseband impulse response.

• Ray arrival follows a dual law composed of two Poisson processes.Accordingly, the model proposes two ray arrival rates λ1 and λ2, as well asa mixing parameter.

• The exponential decay of each cluster increases with the delay. Theintra-cluster exponential decay constant is thus of the following form:

γl = kγTl + γ0 [5.7]

where Tl represents the time of arrival of the lth cluster and kγ accounts forthe increase of the coefficient γl with increasing delay.

The main difference between the IEEE 802.15.4a model and the IEEE802.15.3a model is that the former accounts for a realistic path loss, in boththe distance and frequency domains. The proposed model is independent ofthe transmitter and receiver antennas. After some changes in the proposedvariables, this path loss model can be expressed in the form given in equation[2.35], and the model provides the parameter values equivalent to Nf , Nd,PL(f0, d0) and σS .

In addition, the small scale variations of the ray amplitude are modeled usinga Nakagami distribution (see Appendix B.1.3). As for the Cassioli-Win-Molischmodel, the parameter value m is a delay function.


Nine channel types were identified within the IEEE 802.15.4a work group.Each channel type is defined by a given set of parameters as follows:

• the CM 1 and CM 2 models correspond to the indoor residentialenvironment (respectively in LOS and NLOS configurations);

• the CM 3 and CM 4 models correspond to the indoor office environment(respectively in LOS and NLOS configurations);

• the CM 5 and CM 6 models correspond to the outdoor environment(respectively in LOS and NLOS configurations);

• the CM 7 and CM 8 models correspond to the indoor industrialenvironment (respectively in LOS and NLOS configurations);

• the CM 9 model corresponds to the outdoor environment in an NLOSconfiguration, in the specific case of a farm area or an area covered with snow.

This model is more detailed than the IEEE 802.15.3a model, but isalso somewhat more complex. The provided parameter sets are based onexperimental measurements for each environment: residential [CHO 04b], office[BAL 04a, SCH 04], industrial [KAR 04b] and outdoor [BAL 04a, KEI 04].A survey of the results from the literature complements these measurementcampaigns. It should be noted, though, that the measurements performed inthe office and outdoor environments covered frequency bands limited to 3 or6 GHz.

5.2.1.3. Other models

The Cassioli-Win-Molisch model

The Cassioli-Win-Molisch model [CAS 02] is the result of a joint researchwork performed by the University of Rome “Tor Vergata” (Italy), ViennaUniversity (Austria) and the UltRaLab laboratory from the University ofSouth California (USA). This model is one of the first statistical modelsdescribing the UWB propagation channel. Despite some limitations, it is thusfrequently cited in the studies on UWB. This model is based on a seriesof measurements performed by the UltRaLab laboratory in an indoor officeenvironment, over a frequency band of about 1 GHz [WIN 97b]. 686 impulseresponses were used: 14 antenna locations were selected, and at each location,49 measurements were taken over an area of about 1 m2.

The Cassioli-Win-Molisch model is based on a discrete scale on the delayaxis, with a delay bins defined with a step Δτ of 2 ns. The overall impulseresponse power received between the delays kΔτ and (k + 1)Δτ is integrated,and it is assumed that a ray exists at each delay kΔτ . This corresponds to aray arrival rate λ = 1

Δτ . The power of each ray follows an exponential decay,


but a single cluster is observed. Following the Saleh and Valenzuela formalism(see section 2.4.1), the PDP model can be expressed in the form:

Ph(0, τ) =K∑

k=1

β2kδ

(τ − d

c− (k − 1)Δτ

)[5.8]

where d indicates the distance between the transmitter and the receiver.

The PDP exponential decay is characterized by the coefficient γ (seeequation [2.33]), but the model also introduces an additional coefficient r inorder to account for a significant attenuation between the 1st ray and the 2nd

ray.

The propagation loss is characterized as a function of distance according toa dual-slope law:

PL(d) =

⎧⎪⎪⎪⎨⎪⎪⎪⎩PL(d0

)+ 20.4 log

(d

d0

)+ S(d) d ≤ 11 m

PL(d0

)− 56 + 74 log(

d

d0

)+ S(d) d > 11 m

[5.9]

The fast fading due to the antenna displacement is characterized by a rayamplitude distribution following a Nakagami distribution (see Appendix B.1.3).The Nakagami m parameter decreases with the delay to approach the value of1 for the last rays in the PDP, where the ray amplitude follows a Rayleighdistribution.

This model provides an accurate and reproducible description of theobserved measurements. Its main limitations lie in the low number ofmeasurements on which the statistical study is based, and in the reducedfrequency band.

Frequency domain approach

Most of the research efforts regarding statistical modeling for the UWBpropagation channel concentrate on a time domain approach, where themodel provides a description of the channel impulse response. However, otherapproaches are possible. The model proposed by the researchers from theAT&T Research Laboratory and MIT [GHA 04a] is an interesting exampleof a frequency domain approach. This model is designed from an extensivemeasurement campaign performed in 23 residential houses.

The main concept of this model is to reproduce the channel transfer functionT (f, t) in a statistical way. As for the time domain approach, each parameter


can be described using a statistical law. The value of the frequency domainapproach lies in its opening up the possibility of describing the transfer functioncomponents in a regressive way. The model can be expressed in the form of afilter with infinite impulse response, which can be mathematically representedby:

T(fi, t)

+ a1T(fi−1, t

)+ a2T

(fi−2, t

)= ni [5.10]

where ni represents the input white Gaussian noise. The model can berepresented using five variables: the parameters a1 and a2, the input conditionsT (f1, t) and T (f2, t), and the standard deviation of the Gaussian noise σn.Each of these parameters is then described in a statistical way as a functionof the distance. The model is complemented with a power attenuation law.

Other approaches were proposed regarding UWB channel modeling in thefrequency domain, such as the Prony method used by the Virginia PolytechnicInstitute (USA) [LIC 03]. The value of such a model lies in its low complexity:only a few parameters are required for its description. However, there is nodirect knowledge of the traditional channel characterization parameters, suchas the shape of the PDP or the delay spread. For this reason, the comparisonbetween the two model types is not straightforward.

5.2.2. Empirical modeling principles

This section aims at illustrating UWB channel statistical modeling basedon experimental data. A statistical model based on the Saleh and Valenzuelaformalism is designed from the characteristic parameters observed insection 5.1 [PAG 06d]. The following sections present a propagation loss modeland an impulse response model. Finally, simulation results are compared tothe experimental measurements.

5.2.2.1. Propagation loss model

The first step in the design of the UWB channel model is the definition ofattenuation due to signal propagation. In section 5.1.1.1, it was shown thatwhen the antenna effect is correctly compensated, the channel attenuation inthe frequency domain is close to the theoretical loss of 20 dB per decade. Thepath loss model can thus be expressed in dB in the following form:


)+ 20 log

(f

f0

)+ 10Nd log

(d

d0

)+ S(d) [5.11]

where d0 = 1 m represents a reference distance, f0 = 6.85 GHz correspondsto the center frequency of the FCC analyzed band and S is a Gaussianrandom variable with zero mean. The parameters of this model are defined byexperimental characterization (see section 5.1.1) and are given in Table 5.6.


LOS NLOS

Nd 1.62 3.22

σS (dB) 1.7 5.7

PL(f0, d0) (dB) 53.7 59.4

Table 5.6. Path loss model parameters. Values of PL(f0, d0)are given for f0 = 6.85 GHz and d0 = 1 m

5.2.2.2. Modeling the channel impulse response over an infinite bandwidth

The principle of the UWB impulse response model consists of generatingall constituent rays while maintaining the characteristics observed from theexperimental measurements. Among these characteristics, we mainly aim atreproducing the clustering of multipath echoes, the ray and cluster arrival rates,and the decreasing magnitude of the received power with increasing delay. Fora baseband representation, a ray is described by its delay τ , its amplitude βand its phase θ. By generating these parameters, it is possible to describe theimpulse response over an infinite bandwidth. We then process these parametersin the frequency domain in order to include the effect of the limited observationbandwidth.

In order to account for the clustering of multiple paths, the impulse responseis modeled using the Saleh and Valenzuela formalism (see section 2.4.1). At agiven instant, the UWB channel impulse response is thus described by thefollowing formula:

h(τ) =L∑

l=1

Kl∑k=1

βk,lejθk,lδ

(τ − Tl − τk,l

)[5.12]

where L represents the number of clusters, Kl is the number of rays withinthe lth cluster and Tl corresponds to the arrival time of the lth cluster. Theparameters βk,l, θk,l and τk,l represent the amplitude, phase and arrival timeassociated with the kth ray within the lth cluster.

The experimental observations given in section 5.1.2.3 show that theinter-clusters duration follows an exponential distribution. Hence, the arrivalof a new cluster can be modeled by a Poisson process, and the number ofclusters in the impulse response can be generated by drawing a randomvariable L according to the following law [MOL 04]:

pL(L) =(L)L exp(−L)

L![5.13]


where L represents the average number of clusters. During measurementanalysis, we observed an average number of clusters of L = 5.6 in the LOScase and L = 2.4 in the NLOS case.

Having selected a transmitter-receiver distance d for the simulation, thetime of arrival of the first cluster is given by T1 = d

c , where c is the speed oflight. The time of arrival Tl of the L− 1 remaining clusters is then calculatedby generating inter-cluster durations following an exponential law [SAL 87]:

p(Tl | Tl−1

)= Λ exp

(− Λ(Tl − Tl−1

))[5.14]

where Λ is the cluster arrival rate.

The inter-cluster power decay is accurately modeled by a power function(see section 5.1.2.2). This approach differs from the one followed by Salehand Valenzuela [SAL 87], but presents a closer fit to the experimentalmeasurements. The amplitude of the first ray within each cluster is thus givenby:

β21,l = β2

1.1

(Tl

T1

)−Ω

[5.15]

where Ω represents the inter-cluster power decay constant.

In accordance to the results of the static UWB channel study, it isrecommended to use the values Λ = 36.5 MHz and Ω = 4.4 in the LOS case.In the NLOS case, the recommended values are Λ = 24.9 MHz and Ω = 3.9.

The rays are iteratively generated for each cluster. The arrival time ofeach ray is calculated using inter-ray durations following an exponential law[SAL 87]:

p(τk,l | τk,l−1

)= λ exp

(− λ(τk,l − τk,l−1

))[5.16]

A power function is used to calculate the ray amplitude (see section 5.1.2.2):

β2k,l = 10−

G10 β2

1,l

(τk,l + Tl

Tl

)−ω

[5.17]

where ω represents the intra-cluster power decay constant and G accounts forthe observed attenuation between the first path of each cluster and the followingmultipaths. For each cluster, the ray generation stops when the ray amplitudereaches a given threshold D, fixed at −50 dB.

According to the characterization study presented in section 5.1 and tothe observation of the measured PDP, we recommend using the parametersλ = 5.95 GHz, ω = 11.1 and G = 12 dB in the LOS case. The recommendedvalues in the NLOS case are λ = 6.19 GHz and ω = 10.2.


Finally, the phase θk,l of each ray is generated using a uniform law overthe interval [0, 2π[. This approach was also adopted in the IEEE 802.15.4amodel [MOL 04]. Figure 5.16 presents the rays obtained in a LOS situationfor a transmitter-receiver distance of 6 m, where we may observe 5 clusters. Itmay be noted that this representation corresponds to an infinite observationbandwidth, each ray being represented by a Dirac function.

0 20 40 60 80 100-50

-40

-30

-20

-10

0

Delay (ns)

Rel

ativ

e po

wer

(dB

)

Figure 5.16. Impulse response simulated over an infinite bandwidth. LOS situation,with the parameters d = 6 m, Λ = 36.5 MHz, λ = 5.95 GHz, Ω = 4.4, ω = 11.1 and

G = 12 dB

Table 5.7 summarizes all experimental parameters used in our statisticalmodel of the UWB channel.

LOS NLOS

fmin (GHz) 3.1≤ fmin < fmax

fmax (GHz) fmin < fmax ≤ 10.6

D (dB) 50

Λ (MHz) 36.5 24.9

L 5.6 2.4

λ (GHz) 5.95 6.19

Ω 4.4 3.9

ω 11.1 10.2

G (dB) 12 0

Table 5.7. Parameters of the UWB impulse response model


5.2.2.3. Modeling the channel impulse response over a limited bandwidth

In practice, impulse response is observed on a limited bandwidth, situatedwithin the 3.1–10.6 GHz band. We note by fmin and fmax the minimum andmaximum frequencies in the observation band, and by fc = 1

2 (fmin + fmax)the center frequency. The channel transfer function limited to the observationbandwidth hence appears (for positive frequencies):

Tlim(f)=

⎧⎪⎨⎪⎩fc

f

1∑Ll=1

∑Kl

k=1 β2k,l

L∑l=1

Kl∑k=1

βk,lej(θk,l−2πf(Tl+τk,l)) if fmin≤f≤fmax

0 otherwise[5.18]

where the coefficient PL(fc,d)∑Ll=1∑Kl

k=1 β2k,l

normalizes the power received at the

frequency fc according to the proposed path loss model. In addition, theterm fc

f accounts for the power decrease in −20 log(f) described previously.This transfer function normalization procedure was also proposed in[FOE 03a, ALV 03].

The impulse response observed over a limited bandwidth hlim(τ) is simplyobtained from the transfer function Tlim(f) using an inverse Fourier transform.In order to limit the side lobes level, it is possible to use a Hanning window forinstance at this stage [HAR 78].

Figure 5.17(a) represents an impulse response example observed over the3.1–10.6 GHz frequency band. We may note that the low delay between twoconsecutive rays (see Figure 5.16) naturally induces constructive or destructiveinterferences. Figure 5.17(b) presents the same impulse response observed over3.1–4.1 GHz frequency band: we may note that the multipath resolution is lessaccurate when the observation bandwidth decreases.

5.2.2.4. Simulation results

A series of simulations was conducted using the static UWB radio channelmodel presented in section 5.2.2. A set of 119 PDP was generated usingthe same transmitter-receiver distances as in our measurement campaign(see section 3.4.2.1), for the LOS and NLOS situations. Each PDP wascalculated from a set of 90 impulse responses, simulating the motion of theantenna around a circle of radius 20 cm. The generation of the fast fadingcharacteristics for the 90 locally simulated impulse responses was performedusing an advanced algorithm, taking the ray arrival angle into account. Thisalgorithm is fully described in section 5.3.1.

Figure 5.18 presents two typical PDP obtained by simulation. One of the90 constituting impulse responses is also represented. Note that on the x-axis,


(a)

0 20 40 60 80 100-130

-120

-110

-100

-90

-80

-70

-60

Delay (ns)

Rel

ativ

e po

wer

(dB

)

(b)

0 20 40 60 80 100-130

-120

-110

-100

-90

-80

-70

-60

Delay (ns)

Rel

ativ

e po

wer

(dB

)

Figure 5.17. Impulse response simulated over a limited bandwidth. Identical set ofrays, observed over the 3.1–10.6 GHz band (a) and the 3.1–4.1 GHz band (b)

the delay was converted in path length. As a general observation, simulationsare similar to the measured PDP (see Figure 5.3).

Two parameters representative of the channel temporal dispersion werecalculated for the entire set of generated PDP: the delay spread τRMS and the75% delay window W75%. The average values obtained for these parameters inmeasurement and simulation are compared for the LOS and NLOS situationsin Table 5.8. We may note that the proposed model correctly reproduces thedispersion parameters experimentally measured over the UWB radio channel.The delay spread of the simulated PDP is particularly close to the measurement,in both LOS and NLOS configurations. The values obtained for the delaywindow are somewhat different from the experimental data, but stay in thesame range as the measured characteristics. The proposed model thereforeallows us to reproduce not only the impulse response structure, but also channeldispersion.


(a)

0 20 40 60 80-50

-40

-30

-20

-10

0

Distance-delay (m)

Rel

ativ

e po

wer

(dB

)

IRPDP

(b)

0 20 40 60 80-50

-40

-30

-20

-10

0

Distance-delay (m)

Rel

ativ

e po

wer

(dB

)

IRPDP

Figure 5.18. PDP and impulse responses obtained by simulation.(a) LOS and (b) NLOS configurations

LOS NLOS

Parameter Measurement Simulation Measurement Simulation

τRMS (ns) 4.1 4.0 9.9 9.7

W75% (ns) 7.6 9.7 23.7 21.2

Table 5.8. Comparison of the dispersion parameters: measurement vs. simulation


5.3. Advanced modeling in a dynamic configuration

Section 5.2.2 describes how to simulate an impulse response from statisticalparameters obtained through experimental measurements, in the case of a staticchannel. In instances of practical use for future UWB systems, the antennadisplacement or the motion of people may generate significant variations in thechannel impulse response. This section describes two adaptations to the staticalmodel for an advanced modeling of the spatial and temporal fluctuations of theUWB radio channel [PAG 06c].

5.3.1. Space variation modeling

Spatial variations are due to the displacement of at least one of thetransmitting or receiving antennas. In this case, the lengths of mostpropagation paths undergo significant variation. Only a few studies on thestatistical modeling of the UWB channel spatial variations are available. TheIMST model is one example where a simplified ray tracing algorithm is usedto calculate a fixed delay variation for each cluster [KUN 03]. We here proposeto model these spatial fluctuations by taking the angle formed between theantenna motion and each propagation path into account. In the remainderof this section, we will assume a displacement of the receiving antenna andconsider the arrival angle of each path. For the sake of clarity, the presentedmodel allows an antenna displacement in the (O, x, y) plane only, by takingthe ray azimuth ϕ into account. A 3D model including ray elevation isforwardly derivable.

The first step of this spatial fluctuation model consists of generating animpulse response over an infinite bandwidth h(x0, y0, τ), corresponding to alocation (x0, y0), as described in section 5.2.2. This impulse response observedover an infinite bandwidth may be expressed as in equation [5.12]. In order tocalculate the impulse response observed over an infinite bandwidth at a location(x, y) close to the location (x0, y0), we consider that each ray corresponds toa plane wave. This assumption holds when the receiving antenna is placed inthe far field with respect to the surrounding walls and furniture where thetransmission, reflection or diffraction phenomena occur. Figure 5.19 illustratesthe obtained configuration for a given ray. The path elongation Δl of theincident ray is given by:

Δl = −(x− x0

)cos(ϕ)− (y − y0

)sin(ϕ) [5.19]

where ϕ represents the incident ray azimuth.

A limited number of statistical studies are available in the literatureregarding the departure and arrival angles for UWB channels [CRA 02,


x

y

(x0, y0)

r

Figure 5.19. Path elongation related to an antenna displacement

HAN 05, VEN 05]. To determine the azimuth of each ray in the impulseresponse, we can use the model derived by Spencer et al. from widebandindoor measurements [SPE 97]. In this model, the arrival azimuth of thekth ray within the lth cluster is decomposed in Φl + ϕk,l, where Φl is themean arrival azimuth in the lth cluster. Without further knowledge about theenvironment, we may consider that Φl is uniformly distributed in the [0, 2π[interval. ϕk,l represents the distribution of the ray azimuth within a cluster,and follows a Laplace distribution with zero mean and standard deviation σϕ:

pϕk,l

(ϕk,l

)=

1√2σϕ

e−|√

2ϕk,lσϕ

| [5.20]

In [HAN 05], the standard deviation of the arrival azimuth σϕ is lower thanor equal to 6.7◦.3 As a first approximation, we recommend using this valuefor the parameter σϕ. This value could be refined as more experimental databecomes available. For instance, [VEN 05] proposes a 2-cluster model, wherethe azimuth distribution follows a Laplace law in the first cluster (σϕ = 5◦)and a uniform law in the second cluster.

From the impulse response generated at the location (x0, y0) and knowingthe arrival azimuth Φl +ϕk,l of each ray, we can calculate the transfer function

3. For the indoor LOS and NLOS configurations on a single floor.


over a limited bandwidth at a location (x, y) close to location (x0, y0):

Tlim(x, y, f)

=

⎧⎪⎨⎪⎩fc

f

1∑Ll=1

∑Kl

k=1 β2k,l

L∑l=1

Kl∑k=1

βk,lej(θk,l−2πf(Tl+τk,l+Δτk,l)) if fmin≤f≤fmax

0 otherwise[5.21]

with:

Δτk,l = −1c

((x− x0

)cos(Φl + ϕk,l

)+(y − y0

)sin(Φl + ϕk,l

))[5.22]

The impulse response hlim(x, y, τ) observed over a limited bandwidth issimply obtained using an inverse Fourier transform.

Figure 5.20 presents a simulation of the space varying impulse responseobserved over the 3.1–10.6 GHz band. The delay, amplitude and phase of eachray correspond to the parameters already used in the previous examples. Thespatial variations of the impulse response were calculated for a displacement ofthe receiving antenna along the Ox axis over a distance of 2 m with 1 cm step.We may clearly distinguish the evolution of the main echoes (a-e), dependingon their arrival direction. For instance, the length of the first path shortensfrom approximately 6 m to 4 m.

Location x (cm)

Dis

tanc

e-de

lay

(m)

Rel

ativ

e po

wer

(dB

)

0 50 100 150 200

0

5

10

15

20

25

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

(a)

(b)

(c)

(d)

(e)

Figure 5.20. Simulation of a space variant impulse response. Displacement of thereceiving antenna along the Ox axis over a distance of 2 m


5.3.2. Modeling the effect of people

This section describes a method to model the effect of people, based on theexperimental analysis given in section 5.1.4. The main idea is to reproduce thetime variance observed on each ray of a given impulse response. This modelis based on the results of a real time UWB measurement campaign performedover the 4–5 GHz band (see section 3.4.2.3). As a result, the presented modelis valid for simulating UWB channels with bandwidths up to 1 GHz only.However, the modeling methodology may be used in other configurations asmore experimental characteristics of the time-variant UWB channel will becomeavailable.

The extension of the model to temporal variations is based on an initialimpulse response h(t0, τ) corresponding to a static environment at a giveninstant t0. The method described in section 5.2.2 can be used to obtain adescription of the impulse response over an infinite bandwidth. The initialimpulse response can thus be expressed according to equation [5.12], whereαk,l(t0) = βk,le

θk,l denotes the initial complex magnitude of the kth ray withinthe lth cluster.

As observed in our experimental characterization, we will differentiatebetween (a) the main path of each cluster, where each person generates ashadowing pattern in addition to fast amplitude fluctuations, and (b) theclusters of dense multipath where Rayleigh fading occurs [PAG 06a]. Whenobserving a radio channel over a relatively low bandwidth, in our case lowerthan 1 GHz, the observed main path encompasses not only the first ray ineach cluster, but also several rays situated within the observation resolutionR. This resolution R is equal to 2 ns for a bandwidth of 1 GHz when usinga Hanning window [HAR 78]. For all rays within the main path of eachcluster, the time-variant amplitude αk,l(t) is generated according to thealgorithm below. A more detailed description of this algorithm may be foundin [PAG 05]. Assuming that a group of Np people is interfering with the UWBradio link, the algorithm steps are as follows:

i) Select Np instants {tn}n=1...Npcorresponding to the instants where each

of the Np people are crossing the main path of the cluster. These passinginstants may be randomly chosen, or calculated according to the environmentalgeometry.

ii) Generate Np slow shadowing patterns {sn(t)}n=1...Npcorresponding to

the individual effects of Np moving people, using the following Gaussian-shapedattenuation function:

sn(t) = −As exp

(− 2((

t− tn) 2Ts

)2)

[5.23]


where As represents the maximal shadowing attenuation in dB, Ts representsthe shadowing duration in seconds, and tn represents the shadowing instant.According to our experimental characterization, the parameter values may beselected in the range of 5 dB to 10 dB for As, and in the range of 3 s to 5 s forTs.

iii) Calculate the amplitude variations of the dominant component dl(t) inthe linear scale as follows:

dl(t) =Np∏n=1

10sn(t−tn)

20 [5.24]

iv) Generate additional fast fading fluctuations rk,l(t) following a Rayleighamplitude distribution and having a Laplacian scattering function. As observedfrom the experimental data, the Doppler spread νRMS should be in the rangeof 1–3 Hz. The mean power Pr of the random component rk,l(t) should be 8 dBto 13 dB below the power level of the dominant component αk,l(t0).

v) Finally, calculate the time-variant amplitude αk,l(t) for rays within themain path of the lth cluster as:

αk,l(t) = αk,l

(t0)dl(t) + rk,l(t) [5.25]

Regarding step iv), several methods for the generation of a random signalpresenting a Rayleigh distribution and an arbitrary Doppler spectrum arethoroughly discussed in [PAE 02].

The algorithm presented above allows us to generate the effect thatmoving people have on the main path of each cluster. For the remainingrays, corresponding to regions of dense multipath, we propose to modelthe amplitude αk,l(t) variations by using a Rayleigh distribution. Moreexperimental analysis should be performed to study the exact shape of theDoppler spectrum in the regions of dense multipath. As a first step, wepropose using a Laplacian distribution. Thus, the amplitude αk,l(t) may begenerated as in step iv) of the algorithm.

Having calculated the amplitude αk,l(t) for all impulse response rays, thetime variant transfer function is given as:

Tlim(t, f)

=

⎧⎪⎨⎪⎩fc

f

1∑Ll=1

∑Kl

k=1 β2k,l

L∑l=1

Kl∑k=1

αk,l(t)e−j2πf(Tl+τk,l) if fmin≤f≤fmax

0 otherwise[5.26]


The impulse response hlim(t, τ) observed over a limited bandwidth isobtained using an inverse Fourier transform.

The proposed model was used to simulate the motion of 4 people in thevicinity of a radio link in a LOS situation. For selected realistic passing instantswith respect to the main path of each cluster, the delays Tl and the passinginstants tn were calculated using a ray tracing tool, from which only themost significant rays were extracted. Figure 5.21 illustrates the simulationconfiguration. The five selected paths correspond to the main path and tothe reflections on the four walls. The dashed arrow indicates the motion of thegroup of 4 people and circles present locations where the group crosses one ofthe main echoes.

Rx

Tx

Figure 5.21. Simulation configuration for the effect of people

The time varying impulse response was simulated according to thisinformation, and the results are presented in Figure 5.22. The impulseresponse is observed over the 4–5 GHz frequency band, as in an experiment.The following parameter values were used for the temporal variations model:As = 5 dB, Ts = 4 s, Pr = −13 dB and νRMS = 1 Hz.

As indicated by the circle locations on the graph, the group of peopleinterferes with each main path at a different instant. For each shadowinginstant, we may observe a power attenuation of the corresponding path, fora duration in the order of 3 s to 6 s. In addition, the presence of mobile peoplegenerates fast fading, observable at all impulse response delays. It can be notedthat on occasions, this fast fading significantly interferes with the main paths,as for instance on the second cluster. This proposed model could be refined byanalyzing additional experimental results. In particular, further research couldbe conducted by sounding the UWB channel over a larger bandwidth.


Figure 5.22. Simulation of a time variant impulse response. Circles indicate the grouppassing instants for the five main paths of the impulse response

5.4. Conclusion

Statistical modeling of the UWB channel consists of reproducing themain channel characteristics observed during the measurements using amathematical description. The experimental analyses described in this chapterillustrated the characterization of the UWB propagation channel in an indooroffice environment. Path loss was analyzed in both frequency domain anddistance domain. The measured PDP were characterized through the delayspread, as well as the arrival rate and amplitude decay of the rays and clusters.The fast fading analysis shows that the signal amplitude received at a givendelay follows a Rayleigh distribution, except for the main paths, where thesituation is more deterministic.

Several models of the UWB propagation channel were presented in theliterature. Among the statistical models, the proposals presented in thestandardization groups IEEE 802.15.3a and IEEE 802.15.4a, based on aSaleh and Valenzuela approach, are frequently used for the analysis of UWBcommunication systems. The principles of statistical modeling were presentedusing a practical approach based on experimental data. The described pathloss model can be used directly for dimensioning studies and to evaluate thejamming generated by an UWB terminal. A detailed model has also been givenfor the static impulse response. Simulations show that this model accuratelyreproduces the channel dispersion. It can be used in system simulations, forthe design and development of UWB based radio transceivers.


Two extensions of the impulse response were finally described to account forthe spatial and temporal variations of the UWB channel. The spatial variationsmodel emulates the effects of antenna displacement, by including the arrivaldirection of the delayed wavefronts. The temporal fluctuations model integratesthe effects linked to the motion of people, and can be used to simulate a UWBradio link in realistic conditions.

Appendix A

Baseband Representation of the Radio Channel

A real signal x(t) with spectral components covering a bandwidth centeredon the frequency f0 = 0 can be represented by its complex envelope γx(t)defined by:

x(t) = �{γx(t)ej2πf0t}

[A.1]

There are several ways to define a complex envelope γ(t) able to representthe signal x(t) according to relation [A.1]. We will use here the complex envelopedefined by the analytical form of the signal x(t) as follows [BAR 95]:

γx(t) = x(t)e−j2πf0t [A.2]

where x(t) is the analytical representation of signal x(t).

A real signal possesses a complex spectral structure with a Hermitiansymmetry. All the information concerning this signal is known in thepositive part of the frequency spectrum. The analytical signal is the signalrepresentation using only its positive spectral frequency components. In orderto keep the same signal power, the power spectral density (PSD) of thespectrum’s positive side is multiplied by two. The obtained analytical signal isthus defined in the frequency domain by:

X(f) = F{x(t)}

= 2U(f)X(f) =(1 + sign(f)

)X(f) [A.3]

where F{·} is the Fourier transform operation and U(f) represents the unitstep function (Heaviside step function).


By using the inverse Fourier transform, it leads to the following relation:

x(t) = x(t) + j1πt⊗ x(t) = x(t) + jH{x(t)

}[A.4]

where ⊗ represents the convolution operator and H{·} represents the Hilberttransform.

The signal s(t) is obtained after a convolution of e(t) and h(t):

s(t) = e(t)⊗ h(t) [A.5]

By keeping the same notations as previously, we have [BAR 95]:

S(f) = 2U(f)S(f) = 2U(f)E(f)H(f) =12E(f)H(f) [A.6]

and then:

γs(t) = s(t)e−j2πf0t = F−1{S(f + f0)

}= F−1

{12E(f + f0)H(f + f0)

}=

12γe(t)⊗ γh(t)

[A.7]

There is a second way to represent the equivalent baseband filter [GUI 96].Indeed, relation [A.6] allows us to write:

S(f) = E(f)H(f) [A.8]

So, γs(t) can also be expressed by:

γs(t) = F−1{E(f + f0

)H(f + f0

)}= γe(t)⊗

(h(t)e−j2πf0t

) [A.9]

So, the baseband filtered heq(t) which is equivalent to the real band filterh(t) can be expressed in two ways:

heq1(t) =12γh(t)

heq2(t) = h(t)e−j2πf0t

[A.10]

Baseband Representation of the Radio Channel 179

In the frequency domain, these two baseband filters Heq(f) equivalent tothe real band filter H(f) are expressed by:

Heq1(f) = U(f + f0

)H(f + f0

)Heq2(f) = H

(f + f0

) [A.11]

From a practical viewpoint, the filter Heq1(f) corresponds to a translationof the positive side frequency components of the filter H(f) so that they arecentered around 0 Hz. The filter Heq2(f) corresponds to a simple translation ofall the filter component H(f). These filters are similar when they are appliedto signals expressed in baseband.


Appendix B

Statistical Distributions

B.1. Definition

This section defines the main distribution laws presented in the book. Unlessotherwise mentioned, most of these laws are generally used to characterizethe magnitude of the channel impulse response for a given delay. For eachdistribution of the random variable X, we give the probability density function(PDF) pX(x), the cumulative density function (CDF) F (x) = P (X ≤ x), thefirst and second order moments E[X] and E[X2], and the variance V ar[X]when it can be simply expressed.

B.1.1. Rayleigh distribution

The Rayleigh distribution [PAR 00] is defined from the parameter σ whichis related to the standard deviation of the distribution by a constant value.

pX(x) =

⎧⎨⎩x

σ2e−

x2

2σ2 if x ≥ 0

0 otherwise[B.1]

F (x) =

⎧⎨⎩1− e−x2

2σ2 if x ≥ 0

0 otherwise[B.2]

E[X] =√

π

2σ [B.3]


E[X2]

= 2σ2 [B.4]

Var[X] =(

4− π

2

)σ2 [B.5]

B.1.2. Rice distribution

The Rice distribution [PAR 00, LAU 94] is defined from two parameters, sand σ.

pX(x) =

⎧⎪⎨⎪⎩x

σ2e−

x2+s2

2σ2 I0

(xs

σ2

)if x ≥ 0

0 otherwise[B.6]

where I0 represents the modified Bessel function of type 1.

F (x) =

⎧⎪⎨⎪⎩1−Q

(s

σ,x

σ

)if x ≥ 0

0 otherwise[B.7]

where Q is the Marcum function given by [MAR 60]:

Q(x, r) =∫ ∞

r

ye−x2+y2

2 I0(xy)dy [B.8]

E[X] =√

π

2|σ|L 1

2

(− s2

2σ2

)[B.9]

where L 12

is the Laguerre function, the solution of the differential equation:

xd2y

dx2+ (1− x)

dy

dx+

12y = 0 [B.10]

E[X2]

= s2 + 2σ2 [B.11]

A typical parameter of this distribution is the parameter k expressed by:

k =s2

2σ2[B.12]

Statistical Distributions 183

Numerous estimators exist for the k parameter. The k parameter estimatorconsidered in the book is the one based on the second and fourth order moments,and uses the following m parameter:

m =

(x2)2

x4 − (x2)2 [B.13]

where (·) corresponds to the empirical mean value. So, k is expressed by[ABD 01]:

k �√

1− 1m

1−√

1− 1m

[B.14]

The Rice distribution tends to a Rayleigh distribution when s tends to 0.

B.1.3. Nakagami distribution

The Nakagami distribution [LAU 94] is defined from two parameters, m andΩ.

pX(x) =

⎧⎪⎨⎪⎩2mm

Γ(m)Ωmx2m−1e−

mx2Ω if x ≥ 0

0 otherwise[B.15]

where Γ represents the Gamma function defined for x > 0 by:

Γ(x) =∫ ∞

0

e−ttx−1dt [B.16]

F (x) =

⎧⎪⎨⎪⎩γ

(mx2

Ω,m

)if x ≥ 0

0 otherwise[B.17]

where γ represents the incomplete Gamma function defined for x > 0 by:

γ(a, x) =1

Γ(x)

∫ a

0

e−ttx−1dt [B.18]

E[X] =Γ(m + 1

2

)Γ(m)

√Ωm

[B.19]

E[X2]

= Ω [B.20]


Numerous estimators exist for the parameter m. The one used in the bookis the following [ABD 00]:

m �(x2)2

x4 − (x2)2 [B.21]

The Nakagami distribution tends to a Rayleigh distribution when m tendsto 1.

B.1.4. Weibull distribution

The Weibull distribution [LAU 94] is defined from the two parameters, aand b.

pX(x) =

{abxb−1e−axb

if x ≥ 00 otherwise

[B.22]

F (x) =

{1− e−axb

if x ≥ 00 otherwise

[B.23]

E[X] = a−1b Γ(

1 +1b

)[B.24]

E[X2]

= a−2b Γ(

1 +2b

)[B.25]

The Weibull distribution tends to a Rayleigh distribution when b tends to 2.

B.1.5. Normal distribution

The normal distribution is defined from two parameters, the mean μ andthe standard deviation σ.

pX(x) =1√2πσ

e−(x−μ)2

2σ2 [B.26]

F (x) =12

(1 + erf

(x− μ√

2σ

))[B.27]


where erf represents the error function defined by:

erf(x) =2√π

∫ x

0

e−t2dt [B.28]

E[X] = μ [B.29]

E[X2]

= μ2 + σ2 [B.30]

Var[X] = σ2 [B.31]

B.1.6. Log-normal distribution

The log-normal distribution [WIE 03] is defined from two parameters, μ andσ. This distribution corresponds to the normal distribution of a signal complexenvelope expressed in dB.

pX(x) =

⎧⎨⎩ 10√2πxσ ln(10)

e−(10 log(x)−μ)2

2σ2 if x ≥ 0

0 otherwise[B.32]

F (x) =

⎧⎨⎩12

(1 + erf

(10 log(x)− μ√

2σ

))if x ≥ 0

0 otherwise[B.33]

E[X] = 10 · 10μ10+ 1

2 ( σ10 )2 [B.34]

E[X2]

= 10 · 102( μ10+( σ

10 )2) [B.35]

We can estimate the parameters μ and σ by calculating the first and secondmoments of the variable expressed in dB:

E[XdB

]= μ [B.36]

E[X2

dB

]= μ2 + σ2 [B.37]

Var[XdB

]= σ2 [B.38]

B.1.7. Laplace distribution

The Laplace distribution [SPE 97] is often used to model the arrival angleassociated with the cluster rays. In the book, this distribution is also used todescribe the Doppler spectrum observed on the fast variations of the signals


generated by moving people. This distribution is defined from two parameters,μ and σ.

pX(x) =1√2σ

e−|x−μ|√2

σ [B.39]

F (x) =12

(1 + sgn(x− μ)

(e−

|x−μ|√2σ

))[B.40]

E[X] = μ [B.41]

E[X2]

= μ2 + σ2 [B.42]

Var[X] = σ2 [B.43]

B.2. Kolmogorov-Smirnov goodness-of-fit test

Considering an empirical CDF Fn(x) based on n samples and the theoreticalCDF F0(x) of the random variable from which the random draw is held, wecan study the following variable:

Dn = max{∣∣Fn(x)− F0(x)

∣∣} [B.44]

Figure B.1 illustrates the calculation of the variable Dn, for which thedistribution has been studied by Kolmogorov [KOL 33]. For a decision thresholdα and the critical value dα, we note:

P (Dn > dα) = α [B.45]

or:

P (Fn(x)− dα ≤ F0(x) ≤ Fn(x) + dα,∀x) = 1− α [B.46]

The critical value dα has been tabulated for various values of α and n. Wecan demonstrate for example that for n > 80:

d0.05 � 1.3581 · n− 12

d0.01 � 1.6276 · n− 12

[B.47]

For a sample size n = 100, for example, we can conclude that the probabilityis:

– 95% that F0(x) is totally situated between F100(x) − 0.13581 andF100(x) + 0.13581;


Dn

P(X

x)

x

Fn(x)

F0(x)

Figure B.1. Kolmogorov-Smirnov test: theoretical and empirical CDF

– 99% that F0(x) is totally situated between F100(x) − 0.16276 andF100(x) + 0.16276.

The Kolmogorov-Smirnov test consists of calculating the maximumdeviation between an empirical CDF and a theoretical CDF, for a given decisionthreshold α:

– if this deviation is smaller than the critical value dα, we conclude thatthe empirical CDF follows the same law as the theoretical CDF;

– if this deviation is higher than the critical value dα, we conclude that theempirical CDF does not follow the same law as the theoretical CDF.

Formally, a statistical decision process like the Kolmogorov-Smirnov test canlead to two types of errors. If the test erroneously concludes that the sampleset does not follow the theoretical distribution law, we are faced with an errorof type I. If the test erroneously concludes that the sample set follows thetheoretical distribution law, we are faced with an error of type II. In the case ofthe Kolmogorov-Smirnov test, the type I probability of error is known (α), butthe type II probability of error cannot be directly calculated. In other words,the probability of error is not known when we conclude that some samplesfollow a given law. So, this test is to be used sparingly.


Appendix C

Geometric Optics and UniformTheory of Diffraction

C.1. Geometric optics

C.1.1. Introduction

Geometric optics (GO) have been developed for the analysis of light wavepropagation which corresponds to high frequencies. In propagation problems,the GO is valid only for frequencies higher than 100 MHz.

If we consider a monochromatic electromagnetic pulsation wave ω, theelectric field �E(�s, ω) and magnetic field �H(�s, ω) expressions at an observationpoint P, the spatial position of which is defined by a vector �s, correspond tothe Maxwell equation expressed in an inhomogenous medium free from charges,with a permittivity ε(�s) and a permeability μ(�s) [PET 93] (see equation [C.1]).The Maxwell equations imply a time domain field dependence with e−jωt.

∇× �E(�s, ω) + jωμ(�s) �H(�s, ω) = �0

∇× �H(�s, ω)− jωε(�s) �E(�s, ω) = �0

∇ · [ε(�s) �E(�s, ω)]

= 0

∇ · [ε(�s) �E(�s, ω)]

= 0

[C.1]

For a homogenous dielectric medium, the permittivity and the permeabilityare not dependent on the position (ε(�s) = ε and μ(�s) = μ).


The study of propagation problems in homogenous media is conducted byusing Helmholtz vectorial equations which are derived from Maxwell equations:

∇2�U(�s, ω) + k2�U(�s, ω) = 0 [C.2]

with �U(�s, ω) the electric or magnetic field and k = ω√

εμ = 2πλ = 2π

λ0

√εrμr the

wavenumber of the propagation medium. λ and λ0 are the wavelengths in thepropagation medium and in the free space respectively. εr = ε

′r − j(ε

′′r + 60σλ)

and μr = μ′r − jμ

′′r correspond to the relative permittivities and the

permeabilities of the medium. The conductivity of the medium is representedby σ.

C.1.2. Field locality principle

In a homogenous medium, energy propagates on paths which are straightand orthogonal to the wavefront. These wavefronts are defined by the wavesurfaces which are plane, spherical, cylindrical or any other shape. A group ofrays is a beam or tube which starts and ends with two caustic segments (seeAB and CD in Figure C.1). The energy carried by a ray is persistent in thetime and space domains as well as in magnitude and phase.

A

B

C

DP(0)

P(s)

s

θφ

ρ2ρ1

s

Caustics

propagation

direction

Figure C.1. Ray tubes, caustics and local base

As there is always a scale for which a wave can be considered as locally plane,the properties of transverse electromagnetic plane waves can thus be generalizedto all the electromagnetic waves [GAR 87]. This is the electromagnetic wave

Geometric Optics and Uniform Theory of Diffraction 191

locality principle. The electric and magnetic waves are strictly transverse to thepropagation direction �s. The electric field vector is in the plane orthogonal tothe propagation direction. The trihedron (�E, �H,�s) is orthonormal, direct andfollows relation [C.3].

�E =√

μ

ε( �H × �s) [C.3]

The study can thus be restricted to the case of the electric field �E whichis expressed in a local basis B = (s, θ, φ). This local basis depends on thepropagation direction. For reasons of readability, a simplified notation isadopted in the following text which allows us to mix up the vector �E with itsvectorial representation E.

C.1.3. Field expression in geometric optics

According to the work of Luneberg and Kline, the electric field is expressedin GO by [GLO 99]:

E(s) = A(s, ρ1, ρ2)E(0) e−jkΨ(s) [C.4]

E(s) =

⎡⎣ 0Eθ(s)Eφ(s)

⎤⎦B

= A(s, ρ1, ρ2

)⎡⎣ 0Eθ(0)Eφ(0)

⎤⎦B

e−jkΨ(s) [C.5]

A(s, ρ1, ρ2) corresponds to the ratio between the field magnitudes E(s) andE(0). It is also called the divergence factor:

A(s, ρ1, ρ2) =√

ρ1ρ2

(ρ1 + s)(ρ2 + s)[C.6]

– s is the covered distance between P (0) and P (s).

– Ψ(s) is a phase function at the observation point P (s) and is equal to s.

– E(0) is the electric field at the point P (0).

ρ1 and ρ2 are the two main curvature radii of the wavefront measured on thecentral ray at the reference point P (0). This point corresponds to the sourceposition or the interaction point between the wave and a surface.


As the electric field is transverse to the propagation direction s, thecomponent along s is zero. In the following, the field will be expressed in itsbasis B without its component along s (see equation [C.7]):

E(s) =[Eθ(s)Eφ(s)

]B

= A(s, ρ1, ρ2

) [Eθ(0)Eφ(0)

]B

e−jks [C.7]

The curvature radii ρ1 and ρ2 vary along the ray trajectory. They have tobe recalculated whenever the ray is obstructed because the interactions modifythe ray trajectory. An interaction can be a reflection, a transmission (or doublerefraction) or a diffraction.

C.1.4. Change of local basis

Considering an electric field expressed in a given basis B1, if the wavecorresponding to this field undergoes an interaction, the field has to beexpressed in a new local basis. This new local basis corresponds to the inputbasis B2 of the interaction. To obtain the new expression of the field, we needto use the basis change matrix MB1→B2 (see equation [C.8]).

E(0) =[Eα2(0)Eβ2(0)

]B2

= MB1→B2

[Eα1(0)Eβ1(0)

]B1

[C.8]

B1 = (s1, α1, β1) and B2 = (s2, α2, β2) are the direct orthonormal bases inwhich the incident field is expressed at the interaction input.

MB1→B2 is the transition matrix allowing us to express the incident field inthe new basis. This matrix corresponds to a projection of the vectors α1 andβ1 in the basis B2:

MB1→B2 =[α2 · α1 α2 · β1

β2 · α1 β2 · β1

][C.9]

C.1.5. Incident field

The incident field is the field radiated by a source S in the direction ofan observation point P placed at a distance si. The expression of this field isdeduced from equation (C.7) by applying the transition matrix MBi→Br

:

Er(si)

=[Ei‖(si)

Ei⊥(si)]

Br

= A(s, ρi

1, ρi2

)MBi→Br

[Ei‖(0)

Ei⊥(0)

]Bi

e−jksi

[C.10]


ρi1 and ρi

2 are the main curvature radii of the incident wavefront.

Bi = (si, ei‖, e

i⊥) is a direct orthonormal local basis at the emission. It

corresponds to a basis described by the direction si. If we consider a sphericalframe, ei

‖ and ei⊥ can be assimilated to vectors eθ and eφ which form with si a

direct orthonormal basis.

Br = (−si, er‖, e

r⊥) is a direct orthonormal local basis at the receiver side.

It corresponds to the basis described by the direction −si. If we consider aspherical frame, er

‖ and er⊥ can be assimilated to the vectors eθ and −eφ which

form with −si a direct orthonormal basis.

MBi→Br

is the transition matrix which allows us to express the incidentfield at the point P in the good basis. This matrix corresponds to a projectionof the vectors ei

‖ and ei⊥ in the basis Br.

MBi→Br

=

[er‖ · ei

‖ er‖ · ei

⊥er⊥ · ei

‖ er⊥ · ei

⊥

]=[1 00 −1

][C.11]

Most of the time, we consider that the incident wavefront is spherical. So,the field is expressed by:

Er(si) =1si

MBi→Br

Ei(0)e−jksi

[C.12]

C.1.6. Reflected field

The reflected field is the field received at a point P after the reflection ofa ray at a point Qr placed at a distance si from the source point S and at adistance sr to the point P (see Figure C.2).

C.1.6.1. Expression of the reflected field in GO

The expression of the reflected field Er(sr) is derived from the fundamentalexpression of the field in GO (see equation [C.7]). The reflection law whichcomes from the Fermat principle defines the reflection point Qr. The incidentsi and reflected propagation sr directions are fixed by the interaction surfaceby the normal vector n (see equation [C.13]) [MCN 90].

n× (si − sr)

= 0 [C.13]

The incidence and reflection planes are the same and the incidence angle θi

and reflection angle θr are equal (see Figure C.2). The incidence plane is defined


tangent plane of a surface

θi

θr

n

Qr

S

P

ei‖

siei⊥

local basis Bi

er‖

sr

er⊥ local basis Br

Figure C.2. Incident and reflection local bases

by the normal n and the incident ray given by the vector si. The reflection planeis defined by the normal n and the reflected ray is given by the vector sr. Theuse of the locality principle in the case of the reflected field corresponds tothe introduction of a reflection dyad R which is expressed according to thereflection coefficients R‖ and R⊥ by:

R =[R‖ 00 R⊥

][C.14]

Thus, the reflected field Er(0) at the point Qr and defined in the basisBi only depends on the dyad R and on the incident field Ei(si) defined in thebasis B at this same point. It is thus necessary to express the field in the correctincident local basis Bi = (si, ei

‖, ei⊥).

Er(0) = R MB→Bi

Ei(si) [C.15]

In relation [C.15], B = (si, α, β) corresponds to the orthonormal basis inwhich the incident field Ei(si) is defined. α and β are an arbitrary coupleof orthonormal vectors, such that B is direct. The transition matrix MB→Bi

allows us to describe the field Ei(si) in the basis Bi.

MB→Bi

=

[ei‖ · α ei

‖ · βei⊥ · α ei

⊥ · β

][C.16]


The reflected field Er(sr) at the observation point P is expressed in thereflected local base Br = (sr, er

‖, er⊥) by the equation [C.17]. The main curvature

radii ρr1 and ρr

2 of the reflected wave depend on those of the incident wave. Inthe case of a planar surface, the following equalities are obtained: ρr

1 = ρi1 and

ρr2 = ρi

2.

Er(sr)

= A(sr, ρr

1, ρr2

)RMB→Bi

Ei(si)e−jksr

[C.17]

C.1.6.2. Incident and reflected ray bases

The local bases Bi and Br are defined according to the incident raypropagation direction si and the normal n. In fact, ei

‖ and er‖ are parallel to

the incidence and reflection planes, while ei⊥ = er

⊥ are orthogonal to the sameplanes (see Figure C.2).

C.1.6.3. Reflection coefficients

The dyad R depends on the reflection coefficient components which areparallel R‖ and perpendicular R⊥ to the incidence plane (see equation [C.14]).These coefficients are for the phase and the magnitude changes introducedby the reflection phenomenon on each component of the field. For multi-layerinterfaces with one or more layers, these coefficients have to be adapted inorder to take the stratification into account. Equation [C.18] corresponds to thereflection coefficient in the case of a surface with a thickness e and a permittivityεr. The permeability is considered to be set at 1.

R‖,⊥ =1− e−2jδe2jδ′

1− Γ2‖,⊥e−2jδe2jδ′ Γ‖,⊥ [C.18]

Γ‖,⊥ are the Fresnel coefficients in the case of an infinite plane surface witha permittivity εr:

Γ‖ =εr cos θi −

√εr − sin2 θi

εr cos θi +√

εr − sin2 θi

[C.19]

Γ⊥ =cos θi −

√εr − sin2 θi

cos θi +√

εr − sin2 θi

[C.20]

In the case of a perfect conductor surface (σ →∞), the reflection coefficientsare expressed with a phase difference multiple of π by:

Γ‖ = +1 Γ⊥ = −1 [C.21]


δ = krl and δ′k0

d2 are the phase terms associated with the delays

introduced by each reflected field (see Figure C.3). kr = k0√

εr corresponds tothe wavenumber of the medium with permittivity εr and l = e/ cos θt is theone-way distance in the medium. The incidence θi and refraction θt angles aredefined by:

sin θt =1√εr

sin θi [C.22]

e

Transmitted

rays

Reflected

rays

Incident ray

ε0 εr ε0

θi

θt

θi

e

l

d d

d = 2l sin θi sin θt

ε0 εr ε0

Figure C.3. Reflection of a plane wave on a dielectric interface with thickness e

The expressions of R‖,⊥ do not consider the possible roughness of theencountered surfaces (see equation [C.18]). The roughness is introduced by


multiplying the coefficients Γ‖,⊥ by the roughness factor ρ (see equation [C.23])[BEC 87] [COC 05]. �h is the height standard deviation in the rough interface.

ρ = e−2(kr�h cos θi)2

[C.23]

C.1.7. Refracted and transmitted field

The refracted (or transmitted) field is the received field at the point P afterrefraction (or multiple refractions) of a wave at the point Qt placed on aninterface at a distance si of the source point S and at a distance st of the pointP.

S

P

Qtns t

e ts i

e i

e i

θi θt

local basis B

⊥

i

local basis Bt

e t⊥

Tangent planeat the refractionsurface

Figure C.4. Transmission and incidence local bases

C.1.7.1. Expression of refracted and transmitted field in OG

The expression of the transmitted field Et(st) at the observation point P,placed at a distance st of the transmission point, also follows from the GO fieldmain expression (see equation [C.7]).

The refraction law, also called the Snell-Descartes law, comes from theFermat principle. It establishes the relation between the incidence angle θi andthe transmission angle θt (see Figure C.4) at the interface and in the directionair → medium (see equation [C.22]). The Fermat principle implies that theincidence and transmission planes are the same and defined by the incidentsi ray and transmitted st ray directions, and the reflection surface normal


n. Identically to the reflection example, the transmission can be consideredas a local phenomenon, so the transmitted field is expressed by introducinga transmission dyad T. This dyad is obtained according to the transmissioncoefficients (see equation [C.24]).

T =[T‖ 00 T⊥

][C.24]

The field Et(0) after the transmission point Qt depends on the coefficientT and on the incident field Ei(si) at this same point, taking care to define theincident field in the incident local basis Bi = (si, ei

‖, ei⊥) (see equation [C.25]).

Et(0) = TMB→Bi

Ei(si)

[C.25]

B = (si, α, β) corresponds to the orthonormal basis in which the incidentfield Ei(si) is defined. As in the reflected field case, the transition matrixMB→Bi

allows the expression of the incoming field Ei(si) in the incident localbasis Bi.

The transmitted field Et(st) at the observation point P is expressed in thetransmission local basis Bt = (st, et

‖, et⊥) by:

Et(st)

= A(st, ρt

1, ρt2

)TMB→Bi

Ei(si)e−jkst

[C.26]

In the simple refraction case, st corresponds to the distance between P andQt. As the point P is inside the interface, the propagation constant considersthe propagation speed related to the dielectric properties at the interface. Fora multiple refraction (or transmission), st corresponds to the distance betweenP and Qt at which the propagation distance in the interface is removed. Thislast distance is obtained for propagation in free space. Indeed, in the case ofmultiple refraction, the phase delay associated with propagation in the interfaceis directly introduced in T.

The divergence of a transmitted ray is given by the following relation:

A(st, ρt

1, ρt2

)=

√ρt1ρ

t2

(ρt1 + st)(ρt

2 + st)[C.27]

ρt1 is the first main curvature radius of the transmitted wave. Its expression

is different from the case of simple refraction (see equation [C.28]) and the case


of double refraction (see equation [C.29]).

ρt1 = ρi

1α−1 [C.28]

ρt1 = ρi

1 + αl [C.29]

ρt2 is the second main curvature radius of the transmitted wave. Its

expression is also different from the case of the simple refraction [C.30] andthe case of the second refraction [C.31] [PLO 03].

ρt2 = ρi

2α−1 [C.30]

ρt2 = ρi

2 + αγ2l [C.31]

l =e

cos θtα =

1√εr

γ =cos θi

cos θt[C.32]

C.1.7.2. Incident and transmitted ray bases

The knowledge of the incident ray propagation direction si and the normal nallows us to define the local bases Bi and Bt. In fact, ei

‖ and et‖ are respectively

parallel to the incidence and transmission planes and ei⊥ = et

⊥ are perpendicularto the same planes. ei

‖ and ei⊥ are defined according to the normal n (see

Figure C.2). et⊥ is obtained from equation [C.33]. Generally, after a double

refraction Bi and Bt are the same because si = st.

et‖ = et

⊥ × st [C.33]

C.1.7.3. Transmission coefficient

In the expression of the transmission dyad, the two components T‖ andT⊥ are respectively the transmission coefficients parallel and orthogonal tothe incidence plane. They correspond to the phase and magnitude changesintroduced by the transmission phenomenon on each component of the field. Inthe case of a simple refraction and a plane surface, their expressions are givenby equations [C.34] and [C.35]. Γ‖ and Γ⊥ correspond to the Fresnel reflectioncoefficients defined at equations [C.19] and [C.20].

T‖ =1 + Γ‖√

εr=

2√

εr cos θi

εr cos θi +√

εr − sin2 θi

[C.34]

T⊥ = 1 + Γ⊥ =2 cos θi

cos θi +√

εr − sin2 θi

[C.35]


In the case of a double refraction (transmission), T‖ and T⊥ are expressed byequation [C.36] (see Figure C.3). In [SAG 03], the expression of the transmissioncoefficient for an interface with more than two materials is proposed.

T‖,⊥ =

(1− Γ2

‖,⊥)e−2jδe2jδ′

1− Γ2‖,⊥e−2jδe2jδ′ [C.36]

C.2. Uniform theory of diffraction

C.2.1. Introduction

Electromagnetic waves are continuous, in magnitude and phase, in the timeand space domain. However, the GO does not ensure the total continuity field.It predicts areas where the field is zero (shadow zone). In 1953, Keller proposeda generalization of the GO in order to consider diffracted rays. This led to thebirth of general diffraction theory (GTD) [KEL 62].

The GTD allows us to solve the problem of field existence in the shadowzone of the GO. However, it presents a singularity at the boundary betweena lighted zone and a shadow zone. So in 1962, the theory has been completedby Kouyoumjian and Pathak in order to ensure the total field continuity in allspace points [KOU 74]; henceforth we talk about UTD.

Thereafter, Burnside and Burgener have proposed a formalism of theuniform theory of diffraction (UTD) in the case of the 3D diffraction on acorner of small thickness [BUR 83]. Other authors have also studied thesimple diffraction, the double diffraction as well as the slope diffraction inthe frequency domain [LUE 89, DES 84, ROU 96, ROU 99] and in the timedomain [VER 90, ROU 95]. Then, only the expression of the diffracted field inthe frequency domain is addressed, considering the case of the diffraction bydielectric or metallic dihedron.

C.2.2. Diffracted field

The expression of the diffracted field given by equation [C.37] corresponds tothe diffraction by a dihedron. For this kind of diffraction, the discontinuity lineis mixed up with the one of the diffracted beam caustics and so the curvatureradius ρd

2, also called minor ray, becomes zero.

Ed(sd)

= A(sd, ρd

1, ρd2 → 0

)DMB→Bi

Ei(si)e−jksd

[C.37]


A(s) is the divergence factor of the ray diffracted by the dihedron and isexpressed by:

A(sd, ρd

1, ρd2 → 0

)=

√ρd1(

ρd1 + sd

)sd

[C.38]

D is the dyad introducing the diffraction coefficients. This dyad can bewritten differently according to the diffracted ray’s nature, which can betwo-dimensional (2D) or three-dimensional (3D).

The matrix MB→Bi

makes it possible to describe the incident field,initially expressed in the basis B, in the incidence basis of the diffractionBi = (sd, ei

‖, ei⊥). The diffracted field Ed(sd) is defined in the diffraction basis

Bd = (sd, ed‖, e

d⊥).

The diffraction law, coming from the generalized Fermat principle, connectsthe Keller angle β0 to the incident ray direction si and the diffracted raydirection sd as well as the tangent t of the dihedron wedge (see Figure C.5) atthe diffraction point Qd by:

si · t = sd · t = cos β0 [C.39]

The incidence and diffraction planes are thus defined by the tangent of thewedge t and by the incident and diffraction ray directions. Generally, these twoplanes are not merged, as illustrated in Figure C.5.

The vectors of the bases Bi and Bd are obtained using the followingrelations:

ei‖ = −si × t

sin β0ei⊥ = si × ei

‖

ed‖ = sd × t

sin β0ed⊥ = sd × ed

‖

[C.40]

C.2.3. UTD 2D coefficient

In the case of a 3D ray, the dyad D is diagonal and directly expressed fromthe two components of the diffraction coefficients D‖ and D⊥:

D =[D‖ 00 D⊥

][C.41]

The terms D‖ and D⊥ are the diffraction coefficients initially introduced byKeller and then modified by Kouyoumjian, Burnside and Luebbers.


(2 − n)π

Diffrac

tion

plane

Incidence plane

t

S

P

Qd

local basis Bi

si

ei‖

ei⊥

local basis Bd

sd

ed‖

ed⊥β0

β0

φi

φd

Figure C.5. Incidence and diffraction local bases

C.2.3.1. UTD coefficient – dihedron conductor

Contrary to the GTD, the UTD introduced by Kouyoumjian and Pathak[KOU 74] ensures the field continuity in all the space, especially at the opticboundaries ISB (incident shadow boundary) and RSB (reflection shadowboundary). These authors have taken an interest in the case of a perfectconductor dihedron and have defined two new diffraction coefficients whichintroduce a correcting factor compared to the GTD coefficients:

D//,⊥ = D1 + D2 ± (D3 + D4) [C.42]

D1 = − e−j π4

2n√

2πk sin βo

cot(

π + (φd − φi)2n

)F[kLa+(φd − φi)

]D2 = − e−j π

4

2n√

2πk sin βo

cot(

π − (φd − φi)2n

)F[kLa−(φd − φi)

]D3 = − e−j π

4

2n√

2πk sin βo

cot(

π + (φd + φi)2n

)F[kLa+(φd + φi)

]D4 = − e−j π

4

2n√

2πk sin βo

cot(

π − (φd + φi)2n

)F[kLa−(φd + φi)

][C.43]


β0 is a semi-angle at the diffraction cone head. The normal incidencecorresponds to βo = π

2 (see Figure C.5).

φi and φd are respectively the incidence and diffraction angles. They arespecified from the wedge face 0 (see Figure C.5).

n is a parameter defined so that the dihedron inner angle is given by (2−n)π.

± corresponds to the reflection coefficient in the case of a conductor [C.21].

F (x) corresponds to the transition function which uses the Fresnel integral[LEG 95]:

F (x) = 2j√

xejx

∫ ∞√

x

e−jt2dt [C.44]

L is a distance parameter which corresponds to the incidence type on thewedge. It brings into play the incident wave main curvature radii (ρd

1 and ρd2)

as well as the wedge of curvature radius (ρde) (see equation [C.45]). In the case

of a spherical wave, L is given by equation [C.46].

L = sin2 β0 sd ρde + sd

ρde

ρd1

ρd1 + sd

ρd2

ρd2 + sd

[C.45]

L = sin2 β0sdρd

1

ρd1 + sd

[C.46]

a± is a function defined by:

a± = 2 cos2(2nπN± − (φd ± φi)

2

)[C.47]

with N± an integer corresponding (outside the optic boundaries) to relation[C.48]:

2πnN± − (φd ± φi) = ±π [C.48]

When the cotangent (cot) of one of the Di (i = 1, 2, 3, 4) terms becomessingular for the optic boundary angles φi and φd, the corresponding term isreplaced by −

√L2 sign(ε) [PLO 00].


C.2.3.2. UTD coefficients – dielectric dihedron

Luebbers proposes a more general formulation for the diffraction coefficients.This formulation allows us to consider the dielectric nature of the wedge as wellas its roughness [LUE 89]. These coefficients are heuristic solutions as they arenot obtained by solving Maxwell equations:

D//,⊥ = Gn//,⊥(D1 + ρnRn

//,⊥D3

)+ G0

//,⊥(D2 + ρ0R

0//,⊥D4

)[C.49]

Di (i = 1, 2, 3, 4) are terms reported on equations [C.43].

R0,n//,⊥ corresponds to the Fresnel reflection coefficients [C.19] and [C.20].

The incidence angles θ0i = π

2 − φi and θni = π

2 − (nπ − φi) depend on the faces0 and n of the considered wedge.

ρ0,n corresponds to the roughness coefficient of the considered face [C.23].

G0,n//,⊥ are the correcting coefficients which allow us to consider the grazing

incidences on the faces 0 and n of a dihedron.

G0//,⊥ =

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩1

1 + R0//,⊥

for φi = 0 and |1 + R0//,⊥| > 0

12

for φi = nπ

1 otherwise

[C.50]

Gn//,⊥ =

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩1

1 + Rn//,⊥

for φi = nπ and |1 + Rn//,⊥| > 0

12

for φi = 0

1 otherwise

[C.51]

C.2.4. UTD 3D coefficient

Contrarily to the case of a 2D ray, the dyad D of a 3D ray is no longerdiagonal and is expressed only by two diffraction coefficients, as in the case of2D ray (see equation [C.49]). This 3D dyad has been introduced by Burnsideand Burgener [BUR 83] and reused by Rouviere [ROU 99] in the case of adielectric half-plane with very small thickness.

To obtain the 3D dyad of [BUR 83], field continuity has to be ensured ateach optic limit. So, the boundary conditions at the reflection in incidence


boundaries have to consider relations [C.52] and [C.53]. In these relations, Ui

and Ur correspond to the incident and reflected fields respectively.

RUi(Qd)D(φd + φi)e−jksd

√sd

=

{−1/2Ur area I1/2Ur area II

[C.52]

(1−T)Ui(Qd

)D(φd − φi

)e−jksd

√sd

=

{−1/2(1−T)Ui area II1/2(1−T)Ui area III

[C.53]

with the areas denoted I, II and III illustrated by Figure C.6.

diffracted wedge

Zone III

diffracted + transmitted

Zone II

incident + transmitted

Zone I

incident + reflected + diffracted

ISB

RSB

Figure C.6. Field area around a diffracting wedge

Using these boundary conditions, the following expression is obtained forthe dyad D:

D = (I−T′)D(φd − φi) + R′ D(φd + φi) [C.54]

D(φd − φi) = D1 + D2 [C.55]

D(φd − φi) = D1 + D2 [C.56]

Each of the dyads (D, R′ and T ′) are expressed in their respective localbasis. It is thus necessary to calculate the base change matrices in orderto express all the fields in the local basis of the diffraction. α is the anglebetween the incident-reflection plane as well as the incidence-transmissionplane and the incident plane. The diffraction plane is given by π

2 − α. In 2D,


the incidence-reflection and incidence-transmission planes are perpendicular tothe incidence-diffraction plane (α = 0). In 3D, these planes have no particulardirection (see Figure C.7).

incidence plane - reflection

(2 − n)π

Diffraction

plane

Incidenceplane

t

S

P

Qdsi

ei‖

ei⊥

sd

ed‖

ed⊥

β0

φi

φd

n

θi

θr

π2 − α

Figure C.7. Reflection and diffraction incidence planes

The relations between the reflection and diffraction local bases areillustrated at Figure C.8 allow us to establish the matrix of basis changenecessary to express the reflection R′ (see equation [C.57]) and transmissionT′ dyads in the diffraction local basis (see equation [C.57]). In these equations,the exponent terms correspond to the plane nature (i for incident and d fordiffraction) as well as the interaction specifying the plane (r for reflection andd for diffraction).

MiR→D(α) = M(α) =

⎡⎣ei,d‖ · ei,r

‖ ei,d‖ · ei,r

⊥

ei,d⊥ · ei,r

‖ ei,d⊥ · ei,r

⊥

⎤⎦ =[cos α − sin αsin α cos α

][C.57]

MdR→D(α) = M(−α) =

⎡⎣ed,d‖ · ed,r

‖ ed,d‖ · ed,r

⊥

ed,d⊥ · ed,r

‖ ed,d⊥ · ed,r

⊥

⎤⎦ =[

cos α sin α− sin α cos α

][C.58]


ei,r‖

ei,r⊥

α

α

ei,d‖

ei,d⊥

ed,d‖

ed,d⊥

ed,r‖

ed,r⊥

α

α

after diffractionbefore diffraction

Figure C.8. Incidence reflection and diffraction bases in 3D case

In the case of transmission, the same basis change matrices are used. Theyare denoted M(−α) because we turn conversely. The dyadic matrices are thusexpressed by R′ and T′ by using equations [C.59] and [C.60].

R′ = MdR→D(α) R

(Mi

R→D(α))−1

= M(−α) R M(−α)

=[

R‖ cos2 α−R⊥ sin2 α (R‖ + R⊥) cos α sin α−(R‖ + R⊥) cos α sin α R⊥ cos2 α−R‖ sin2 α

] [C.59]

T′ = MdT→D(α)T

(Mi

T→D(α))−1

= M(α)TM(−α)

=[T‖ cos2 α + T⊥ sin2 α (T‖ − T⊥) cos α sin α(T‖ − T⊥) cos α sin α T⊥ cos2 α + T‖ sin2 α

] [C.60]

(I−T′) =[1− T‖ cos2 α− T⊥ sin2 α −(T‖ − T⊥) cos α sin α−(T‖ − T⊥) cos α sin α 1− T⊥ cos2 α− T‖ sin2 α

][C.61]

Expressions [C.59] and [C.61] inserted in equation [C.54] underline thenon-diagonal structure of the dyad D which is expressed by [BUR 83] [GLO 99]:

D =[Da Db

Dc Dd

][C.62]

Da =[1−T‖ cos2 α−T⊥ sin2 α

]D(φi − φd

)−[R‖ cos2 α−R⊥ sin2 α]D(φi + φd

)[C.63]


Db = cos α sin α [(T⊥ − T‖)D(φi − φd) + (R‖ + R⊥)D(φi + φd)] [C.64]

Dc = cos α sin α [(T⊥ − T‖)D(φi − φd)− (R‖ + R⊥)D(φi + φd)] [C.65]

Dd =[1−T‖ sin2 α−T⊥ cos2 α]D(φi − φd)−[R⊥ cos2 α−R‖ sin2 α]D(φi + φd)[C.66]

In equations [C.63] [C.64] [C.65] and [C.66], the terms R‖,⊥ and T‖,⊥ arethe reflection and transmission coefficients, the expressions of which are givenby [C.18] and [C.36].

Appendix D

Ray Construction Techniques

D.1. Ray launching

Ray launching is a forward approach which consists of sending rays in all thedirections from a transmission position of coordinates (Tx) with an incrementalangular step (Δα) which can be set to various values. Then, the receiver positioncoordinates (Rx) are specified (see Figure D.1) [CHE 96, KIM 97, STA 98,LIN 89].

The speed of ray determination with the ray launching approach is directlyrelated to the chosen Δα. When the Rx position is fixed, the rays connectingthe transmitter Tx and the receiver Rx are obtained considering a receiversphere of diameter Δd which can be set to various values. So, the launched raysconnecting Tx to Rx will be considered if they intersect the receiver sphere (seeFigure D.1). The number of rays obtained increases with the sphere diameterΔd (for a given Δα), but the precision of the calculated field and the receivedsignal decreases.

D.2. Ray tracing

Ray tracing is a backward approach which consists of applying the imageprinciple from Tx and Rx position in order to obtain reflected rays (seeFigure D.2) [HUM 03, MCK 91, CHA 03].

The specificity of this approach is the increase of the number of the potentialimages combinations with the complexity of the considered environment. Thiscan lead to important ray calculation time.


Tx

δα

(a)

Tx

Rxδd

δα

(b)

Figure D.1. Ray launching principle: (a) rays launched from the transmitterand (b) rays obtained considering intersection of receiver sphere

Im(Tx

)/s1

Im(Im

(Tx

)/s1

)/s2

s1

s2Tx Rx

Figure D.2. Ray tracing principle

Ray Construction Techniques 211

D.3. Other techniques

In the literature, other techniques are also proposed and used for raydetermination. Some of these techniques are hybrid and combine ray launchingand ray tracing [TAN 95, TCH 03, AVE 04], while others require a visibilitytree to be built [AGE 97, AGE 00], or rely upon calculation time speedimprovement techniques borrowed from the image processing domain. Theselast techniques use octree, raster or Voxel matrices for ray determination[FOL 84, LEG 05].


Appendix E

Description of the Time-Frequency Transform

The determination of a time domain signal x(τ) from its frequency domainexpression X(f) is generally made using an inverse Fourier transform (seeequation [E.1]). As the frequency domain expression X(f) of the signal x(τ)shows a Hermitian symmetry (see equation [E.2]), the obtained signal x(τ) isreal.

x(τ) =∫ +∞

−∞X(f) ej 2 π f τ df [E.1]

X∗(f) = X(−f) ∀ f ∈ R [E.2]

From frequency domain measurements, the obtained channel transferfunction H(f) is defined on a finite frequency band from fmin to fmax, forNf frequency points. As H(f) is discrete, the determination of h(τ) is madeusing an inverse Fourier transform (see equation [E.3]). δf = fmax−fmin

Nfis the

frequency sampling step and fk corresponds to a frequency value given byfk = fmin + k δf .

h(τ) = δf

Nf−1∑k=0

H(fk) ej 2 π fk τ [E.3]

The transfer function H(f) does not show a Hermitian symmetry because itis only defined between fmin and fmax. The signal obtained after discrete inverseFourier transform is complex and corresponds to h(τ)+j h(τ) (see Figure E.1).


010

2030

4050

−0.0

8

−0.0

6

−0.0

4

−0.0

20

0.02

0.04

0.06

0.08

dela

y (n

s)

real

par

t

010

2030

4050

−0.0

8

−0.0

6

−0.0

4

−0.0

20

0.02

0.04

0.06

0.08

dela

y (n

s)

imag

inar

y pa

rt

Fig

ure

E.1

.In

vers

eFouri

ertransf

orm

of

H(f

)

Description of the Time-Frequency Transform 215

To obtain a real signal h(τ), it is mandatory to use a transfer function H2(f)presenting by construction a Hermitian symmetry. Moreover, to improve theprecision of the reconstructed h(τ), we can expand the spectral support ofH2(f) in comparison to H(f). This consists of making an operation of zeropadding. Indeed, the product δτ δf Nf is equal to 1, so the increase of Nf

necessary leads to a reduction of δτ and consequently improves the time domainprecision of the signal h(τ) obtained after the discrete inverse Fourier transform.

The reconstruction of a real h(τ) from H(f) is made by applyingtwo successive operations on H(f) before the discrete inverse Fouriertransformation: zero padding and Hermitian symmetric forcing.

Operation of zero padding

The operation of zero padding consists of obtaining a new transfer functionH1(f) from H(f) (see Figure E.3). The new transfer function H1(f) containsfar more samples than H(f). H1(f) is constructed according to the followingrelation with fe = 1

2 δτ .

H1(f) =

{H(f) f ∈ [fmin, fmax

]0 f ∈ [δf, fmin − δf

] ∪ [fmax + δf, fe

] [E.4]

So, the new transfer function H1(f) is constructed as shown in equation[E.5]) with N1 = Nr +Nf +Nl samples where Nl = fmin

δf −1 and Nr = fe−fmaxδf .

H1(f) =[zeros(1, Nl) H(f) zeros(1, Nr)

][E.5]

Figure E.2 shows the time domain signal obtained after discrete inverseFourier transformation is applied on H1(f). We can notice that the samplingof the obtained time domain signal is improved. Nevertheless, it is still complex.

Operation of Hermitian symmetric forcing

The operation of forcing the Hermitian symmetry consists of creating atransfer function H2(f) from H1(f). This new transfer function H2(f) is definedfrom −fe to fe (see equation [E.6]) as illustrated in Figure E.3. Figure E.4represents a real impulse response h(τ) obtained after a discrete inverse Fouriertransform applied on H2(f).{

H2(f) = H1(f) for f > 0H2(−f) = H∗

2 (f) ∀f ∈ [δf, fe

] [E.6]


010

2030

4050

−0.0

8

−0.0

6

−0.0

4

−0.0

20

0.02

0.04

0.06

0.08

dela

y (n

s)

imag

inar

y pa

rt

010

2030

4050

−0.0

8

−0.0

6

−0.0

4

−0.0

20

0.02

0.04

0.06

0.08

dela

y (n

s)

real

part

Fig

ure

E.2

.Zer

opa

ddin

gand

inve

rse

Fouri

ertransf

orm

on

H1(f

)

Description of the Time-Frequency Transform 217

Operationofsymmetrf

icorcing

fm

inf

max

ff e

±f

H(f

)+zeropadding

fm

inf

max

−fm

in−f

max

ff e

−fe

0

H(f

)+zeropadding

H*(f)+flipzeropadding

Fig

ure

E.3

.Illu

stra

tion

ofth

eH

erm

itia

nsy

mm

etri

cfo

rcin

g


010

2030

4050

−0.0

8

−0.0

6

−0.0

4

−0.0

20

0.02

0.04

0.06

0.08

dela

y (n

s)

real

par

t

010

2030

4050

−0.0

8

−0.0

6

−0.0

4

−0.0

20

0.02

0.04

0.06

0.08

del

ay (

ns)

imag

inar

y pa

rt

Fig

ure

E.4

.Rec

onst

ruct

ion

of

h(τ

)after

dis

cret

ein

vers

eFouri

ertransf

orm

applied

on

H2(f

)

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Index

A

Antenna

diversity, 102

effective area, 44, 134

isotropic, 111

polarization, 107

radiation efficiency, 107

return loss, 107

Arrival rate

cluster, 61, 145

ray, 146

rays, 61

Average fade duration, 64

B

BER, 24

Bluetooth, 26, 27, 29, 30

BPSK, 39, 40

C

CDMA, 38, 40

Channel

characteristic parameters, 58, 134,137

definition, 43

deterministic, 52

impulse response, 181

linear random, 54

matrix, 108

propagation, 25

representation, 51, 177

sounding, 67

transfer function, 213

US, 56

variations, 47, 148, 150

WSS, 55

WSSUS, 57

Channel capacity, 24

Channel equalization, 49

Channel modeling

statistical, 133

Chirp sounder, 72

Coherence bandwidth, 49, 59

Correlation bandwidth, 49

Correlation sounder, 75

sliding correlation, 76

D

DAA, 33

Delay interval, 60

Delay window, 60

Delay-Doppler spread function, 54

Deterministic model, 99

Diffraction, 47

Diffusion, 47

DoA, 104

DoD, 104

Doppler

effect, 50

shift, 50, 69, 156

spectrum, 64, 173

spread, 64, 156, 173

DS-UWB, 35, 39, 40, 42


Duty cycle, 23

E

ESD (Energy spectral density), 110

Exponential decay constants, 61, 141

F

Fading

fast, 48, 63, 148, 153, 172

flat, 48

slow, 48, 152, 172

Far field, 45

FCC, 22, 25, 31, 33, 34, 40, 111

FDTD, 100

Fourier transform, 103, 178, 213

Fraunhofer distance, 45

Free space propagation, 44

Frequency correlation function, 59

Frequency domain function, 53

Fresnel law, 46

Friis formula, 45, 134

G

General theory diffraction, 200

Geometric optic, 189, 200

field expression, 191

field locality, 190

GO, 101

GPS, 31, 32

GSM, 30

H

Hermitian symmetry, 177, 213, 215

Hilbert transform, 178

Huygens’ principle, 47

I

Impulse radio, 35, 38–40

Impulse response, 51, 103, 137, 163,166

time varying, 53

Intersymbol interference, 50, 59

Inversion sounding technique, 78

ISB, 202

K

Kolmogorov-Smirnov, 186

Kolmogorov-Smirnov test, 64

L

Laplace distribution, 170, 173, 185

Level crossing rate, 64

Log-normal distribution, 64, 150, 185

LOS, 105

M

M-BOK, 39

m-sequence, 75

Maxwell equation, 189, 204

MB-OFDM, 35, 40–42

Mean delay, 59

Measurement campaigns, 85

examples, 91

overview, 85

Model

statistical, 157

Cassioli-Win-Molisch, 160

dynamic, 169

frequency domain, 161

IEEE 802.15.3a, 158

IEEE 802.15.4a, 159

principles, 162

MoM, 100

N

Nakagami distribution, 64, 150, 159,161, 183

NLOS, 105

Normal distribution, 184, 185

O

OOK, 39

P

PAM, 38, 39

Path loss, 62, 134, 162

exponent

distance dependent, 48, 63, 136

frequency dependent, 63, 134

Power decay constants, 144

Power delay profile, 57, 58, 137

Power spectral density, 25, 33, 37, 177

PPM, 35, 38, 39

Processing gain, 25

Index 239

Propagationfree space, 44, 134model, 99multipath, 45, 48phenomena, 45

PSD (Power spectral density), 111Pulse sounder, 73

QQPSK, 40

RRadio channel, 26RAKE reception, 49Ray launching, 209, 211Ray tracing, 209, 211Rayleigh distribution, 64, 150, 155,

161, 173, 181, 183, 184Rays launching, 101Rays tracing, 101Reflection, 46Rice distribution, 64, 150, 155, 182,

183RIR, 105RMS delay spread, 59, 137RSB, 202RUN method, 58

SS-parameters, 71Saleh and Valenzuela model, 61Scattering function, 57, 64, 156, 173Selectivity

frequency, 48, 58spatial, 48

Shadowing, 48SHF, 30SISO, 104Snell-Descartes law, 46Sounding

analyzed bandwidth, 68CIR dynamic, 69CIR length, 69maximum Doppler shift, 69

measurement techniques, 70frequency domain, 71multiple-band time domain, 78time domain, 73

time resolution, 68Standing wave ratio, 92

TTime hopping, 23Transfer function, 125

time varying, 54Transmission, 47

UUHF, 30UMTS, 23, 30, 40Uncorrelated scattering, 56Uniform theory of diffraction, 200UNII, 30, 34, 39UTD, 101UWB

applications, 27, 29, 30characteristics, 24definition, 21, 22history, 23regulation, 30

VVariations

spatial, 51, 150, 169temporal, 51, 150, 172

Vector network analyzer, 71

WWaveguide effect, 47, 137Weibull distribution, 64, 184Wide sense stationary, 55WiFi, 26, 27, 29, 30, 39WLAN, 27WPAN, 27

ZZero padding, 215Zigbee, 26, 29

Date post:	09-Apr-2015
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Ultra-Wideband Radio Propagation Channels

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