ULTRA-WIDEBAND RADIO TECHNOLOGIES FOR COMMUNICATIONS, LOCALIZATION AND SENSOR APPLICATIONS ppt

Contents Editors IX Preface XIX Chapter 1 MIRA – Physical Layer Optimisation for the Multiband Impulse Radio UWB Architecture 1 Rainer Moorfeld, Adolf Finger, Hanns-Ulrich Dehner, Ho

ULTRA-WIDEBAND RADIO

TECHNOLOGIES FOR COMMUNICATIONS, LOCALIZATION AND SENSOR APPLICATIONS Edited by Reiner Thomä, Reinhard H Knöchel, Jürgen Sachs, Ingolf Willms and Thomas Zwick

Localization and Sensor Applications

Publishing Process Manager Viktorija Zgela

Typesetting InTech Prepress, Novi Sad

Cover InTech Design Team

First published February, 2013

Printed in Croatia

A free online edition of this book is available at www.intechopen.com

Additional hard copies can be obtained from orders@intechopen.com

Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications, Edited by Reiner Thomä, Reinhard H Knöchel, Jürgen Sachs, Ingolf Willms and Thomas Zwick

p cm

ISBN 978-953-51-0936-5

Contents

Editors IX

Preface XIX

Chapter 1 MIRA – Physical Layer Optimisation for the Multiband

Impulse Radio UWB Architecture 1

Rainer Moorfeld, Adolf Finger, Hanns-Ulrich Dehner, Holger Jäkel, Martin Braun and Friedrich K Jondral Chapter 2 Pulse Rate Control for Low Power and Low Data Rate Ultra

Communications 153

Markus Grimm and Dirk Manteuffel

Chapter 8 Power Allocation Procedure for Wireless Sensor Networks

with Integrated Ultra-Wide Bandwidth Communications and Radar Capabilities 165

Gholamreza Alirezaei, Rudolf Mathar and Daniel Bielefeld Chapter 9 Cooperative Localization and Object Recognition

in Autonomous UWB Sensor Networks 179

Rudolf Zetik, Honghui Yan, Elke Malz, Snezhana Jovanoska, Guowei Shen, Reiner S Thomä, Rahmi Salman, Thorsten Schultze, Robert Tobera, Hans-Ingolf Willms, Lars Reichardt,

Malgorzata Janson, Thomas Zwick, Werner Wiesbeck, Tobias Deißler and Jörn Thielecke

Chapter 10 Pedestrian Recognition Based on 24 GHz Radar Sensors 241

Steffen Heuel and Hermann Rohling Chapter 11 ultraMEDIS – Ultra-Wideband Sensing in Medicine 257

Ingrid Hilger, Katja Dahlke, Gabriella Rimkus, Christiane Geyer, Frank Seifert, Olaf Kosch, Florian Thiel, Matthias Hein, Francesco Scotto di Clemente, Ulrich Schwarz, Marko Helbig and Jürgen Sachs

Chapter 12 ISOPerm: Non-Contacting Measurement of Dielectric

Properties of Irregular Shaped Objects 323

Henning Mextorf, Frank Daschner, Mike Kent and Reinhard Knöchel Chapter 13 Concepts and Components for Pulsed Angle Modulated Ultra

Wideband Communication and Radar Systems 343

Alexander Esswein, Robert Weigel, Christian Carlowitz and Martin Vossiek Chapter 14 HaLoS – Integrated RF-Hardware Components

for Ultra-Wideband Localization and Sensing 369

Stefan Heinen, Ralf Wunderlich, Markus Robens, Jürgen Sachs, Martin Kmec, Robert Weigel, Thomas Ußmüller, Benjamin Sewiolo, Mohamed Hamouda, Rolf Kraemer, Johann-Christoph Scheytt and Yevgen Borokhovych Chapter 15 UWB in Medicine – High Performance

UWB Systems for Biomedical Diagnostics and Short Range Communications 439

Dayang Lin, Michael Mirbach, Thanawat Thiasiriphet, Jürgen Lindner, Wolfgang Menzel, Hermann Schumacher, Mario Leib and Bernd Schleicher

Reiner Thomä received the Dipl.-Ing (M.S.E.E.), Dr.-Ing (Ph.D.E.E.), and the Dr.-Ing

habil degrees in electrical engineering and information technology from Technische Hochschule Ilmenau, Germany, in 1975, 1983, and 1989, respectively

From 1975 to 1988, he was a Research Associate in the fields of electronic circuits, measurement engineering, and digital signal processing at the same university From

1988 to 1990, he was a Research Engineer at the Akademie der Wissenschaften der DDR (Zentrum für Wissenschaftlichen Gerätebau) During this period he was working

in the field of radio surveillance In 1991, he spent a three-month sabbatical leave at the University of Erlangen-Nürnberg (Lehrstuhl für Nachrichtentechnik) Since 1992, he has been a Professor of electrical engineering (electronic measurement) at TU Ilmenau where he was the Director of the Institute of Communications and Measurement Engineering from 1999 until 2005 With his group, he has contributed to many European and German research projects and clusters such as WINNER, PULSERS, EUWB, NEWCOM, COST 273, 2100, IC 1004, EASY-A, EASY-C Currently he is the speaker of the German nation-wide DFG priority funding project UKoLOS, Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications (SPP 1202)

His research interests include measurement and digital signal processing methods (correlation and spectral analysis, system identification, sensor arrays, compressive sensing, time-frequency and cyclostationary signal analysis), their application in mobile radio and radar systems (multidimensional channel sounding, propagation measurement and parameter estimation, MIMO-, mm-wave-, and ultra-wideband radar), measurement-based performance evaluation of MIMO transmission systems including over-the-air testing in virtual electromagnetic environments, and UWB sensor systems for object detection, tracking and imaging

Since 1999 he has been serving as chair of the IEEE-IM TC-13 on Measurement in Wireless and Telecommunications In 2007 he was awarded IEEE Fellow Member and received the Thuringian State Research Award for Applied Research both for contributions to high-resolution multidimensional channel sounding

Reinhard H Knöchel received the Dipl.-Ing in Electrical Engineering in 1975, and the

Dr.-Ing in 1980 from the Technical University of Braunschweig, Germany From 1980

to 1986 he was a principal scientist at the Philips Research Laboratory, Hamburg, Germany In 1986 he joined the Technical University Hamburg-Harburg, where he was a Full Professor in Microwave Electronics until November 1993 Since December

1993 he holds the Chair in Microwave Engineering with the University of Kiel, Kiel, Germany From July 2010-July 2012 he was Dean of the Department His research interests include active and passive microwave components, ultra-wideband technology, microwave and field measurement techniques, industrial microwave sensors, radar and magnetic field sensors Dr Knöchel is a Fellow of the IEEE “for contributions to microwave systems and sensors for industrial process control”

Jürgen Sachs is a Senior Lecturer at Ilmenau University of Technology, Germany He

teaches “Basics of Electrical Measurement Technology”, “Measurements in Communications” and “Ultra-Wideband Radar Sensing” He is a head of several research projects, and inter alia coordinator of European projects for humanitarian demining and disaster relief His research areas cover RF-signal analysis and RF-system identification; Surface Penetrating Radar for non-destructive testing and medical engineering, ultra wideband methods and their application in high resolution radar and impedance spectroscopy, digital processing of ultra wideband signals, array processing; and design and implementation of new RF device approaches

Ingolf Willms received the diploma degree in electrical engineering from the RWTH

Aachen University in 1977 and the Ph.D with honours from the former Mercator University Duisburg in 1983 He was awarded for both degrees He then worked for Dräger in Lübeck for 6 years before he returned to University Duisburg-Essen in 1990 taking up the position of Professor in Information Technology His research interests include automatic fire alarm systems, especially video detectors and detector test systems, and ultra-wideband radar systems for fire and security

Gerhard-He is co-recipient of the Best Paper Award presented at 2011 IEEE International Conference on Ultra-Wideband Since 1996 he is member of the Executive Committee

of the European Society for Automatic Alarm Systems (EUSAS) and is secretary of this society since 2006

Thomas Zwick received the Dipl.-Ing (M.S.E.E.) and the Dr.-Ing (Ph.D.E.E.) degrees

from the Universität Karlsruhe (TH), Germany in 1994 and 1999, respectively From

1994 to 2001 he was a Research Assistant at the Institut für Hochfrequenztechnik und Elektronik (IHE) at the Universität Karlsruhe (TH), Germany February 2001 he joined IBM as research staff member at the IBM T J Watson Research Center in Yorktown Heights, NY, USA From October 2004 to September 2007 T Zwick was with Siemens

AG, Lindau, Germany During this period he managed the RF development team for automotive radars In October 2007 he became appointed as a Full Professor at the Karlsruhe Institute of Technology (KIT), Germany T Zwick is the Director of the Institut für Hochfrequenztechnik und Elektronik (IHE) at the KIT

His research topics include wave propagation, stochastic channel modeling, channel measurement techniques, material measurements, microwave techniques, millimeter wave antenna and system design, wireless communication and radar system design

He participated as an expert in the European COST231 Evolution of Land Mobile Radio (Including Personal) Communications and COST259 Wireless Flexible Personalized Communications For the Carl Cranz Series for Scientific Education he served as a lecturer for Wave Propagation He received the best paper award on the Intern Symp on Spread Spectrum Techn and Appl ISSSTA 1998 In 2005 he received the Lewis award for outstanding paper at the IEEE International Solid State Circuits Conference Since 2008 he is president of the Institute for Microwaves and Antennas (IMA) T Zwick became selected as a distinguished microwave lecturer for the 2013 –

2015 period He is author or co-author of over 200 technical papers and over 20 patents

Preface

Sometimes history seems to repeat Even in the so-called ‘mature’ technological fields When the radio pioneers such as Heinrich Hertz, Guglielmo Marconi, and Alexander Stepanovich Popov made their first experiments of wireless transmission more than a hundred years ago using spark-gap transmitters with simple coherer-detectors they did not care which ‘frequency band’ they were using, nor did they worry about their signals being ‘spectrally efficient’ or ‘band limited’ The world of radio frequency regulation was very simple then since regulations have not yet existed Over the years this has dramatically changed The frequency band was subdivided into small ‘boxes’

of different sizes, regulated and supervised The rules governing these ‘bands’ are strict and vary with the respective region, time and demand Sometimes even frequency bands of a few tens or hundreds MHz are sold by auction for millions or even billions of dollars Hence ‘Spectral Dividend’ became a key word in the media Scientists worldwide have begun an intensive search for a more efficient usage of the available frequency spectrum One of the ideas, which came more and more into the center of attention, was to use signals with very low spectral density yet huge instantaneous bandwidth This ‘underlaying’ technique allows the reuse of the spectrum, which is already occupied by other narrowband users The proactive release

of a ‘new’ frequency band of several GHz (3.1 GHz – 10.6 GHz) in February 2002 by the Federal Communications Commission (FCC) hastened research in this field immensely With such a technique the ultra-wide frequency band can be used without any further spectral slicing even though there are already a large number of established users and services within it! Thus, contrary to the mainstream of contemporary wireless technology, bandwidth efficiency becomes of minor concern again for interference mitigation as in the early days of Hertz and Marconi However, severe limitations in terms of power spectral density emission are placed on the emitted signals as the first measure of interference mitigation and to avoid a slipshod use of our limited spectral resources as in the early days of Marconi

So, what is it that makes ultra-wideband (UWB) so interesting for research and emerging applications? What are the paradigm shifts and challenges for circuit and system design? What does it hold for new and pioneering applications? In order to answer these questions the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) has funded a nation-wide priority-funding program called ‘Ultra-Wideband Radio Technologies for Communications, Localization and

Sensor Applications (UKoLoS)’ UKoLoS started in 2006 and ended in 2012 Altogether

14 research partners participated in the research program, which are mainly universities Most of the projects are conducted as a cooperative research between two

to four partners The initial aim of UKoLoS was the joint UWB research in the areas of communications, localization, and sensors Remarkable synergy effects and technological advancement and development are expected This book gives an overview of the scope and results of the UKoLoS program

In contrast to the conventional frequency multiplexed radio approach, ultra-wideband radio systems earmark a completely new technological philosophy Since UWB frequencies are already occupied by other radio services, coexistence with the existing systems is a serious concern Hence it must be made clear that the aim of the UWB technologies is not to replace the current existing systems but to simply coexist with them Therefore, the transmit power for UWB systems is strictly limited and intelligent interference mitigation methods and cognitive access schemes are being investigated and developed

For short-range communication and sensor networks, the UWB technology offers a very interesting alternative to the current conventional systems since very high data rates at low power radio interfaces can be achieved The current research in UWB communications addresses optimal energy-efficient modulation-, access-, coding-, and detection schemes New results from information theory are needed to determine the basic capabilities of UWB systems under real network- and propagation conditions as well as to unveil optimal system concepts Further research into variable data rates in sensor networks, dedicated short-range access, secure communication, cooperative detection and integrated communication, sensor and location functions for sensor networks, etc., are also being done

For localization and sensing applications, the huge UWB bandwidth allows the unprecedented time delay resolution Precise range estimates in strong multipath environments become possible making UWB the key technology for indoor radio localization, be it infrastructure-based localization, relative inter-terminal localization

in ad-hoc networks, or passive localization (e.g radar imaging) Interaction of the UWB wave field with materials and objects delivers vast information about object’s shape, position, motion dynamics, structural time variance, material composition, etc Since the extremely large bandwidth of UWB is provided at a comparably low frequency (for sensor applications the lower frequency limit may be as low as several hundreds of MHz), UWB can also penetrate materials and obstacles Information about the inner structure of objects can be made available and the investigation of objects that are hidden by obstacles becomes feasible Such capabilities open up many applications for use in the industry, e.g in civil engineering, surveillance, security and safety operations, and even medicine However basic research is still required to investigate the theory behind the interaction between UWB radio signals and objects, material, environments, technical, or biomedical processes, etc This will then lead to

many different interdisciplinary questions, since non-electrical properties and their relation to the ultra-wideband electro-magnetic field will become essential knowledge

As mentioned before, UWB utilizes an extremely large bandwidth of potentially several GHz at a comparably low frequency of a few GHz Associated with the extremely large bandwidth is the potential for super high data rates, yet limited by low power constraints Therefore, and especially due to the extremely high relative bandwidth, the UWB technology not only promises new and outstanding performance features but also adds new and highly challenging design demands on the envisioned UWB circuits and systems UWB radio interfaces require innovative integrated hardware architecture, design and implementation This includes UWB front-ends, antennas and data processing units as a whole Efficient small antennas with optimal time-domain behavior in real propagation environments are just but one example Known space-time signal processing algorithms must be tested against the properties of UWB signals and subsequently improved and new processing schemes have to be developed as well Generally speaking, UWB requires a change

of paradigm from narrowband to wideband principles in both algorithms and hardware Linearity, impulse response, stability, robustness, and power consumption are very important properties, which lead to new requirements in design strategies for UWB circuits Modern microwave semiconductor technologies such as Silicon-Germanium (SiGe) together with new manufacturing processes and packaging technologies play a key role in the implementation of complex UWB systems on a single integrated circuit

When the FCC published their report and order that authorizes the unlicensed use of the ultra-wideband (UWB) of 3.1–10.6 GHz a great storm of research, publications, standard proposals, etc emerged The usage of the UWB band seemed extremely promising since the very large bandwidth could support high data rates in wireless communications or a good range resolution in sensors However the hype is now over

On one hand, there are indeed some UWB radio access devices on the market UWB has become the foundation of Wireless USB and WiMedia access Yet the anticipated big economic success of UWB still remains to be seen The last ten years of UWB research has however brought us many insights to a completely new and alternative radio access philosophy Whereas the first hype was driven by the expectation of a big economic success in the electronic mass market, now the motivation is clearly driven

by the physical advantage of such a huge bandwidth at low frequencies New and innovative applications are generated, which are not yet mainstream So the initial idea of high data rate wireless UWB systems may have taken a backseat in favor of UWB based systems for medical diagnostics, localization, sensing etc But the coming years will show if these new ideas will launch UWB into a broad commercial success

or at least as indispensable technology in the niche markets This book at hand is meant to provide some important basics for that goal

Acknowledgement

All the authors and their corresponding researchers from the various institutions supported by this program would like to express their utmost gratitude to DFG for funding these research projects over 6 years and to enable many revolutionary discoveries to be made in the field of UWB We would also like to thank the panel of reviewers for their time and effort in reviewing all the submitted project proposals Last but not least much appreciation goes to Dr Klaus Wefelmeier and his successor

Dr Damian Dudek for their great support and their personal commitment We hope that this collective research effort will propel the technology to greater heights and to inspire new innovations

Reiner Thomä, Reinhard Knöchel, Jürgen Sachs, Ingolf Willms, Thomas Zwick

Chapter 1

MIRA – Physical Layer Optimisation for the

Multiband Impulse Radio UWB Architecture

Rainer Moorfeld, Adolf Finger, Hanns-Ulrich Dehner, Holger Jäkel,

Martin Braun and Friedrich K Jondral

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/55076

1 Introduction

Future wireless communication systems have to be realised in a simple and energy efficientmanner while guaranteeing sufficient performance Furthermore, the available frequencyresources have to be used flexibly and efficiently In this context two different approacheshave been considered in recent years: On one hand OFDM-based overlay systems in which

a primary user dynamically allocates unused frequencies to one or more secondary users[57] and on the other hand unlicensed, easy-to-realise and low-cost ultra-wideband (UWB)systems This underlying technology operates with an extremely low transmission powerover a wide frequency range and does not interfere with existing licensed systems [15]

In order to establish UWB on the consumer market it has to get along with some challenges.Such challenges are, e.g., the realisation of practical, low-complex and energy-efficienttransceiver architectures, the investigation of methods for accurate synchronization andchannel estimation or the handling of high sample rates To meet these requirementsthis chapter considers a non-coherent multiband impulse radio UWB (MIR-UWB) system[11, 45, 46] The MIR-UWB system focuses on short-range high data rate communicationapplications The MIR-UWB system is an alternative to the architectures Multiband OFDMUWB [2] and Direct Sequence UWB [16] which have been proposed within the IEEE 802.15.3astandardization process

The chapter is organised as follows: Section 2 gives a short introduction into the physical layerarchitecture of the non-coherent MIR-UWB system In the following section 3 the performance

of the energy detection receiver is analysed with respect to different aspects In contrastsection 4 deals with interference investigations for the non-coherent MIR-UWB system aiming

at an efficient and intelligent interference handling The chapter concludes with section 5 inwhich a summary is given

©2013 Dehner et al., licensee InTech This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly

Chapter 1

2 Multiband impulse radio

The idea of the MIR-UWB architecture is based on [45, 46] The architecture proposedthere comprises a transmitter using multiple bands and impulse radio within the bands totransmit data and a receiver, which detects only the energy of the transmitted impulses Thecombination of energy detection receiver and multiband enables a flexible high data ratesystem with low power consumption

2.1 Transmitter

The MIR-UWB transmitter is based on a multiband pulse generation followed by a modulator.The multiband pulse generator generates a pulse with a specified bandwidth for everysubband Subbands can be activated or deactivated using the bandplan Different possibilities

to generate theses pulses are shown in [30] Each subband pulse will be modulated withdifferent data, all subband pulses are summed up to a multiband pulse, amplified and

transmitted Figure 1 shows a transmitter based on an oscillator bank pulse generator.

PAM/PPM

PAM/PPM Modulator 2

The MIR-UWB receiver is based on N parallel energy detection receivers A filter bank

separates the individual subband pulses and an energy detector measures the energy in everysubband Based on the measured energy, the demodulator makes his decision For pulseamplitude modulation (PAM) and its special case of on-off-keying (OOK) the demodulationprocess needs to know the SNR in each subband This can be estimated using a preamble [46].The channel state information can be used for Detect and Avoid (DAA) algorithms [34] and toincrease the performance of the multiband system [28] Pulse position modulation (PPM) andtransmit reference (TR) do not need any channel state information

3 Energy detection

The MIR-UWB architecture is based on energy detection Thus the receiver detects only the

energy of the received signal in a specified window The disadvantage in performance is

MIRA – Physical Layer Optimisation for the Multiband Impulse Radio UWB Architecture 3

Channel- nisation

Synchro-binary data

Figure 2 MIR-UWB receiver

accompanied by a very simple receiver design [36, 38, 54] The performance measure isbased on the average symbol error probability (SEP) or bit error probability (BEP) and will

be derived in the following section

with the rangeA = { a0, , a M−1 } describes a transmitted symbol with the amplitude a m

Without loss of generality the integration starts at t0=0 In order to measure the energy, the

detector squares the received signal R( t)and integrates the result over the time interval T i

The received energy, normalized by the power spectral density N0/2, is:

A time discrete representation of the received energy Y is:

where W i := W(i/(2B)) If the symbol energy is ES =0, the received energy Y will be χ2

distributed with the degree of freedom of 2D If the symbol energy E S >0, the received energywill be noncentralχ2 distributed with the degree of freedom of 2D and the noncentrality

The conditional probability density function f Y|A (·| a m) with a m > 0 and E S > 0 of the

received energy Y is:

whereΓ is the gamma function [18, eq 8.310.1] and Inis the modified Bessel function of the

first kind of order n [1, eq 9.6.3].

3.2 AWGN channel

First we calculate the bit error probability of the energy detection receiver in the AWGNchannel (1) This receiver detects only the energy of the received signal (2), (3)

3.2.1 Pulse amplitude modulation

The M-PAM modulated signal is:

s(t) = ∑∞

k =−∞ a m,k p(t − kT r)and transmits log2(M)bit per symbol The energy of the mthsymbol is:

MIRA – Physical Layer Optimisation for the Multiband Impulse Radio UWB Architecture 5

where E p is the energy of an unmodulated pulse p The demodulator has to decide, which symbol m with the energy E S m and the amplitude a m has been transmitted, based on the

observation of the random variable Y The optimal receiver, i e the receiver with the lowest

probability to make a wrong decision, makes the decision for the symbol that has been sent

most likely, given a certain energy y at the receiver Thus, the receiver makes the decision for the symbol m with the amplitude a m, when [25]:

P{ A=a m | Y=y } ≥P{ A=a k | Y=y }, ∀ m = k. (7)This is the maximum a posteriori probability (MAP) decision rule If all transmitted symbolsare equal probable, it can be reduced to the maximum-likelihood (ML) decision rule:

m= arg max

with the conditional probability density function f Y|Abased on (5) and (6)

The SEP P e for the energy detection receiver in the AWGN channel with M-PAM signals can

be calculated as:

P e(γ, a, ρ, D) =1− P c(γ, a, ρ, D)

=1− M−1∑

m=0P(ρ m ≤ Y < ρ m+1| A=a m)P(A=a m), (9)

where P c is the probability of a correct decision and P(ρ m < Y ≤ ρ m+1| A = a m) is the

conditional probability, that the received energy Y is in the interval [ρ m,ρ m+1), with theoptimal interval thresholdsρ Thus, the decision has been made using the ML decision rule (8).

P(A=a m)is the a priori probability, that the symbol m has been sent andP(A=a m) =1/M for all m ∈ { 0, 1, , M −1} The conditional probabilityP(ρ m ≤ Y < ρ m+1| A=a m)is:

where Γ(·)is the Gamma function [18, eq 8.310.1] and Γ(·,·)is the incomplete Gammafunction [18, eq 8.350.1] The distribution function (11) can be also displayed with the help ofthe Marcum-Qfunction:

F Y|A(y |0) =1− Q D(0,√ y) (13)

If a symbol with an amplitude a m > 0 has been sent, the conditional probability density

function f Y|A (·| a m)has the form (6) There does not exist a closed form for the distribution

function in general But for D ∈Z+it can also be solved in closed form with the help of theMarcum-Qfunction (12):

F Y|A(y | a m) =y

0

12

3.2.1.1 Optimal interval thresholds

The optimal interval thresholds to minimise the SEP have to fulfil the following optimisationproblem:

MIRA – Physical Layer Optimisation for the Multiband Impulse Radio UWB Architecture 7

Figure 3 BEP for OOK and 2-PPM with different degrees of freedom

Figure 4 BEP for multilevel M-PAM and M-PPM for D=2

minimise

ρ P e(γ, a, ρ, M, D)subject to 1

has to fulfil the following equation:

f Y|A(ρopt| a m) = f Y|A(ρopt| a m+1), (17)

where f Y|A are the conditional probability density functions based on (5) and (6) Withthese optimal interval thresholds, the symbol decision is based on the ML-criteria (8).Unfortunately, there is no closed form solution for determining the optimal intervalthresholds Thus, they have to be calculated numerically Figure 5 shows the conditional

probability density functions with equidistant symbol amplitudes a m and optimal intervalthresholdsρ1,ρ2andρ3with an SNR ofγ=10 dB

7 MIRA – Physical Layer Optimisation for the Multiband Impulse Radio UWB Architecture

Figure 6 Sensitivity of the BEP related to the interval thresholdρ1 for OOK

Figure 6 shows the influence of a non optimal interval thresholdρ1on the SEP for OOK (M=2) In such a case, the SEP gets more sensitive for high SNR

optimal interval thresholdsρ (17) For OOK (M=2) the optimal amplitudes areaopt= (0, 2)

In this case they are independent of the SNRγ For M >2 it is possible to calculate a set ofoptimal amplitudesaopt for every SNRγ Figure 7 shows the SEP for 4-PAM for different

symbol amplitudes a1 and a2 for a SNR of 16 dB For figure 7 the amplitudes a0 = 0 and

MIRA – Physical Layer Optimisation for the Multiband Impulse Radio UWB Architecture 9

a3 =1 are set The minimal SEP has been reached fora= (0, 0.35, 0.67, 1) Figure 8 shows

0,5 1

10 -4

10 -2

10 0

Figure 7 SEP for 4-PAM with different interval thresholds

the gain for 4-PAM with optimal amplitudes for different degrees of freedom The resultsshow impressive gains for large degrees of freedom Figure 9 shows the optimal amplitudes

for different degrees of freedom For D = 2 the amplitudes are almost equidistant but for

D=200 the amplitudes are adjusted and not equidistant any more

Figure 8 BEP for 4-PAM with equidistant and optimal amplitudes

3.3 Flat fading channel

To analyse the performance of an energy detection receiver we need a channel model thatenables a good approximation of the energy at the receiver Investigations of the IEEE channelmodel (802.15.3a) show that the energy at the receiver can be approximated by a randomvariable which is constant for one symbol

Figure 10 compares the channel’s magnitude (denoted as CIR) to a moving average of width

100 MHz and 1 GHz of the energy in the IEEE channel model Figure 11 shows the magnitude

at the receiver for a detector with 100 MHz and 1 GHz bandwidth Thus we can use the

9 MIRA – Physical Layer Optimisation for the Multiband Impulse Radio UWB Architecture

E b/N0in dB

a m

a0 a1 a2 a3

Figure 9 Optimal amplitudes for different degrees of freedom (D=2, D=200)

flat fading channel model to model the energy at the receiver in a frequency selective fadingchannel

CIR CIR – 100 MHz CIR – 1 GHz

Figure 10 Moving average of the energy at the receiver (IEEE 802.15.3a, CM1)

MIRA – Physical Layer Optimisation for the Multiband Impulse Radio UWB Architecture 11

In a flat fading channel, the random path attenuation H is assumed to be constant for the duration of a symbol Thus, the received signal R( t)in the interval 0≤ t ≤ T Sis:

3.3.1 Pulse amplitude modulation

Using the SEP in the AWGN channel (16) and the probability density function of the randomSNRΓ in the flat fading channel, the average SEP for M-PAM is:

3.3.2 Rayleigh fading

Rayleigh distributed path gains are used to model fading channels with no line-of-sight

(NLOS) [49, 50, 55] Thus, the random variable H is Rayleigh distributed:

In UWB channels with a large bandwidth and a corresponding high temporal resolution, it

is questionable, if the central limit theorem is applicable [4, 32, 59] Nevertheless, some UWB

channel measurements show a good fit to the Rayleigh distribution [17, 24, 51] Using (18), the

probability density function of the random SNR is:

Combining (20) and (24) yields to the closed form solution for the energy detection receiver in

a Rayleigh fading channel with M-PAM:

Rice distributed path gains are used to model line-of-sight (LOS) fading channels [49, 50, 55].

Thus, the random variable H is Rice distributed:



MIRA – Physical Layer Optimisation for the Multiband Impulse Radio UWB Architecture 13

where I0 denotes the modified Bessel function of the first kind of order zero The

Rician-k-factor is the ratio between the power in the direct path and the power in the scattered

paths For k=0 the Rice distribution is equal to the Rayleigh distribution For k → ∞ the Rician

fading channel converges to the AWGN channel Different UWB measurement campaigns

show a good fit with the distribution of the path gains with a Rice distribution [20, 26, 43].

Using (18), the probability density function of the random SNR is:



k(k+1)γ γ

A closed form solution for the integral in (28) is not known for D >1 In this case, the integralhas to be calculated numerically

3.3.4 Nakagami-m fading

The probability density function of the Nakagami-m distribution of the random path gains is

related to theχ2distribution:



− mΩh2



where m denotes the Nakagami-m fading parameter with m ∈ [1/2,∞) andΓ denotes the

Gamma function The Nakagami-m distribution includes as special cases the one-sided normal distribution (m = 1/2) and the Rayleigh-distribution (m = 1) For m → ∞ the Nakagami-m

fading channel converges to the AWGN channel Different UWB measurement campaigns

show a good fit to the Nakagami-m distribution [4, 19] Nakagami-m distribution is also used

13 MIRA – Physical Layer Optimisation for the Multiband Impulse Radio UWB Architecture

in the IEEE channel model 802.15.4a to model the path gains [31] The probability densityfunction of the random SNRΓ is with (18) and (31):

fΓ(γ) = γΓ(m−1

m)



m γ

mexp

(33) can be solved recursively [13] The average symbol error rate in a fading channel with

Nakagami-m distributed fading gains is:



− (1− β)ρ

2

+ (1− β)m−2∑

2m+a ν γ.

L i is the Laguerre polynomial of degree i [18, eq 8.970] and1F1is the confluent hypergeometricfunction [18, eq 9.210.1]

Figure 12 shows the bit error probability in a flat fading channel with Rayleigh and Rice

distributed channel gains Figure 13 shows the bit error probability in a flat fading channel

with Nakagami-m distributed channel gains.

3.4 Diversity reception

Now we analyse the SEP of an energy detection receiver with diversity reception The goal

is to increase the SNR to improve its performance Because of the architecture of the receiver,detecting only the energy of the received signal, the possibilities to improve its performanceare limited and many combining techniques like maximum ratio combining (MRC) or equalgain combining (EGC) are not feasible Thus we concentrate on square law combining (SLC)and square law selection (SLS) [29]

MIRA – Physical Layer Optimisation for the Multiband Impulse Radio UWB Architecture 15

Figure 12 BEP in a flat fading channel with Rayleigh and Rice distributed channel gains (OOK, D=2)

Figure 13 BEP in a flat fading channel with Nakagami-m distributed channel gains (OOK, D=2)

The channel model used here is based on flat fading with independent and correlated fading

gains H l for all l diversity paths The instantaneous SNR at the energy detector l is:

γ l=h2l E S /N 0,l and the average SNR at the lthdetector is:

γ l=Ωl E S /N 0,l

withΩl=E(H2

l) Figure 14 shows the model of multichannel receiver

3.4.1 Square law combining

At the SLC receiver we have a new SNR YSLCat the receiver output based on the sum of the

SNR Y l at the l detectors:

15 MIRA – Physical Layer Optimisation for the Multiband Impulse Radio UWB Architecture

The new random variable YSLChas a centralχ2distribution for a0 = 0 and a noncentralχ2

distribution for a m > 0 with the degree of freedom of 2LD The conditional distribution

function for SLC is:

YSLC