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Ultra Wide Band Ad-Hoc Sensor Networks: A
Multi-Layer Analysis
Dorin Panaitopol
To cite this version:
Dorin Panaitopol. Ultra Wide Band Ad-Hoc Sensor Networks: A Multi-Layer Analysis. Signal and Image processing. National University of Singapore; Supélec, 2011. English. �tel-00840023�
PhD THESIS
in Signal Processing and Telecommunications
Ultra Wide Band Ad-Hoc Sensor Networks:
A Multi-Layer Analysis
Dorin PANAITOPOL
OFFICIAL NUMBER: 2011-05-TH
Ecole Supérieure d’Électricité (SUPÉLEC) National University of Singapore (NUS)
PhD Thesis
Field: Signal Processing and Telecommunications
presented by Dorin PANAITOPOL
for the title of Joint-PhD SUPÉLEC-NUS
on the subject
Ultra Wide Band Ad-Hoc Sensor Networks:
A Multi-Layer Analysis
PhD Supervisors Jocelyn FIORINA Chen-Khong THAM
Peng-Yong KONG
presented on 5th of July 2011, in front of the Jury composed of:
Hikmet SARI Laurent CLAVIER
Jocelyn FIORINA Stephen Vaughan HANLY
Chen-Khong THAM Peng-Yong KONG
in the memory of my father..
Abstract and Thesis Overview
Abstract
The Ultra Wide Band (UWB) technology represents a promising approach al- lowing the development of new types of wireless Local Area Networks (LANs) and Wireless Sensor Networks (WSNs). For twenty years, UWB has been an active field of research and it could be the physical layer for future multiple access wireless net- works with very high bit rates, as well as low bit rate low power networks with high accuracy positioning abilities.
Ad-hoc networks are expected to play an important role in future communication systems. They are self-organizing, rapidly deployable, and require no fixed infrastruc- ture. In ad-hoc networks, the wireless nodes cooperate in order to dynamically set up communications with distributed management and administration.
Sensor networks will provide the capacity to sense the surroundings, therefore in- troducing a high degree of visibility into the real physical world. This research project entitled ‘Ultra Wide Band ad-hoc sensor networks: a multi-layer analysis’ studies and analyzes protocols adapted to the UWB ad-hoc sensor networks, and also the opti- mization of layers (PHY, MAC and network). The various points to be approached in this thesis are from the physical layer toward the upper layers: antenna optimiza- tion issues, interference modeling, Impulse Radio UWB (IR-UWB) advanced receivers and transmitters with efficient wireless communication, throughput optimization, and cooperation issues.
The synthesis of these elements into a UWB-based ad-hoc sensor network will help in developing powerful optimized networks for which there are countless appli- cations and can lead to breakthroughs in areas such as healthcare, surveillance and environmental monitoring.
Thesis Overview
In this thesis we have addressed the problems of interference modeling, throughput maximization with several applications for IR-UWB ad-hoc sensor networks, antenna optimization, receiver and transmitter design, and relay cooperation.
After the introductory chapter, Chapter 2 presents the Impulse Radio system.
In Chapter2 we describe the Impulse Radio signal model, the classical transmission schemes, and some generalities on UWB channel model and receiver schemes. An- other part of this chapter is concerned with multiuser interference for IR-UWB and its
impact on the network organization. The network is simplified to some basic topolo- gies (e.g., two cells in uplink mode or two links T x − Rx transmitting and interfering with each other) that are further used in the manuscript to analyze the impact of some system parameters (e.g., slots, users, pulse shapes, spreading factors) on capac- ity and throughput. Thus, Section 2.3 details the IR-UWB interference model and applies it further in some interesting applications in Chapter4.
Our scientific contribution starts in Chapter3which deals with the IR-UWB non- Gaussianity of the MUI distribution. In this chapter we first recall that generalized Gaussian is a better approximation model for IR-UWB Multi User Interference. Note that there are several cases where the Gaussian distribution could be used to approxi- mate the IR-UWB MUI distribution but these cases are not representative and cannot be generalized. Another part of this chapter deals with a performance criterion for IR-UWB communication (see Section 3.4), that takes into account the MUI shape distribution and several signal parameters in order to compute the capacity of the communication and its throughput.
Chapter 4 deals with several applications of the performance criterion developed in Chapter 3. Each of these applications uses one of the interference models pre- sented in Chapter 2 (i.e., Section 2.3). In Chapter 4 we present the effect of tuning impulsiveness on throughput of IR-UWB Communications. In Sections 4.3, 4.4, 4.5 and 4.6we have presented different applications of several impulsiveness methods for double-cell scenarios, double-link communications, cognitive networks and IR-UWB antenna design respectively. While Sections4.3 and4.4 show that throughput can be maximized by controlling the impulsiveness of the interference, Section 4.6 presents the impact of antenna design on the impulsiveness and so on the capacity of an IR- UWB system in a Multi-User Interference environment, and proposes a new antenna design and pulse shape optimizations.
Chapter 5 is concerned with Impulse Radio UWB receivers and transmitters.
Section 5.1 describes the design of a novel simple IR-UWB receiver that could be used for sensor networks and compares it with previous works presented in Section 2.2.5. This receiver assumes that the probability density function describing the statistic of the interference is a mixture-based distribution. Section5.2 investigates a novel transmitter design based on Time Reversal (TR). We chose here to investigate the trade-off between the number of fingers in the prefilter (i.e., at the transmitter side) of a TR-IR-UWB system versus the number of fingers in the Rake receiver. This allows studying the gain brought by time reversal when the complexity is switched from the receiver to the transmitter i.e., when the number of fingers is increased in the prefilter while it is reduced in the Rake receiver. Moreover, it seems that TR combined with Rake technique changes the Probability Density Function (PDF) of the MUI. This chapter led to the development of a C++ platform used under Cygwin.
The work focuses further on the cooperation for wireless networks in Chapter 6. While Section 6.1 proposes an incremental relaying scheme that uses multiple relays, Section 6.2 proposes a novel and practical incremental relaying scheme that deals with the imperfect feedback. Section 6.3 describes a simple distributed relay selection policy without any need of information exchange between the relays.
Publication List
A part of the work from the Chapters 3, 4,5, 6has been published as follows:
1. D. Panaitopol, J. Fiorina, A. Diet, N. Ribière-Tharaud, ‘A New Criterion to Jointly Design the Antenna and Optimize the Communication Capacity in IR-UWB’, IEEE Wireless Communications and Networking Conference, IEEE WCNC, Budapest, Hungary, 2009.
2. D. Panaitopol, J. Fiorina, A. Diet, N. Ribière-Tharaud, ‘Impact of the Design of an UWB Antenna on the Maximum Achievable Rate of the Communication in Presence of Multi User Interferences’, Asia Pacific Microwave Conference (APMC 2008), Hong Kong, China, 2008.
3. D. Panaitopol, J. Fiorina, M. -G. Di Benedetto, ‘Trade-off Between the Number of Fingers in the Prefilter and in the Rake Receiver in Time Reversal IR-UWB’, IEEE ICUWB’09, Vancouver, Canada, 2009.
4. D. Panaitopol, J. Fiorina, P.-Y. Kong, C.-K. Tham, ‘The Effect of Impulsive- ness in Inter-Cell Interference on Throughput of TH-IR-UWB Networks’, IEEE WCNC, Sydney, Australia, 2010.
5. D. Panaitopol, J. Fiorina, T. Erseghe, ‘A Comparison of IR-UWB Receivers Adapted to MUI with Mixture Based Distributions’, IEEE WCNC, Sydney, Aus- tralia, 2010.
6. D. Panaitopol, P.-Y. Kong, C.-K. Tham, J. Fiorina, ‘An Efficient Cooperative Transmission Scheme Using Multiple Relays Incrementally’, IEEE PIMRC, Is- tanbul, 2010.
7. J. Fiorina, D. Panaitopol, D. Domenicali, ‘On the necessity of sensing the non- Gaussianity of the interferences: application to UWB systems’, CogART, Aal- borg, Denmark, 2009.
8. Patent Filed with NEC Technologies (UK), ‘Cooperative Transmission’ (submit- ted to the patent agent with the title ‘A Practical Multiple-Relaying Incremental Scheme for Wireless Networks’), Reference Number GB1105487.1.
9. D. Panaitopol, J. Fiorina, ‘Impact of the Generalized Gaussian Approximation on the design of IR-UWB systems’, Submitted to IEEE Transactions on Wire- less Communications Journal.
10. L. De Nardis, J. Fiorina, G. Capodanno, D. Panaitopol, and M.-G. Di Benedetto,
‘Combining UWB with Time Reversal for improved communication and posi- tioning’, to appear in Telecommunication Systems Journal (Springer), Special Issue on Recent Advances in UWB Systems: Theory and Applications.
Résumé
Les systèmes Ultra Wide Band (UWB) représentent une solution prometteuse pour le développement de nouveaux types de réseaux locaux sans-fils. L’UWB a été un domaine de recherche actif depuis 20 ans et pourrait être la couche physique pour de futurs réseaux sans fils à accès multiples à très haut débit ainsi qu’à bas débit avec consommation énergétique minimale, tout en offrant des possibilités de localisation à haute précision.
Nous nous intéressons dans cette thèse aux réseaux ad-hoc de capteurs UWB en partant de la couche physique pour remonter aux couches plus élevées : optimisation d’antenne, modélisation d’interférence, conception de récepteurs et transmetteurs, optimisation de débit et schémas coopératifs.
Une première contribution concerne la non Gaussianité des interférences multi utilisateurs : nous avons développé un critère de performance qui prend en compte les paramètres du système et la distribution des MUI afin de calculer la capacité des communications et le débit utile. Nous avons montré que le débit peut être maximisé en contrôlant l’impulsivité des interférences et nous avons montré l’impact de la conception de l’antenne sur cette impulsivité et par conséquent sur la capacité des systèmes UWB.
A partir de l’étude des MUI, une autre contribution concerne de nouveaux récep- teurs et émetteurs IR-UWB. Le récepteur proposé modélise la densité de probabilité des interférences comme une distribution mélangée. Nous avons également étudié un nouvel émetteur basé sur le retournement temporel combiné à l’IR UWB et étudié le gain apporté par le retournement temporel lorsque la complexité est assumée par le transmetteur à la place du récepteur, i.e. quand le nombre de doigts du pré-filtre est augmenté et quand le nombre de doigts du récepteur à râteau est diminué. Nous avons également montré que le time réversal combiné à l’IR UWB change la distribution des interférences.
Les recherches ont ensuite porté sur des schémas coopératifs. Nous avons proposé dans une première étude un schéma de relayage incrémental qui utilise plusieurs relais mais avec un retour imparfait et proposé finalement une règle simple de sélection distribuée des relais.
Contents
Thesis Overview iii
Résumé vii
Abbreviation List xiii
1 Introduction 1
1.1 History of Ultra Wide Band . . . 1
1.2 Applications of UWB . . . 4
1.3 Contribution with Respect to the State of the Art . . . 7
2 Signal Model and Interference Scenarios 13 2.1 Introduction on IR-UWB Signal . . . 13
2.1.1 PPM-TH-UWB . . . 14
2.1.2 PAM-TH-UWB . . . 15
2.1.3 DS-UWB . . . 15
2.1.4 Generalized PAM-PPM. . . 15
2.1.5 Useful Physical Quantities for Impulse Radio. . . 16
2.2 System Model . . . 16
2.2.1 Impulse Radio Transmitted Signal. . . 16
2.2.2 Channel Model . . . 17
2.2.3 Transmission Scheme and Received Signal . . . 18
2.2.4 Types of Interference . . . 19
2.2.5 Impulse Radio Receiver Generalities. . . 19
2.3 Interference Model . . . 24
2.3.1 Single-Cell Scenario . . . 24
2.3.2 Double-Cell Scenario . . . 27
2.3.3 Double-Link Scenario . . . 29
3 On the Non-Gaussianity of the IR-UWB MUI 31 3.1 Introduction . . . 31
3.2 Simulation Results . . . 33
3.3 Kurtosis Computation in Perfect Power Control and Lack of Power Control Scenarios . . . 39
3.3.1 General Issues . . . 39
3.3.2 Perfect Power Control Scenario . . . 42
CONTENTS
3.3.3 Lack of Power Control Scenario . . . 43
3.4 Channel Capacity Computation Using a Generalized Gaussian Appro- ximation . . . 45
3.4.1 Kurtosis Expressions . . . 45
3.4.2 SINR Expressions . . . 47
3.4.3 The Capacity of a Discrete Memoryless Channel with Continuous- Valued Output . . . 49
4 The Effect of Tuning Impulsiveness on Throughput of IR-UWB Communications 51 4.1 Introduction . . . 51
4.2 Tuning the Impulsiveness. . . 52
4.3 Application in Double-Cell Scenario . . . 53
4.3.1 Novel Metrics Based on the Communication Capacity . . . 54
4.3.2 Tuning the Impulsiveness of the Signal through Nh,I and Nh,II 54 4.3.3 Numerical Results . . . 55
4.3.4 Conclusions . . . 59
4.4 Application in Double-Link Communications . . . 60
4.5 Application in Cognitive Networks . . . 64
4.5.1 Sensing the MUI . . . 64
4.5.2 Tuning w(t) in the Cognitive Network . . . 65
4.5.3 Conclusions . . . 66
4.6 Application in IR-UWB Antenna Testing . . . 67
4.6.1 An Antenna for IR-UWB . . . 69
4.6.2 A Novel IR-UWB Antenna Performance Criterion . . . 70
4.6.3 Results. . . 74
4.6.4 Conclusions . . . 77
5 Receiver and Transmitter Designs for IR-UWB 81 5.1 A Comparison of IR-UWB Receivers Adapted to MUI with non Gaus- sian Distributions . . . 82
5.1.1 Introduction . . . 82
5.1.2 Receiver . . . 82
5.1.3 Modeling MUI . . . 83
5.1.4 What is the Point of Using Receivers Adapted to Atypical MUI Distributions? . . . 85
5.1.5 The Receiver Structure for Generalized Gaussian MUI and a Novel Block Scheme . . . 86
5.1.6 The Receiver Structure for Mixture MUI . . . 87
5.1.7 Conclusions . . . 94
5.2 A Study on a Novel Type of Transmitter Using Time Reversal . . . . 96
5.2.1 Introduction . . . 96
5.2.2 TR-SRake Model . . . 96
5.2.3 Simulations and Results . . . 98
5.2.4 Conclusions . . . 105
CONTENTS
6 Cooperation in Wireless Networks 107
6.1 Cooperative Transmission Scheme Using Incremental Relaying with
Multiple Relays . . . 108
6.1.1 Introduction . . . 108
6.1.2 System Model . . . 109
6.1.3 Incremental AF with Multiple Relays . . . 110
6.1.4 Numerical Results . . . 116
6.1.5 Conclusions . . . 121
6.2 A Practical Incremental Relaying Scheme with Imperfect Feedback for Wireless Networks . . . 121
6.2.1 Introduction . . . 121
6.2.2 Practical Incremental Relaying with Imperfect Feedback . . . 122
6.2.3 Numerical Results . . . 133
6.2.4 Conclusions . . . 135
6.3 On the Relay Selection and Cooperation for UWB . . . 137
6.3.1 Introduction . . . 137
6.3.2 Theoretical Model . . . 139
6.3.3 Packet Success Probabilities . . . 139
6.3.4 To Cooperate or Not to Cooperate? . . . 141
6.3.5 Matlab Results and C++ Implementation . . . 142
6.3.6 Further Investigation . . . 145
Conclusions and Perspectives 147
Acknowledgement 157
Remerciements 159
Bibliography 161
Abbreviation List
ACK ACKnowledgement AF Amplify and Forward AOA Angle Of Arrival BER Bit Error Rate
BPSK Binary Phase Shift Keying BS Base Station
CDMA Code Division Multiple Access CF Characteristic Function
CH Cluster Head or CHannel CM Channel Model
CNODE Cognitive NODE
CSI Channel State Information DF Decode and Forward
DS Direct Sequence
Eb/N0 Energy per bit to Noise power spectral density EM Expectation Maximization
FIR Finite Impulse Response FRake Full Rake
GG Generalized Gaussian
GGM Generalized Gaussian Mixture GM Gaussian Mixture
IAF Incremental Amplify and Forward IR Impulse Radio
ISI Inter-Symbol Interference LM Laplacian Mixture
LOS Line Of Sight
LPI/D Low Probability of Interference and Detection LSE Least Square Estimator
MAC Medium Access Control (Layer) MAI Multiple Access Interference MANET Mobile Ad-hoc NETwork
MB Multi Band
MEB Mixture Estimation Block
MEM Modified Expectation Maximization MF Matched Filter
MLE Maximum Likelihood Estimator MMSE Minimum Mean-Square Error
MRC Maximal Ratio Combining MUD Multi User Detection
MUI Multi User Interference NACK Not ACKnowledgement
NLOS Non Line Of Sight
PAM Pulse Amplitude Modulation PDF Probability Density Function PIAF Practical IAF
PHY PHYsical (Layer)
PPM Pulse Position Modulation PRake Partial Rake
PULSERS Pervasive UWB Low Spectral Energy Radio Systems
RF Radio Frequency RSS Radio Signal Strength
Rx Receiver
QoS Quality of Service
QPSK Quaternary Phase Shift Keying SE Spectral Efficiency
SGA Standard Gaussian Approximation SINR Signal to Noise and Interference Ratio
SIR Signal to Interference Ratio SNR Signal to Noise Ratio SRake Selective Rake
TDOA Time Difference Of Arrival TH Time Hopping
TOA Time Of Arrival TR Time Reversal
TRef Transmitted Ref erence or Time Ref erence Tx Transmitter
UWB Ultra Wide Band WMN Wireless Mesh Network
WPAN Wireless Personal Area Network WSN Wireless Sensor Network
Chapter 1
Introduction
1.1 History of Ultra Wide Band
The concept of Ultra Wide Band communications originated with the first experi- ments made by Marconi and Hertz [141]. At the end of the 1890s, Marconi developed the spark gap transmitter and he is therefore considered to be the parent of spread spectrum systems [74,176,184]. The Impulse Radio based Ultra Wide Band commu- nication systems became an interesting research field twenty years ago, with the first publications by P. Withington and L. Fullerton [182] and by R. A. Scholtz [158,159].
Previously, the UWB systems have been classified by the US military which used them because of their many properties such as resistance to jamming and interference.
We can also quote as an historical invention the radio systems using Pulse Posi- tion Modulation (PPM), whose prototypes exist since 1943 [8,15]. After the second world war, J. R. Pierce published the principle of IR-UWB in a Bell Labs memoran- dum [138]. We find in this article the basic ideas of the TH-IR-UWB, although the transmitted signals are not digital but analog.
The evolutions in radar systems have also allowed the development of the UWB systems for communications although, contrary to UWB radars [6,106], UWB com- munication technique uses short impulses with low power. In 1987, Ross and Fontana designed, developed and implemented a Low Probability to Intercept and Detection (LPI/D) communications system [58], funded by the United States government.
The term UWB was first introduced by DARPA in 1990 for radar applications, and in 2002 FCC (US) established the first regulation for UWB devices. Just after that, European and Japanese standards followed - see Fig. 1.1.
Nowadays, not only that UWB is a physical transmission technique suitable for a great number of applications, but is also expected to be very advantageous (see Table 1.1). UWB has emerged as a particularly appealing transmission technique for applications requiring either high bit rates over short ranges (on the right hand side of Table 1.1) or low bit rates over medium to long ranges (on the left hand side of Table 1.1). While the first area of interest is suitable for multimedia and high rate applications, the latter makes UWB appealing for such applications as sensor networks.
1.1 History of Ultra Wide Band
(a)
(b) (c)
Figure 1.1Standard - UWB Emission Limit: (a) FCC (US) emission limits for indoor and outdoor UWB systems (b) European Commission emission limits for UWB systems (c) Japanese emission limits for indoor UWB systems
1.1 History of Ultra Wide Band
Table 1.1 The position of UWB Communications
← Sensors Multimedia, High Rate
Applications Applications →
Technology UWB Low Zigbee Bluetooth Wi-Fi UWB High
Rate Rate
Protocol 802.15.4a 802.15.4 802.15.1 802.11 802.15.3a
IEEE a/b/g
Memory 4Kb+ 4-32Kb 250Kb+ 1Mb+ 1Mb+
Autonomy Years months Days up to >hours
4 hours
Number thousands hundreds 7 32 >32
of nodes
Transfer 250Kb/s- 250Kb/s 1Mb/s 11-54- >110-200Mb/s
Speed 1Mb/s 108Mb/s
Range Hundred- 100m 10-100m 300m 10m-4m
tens of m
Among the various modulations schemes that have been proposed for the UWB technology, we can cite the most important ones: Impulse Radio UWB (IR-TH-PAM and IR-TH-PPM), Direct Sequence CDMA and Multi Band UWB (i.e., MB-OFDM).
To understand the steps taken towards the UWB technology, the future devel- opment and the applications envisaged it is imperative to discuss about the IEEE standard 802.15 and more precisely about the Task Group 3a (i.e., 802.15.3a) and the Task Group 4a (i.e., 802.15.4a).
The 802.15.3a standard was withdrawn in Jan 2006 due to a long lasting fight between the two proposals MB-UWB (sustained by WiMedia Alliance) and DS-UWB (sustained by UWB Forum). The only important task achieved was the selection of two candidate proposals out of 23. The final goal was to provide a High Rate UWB standard.
It is important to say that the weakness of the MB-OFDM UWB approach is a more complex transceiver structure if compared to the original impulse radio work- ing at the baseband - a very simple radio concept. The basic idea of cheap, low power consumption UWB devices is lost since new functional blocks like mixers and amplifiers are needed for the up-converter and down-converter. On the other hand, the technique can offer higher data rates for medium distances than the single-band approach, and commercial OFDM technology is quite mature, nowadays with com- ponents available on the shelf.
On the other hand, the 802.15.4a is now complete. The first goal is to provide communications and high precision ranging/location capability (1 meter accuracy and better), high aggregate throughput, and ultra low power; as well as adding scalability to data rates, longer range, and lower power consumption and cost. These additional capabilities over the existing 802.15.4 standard are expected to enable significant new applications and market opportunities. The physical layer of this standard is based on Low Rate UWB.
1.2 Applications of UWB
In particular, for ad-hoc and sensor networks, the UWB ranging capability (at the PHY layer) is an attractive feature for location-aware applications (for MAC layer and above). Therefore, introducing positioning in low data rate networks has recently become the main goal of the 802.15.4a, where impulse radio ultra wide-band (IR-UWB) emerges as a most appealing principle.
Another standard with some relevance to our work is IEEE 1451.5, or the wireless smart sensor standard. This standard does not specifically address UWB but the main principles for wireless sensors are there.
1.2 Applications of UWB
UWB systems have potentially low complexity and low cost, are resistant to jam- ming and have very good time resolution allowing for precise location and tracking.
Furthermore, as a result of their good signal properties, the UWB interference appears as a low power spectral density noise, and therefore UWB systems should create little interference to other systems. Nevertheless, this interference still has to be taken into account in interference management.
Among other possible applications, the inherent properties of Impulse Radio UWB technology make it well suited to wireless sensor network applications [32,67,76,173, 187] and its feasibility has been studied on real chip designs [7, 126, 150, 172].
A sensor network is a computer network composed of a large number of sensor nodes. The sensors should be heterogeneous devices with low cost, low energy consumption, small, robust with variable data rate enhancements suitable for different applications. There are different sensors such as accelerometer, camera, microphone, pressure, thermal, etc. They monitor conditions such as the chemical composition, direction, lightning, humidity, noise level, mechanical stress levels, move- ment, pressure, size, speed, and temperature of an habitat, highways, bridges, and other civilian infrastructure [123]. This capability leads to innovative applications such as in-vehicle sensing, intrusion detection [187], weather forecast, etc. These sen- sor nodes usually contain three components: sensing, processing and communicating [4].
While sensing represents an amazing way of interacting with the physical world, with a huge number of applications, nowadays it may still be an expensive opera- tion in terms of energy consumption. For the sensing operation a sensing capable device usually consumes 1mJ/sample for Light (Taos [88] TSL2550 ambient light sensor), 3mJ/sample for Humidity and Temperature (Sensirion [87] SHT1x relative humidity sensor), while operating typically at 3V . Some other sensing features of more complex devices consume 3 − 5mJ for an accelerometer (Analog Devices [82]
ADXL202E low-cost 2g dual-axis accelerometers), 3mJ for a barometer (Intersema [84] MS5534A barometer module) or around 10mJ for a magnetometer (Honeywell [83] HMC1001/1002 and HMC1021/1022 1-and 2-axis magnetic sensors).
Sensors networks have military applications [31] (DSN and SenIT from DARPA), environmental applications [4,85], healthcare applications (A*STAR, Singapore), and even home applications like "Smart Environment" [43], "Smart Kindergarten" [168] or
1.2 Applications of UWB
"The Intelligent Home". For most of these we need high-precision localization systems [59].
Some companies already started to commercialize UWB applications for retail marketing, manufacturing and healthcare such as PLUS from Time Domain [89], used to tag or locate everything in real time from consumables and equipment to staff and even workflow processes. Ubisense [90] also commercializes systems using Angle of Arrival (AoA) and Time Difference of Arrival (TDoA) for precise real-time location.
SandLinks [86] is developing a low-cost UWB RTLS chip that could dramatically reduce the cost of equipment.
In Singapore, the Agency for Science, Technology & Research (A*STAR) finances the Ultra Wide Band-enabled Sentient Computing (UWB-SC) pro- gram [81,128] in order to extend Singapore’s R&D capabilities relevant to Sentient Computing and Ultra Wide Band. Sentient computing is defined as a form of ubiq- uitous computing which emphasizes the use of sensors to perceive its environment and react accordingly, performing intelligent actions which affect and benefit peo- ple. Research is being carried out at the Institute for Infocomm Research (I2R), Institute of Microelectronics (IME), Nanyang Technological University (NTU) and National University of Singapore (NUS).
There are eight projects in the UWB-SC program handling research subjects from the physical layer to the application layer:
1. UWB Antennas and Channel Characterization,
2. Reconfigurable RF Transceiver IC Platform for Communication and Localiza- tion,
3. Adaptive Power Aware Digital Signal Processing Circuits,
4. Ranging and Low Rate Communication for an IR-UWB RFID System,
5. Localization and Identification: System architectural components and core ca- pability development for UWB-SC,
6. UWB-enabled Sentient Computing Architecture and Middleware with Coordi- nated QoS (USCAM-CQ),
7. Smart Space enabled by Sentient Computing,
8. Context Aware Middleware Services and Programming Support for Sentient Computing.
The goal of the UWB-SC research program is to provide a smart space environment for use in indoor applications such as healthcare monitoring, customer and/or incident monitoring in shopping mall, etc.
Localization joint with communication is an important application for a sensor network and, because of their high ranging capabilities, it is particularly important for sensor networks using IR-UWB technology. When a technology like UWB comes along, providing better location estimation due to its short impulses and higher band- width, having accurate information about the position of the nodes inside the network becomes fundamental. The benefits of knowing the position of the nodes are divided into two important categories:
1.2 Applications of UWB
– for the enhanced protocols and algorithms used in the MAC layer and above:
to provide location stamps for individual sensor measurements that are being gathered, to determine the quality of coverage, to achieve load balancing in topology control mechanism, to form clusters, to facilitate routing of information through the network, to perform efficient spatial querying, or to manage the cooperation between nodes based on geographical position.
– for future applications that could be envisaged: to locate and track objects in the environment, to secure a military area, to monitor the spatial evolution of a diffuse phenomenon over time, for search and rescue missions, for the supervision of children or of the patients in a hospital (healthcare).
While it is not the main focus of the thesis, and therefore it is not presented in this manuscript, we have addressed the subject of localization for Wireless Sensor Networks (WSN) during the initial phase of this study. Our contribution is about the use of Spring Force Algorithm (SFA) for localization which has been presented in the First French-Singapore Workshop on Signal Processing, S2.2-B2-53/NTU, Singapore, 2007 [130]. The novelty about this credibility-based algorithm is that it applies a simple principle of equivalence with a spring network: the difference between the range estimate and the real distance is seen as a compression or as an extension of a spring. The algorithm is very simple and also it helps gathering a 3D map (please note the difference between the term "ranging" [23, 75] which refers to point-to-point distance estimation and the term "localization" [16, 113,129,155] which refers to 2D or 3D position estimation).
In this section we have shown that there are many possible IR-UWB applications and technological breakthroughs in the field, but IR-UWB still remains technologi- cally unavailable for WSN in the sense that there are only a few (and costly) WSN IR-UWB research platforms. For this reason, many WSN scientific studies such as those on the MAC and network related layers (e.g., issues in network topology, which is applicable to different PHY layers) are nowadays done using research platforms that are not IR-UWB capable. We could cite, for example, a few motes (i.e., devices similar to sensors, used as research platforms for WSN scientific purposes) that do not exploit the UWB technology yet: TelosB, Mica2/MicaZ, Mica2dot (see Fig.1.2).
For instance, TelosB and MicaZ [91] have IEEE 802.15.4 compliant RF transceivers operating in a bandwidth not larger than 85MHz (in steps of 5MHz).
1.3 Contribution with Respect to the State of the Art
(a) (b)
(c)
Figure 1.2 (a) TelosB, (b) Mica2/MicaZ, (c) Mica2dot
1.3 Contribution with Respect to the State of the
Art
In this thesis we are concerned with Impulse Radio UWB communications and we have addressed the problems of interference modeling, throughput optimization, receiver and transmitter design, cooperation, and antenna optimization for ad-hoc sensor networks.
Interference modeling is a major research issue for any wireless network. Many works [11, 22, 142, 158] studied the IR-UWB interference using models provided by the research done on CDMA networks. As we will show in the next paragraphs and in the rest of this thesis, Impulse Radio (IR) UWB interference has different properties from any other type of interference previously studied.
The discussions around the validity of Standard Gaussian Approximation (SGA) for Impulse Radio UWB interference has recently intensified. Results suggest that the validity of SGA for IR schemes increases with the number of interfering users [179], but SGA may not be fully valid even with an asymptotic number of users [48,50]. It has also been shown that SGA does not drive to adequate Bit Error Rate derivations [36,56]. The analyses presented in [36,73] show that for Time Hopping UWB systems with and without perfect power control, when a classical correlation receiver is used, the SGA leads to more optimistic predictions of the BER floor than results obtained by simulation. In [71] it is shown that for random uniform distributed delays and a low number of interferers, the interference will act as a "collision model". The above
1.3 Contribution with Respect to the State of the Art
studies are based on experimental data obtained by simulation, and they are showing the non-validity of the standard Gaussian approximation.
The SGA hypothesis seems to cease having validity when the number of pulses in a transmission frame is not sufficiently high. A reduced number of pulses can be associated with scenarios with a reduced number of transmitters (e.g., low density networks) or scenarios with several dominant interferers (e.g., transmitters with fixed powers and lack of power control scenarios), or combinations of the above conditions.
The transmitters may also be characterized by a low data rate with low number of pulses per bit. All these scenarios have applications in sensor networks, which are typically characterized by low data rates and sparse topologies. Therefore, one may conclude that for sensor networks the Gaussian approximation is no longer valid and it has to be replaced with some other distributions that better approximate the data obtained from experiments. Note that for high density of users (e.g., networks with many transmitting sensors) it has also been shown that SGA may not be valid [46].
There are several works [92,93,152] proposing analytical approaches for IR-UWB system performance estimation, taking into account the non-Gaussianity of the inter- ference. In particular, [92, 93] are using the Characteristic Function (CF) technique following a consolidated procedure from CDMA systems.
Sometimes it may be very difficult to analytically compute BER under non- Gaussian approximation. One can still use different approximation methods [35]
and experimental results from Monte-Carlo simulations, but the results may not be precise. Therefore we may need to introduce novel concepts and performance criteria.
Our contribution starts with Chapter 3, which is concerned with multiuser inter- ferences for IR-UWB and its impact on the network organization. Chapter3proposes to further develop an IR-UWB performance criterion which we apply in some interest- ing applications in Chapter4. This performance criterion takes into consideration not the BER of the network but instead the achievable communication capacity of a dis- crete memoryless channel with continuous-valued output. The capacity is dependent on two important parameters: SINR and kurtosis. We give the kurtosis expression as a function of the system parameters (it is an extension of its existing expression in the very basic case of power control [47, 51, 133]), so our contribution allows to see the impact of the parameters on the capacity when SGA is not valid. In Chapter 3 it is also shown that kurtosis is related to physical parameters such as the distance between pulses and the number of users, the duty cycle of the pulse and so on. This is the reason for which we frequently refer to impulsiveness instead of kurtosis, as we could see in the rest of the manuscript. In the different context of CDMA cells and using a different approach, results were found which prove that changing the system’s impulsiveness can be used as an alternative for power control in terms of achievable better network capacity [64, 65]. With our performance criterion we have reached new results which are in agreement.
In the same area of interest, Section4.6 presents an antenna design that increases the capacity of an IR-UWB system in a Multi-User Interference environment. As it has been suggested by [45], the interference in IR-UWB could be decreased by pulse shape optimizations. This part of the work proposes a statistical signal-processing tool to optimize an IR-UWB antenna, taking into account the impact of antenna’s
1.3 Contribution with Respect to the State of the Art
time domain response over the capacity of the discrete memoryless channel. This tool could be also used to optimize some other basic pulse shapes.
In an IR-UWB system, both transmitters and receivers have to use pulse genera- tors. For instance, Impulse Radio receivers use Matched Filter (MF) correlation and therefore must generate a template pulse that matches the incoming waveform. Even if the heart of any IR-UWB system is the pulse generator, the performance of the pulse generators it is not the goal of this thesis. From our point of view, the most im- portant receiver design concerns the minimization of the bit error rate through signal processing tools but also of the complexity and of the power consumption. For appli- cations such as sensor networks, where low complexity and low power consumption is a powerful demand, suboptimal receivers might be very good candidates.
Receivers for impulse IR-UWB can be broadly categorized as energy detectors [61, 149,165] (i.e., threshold detectors), correlation detectors known also as matched filter (MF) receivers [94, 144, 186], and Rake receivers [119, 140, 146, 181]. Multi- user detectors (MUD) [37,114] and hybrid Rake/MUD-UWB [115] receivers for robust narrowband interference suppression are also becoming popular.
The Rake receiver is used in any kind of spread spectrum communication system to accumulate the energy in the significant multipath components. The Rake receiver consists of multiple correlators (i.e., bank of correlators). Each finger of the Rake is synchronized to a multi-path component, and the output of each finger is coherently combined using MRC (maximal ratio combining). Obviously, channel estimation is required in the combining scheme and therefore when it is applied to UWB systems, the Rake receiver suffers from a major drawback if the distortion of the pulse through the multipath channel changes very fast (i.e., for each transmitted pulse). In this situation, the template in the receiver has to be recomputed faster [11]. An optimal maximum likelihood (ML) detector is far too complex to be implemented for a realistic system, so in practice suboptimal coherent Rake receivers are used. Another way to reduce the complexity is to reduce the number of fingers (e.g., the number of paths), but as we will see later in Section 5.2, when the second derivative of the Gaussian pulse is used, the energy capture is relatively low for a moderate number of fingers [177].
MUD receivers usually consider minimum mean square error (MMSE) techniques.
Adaptive MMSE MUD receivers are very efficient, being able to gather the multipath energy and reject interference to a much greater extent than conventional Rake re- ceivers. The Hybrid Rake MUD UWB receivers are enhancements of Rake reception, replacing MRC combining with optimum combining based on MMSE. Unfortunately, MUD is a complex solution [185], even when suboptimal methods such as successive interference cancellation are used [52].
It is important to mention that the number of paths in IR-UWB is huge, making the estimation of the channel difficult to compute. If we cannot rely on a high number of fingers in a Rake receiver, neither on a very frequent estimation, an alternative approach is the use of an autocorrelation receiver that correlates the received signal with a previously received template [30,80]. Under the assumption that the channel is varying slowly, this receiver is not requiring channel estimation, as both template and useful signal are affected by the same propagation parameters. However, even
1.3 Contribution with Respect to the State of the Art
if the channel is varying slowly, the noise is not and it affects the demodulation.
More precisely, the Time Reference (TRef) system is always suffering from the use of a noisy received template. Anyway, a potentially attractive feature of TRef UWB autocorrelation receivers is their relative robustness to synchronization problems [80].
Our contribution in the field of receiving and transmitting techniques for Impulse Radio UWB can be found in Chapter 5, which is concerned with IR-UWB receivers and transmitters. This chapter led to the development of a C++ platform used under Cygwin. As a consequence of the atypical MUI aspect in IR-UWB [34], we chose to model the MUI distribution in order to derive an appropriate single user receiver. The results in [11, 47, 50] prove that the MUI in IR-TH are not Gaussian. It has been empirically shown [46] that after the correlation part of the receiver, the MUI (for each impulse of the received signal) may be modeled as a generalized Gaussian. The receiver adapted to generalized Gaussian was developed in [46], but the parameter estimation block was not detailed. In Subsection 5.1.5 we contribute by detailing it and giving an iterative structure.
The advantage of modeling or fitting the MUI distribution with an appropriate distribution [10, 104] is that it gives the possibility to develop a simple yet efficient receiver [9,45,68,69]. We privilege this approach in contrast with heavier multi user detection, as the low complexity receiver is one of the targeted advantage of Impulse Radio systems.
Section5.1presents the design of a novel IR-UWB receiver which assumes that the probability density function describing the statistic of the interference is a mixture- based distribution.The receiver for Gaussian Mixture was developed in [41, 42], and in Subsection 5.1.6 we contribute by extending it to generalized Gaussian Mixture and by giving a more simple architecture in an iterative structure where the mixture estimation is separated from the channel estimation - which is supposed to be already done and used by the Matched Filter.This simple IR-UWB receiver could be used for sensor networks and its performance is compared with previous works presented in Section2.2.5.
In Chapter 5, we also propose a novel transmitter design based on Time Reversal (TR) Impulse Radio Ultra Wide Band which we describe in Section5.2. Many studies have been made on the number of fingers to be used in the Rake receiver in order to obtain good performance [11, 24,124,143,178]. Time Reversal IR-UWB systems use a prefilter at the transmitter side [139, 170], that has the function of convolving the UWB pulse with the impulse response of the channel reverted in time; when the signal traverses the channel, the output of the channel presents the correlation of the channel with itself. The "fingers" from the transmitter (i.e., prefilter) could be seen similar to the fingers from the Rake. In this section, a trade-off between the number of fingers in the prefilter versus the number of fingers in the Rake receiver has been done. This allows us to study the gain brought by Time Reversal when the complexity is switched from the receiver to the transmitter i.e., when the number of fingers is increased in the prefilter while at the same time it is reduced in the Rake receiver.
Going toward upper layers, cooperative communication techniques are used (at the MAC layer) to improve wireless link performance. As explained in Section1.2 on
1.3 Contribution with Respect to the State of the Art
the applications for UWB, one of the advantages of UWB is the positioning ability (due to the high bandwidth). The geographical informations can be used to manage cooperation between adjacent nodes [161, 162, 163].
Compared to direct transmission between a source node and a destination node, cooperative transmission involves relay (neighbor) nodes that are within the radio range of both source and destination to retransmit an overheard transmission to the destination. Cooperative communications have some advantages in terms of through- put, connectivity, and energy consumption [153]. In literature, this type of cooper- ative communication technique is also called (cooperative) relaying. There are two common types of relaying, namely the decode-and-forward (DF) and amplify-and- forward (AF) [118]. In AF, a relay simply amplifies an overheard transmission with- out decoding it, before retransmitting to the destination [95]. On the other hand, in DF, the relay needs to fully decode an overheard transmission before retransmitting it to the destination, which limits DF’s performance.
In a simple AF scheme, a fixed time slot is allocated to the source and to the relay.
In this fixed time slot structure, the relay retransmits the overheard transmission to the destination node even if the original transmission from the source has been successfully received. This type of simple AF scheme has been shown not to be the best alternative in terms of spectral efficiency [108]. In [110], the authors chose to improve the performance of AF in terms of lower outage probability by using multiple relays that transmit concurrently in the single allocated time slot. However, this improvement does not help in achieving a higher spectral efficiency.
A few incremental relaying schemes have been proposed in order to improve spec- tral efficiency. In these schemes, a relay is dynamically allocated a time slot to retransmit an overheard transmission only if the destination has not received the original transmission from the source. In order to perform incremental relaying, it is assumed that there is immediate feedback from destination to relay. When im- mediate feedback is not available, [188] proposed to dynamically allocate time slots to the relay based on an estimated channel state information. While these existing incremental relaying schemes help in achieving a higher spectral efficiency [99], only a few exploit the existence of multiple relay nodes [97]. Nevertheless, there are several references employing multiple relay strategies but they treat mainly non-incremental schemes (e.g., AF or DF) [77, 166], while those dealing with multiple relay incremen- tal schemes [17,19,98,101,102] are referring to best single-relay selection technique (i.e., only one best relay is picked up to help) or to space time coding techniques [121]
(i.e., virtual antenna array).
We would like to point out that the literature for relay cooperation schemes is vast and one can find AF schemes with multiple relays, or incremental AF schemes with best relay selection (or half-duplex), but we were not able to find existing results for incremental AF schemes with multiple relays where all the relays incrementally participate in cooperation.
The work in Chapter6focuses on the cooperation in wireless networks. In Section 6.1, we propose an incremental AF relaying scheme that uses multiple relay nodes to achieve higher spectral efficiency and lower outage probability.
Even if they are the best options in terms of spectral efficiency [108], incremental
1.3 Contribution with Respect to the State of the Art
relaying techniques are not practical and there are difficulties to be implemented for reasons such as non-availability of the channel state information (CSI) or the imperfect feedback [110] from the destination. There are two ways to do the dynamic time slot allocation in IAF: (a) the first way is to use the estimated channel state information [17, 18, 188], and (b) the second way is to use immediate feedback from destination [97, 98, 99,101].
Because of feasibility reasons related to determining the instantaneous channel state information, in Chapter 6 we consider the use of immediate feedback from destination, but which can be affected by propagation impairments. In practical wireless networks, in the presence of such imperfect feedback information, both the source and the relay may over-react resulting in packet collisions. Therefore, in Section 6.2 we propose a novel and practical incremental AF (PIAF) scheme that deals with the imperfect feedback information. Section 6.3 describes a simple distributed relay selection policy without any need of information exchange between the relays.
This thesis covers various domains from PHY to MAC and network layers. Each contribution can be seen as a small piece of the whole complex puzzle which is the field of wireless networks. The work from this thesis led to a certain number of publications enumerated at the beginning of this manuscript.
Chapter 2
Signal Model and Interference
Scenarios
Chapter Overview
This chapter presents the overall system model and the IR-UWB notation con- vention that will be used throughout the manuscript. While Section2.1 describes the classical Impulse Radio transmission schemes (e.g. PPM-TH, PAM-TH, DS-UWB), Section 2.2 deals with the transmitter, the channel model, and basic Impulse Radio receivers.
We further show in Section 2.3 the primary interference scenarios that can affect our network’s performance. This section presents the basic topologies encountered in sensor networks and theoretically develops the interference expression for all of the considered topologies. All topologies are further used in Chapters 4 and 5 for different applications of single-cell, double-cell and double-link scenarios, or cognitive networks.
2.1 Introduction on IR-UWB Signal
In this introductory section we briefly describe the existing Impulse Radio UWB modulations techniques, emphasizing on Pulse Position Modulations (PPM) and Pulse Amplitude Modulations (PAM) [5, 11, 70, 147]. We are also showing that all of the IR-UWB techniques are similar: all of these techniques use pulses to transmit and therefore share similar expressions, similar interference models or similar receiv- ing methods. For instance, later in Section3.3.1we use this similarities between PPM and PAM to compute some important quantities necessary further in our study (e.g., kurtosis, SINR).
2.1 Introduction on IR-UWB Signal
2.1.1 PPM-TH-UWB
The signal sent in Pulse Position Modulation Time Hopping Ultra Wide Band (PPM-TH-UWB or simply called PPM-UWB) may be written as
x(t) = +∞X
j=−∞
w(t − jTf − cjTc− bitjδP P M), (2.1) where w(t) is the function describing the shape of the pulse, and has non-zero values only inside an interval of length Tp. Tf is the frame period and usually equals NhTc
where Tc is the slot (i.e., chip) time period and Nh is the number of slots (i.e., chips) in a frame. bitj is the bit we would like to transmit, bitj ∈ {0, 1} and δP P M is the additional time shift used for the pulse position modulation. The time hopping code cj is a number from a sequence Cn that defines the position of the chip into the frame. Usually cj is chosen relative to the length of only one frame so cj ∈
n0, 1, . . . ,jTTf
c
k− 1o.
Note that different users are using different time hopping codes, which gives multi- ple access ability and resistance to interference. One refers to orthogonal time hopping code when the time hopping codes of different synchronized users are such that the pulses of the different users are received in different slots: so there are no overlapping pulses and no interferences between them.
In this generation scheme we have assumed that we transmit only one bit per frame for a given user. An entire symbol could be spread into multiple frames, upon a redundancy code included into [bitj]. Also, cj could be cyclic, random, or repetitive on some portions and cyclic at the same time. On the other hand, the data bitj could be coded using some sophisticated methods or simply coded by repetition. w(t) is usually (but not necessary) considered as the second derivative of the Gaussian pulse, therefore
w(t) =
"
1 − 4πt τ
2#
· exp
"
−2π
t τ
2#
. (2.2)
Note that the pulse to be transmitted is considered to be the Gaussian pulse and the passive components from the system of two antennas are considered to generate a second derivative operation. Therefore, w(t) already incorporates the effect of the two antennas (i.e., one at the transmitter side and one an the receiver side) [70]. This pulse it is also called "Scholtz’s pulse" [180] after the name of the one who used it for the first time in UWB communications. For this special type of pulse, the length of the pulse Tp = 2τ.
Usually Tp ≤ Tc for orthogonality reasons, and in many systems Tc is chosen equal to Tp (i.e., Tc = Tp).
2.1 Introduction on IR-UWB Signal
2.1.2 PAM-TH-UWB
The signal sent in Pulse Amplitude Modulation Time Hopping Ultra Wide Band (PAM-TH-UWB) may be written as
x(t) = +∞X
j=−∞
(2 · bitj − 1) · w(t − jTf − cjTc). (2.3) PAM-TH-UWB is a hybrid modulation using both the properties of PAM and TH. The code cj gives the time hopping [38, 39] property but the data information is contained in the amplitude of the signal. Again, different users are using different time hopping codes [109].
2.1.3 DS-UWB
Pulse Amplitude Modulation Direct Sequence UWB (PAM-DS-UWB) or simply called DS-UWB can be schematized as
x(t) =
+∞
X
j=−∞
(2 · bitj− 1)
Nh−1
X
i=0
biw(t − jTf − iTc), (2.4) where we suppose we send one bit bitj per one frame Tf, which is composed of Nh
slots. In this description, the code bi ∈ {−1, +1} and it comes from a binary spreading sequence Bn. Different users are using different spreading sequences. Note that in the expression (2.4), w(t) is present on each chip from the frame (and not one per frame).
The inconvenience for this method is that the multi-path performance is degraded due to inter chip interference (ICI) and inter symbol interference (ISI). Since the pulse positions are fixed in frames, if one pulse was interfered with another pulse, the subsequent pulses will be interfered too and this may cause the error bits burst. In [3], a hybrid DS-TH-UWB scheme that uses both direct sequence and time hopping codes has been proposed.
2.1.4 Generalized PAM-PPM
Generalized PAM-PPM [11] is a form of representation of both PAM and PPM techniques and the generalized signal expression is
x(t) = +∞X
j=−∞
(2 · bitP AMj − 1) · bj· w(t − jTf − cjTc− bitP P Mj δP P M), (2.5)
where
– bitP AMj = bitj and bitP P Mj = 0 for all j if the signal is PAM or
– bitP P Mj = bitj and bitP AMj = 1 for all j if the signal is PPM.
2.2 System Model
In equation (2.5) we have used a scrambling sequence bj with its values belonging to the set {−1, +1} [49, 184]. The symbol is transmitted over Ns frames of duration Tf and each frame is decomposed into Nh slots (i.e., chips) of duration Tc. Note that the symbol period Ts = NsTf = NsNhTc.
If we consider that the length of the code defines one symbol or that the code is cyclic with the period Ts, the representation becomes
x(t) = +∞X
j=−∞
(2 · bitP AMj − 1)
NS−1
X
i=0
bj· w(t − jTs− iTf − ciTc− bitP P Mj δP P M). (2.6) In literature there are several other modulation techniques for example Pulse Or- der Time-Hopping Multiple Access ultra wide band (PO-THMA UWB) (a technique using Hermite polynomial MHP pulses [96]), or On-Off Keying (OOK), but all these techniques used for Impulse Radio are somewhat similar because all of them use pulses to transmit and share the same signal characteristics.
2.1.5 Useful Physical Quantities for Impulse Radio
If we transmit a single pulse w(t) in a frame Tf, then we can define the instanta- neous power pw(t), the peak power Ppeak, the average power Pavg and the energy of the pulse εpulse as follows:
pw(t) = |w(t)|2 (2.7)
Ppeak = max(pw(t)) = P0 (2.8)
Pavg = 1 Tf
Z Tf
0 pw(t)dt = εpulse
Tf
(2.9) εpulse = Pavg · Tf =Z Tf
0 pw(t)dt (2.10)
2.2 System Model
In Section 2.2 we present the Impulse Radio signal that we use (see Subsection 2.2.1), the channel model (see Subsection2.2.2), and the Impulse Radio receiver (see Subsection 2.2.5). The most common types of interference are briefly described in Subsection2.2.4. Please note that interference modeling it shall be presented in depth in Section 2.3.
2.2.1 Impulse Radio Transmitted Signal
We consider an Impulse Radio Time-Hopping Pulse Amplitude Modulation (bi- nary IR-TH-PAM) UWB system [11]; as presented before, the time is divided into frames, each frame is divided into Nh slots with Tc being the duration of a slot (the chip time interval), and a user sends one impulse per frame in a slot position given
2.2 System Model
by a pseudo-random time-hopping code. This impulse is repeated over Ns frames of duration Tf = NhTc each, therefore Ns is so-called the repetition factor.
To distinguish between users, we add the subscript k, so the time hopping code for the user k is represented by the sequence (ck,l)l∈Z whose elements belong to {0, . . . , Nh− 1}. There is a user-specific “scrambling code” bk,l with values belonging to the set {−1, 1} [49, 184]. Note that both codes bk,l and ck,l have to be known by the receiver when receiving signal from user k (see Fig. 2.1). The user k transmits the signal
xk(t) =
sεk
Ns +∞
X
m=−∞
ak,mpk,m(t − mNsTf) (2.11) with
pk,m(t) = XNs
n=1
bk,mNs+n· w(t − (n − 1)Tf − ck,mNs+nTc), (2.12) where ak,mis the mthsymbol’s information of the kthuser, bk,mNs+nis the randomizing code and εk is the average energy per sent symbol. w(t) is the unit-energy basic pulse waveform and is considered to be the second derivative of the Gaussian pulse, as defined in equation (2.2).
2.2.2 Channel Model
The signal xk(t) is transmitted through the physical channel hk(t) between the user k and the receiver. While in Subsection 2.2.2.1 we present the multi-path channel model, in Subsection 2.2.2.2 we present a simplified channel model for free-space propagation.
2.2.2.1 Multi-path Channel
We consider a frequency-selective channel of the form
hk(t) =L−1X
i=0
αk,iδ(t − iTw) (2.13)
where L is the maximum number of multi-path components in the system, and αk,iis the attenuation of the ith path. As expected, L is a function of the imposed Channel Model (CM), while LTw is equal to the maximum delay spread of the channel. In our simulations we have considered the IEEE CMs proposed by Foerster and Molisch [55, 57, 116], and we have considered CM1 (LOS), CM2 and CM3 (NLOS). These CMs are actually a modification of the Saleh-Valenzuela channel model described in [154] that takes into account the clustering phenomenon observed in several UWB channel measurements [107].
2.2.2.2 Single-path Channel
The single-path channel is a simplified channel model in which αk,i= 0 for every i 6= 0. A particular case of the single-path channel is the free-space propagation
2.2 System Model
channel where αk,0 = 1. The single-path and the free-space propagation channels are often used for theoretical derivations [179,180] to show the influence of various signal parameters. In the case of multi-path channel such analytical derivations would lead to complex formulas hardly readable and handleable.
2.2.3 Transmission Scheme and Received Signal
The classical transmission-reception chain is presented in Fig.2.1 [179,180]. The bits ∈ {0, 1} are transformed into polar values a, and after the repetition and multipli- cation with the scrambling code b (cf. equation (2.12)) each value is time shifted after a Time-Hopping Code (TH Code) and finally Pulse Amplitude Modulated (PAM) and sent. We assume that the receiver is perfectly synchronized with the first user and thus △1 = 0. As a consequence the received signal becomes
r(t) = r1(t) +XNu
k=2
rk(t − △k) + v(t) (2.14) where rk(t) = xk(t) ⋆ hk(t) takes into consideration the effect of the channel hk(t), with ’⋆’ denoting the convolution operation. v(t) is the additive white Gaussian noise (AWGN) and the delay △k accounts for the absence of synchronization between user k and user 1, or in other words for the timing offset between the user k and the receiver.
Figure 2.1 Classical Transmission Scheme
