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UNIVERSIDAD POLITÉCNICA DE MADRID
ESCUELA TÉCNICA SUPERIOR DE INGENIEROS DE
TELECOMUNICACIÓN
TESIS DOCTORAL
Sobre el Desarrollo de un Simulador Rápido para
los Sistemas TH-UWB
PHD THESIS
On the Development of a Very Fast Simulator for
TH-UWB Systems
Autora: MARINA MARJANOVIĆ
Director: DR. JOSÉ MANUEL PÁEZ BORRALLO
Madrid, Mayo de 2007
UNIVERSIDAD POLITÉCNICA DE MADRID
ESCUELA TÉCNICA SUPERIOR DE INGENIEROS DE
TELECOMUNICACIÓN
DEPARTAMENTO DE SEÑALES, SISTEMAS Y RADIOCOMUNICACIONES
TESIS DOCTORAL
Sobre el Desarrollo de un Simulador Rápido para
los Sistemas TH-UWB
Autora: MARINA MARJANOVIĆ
Director: DR. JOSÉ MANUEL PÁEZ BORRALLO
Madrid, Mayo de 2007
UNIVERSIDAD POLITÉCNICA DE MADRID
ESCUELA TÉCNICA SUPERIOR DE INGENIEROS DE
TELECOMUNICACIÓN
DEPARTAMENTO DE SEÑALES, SISTEMAS Y RADIOCOMUNICACIONES
TESIS DOCTORAL
Sobre el Desarrollo de un Simulador Rápido para
los Sistemas TH-UWB
Autora: MARINA MARJANOVIĆ
Director: DR. JOSÉ MANUEL PÁEZ BORRALLO
El tribunal nombrado para juzgar la tesis arriba indicada, compuesto de los siguientes Doctores:
Presidente: _______________________________________________________
Secretario: _______________________________________________________
Vocales: _______________________________________________________
_______________________________________________________
_______________________________________________________
Acuerdan otorgarle
Calificación ______________________________________________________
En Madrid, a de de 2007
UNIVERSIDAD POLITÉCNICA DE MADRID
ESCUELA TÉCNICA SUPERIOR DE INGENIEROS DE
TELECOMUNICACIÓN
DEPARTAMENTO DE SEÑALES, SISTEMAS Y RADIOCOMUNICACIONES
PHD THESIS
On the Development of a Very Fast Simulator for TH-UWB Systems
Author: MARINA MARJANOVIĆ
Adviser: DR. JOSÉ MANUEL PÁEZ BORRALLO
Madrid, May 2007
ACKNOWLEDGMENTS
I
Acknowledgments
There are a number of people who had a major influence in my life for the past
four years. Personally, I believe that they have brought out the best in me and also have
provided the financial and moral support, which played a significant role in my life.
First and foremost, I would like to thank to my supervisor Dr. José Manuel Páez
Borrallo. It was indeed a stroke of enormous good fortune that led me to work with him.
Although extremely busy, professor Páez always could find a time to help me think
about research from a wider perspective. For all his advices, constant encouragements,
giving me the chance to participate in various international conferences where I had met
many interesting people that also had influenced on my work. It has been my privilege
and honour to collaborate with Páez from his days as an energetic professor and director
of ETSIT to his new role as a vice dean of Technical University of Madrid.
Furthermore, I can not skip mentioning many thanks to Dr. Enrique Calleja and
Dr. Angel Álvarez who helped me to become the part of research group GAPS, made
my life in a new country much easier and introduced me to professor Páez.
I like to thank to Dr. Santiago Zazo Bello especially, for offering me good
advices throughout these years, and for getting me project that enable me to cover my
living expenses for the last year.
I am thankful to “Telefónica Móviles” for providing financial support by
granting me a scholarship during the first two and half years; and my sincere gratitude
to “CEDINT”, particularly to its director Ms. Asunción Santamaría for giving me the
chance to attend several international conferences.
I like to thank to Dr. Mariano García Otero for reviewing my first accepted
paper that gave me encouragement to go on. Additionally, I would like to thank to all
anonymous reviewers at conferences who have taken the time to review my work and
provided constructive criticisms and positive feedbacks which have certainly raised the
standard of my work.
I thank to Dr. Santiago Zazo Bello from UPM, to Dr. Javier Ramos López from
University ‘Rey Juan Carlos’ and to Dr. Rafael Pérez Jiménez from University ‘Las
ACKNOWLEDGMENTS
II
Palmas de Gran Canaria’ for their interest in my work and for accepting to be members
of my thesis committee.
Friends that I like to thank include people from GAPS, especially Alberto
Jiménez Pacheco, José Manuel Diaz and Galo Nuño Barrau. Alberto has been very
helpful giving me many fruitful comments and criticism on various versions of my
papers and programs. José Manuel contributed with many handful advices. Of course, I
am thankful to Galo for starting with a wonderful idea and leaving me a space to
continue with working in a very young, interesting and fertile area.
Thanks to my friends Milica, Shiki, Goga, Vlada, Mare, Mica, Marija, Sale,
Jelena Ristic, Jelena Urosevic, Zorana, Zarko, Vaske, Vule, Maja, Grabi, Kum and
Kuma, Sofia, Ful for supporting me during the years towards this dissertation.
I want to thank Mar Díaz Peñalver, Julian Ayuso, Dolores Ajates Abellán, and
Ana Nohales for helping me out with all the administrative issues.
Deepest gratitude should go to my parents and grandparents since they always
have loved me, believed in me, and encouraged me in my study.
Finally, my special thanks should go to Milosh who has been with me and has
been so supportive all these years. Without his love, presence beside me, his
encouragement, support, and technical guidance, this thesis would never have started or
ended.
RESUMEN
III
Resumen
Los impulsos de radio de banda ultra ancha y salto en el tiempo (IR-TH-UWB)
es una tecnología relativamente nueva que puede tener un fuerte impacto en el
rendimiento de las comunicaciones inalámbricas. Resistencia a la propagación multi-
trayecto, bajos niveles de potencia, elevada capacidad, coexistencia con otros sistemas,
capacidad de penetración en paredes, son algunas de las características que hacen que
este sistema sea muy atractivo para Comunicaciones Inalámbricas de corto alcance,
tales como Redes de Área Local inalámbricas (WLAN) y Redes de Área Personal
inalámbricas (WPAN). Esta tecnología hace uso de pulsos de muy corta duración para
transmitir grandes cantidades de datos digitales sobre un rango de frecuencias muy
amplio a muy bajos niveles de potencia. Desafortunadamente, para el procesamiento de
señales de banda ultra ancha, es necesaria una razón de muestreo extremadamente
grande. En una aproximación sencilla, con una razón de muestreo constante, la longitud
del array que contiene las muestras de bits, puede ser muy grande, dependiendo de la
relación entre el ciclo útil y la tasa binaria. Ya que este array tiene que pasar a través de
la cadena de bloques que modela el canal y la respuesta del receptor, es obvio que un
elevado número de convoluciones tienen que ser realizadas. Por lo tanto, aun en
ordenadores muy rápidos, el tiempo total de cómputo para estimar la BER puede ser
muy alto. Este hecho reduce considerablemente la eficiencia del simulador. Además,
como se menciona en esta tesis, aplicando descomposición de señal directa/ en
cuadratura a las señales de UWB, que es una técnica fundamental usada para acortar el
tiempo de simulación requerido, no es posible mitigar una elevada frecuencia de
muestreo.
En esta tesis, un sistema TH-UWB con modulación por posición de pulsos
(PPM) es simulado utilizando el simulador de sistema de alta velocidad, el cual
constituye una innovación de nuestro grupo de investigación. Este método aprovecha las
ventajas de algunas de las propiedades de estos tipos de sistemas para facilitar un
proceso rápido y directo que supere los diseños previos varios órdenes de magnitud,
RESUMEN
IV
independientemente de la razón de muestreo. Comparándolo con los simuladores
previos, la frecuencia de muestreo puede ser tan elevada como se necesite, ya que el
tiempo de simulación no depende de esta. La señal transmitida es almacenada en el
vector de forma de onda llamado Transmitted Distorted Received (TDR), por lo tanto,
no es necesario operar con las muestras de señal en cada simulación. La única influencia
de la razón de muestreo es en la longitud del vector de forma de onda TDR. La
complejidad del algoritmo es lineal con el número de usuarios, tramas, componentes
multitrayectos y ramas del receptor RAKE.
Para desarrollar el código de simulación, un paso importante en cada proceso de
simulación, es la definición de los atributos del dispositivo físico que afecta los
productos de simulación requeridos, esto es, la tasa de bits erróneos (BER). Uno de
estos atributos en sistemas IR-TH-UWB es la sincronización que produce la alineación
de los relojes de relojes en transmisión y en recepción, de manera tal que la información
puede ser intercambiada con exactitud. Particularmente con PPM, la sincronización es
esencial para la correcta demodulación de las señales recibidas, ya que la información es
portada en la posición que tienen los pulsos en el tiempo.
Otra tarea crítica para la operación satisfactoria de los sistemas de UWB es la
detección multi-usuario. Algunas publicaciones muestran que el receptor MMSE tiene
el mejor rendimiento en términos de SINR a expensas de una elevada complejidad de
cómputo, ya que requiere de la inversión de la matriz cada vez que la secuencia de
esparcimiento cambia. Por lo tanto, no existe mucha literatura relacionadas con estos
tópicos, especialmente en sistemas de UWB en la presencia de entornos reales con
multitrayecto.
Desafortunadamente, ya que la señal transmitida es almacenada en el vector de
forma de onda TDR, resulta difícil extraerla. Por lo tanto la implementación de aquellas
tareas (sincronización, estimación de canal y detección multi-usuario) podrían ser un
gran problema en la simulación del sistema.
Por lo tanto, la presente tesis se compone de dos partes. En la primera parte se
propone un sistema del tipo PPM IR-TH-UWB con un procedimiento de sincronización
conjunta de símbolo, trama y chip, en un entorno multitrayecto denso. Se asume que el
canal es estimado usando Modulación Asistida por Formas de onda Pilotos (PWAM) y
RESUMEN
V
dicha sincronización es lograda a partir de maximizar la energía del canal multitrayecto
estimado. Basado en este método para la sincronización en combinación con el método
PWAM para la estimación de canal, las operaciones FFT que son usadas en muchos
trabajos, son evitadas y el algoritmo presenta muy baja complejidad. Adicionalmente y
con la finalidad de incrementar aun más la velocidad del proceso de simulación, este
método es implementado en un algoritmo de ensanchamiento temporal. Por lo tanto, los
algoritmos que esta tesis propone, puede relacionarse con canales con un gran numero
de taps que son difíciles de estimar usando los algoritmos existentes. Gracias a esta
aproximación, una baja complejidad para la implementación en tiempo real y un buen
rendimiento en términos de BER contra relación señal a ruido (SNR) es obtenido. Las
simulaciones muestran que estos sistemas sincronizados contribuyan a mitigar los
efectos del corrimiento temporal.
En la segunda parte de la tesis, el receptor MMSE para sistemas IR-TH-UWB
usando un simulador de sistema de alta velocidad, es simulado. La implementación de
cualquier detector multi-usuario fue también una tarea difícil (como lo fue para la
sincronización) ya que una señal transmitida es ‘rechazada’ en los TDR y no existe una
estructura multi-usuario típica con matriz de correlación. Por lo tanto, aplicando este
método en esta tesis, es lograda una nueva aproximación de una detección multi-
usuario. Ya que la forma de onda es almacenada en los TDR, no es necesario operar con
las muestras de señal en cada simulación. Por lo tanto, la matriz de correlación tiene que
ser recalculada solamente cuando las condiciones del canal cambian. Dependiendo del
tiempo de coherencia del canal y de la tasa binaria, es posible encontrar el número de
bits que pueden ser simulados sin alterar la matriz de correlación. La única influencia de
la razón de muestreo es en la longitud de los TDR. Los resultados derivados demuestran
que este efecto es despreciable. Por consiguiente, puede ser considerado que la
velocidad de simulación es aproximadamente independiente de la razón de muestreo.
Ventajas adicionales de esta aproximación es que la complejidad del algoritmo es lineal
con el número de usuarios, las tramas, las componentes multitrayecto y las ramas del
receptor RAKE.
Además, con esta aproximación, es posible reducir el proceso de simulación
significativamente, evitando cualquiera operación de convolución que representa el
RESUMEN
VI
mayor consumo de tiempo. Basados en esta aproximación, un número de operaciones de
simulación necesarias para evaluar la matriz de recepción MMSE son reducidas. Por lo
tanto, es posible procesar un gran número de muestras y estimar exactamente bajos
valores de BER en un corto tiempo. Además, se deriva una fórmula teórica del
rendimiento del detector MMSE para PPM IR-TH-UWB basados en esta nueva
aproximación. Esta fórmula es validada a partir de la comparación de los resultados con
otros obtenidos en investigaciones previas.
Ambas tareas, sincronización y la nueva aproximación de detección multiusuario
propuestas en esta tesis, aportan una buena realización en términos de baja complejidad,
procesamiento rápido y un adecuado comportamiento de la BER en función de la
relación señal a ruido (SNR).
Todos los resultados son evaluados usando el algoritmo propuesto y las
simulaciones son facilitadas para validar esta implementación. Estas demuestran que el
tiempo de simulación crece linealmente con el número de usuarios y el número de
tramas. El principal logro de esta tesis es un algoritmo para el cálculo de un sistema
completo PPM IR-TH-UWB cuya complejidad es Nh veces inferior comparado con
resultados previos, donde Nh es un número de chips en aquellos sistemas. Por lo tanto,
asumiendo un factor de esparcimiento grande de las señales de UWB, este algoritmo
consigue salvar un elevado tiempo de cómputo comparado con los diseños previos.
Esta tesis está constituida por seis capítulos. En el primer capítulo se ofrece una
panorámica de los fundamentos de los sistemas de UWB y dentro de este, algunos
tópicos incluyen: historia de UWB, características y aplicaciones de estos sistemas.
En el segundo capítulo se incluye el diseño de un sistema de acceso múltiple
UWB, incluyendo el diseño de un transmisor es revisado. Este capítulo presenta el
modelo completo del sistema y el convenio de notaciones empleadas a lo largo de la
tesis.
También en el segundo capítulo se incluyen dos modelos estadísticos para
canales de UWB son presentados, basados en datos reunidos a partir de medidas
extensivas de la propagación UWB. Saleh-Valenzuela y basado en Saleh-Valenzuela,
modelo propuesto por Intel que será empleado con estos propósitos en la tesis, será
descrito.
RESUMEN
VII
En adición, se proporciona una descripción de una estructura receptora de simple
usuario y multiusuario, asumiendo una sincronización y una estimación de la canal
perfecta que constituyen la contribución de esta tesis.
El capítulo cuatro cubre las siguientes tareas:
• Diferencias entre UWB y sistemas tradicionales de banda estrecha y dificultades
en el desarrollo del modelo.
• Una breve revisión de los fundamentos de las metodologías de simulación.
• Un nuevo simulador del sistema IR-TH-UWB que constituye un aporte de
nuestro grupo de investigación y que será utilizado en interés de esta tesis.
El capítulo cinco presenta la segunda parte de la contribución de esta tesis donde
he implementado un receptor RAKE MMSE para sistemas de UWB usando un nuevo
simulador de sistema de salto en tiempo, logrando una novedosa aproximación de
detector multiusuario (MUD). Adicionalmente, es presentada una nueva fórmula teórica
del rendimiento del detector MMSE para PPM IR-TH-UWB basado en esta nueva
aproximación y en investigaciones previas es presentado.
El capítulo seis presenta resultados de las simulaciones para verificar este
acercamiento.
ABSTRACT
IX
Abstract
Impulse Radio-Time Hopping-Ultra Wideband (IR-TH-UWB) is a relatively
new technology that might have a big effect on improving wireless communication.
Multipath resistance, low power, high capacity, coexistence with other systems, ability
of penetrating walls are some of the characteristics that make this system very attractive
for a Short Range Wireless Communications, such as deployed in Wireless Local Area
Network (WLAN) and Wireless Personal Area Network (WPAN). This technology uses
short pulses in order to transmit large amounts of digital data over a wide spectrum of
frequency bands with a very low power. Unfortunately, in order to process ultra-
wideband signals, an extremely large sampling rate is mandatory. In a straightforward
approach, with the constant sampling rate, the length of the array that contains the bit
samples can be very large, depending on the relationship between the duty cycle and the
bit rate. Since this array should pass through the chain of blocks that model the channel
and receiver responses, it is obvious that a large number of convolutions should be
done. Thus, even in very fast workstations, the total computing time in order to estimate
BER can be very high. This fact significantly reduces the efficiency of the simulator.
Furthermore, as mentioned in this thesis, applying direct/quadrature signal
decomposition to UWB signals, which is fundamental technique used to shorten the
required simulation runtime, it is not possible to mitigate a large sampling frequency. In this thesis, a complete Pulse Position Modulation (PPM) TH-UWB system is
simulated using the high-speed system simulator, which is the innovation of our
research group. This method takes advantage of some of the properties of this kind of
systems in order to provide a very straightforward and fast processing that improves all
the previous designs several orders of magnitude, independently on the sampling rate.
Comparing to previous simulators, sampling frequency can be as high as needed, since
the simulation run-time does not depend on it. Transmitted signal is stored in the
Transmitted Distorted Received (TDR) waveform vector, thus it is not necessary to
operate with the signal samples in every simulation. The only influence of the sampling
ABSTRACT
X
rate is on the length of the TDR waveform vector. The algorithm complexity is linear
with the number of users, frames, multipath components, and rake fingers.
In order to develop the simulation code, an important step in every simulation
process is definition of the attributes of the physical device that affect the required
simulation products, i.e. Bit Error Rate (BER). One of those attributes in IR-TH-UWB
systems is synchronization that produces alignment of transmitter and receiver clocks,
so information can be accurately exchanged. Particularly with PPM, synchronization is
essential to correct demodulation of the received signals because information is
conveyed in the time position of the pulse.
Another critical task for successful operation of UWB systems is a multiuser
detection. Some papers show that MMSE receiver has the best performance in terms of
SINR at the expense of high computational complexity since it requires the matrix
inversion every time the spreading sequence changes. Thus, there are no many
literatures dealing with this topic, especially not in UWB systems in the presence of real
multipath environment.
Unfortunately, since the transmitted signal is stored in the TDR waveform
vector, it is very difficult to extract it. Thus, implementation of those tasks
(synchronization, channel estimation and multiuser detection) might be a big problem
for system simulation.
Therefore, this thesis has two main parts. In the first part of the thesis, a joint
symbol, frame and chip synchronization method for PPM IR-TH-UWB system in the
presence of dense multipath environment is proposed. It is assumed that the channel is
estimated using Pilot Waveform Assisted Modulation (PWAM), and that
synchronization is achieved by maximizing the energy of the estimated multipath
channel. Based on this method for synchronization in combination with PWAM method
for channel estimation, FFT operations that are used in many works are avoided and the
algorithm has a very low complexity. Additionally, in order to even more increase the
speed of simulation process; this method is implemented in the enhanced time
algorithm. Therefore, algorithm that this thesis proposes can deal with channels with a
large number of taps that are difficult to estimate using the existing algorithms. Thanks
to this approach, low complexity for real time implementation and the good
ABSTRACT
XI
performance in terms of BER versus Signal to Noise Ratio (SNR) are achieved.
Simulation shows that this synchronization system helps to mitigate the negative effects
of timing offset.
In the second part of the thesis, MMSE receiver for PPM IR-TH-UWB systems
using a high-speed system simulator is implemented. Implementation of any multiuser
detector in this algorithm was also a difficult task (as was for synchronization), since a
transmitted signal is ‘hidden’ in TDR and a typical multiuser structure with a correlation
matrix does not exist. Therefore, applying this method, in this thesis, a new approach of
multiuser detection is achieved. Since the transmitted waveform is stored in the TDR, it
is not necessary to operate with the signal samples in every simulation. Thus,
correlation matrix should be recalculated only when the channel conditions change.
Depending on the channel coherence time and the bit rate, it is possible to find the
number of bits that can be simulated without alerting the correlation matrix. The only
influence of the sampling rate is the length of the TDR. Derived results show that this
effect is disregarded. Therefore, it can be considered that the simulation speed is
approximately independent on the sampling rate. Additional advantage of this approach
is that the complexity of the algorithm is linear with the number of users, frames,
multipath components, and RAKE fingers.
Furthermore, with this approach, it is possible to reduce the simulation process
significantly by avoiding any convolution operation, which is the most time-consuming.
Relaying on this approach, number of simulation operations needed to evaluate MMSE
receiver matrix are reduced. Thus, it is possible to process a large number of samples
and to estimate accurately low BER in a short time application. In addition, I derived a
theoretical formula of the performance of the MMSE detector for PPM IR-TH-UWB
based on this new approach. This new formula is validated by comparing results to
some other results based on some previous researches.
Both tasks, synchronization and the new approach of multiuser detection
proposed in this thesis, give a good performance in terms of low complexity, fast
processing and BER versus Signal to Noise Ratio (SNR) performance.
All results are evaluated using the proposed algorithm and simulations are
provided in order to validate this implementation. They demonstrate that the simulation
ABSTRACT
XII
time linearly grows with the number of users and the number of frames. The main gain
of this thesis is that the complexity of the algorithm in order to calculate the complete
PPM IR-TH-UWB system is Nh times lower comparing to previous methods, where Nh
is a number of chips in those systems. Therefore, assuming a large spreading factor of
the UWB signals, this algorithm yields a large saving of computational time comparing
to the previous designs.
With this accurate flexible simulation model; we might analyze the performance
of the TH-UWB system and the impact of different factors of TH-UWB systems (the
number of users, waveform design time-hopping codes, channel models, receivers…)
and achieve a low BER in a real time application even in the presence of reach multipath
environment.
This thesis consists on five chapters. In the first chapter of this thesis, the
fundamentals of UWB system are overviewed. Within the following sections, topics
covered are UWB history, features and applications of UWB system, types of UWB
signals, UWB spectrum and regulations and some of the possible problems of this
system.
The second chapter gives an overview of MA UWB system design, including a
transmitter design. Additionally, this chapter presents the overall system model and
notation convention that I have used throughout this thesis.
In addition, two statistical models for UWB channel are presented based on data
collected from extensive UWB propagation measurements. Saleh-Valenzuela and based
on Saleh-Valenzuela, model proposed by Intel that will be employed for the purposes of
this thesis are described. This channel model was made with one slight modification
since the observations have shown that the lognormal distribution better fits the
measurement data.
Additionally, the second chapter provides a description of a single user and
multiuser receiver structure, assuming perfect synchronization and perfect channel
estimation. As an optimum single user receiver, selective RAKE receiver is used for the
purposes of this thesis and as a multiuser receiver, MMSE RAKE is employed.
In addition, as a one part of the contribution of this thesis low complexity
method for synchronization is presented. With this approach, a low complexity for real
ABSTRACT
XIII
time implementation and the good performance in terms of BER versus SNR are
achieved.
Since the UWB system requires taking a second look at simulation
methodology, the chapter three covers the following tasks:
• Differences between UWB and traditional narrowband systems and difficulties
in model development
• A brief review of the fundamental simulation methodologies.
• New IR-TH-UWB system simulator that is the innovation of our research group
and will be used for the purposes of this thesis.
In Chapter four, I implemented a MMSE RAKE receiver for Ultra-Wideband
(UWB) system using a new time-hopping system simulator, achieving a novel approach
of MUD. With this approach, it is possible to reduce the simulation time significantly by
avoiding any convolution operation, which is the most time-consuming. Relaying on
this approach, number of simulation operations needed to evaluate MMSE receiver
matrix are reduced. Complexity of this algorithm is O(Nu*Nf*L*Lmax), while using
Monte Carlo method complexity is Nh times higher. Thus, for systems with a very large
spreading factor, as UWB is, this provides a large computational time saving.
Additionally, I have derived a theoretical formula of the performance of MMSE
RAKE receiver detector for PPM IR-TH-UWB based on this new approach and some
previous researches.
In chapter five, simulation results are provided in order to validate this approach.
And it is shown that is possible to achieve very low BER for a certain system loading in
a real time application.
XIV
TABLE OF CONTENTS
XV
Table of Contents
1. Summary............................................................................................................................. 31
1.1. Introduction.................................................................................................................. 31
1.2. UWB History ............................................................................................................... 32
1.3. Features and Applications of UWB............................................................................. 34
1.4. UWB Signal Definition ............................................................................................... 36
1.4.1. Types of UWB Signals ..................................................................................... 36
1.4.1.1. IR-UWB Versus MC-UWB ................................................................ 36
1.5. UWB Compatibility with Other Services .................................................................... 40
1.6. UWB Problems ............................................................................................................ 42
1.7. Conclusion ................................................................................................................... 43
2. UWB System Model........................................................................................................... 45
2.1. Introduction.................................................................................................................. 45
2.2. Multiple Access IR-UWB Signal Structure and Signal Model ................................... 46
2.2.1. Pulse Shapes ..................................................................................................... 47
2.2.2. Modulation Schemes ........................................................................................ 49
2.2.3. TH Sequences ................................................................................................... 50
2.3. The MC-UWB System Model ..................................................................................... 51
2.3.1. Overview of the MC-UWB System ................................................................. 51
2.3.2. OFDM UWB .................................................................................................... 52
2.4. UWB Multipath Channel ............................................................................................. 52
2.4.1. Introduction ...................................................................................................... 52
2.4.2. Saleh-Valenzuela Model .................................................................................. 53
2.4.2.1. Proposed Model Based on Intel Measurements .................................. 57
2.5. Single User Receiver Structure.................................................................................... 65
2.5.1. Introduction ...................................................................................................... 65
2.5.2. Selective RAKE Receiver ................................................................................ 66
2.5.2.1. Performance of a PPM TH-UWB System employing RAKE
Receiver ............................................................................................. 68
2.6. Multiuser Detection (MUD) Receivers........................................................................ 71
2.6.1. Performance of a PPM TH-UWB System employing MMSE RAKE
Receiver 74
2.6.2. Synchronization and Channel Estimation ........................................................ 75
2.6.3. Transmitted Reference UWB Receiver ............................................................ 77
2.6.4. Channel Estimation using Pilot Waveform Assisted Modulation
(PWAM)........................................................................................................... 79
TABLE OF CONTENTS
XVI
2.6.5. Synchronization................................................................................................ 82
2.6.6. Conclusion........................................................................................................ 84
3. The Slowness of Simulating TH-UWB System................................................................ 87
3.1. Introduction.................................................................................................................. 87
3.2. Differences between UWB and Traditional Narrowband Systems ............................. 88
3.2.1. Large Sampling Frequency............................................................................... 88
3.2.2. Difficulties in Model Development.................................................................. 91
3.3. A Brief Review of BER Estimation Techniques ......................................................... 92
3.3.1. Monte Carlo Simulation Techniques................................................................ 93
3.3.2. Importance Sampling Technique...................................................................... 94
3.3.3. Semi-Analytic Simulation Technique .............................................................. 96
3.4. High Speed System Simulator ..................................................................................... 98
3.4.1. Signal and noise separation. Signal processing................................................ 99
3.5. Conclusion ................................................................................................................. 105
4. A Novel Approach of Multiuser Signal Model for Simulation Purposes.................... 107
4.1. Introduction................................................................................................................ 107
4.2. A Novel Approach of Multiuser Signal Model for AWGN Channel ........................ 108
4.3. A Novel Approach of Multiuser Signal Model for Synchronous Channel................ 111
4.4. MMSE RAKE Receiver Implementation .................................................................. 112
4.5. Theoretical Performance of the MMSE Receiver-Based on the Novel Approach .... 116
4.6. Conclusion ................................................................................................................. 118
5. Simulation Results ........................................................................................................... 121
5.1. Introduction................................................................................................................ 121
5.2. Single User Receiver ................................................................................................. 122
5.2.1. Number of Users Influence on BER Performance in AWGN Channel.......... 122
5.2.2. Number of Chips Influence on BER Performance in AWGN Channel.......... 123
5.2.3. Type of the Monocycle Influence on BER Performance in AWGN
Channel 124
5.2.4. Sampling Frequency Influence on BER Performance in AWGN Channel .... 125
5.2.5. Influence of Different Parameters on BER Performance in the Multipath
Channel 126
5.2.6. Synchronization and Channel Estimation ...................................................... 127
5.3. Time Performance and Complexities of the algorithm.............................................. 132
5.4. Multiuser Receiver..................................................................................................... 134
5.4.1. Number of Users Influence on BER Performance in the AWGN Channel
Employing MMSE RAKE Receiver .............................................................. 135
5.4.2. Number of Chips Influence on BER Performance in AWGN Channel
employing MMSE Receiver ........................................................................... 136
TABLE OF CONTENTS
XVII
5.4.3. Sampling Frequency Influence on BER Performance in AWGN Channel
employing MMSE Receiver ........................................................................... 137
5.4.4. Number of Users Influence on the BER Performance in the Channel2
Employing MMSE RAKE Receiver .............................................................. 138
5.4.5. Number of Chips Influence on BER Performance in the Channel2
Employing MMSE RAKE Receiver .............................................................. 139
5.4.6. Sampling Frequency Influence on BER Performance in the Channel 2
employing MMSE Receiver ........................................................................... 140
5.4.7. Number of Users Influence on BER Performance in the Channel 3
Employing MMSE RAKE Receiver .............................................................. 141
5.4.8. Number of Chips Influence on BER Performance in the Channel 3
Employing MMSE RAKE Receiver .............................................................. 142
5.4.9. Number of RAKE Fingers Influence on BER Performance in the
Channel 2 Employing MMSE RAKE Receiver ............................................. 145
5.4.10. Effect of the Synchronization on BER Performance for a PPM-TH-UWB
System with MMSE Receiver in the presence of Channel 2.......................... 146
5.5. Time Performance and Complexities of the Algorithm............................................. 147
6. Conclusions....................................................................................................................... 153
6.1. Thesis Summary ........................................................................................................ 153
6.2. Summary of the Contributions................................................................................... 155
6.3. Future Research ......................................................................................................... 158
XVIII
ABBREVATIONS
XIX
Abbreviations
AGN Additive Gaussian Noise
AWGN Additive White Gaussian Noise
BEP Bit Error Probability
BER Bit Error Rate
DS Direct Sequence
FCC Federal Communications Commission
FH Frequency Hopping
FT Fourier Transform
GPS Global Positioning System
GSM Global System for Mobile
LAN Local Area Network
LPD/I Low Probability of Detection/Interception
MAC Medium Access Control
MC Multi Carrier
MMSE Minimum Mean Square Error
MRC Maximum Ratio Combining
MSE Mean Square Error
MUD Multi-User Detection
MUI Multiuser Interference
(N)LOS (Non) Line Of Sight
OFDM Orthogonal Frequency Division Multiplexing
OMAN Open Mobile Access Network
PAM Pulse Amplitude Modulation
PDF Probability Distribution Function
PPM Pulse Position Modulation
PSD Power Spectral Density
PWAM Pilot Waveform Assisted Modulation
ABBREVIATIONS
XX
RF Radio Frequency
QoS Quality of Service
SINR Signal-to-Noise-plus-Interference-Ratio
SNR Signal-to-Noise-Ratio
SS Spread Spectrum
SUD Single-User Detection
TDMA Time Division Multiple Access
TDR Transmitted-Distorted-Received
TEM Transverse Electromagnetic
TH Time Hopping
TR Transmitted Reference
UAV Unmanned Aerial Vehicle
UGV Unmanned Ground Vehicle
UMTS Universal Mobile Telecommunication System
UWB Ultra-Wideband
WAN Wide Area Network
WLAN Wireless Local Area Network
WPAN Wireless Personal Area Network
WSN Wireless Sensor Network
LIST OF FIGURES
XXI
List of Figures
Figure 1.1 Comparison of the Fractional Bandwidth of a Narrowband and Ultra
Wideband Communication System ..............................................................37
Figure 1.2. Spectrum of a Gaussian Monocycle- Based Impulse UWB Signal
(Data taken from [48])..................................................................................38
Figure 1.3. Spectrum of an OFDM based MC-UWB Signal (Data taken from [48]) ....39
Figure 1.4. UWB Spectral Mask and FCC Part 15 Limits. (Data taken from [49]).......40
Figure 1.5. WPAN, WLAN, and Cellular Networks: Typical Link Ranges. (Data
taken from [49])............................................................................................41
Figure 2.1. Frame Structure for TH Signals ...................................................................46
Figure 2.2. Example UWB Pulses ..................................................................................47
Figure 2.3. PSD of the Different UWB Pulses ...............................................................48
Figure 2.4. Example of a PPM Modulate UWB Signal Using the Data Sequence
1 -1 ............................................................................................................50
Figure 2.5. Example of a PAM Modulate UWB Signal Using the Data Sequence
1 -1 ............................................................................................................51
Figure 2.6. Channel Impulse Response ..........................................................................55
Figure 2.7. Exponential Decay of Mean Cluster Power and Ray Power Within
clusters (taken from [76]) .............................................................................56
LIST OF FIGURES
XXII
Figure 2.8. One LOS Channel Realization Generated From Intel Model Using the
Same Parameter as the Ones in Table 2.2. (Experimental Data taken
from [76]) .....................................................................................................61
Figure 2.9. One NLOS Channel Realization Generated from Intel Model Using
the Same Parameter as the Ones in Table 3.3. (Experimental data taken
from [76]) .....................................................................................................62
Figure 2.10. RAKE Receiver Structure Scheme ............................................................67
Figure 2.11 Histogram of the distribution of the MUI for a PPM TH-UWB system
with Tc=1 ns, Nh= 1024 slots, Nu=900 links, λ = 180 ps, Nf =64 and no
multipath. The number of simulations is 330.503. It can be noticed the
Gaussian distribution of the interference. (Data taken from [83]) ...............69
Figure 2.12. Theoretical BER Performance versus SNR of a PPM TH-UWB
System Downlink Employing RAKE Receiver in a Multipath Channel;
L=100, Nf=64; Nh=128..................................................................................70
Figure 2.13. Theoretical BER Performance of a PPM TH-UWB System
Employing RAKE Receiver vs. BER Performance of a PPM TH-UWB
System Employing MMSE Receiver in AWGN Channel; Nf=8; Nh=4;
Nu=5..............................................................................................................75
Figure 2.14. Block Scheme of the Receiver (with Channel Estimation and Joint
Synchronization)...........................................................................................77
Figure 2.15. Illustration of the Transmitted Reference System......................................78
Figure 2.16. Illustration of the PWAM Scheme.............................................................79
Figure 2.17. Pilot Based Receiver ..................................................................................82
LIST OF FIGURES
XXIII
Figure 2.18. Timing Offset Presentation ........................................................................84
Figure 3.1. Wideband Signal Spectrum..........................................................................90
Figure 3.2. Schematic Representation of Implementation of Monte Carlo Method ......94
Figure 3.3. Importance Sampling Illustration.................................................................95
Figure 3.4. Diagram of a Semi-Analytic BER Calculation for BPSK............................97
Figure 3.5. Conceptual Model of the UWB Receiver for the qth
User .........................103
Figure 3.6. Signal Processing Flowchart ......................................................................104
Figure 4.1. Signal Processing Flowchart (as in [83]) ...................................................112
Figure 4.2. Error Vector Calculation Flowchart...........................................................114
Figure 4.3. Simulator Flowchart...................................................................................115
Figure 4.4. Position Vector Calculation Flowchart ......................................................116
Figure 4.5.Comparison Between the Theoretical and Results Obtained with New
Approach for AWGN and NLOS Channel; Γ =16 γ =8.5, 1/ Λ =11 ns,
1/ λ =0.35 ns, L=400, Lmax=400;Nu=5; Nf=8; Nh=4 ....................................118
Figure 5.1. Number of Users Influence on BER performance employing Single
User Receiver; Second Derivative of the Gaussian Monopulse; AWGN
channel ; Nf=32, Nh=64, fs=200/Tc.............................................................122
Figure 5.2. Number of Chips Influence on BER performance employing Single
User Receiver; Second Derivative of the Gaussian Monopulse; AWGN
channel; Nu=64, Nf=64, fs=200/Tc,..............................................................123
Figure 5.3. Monocycle Shape Influence on BER performance employing Single
User Receiver; AWGN channel ; Nu=64, Nh=64, Nf=8, fs=200/Tc, ............124
LIST OF FIGURES
XXIV
Figure 5.4. Sampling Frequency Influence on BER performance employing Single
User Receiver; Second Derivative of the Gaussian Monopulse; AWGN
channel; Nu=64, Nh=64, Nf=8, Nh=4 ...........................................................125
Figure 5.5. BER performance employing Single User Receiver; Second Derivative
of the Gaussian Monopulse; Multipath Channel L=400, Nu=2, Nh=64,
Nf=32, fs=200/Tc..........................................................................................126
Figure 5.6. UWB Downlink System Model .................................................................127
Figure 5.7. UWB Uplink System Model ......................................................................127
Figure 5.8. Channel Estimation Performance in the PPM TH-UWB System
Downlink employing RAKE Receiver in NLOS Multipath Channel
based on Intel Measurements from Figure 3.4; Lmax=18, Nu=13, Nf=32,
Nh=128, fs=200/Tc, Perfect Synchronization .............................................128
Figure 5.9. Channel Estimation Performance in the PPM TH-UWB System
Uplink employing RAKE Receiver in NLOS Multipath Channel from
Figure 3.4 based on Intel Measurements; Nu=13, Nf=32, Nh=128,
fs=200/Tc, Perfect Synchronization.............................................................129
Figure 5.10. BER Performance versus SNR of a PPM TH-UWB System Downlink
employing RAKE Receiver in NLOS Multipath Channel from Figure
3.4 based on Intel Measurements; Lmax=18, Nu=13, Nf=32, Nh=128,
Np=10000, fs=200/Tc ...................................................................................130
Figure 5.11. BER Performance versus SNR of a PPM TH-UWB System Uplink
Employing RAKE Receiver in a NLOS Multipath Channel from
LIST OF FIGURES
XXV
Figure3.4 based on Intel Measurements; Nu=13, Nf=32, Nh=128,
Np=10000, fs=200/Tc ...................................................................................131
Figure 5.12. Relation between the Sampling Frequency and the Simulation Time
per Bit for a PPM-TH-UWB System with PWAM assuming
Synchronization; SNR=5dB, Np=1, fs=200/Tc.............................................132
Figure 5.13. Effect of the Number of Multipath Components on the Simulation
Time per Bit for a PPM-TH-UWB System with PWAM assuming
Perfect Synchronization; SNR=5dB, Np=1, fs=200/Tc ................................133
Figure 5.14.Comparison Between Results from [85] and Results Obtained with a
New Approach; L=1 (AWGN); Nu=5, Nf=8, Nh=4, fs=200/Tc ....................134
Figure 5.15. Effect of the Number of Users on BER Performance for a PPM-TH-
UWB System with MMSE Receiver; Nh=4, Nf=8, Tc=2 ns, fs=200/Tc,
L=1 .............................................................................................................135
Figure 5.16. Effect of the Number of Chips on BER Performance for a PPM-TH-
UWB System with MMSE Receiver; Nu=5, Nf=8, Tc=2 ns, fs=200/Tc,
L=1 .............................................................................................................136
Figure 5.17. Sampling Frequency Influence on BER performance employing
MMSE Receiver; Second Derivative of the Gaussian Monopulse;
AWGN channel; Nu=64, Nh=64, Nf=8, Nh=4..............................................137
Figure 5.18. Effect of the Number of Users on BER Performance for a PPM-TH-
UWB System with MMSE Receiver; Nh=4, Nf=8, Tc=2 ns, fs=200/Tc,
Γ =16, γ =8.5, 1/ Λ =11 ns, 1/ λ =0.35 ns, L=400, Lmax=400
(Channel2) ..................................................................................................138
LIST OF FIGURES
XXVI
Figure 5.19. Effect of the Number of Chips on the BER Performance for a PPM-
TH-UWB System with MMSE Receiver; Nu=5, Nf=8, Tc=2 ns,
fs=200/Tc, Γ =16, γ =8.5, 1/ Λ =11 ns, 1/ λ =0.35 ns, L=400, Lmax=400
(Channel2) ..................................................................................................139
Figure 5.20. Sampling Frequency Influence on BER performance employing
MMSE RAKE Receiver; Second Derivative of the Gaussian
Monopulse; Channel 2; Nu=5, Nh=4, Nf=8 .................................................140
Figure 5.21. Effect of the Number of Users on BER Performance for a PPM-TH-
UWB System with MMSE Receiver; Nh=4, Nf=8, Tc=2 ns, fs=200/Tc,
Γ =33, γ =5, 1/ Λ =2 ns, 1/ λ =0. 5 ns, L=400, Lmax=400 (Channel3)........141
Figure 5.22. Effect of the Number of Chips on BER Performance for a PPM-TH-
UWB System with MMSE Receiver with Nh=4, Nf=8, Tc=2 ns,
fs=200/Tc, Γ =33, γ =5, 1/ Λ =2 ns, 1/ λ =0. 5 ns, L=400, Lmax=400
(Channel3) ..................................................................................................142
Figure 5.23. Effect of the Number of Users on the BER Performance for a PPM-
TH-UWB System with MMSE Receiver in the presence of AWGN
channel vs. BER Performance for a PPM-TH-UWB System in the
presence of Channel 2; Nh=8, Nf=8, Tc=2 ns, fs=200/Tc, L=400,
Lmax=400 .....................................................................................................143
Figure 5.24. Effect of the Number of Chips on BER Performance for a PPM-TH-
UWB System with MMSE Receiver in the presence of AWGN
channel vs. BER Performance for a PPM-TH-UWB System with
LIST OF FIGURES
XXVII
MMSE Receiver in the presence of Channel 2; Nu=8, Nf=8, Tc=2 ns,
fs=200/Tc, L=400, Lmax=400........................................................................144
Figure 5.25. Effect of the Number of RAKE Fingers on BER Performance for a
PPM-TH-UWB System with MMSE Receiver in the presence of
Channel 2; Nu=8, Nf=8, Nh=4, Tc=2 ns, fs=200/Tc, L=400..........................145
Figure 5.26. Effect of the Synchronization on BER Performance for a PPM-TH-
UWB System with MMSE Receiver in the presence of Multipath
Channel (Channel2) Nu=13, Nf=8, Nh=8, Tc=2 ns, fs=200/Tc, L=400,
Lmax=400. ....................................................................................................147
Figure 5.27. Relation between the Sampling Frequency and the Simulation Time
per Bit for a PPM-TH-UWB System employing MMSE RAKE
Receiver; Nu=5, Tc=2 ns, fs=200/Tc, Nf=8, Nh =4, L=400, Lmax=100...........148
Figure 5.28. Effect of the Number of Users on the Simulation Time per Bit for a
PPM-TH- UWB System employing MMSE RAKE Receiver; Tc=2 ns,
fs=200/Tc, Nf=8 Nh=4, L=400, Lmax=100......................................................149
Figure 5.29. Effect of the Number of Multipath Components on the Simulation
time per Bit for a PPM-TH- UWB System with MMSE Receiver;
Nu=5, Tc=2 ns, fs=200/Tc, Nf=8, Nh =4, Lmax=L............................................149
Figure 5.30. Effect of the Number of Frames on the Simulation Time per Bit for a
PPM-TH- UWB System with MMSE Receiver; Nu=5, Tc=2 ns,
fs=200/Tc, Nh =4, L=400, Lmax=100. ............................................................150
Figure 5.31. MMSE Matrix Calculation Flowchart using our Algorithm vs.
MMSE Matrix Calculation Flowchart using Monte Carlo Method. ..........150
LIST OF FIGURES
XXVIII
Figure 6.1. Conceptual Model of the UWB Signal Generation....................................157
Figure 6.2. Conceptual Model of the UWB Receiver for the qth
User .........................158
Figure 6.3 Optimum Combining UWB RAKE Receiver for IR-TH-UWB.................161
Figure 6.4. Error Vector Calculation Flowchart when Optimum RAKE Receiver
is employed.................................................................................................161
LIST OF TABLES
XXIX
List of Tables
Table 2.3. Simulated and Measured Results for NLOS UWB Channels Using
Intel’s Model. Simulation Results are Generated from Intel Model with
Γ=16 ns, γ=8.5 ns, Λ=1/11 ns, λ=1/0.35 ns, σ =4.8 dB. (Experimental
data taken from [76]) ....................................................................................61
Table 2.4. Example Multipath Channel Characteristics and Corresponding Model
Parameters (Experimental data taken from [76]). ........................................63
Table 5.1 Channel Estimation Performance in the PPM TH-UWB System
Downlink employing RAKE Receiver in NLOS Multipath Channel
based on Intel Measurements from Figure 3.4; Lmax=18, Nu=13, Nf=32,
Nh=128, fs=200/Tc, Perfect Synchronization .............................................128
Table 5.2 Channel Estimation Performance in the PPM TH-UWB System Uplink
employing RAKE Receiver in NLOS Multipath Channel from Figure
3.4 based on Intel Measurements; Nu=13, Nf=32, Nh=128, Perfect
Synchronization ..........................................................................................129
Table 5.3. BER Performance versus SNR of a PPM TH-UWB System Downlink
employing RAKE Receiver in NLOS Multipath Channel from Figure
3.4 based on Intel Measurements; L=400; Lmax=18; Nu=13; Nf=32;
Nh=128; Np=10000......................................................................................130
Table 5.4. BER Performance versus SNR of a PPM TH-UWB System Uplink
employing RAKE Receiver in NLOS Multipath Channel from Figure
LIST OF TABLES
XXX
3.4 based on Intel Measurements; Lmax=18, Nu=13, Nf=32, Nh=128,
Np=10000, fs=200/Tc ...................................................................................131
Table 5.5. Comparison of the Algorithms Complexities..............................................133
Table 5.6 Comparisons of the Algorithms Complexities in Single User Receiver ......151
Table 5.7 Comparisons of the Algorithms Complexities in Multiuser Receiver .........152
CHAPTER 1 SUMMARY
31
Chapter 1
1. Summary
1.1. Introduction
Ultra wideband (UWB) communication systems can be broadly classified as any
communication systems whose instantaneous bandwidth is many times greater than the
minimum required to deliver particular information. This large bandwidth is the
defining characteristic of those systems.
Within the past 40 years, advances in analog and digital electronics and UWB
signal theory have enabled system designers to propose some practical UWB
communications system. Over the past decade, many individuals and corporations
began asking the FCC for permission to operate unlicensed UWB system concurrent
with existing narrowband signals. In 2002, FCC decided to change the rules to allow
UWB system operation in a broad range of frequencies. In some of the FCC UWB rule-
making process proceedings, one of them can find a vast array of claims relating to the
expected utility and performance of UWB systems, some of them almost perfect.
Testing by the FCC, FAA, and DARPA has uniformly shown that UWB still conforms
to Maxwell’s Equations and the laws of physics.
It is a relatively new technology that might have a big effect on improving
wireless communications. Multipath resistance, low power, high capacity, coexistence
with other systems, ability of penetrating walls are some of the characteristics that make
this system very attractive for a Short Range Wireless Communications, such as
deployed in WLAN and WPAN [1]-[3]. This technology uses short pulses in order to
transmit large amounts of digital data over a wide spectrum of frequency bands with a
very low power [4].
SUMMARY CHAPTER 1
32
In this chapter, the fundamentals of UWB system are overviewed. Within the
following sections, topics covered are UWB history, features and applications of UWB
system, types of UWB signals, UWB spectrum and regulations and some of the possible
problems of this system.
1.2. UWB History
There is a comprehensive bibliography about the origins of the UWB technology
as in [5]-[34]. Dr. Henning F. Harmuth gave a descriptive history of no sinusoidal
electromagnetic technologies in [13]-[19]. In his work, it was found that in late 1950's,
there was a first effort made by Lincoln Laboratory and Sperry to develop phased array
radar system.
The analysis started in attempting to understand the wideband properties of the
needed network. The four-port interconnection of quarter wave TEM mode lines was
analysed.
The impulse response of these networks was a train of weighted and equally
spaced impulses, thus the response resembled what one would find at the output of a
sampled data system. About the same time, Schmidt and RWP King were measuring the
impulse response of the dipole and resonant ring radiating elements in the time domain.
The response in the far field and the driving ports was approximately a train of
uniformly spaced impulses that was well correlated with the work of Hallen. Dr. Hallen
found in the frequency domain that this class of radiating element had a periodic
amplitude spectrum. This fact made clear that working in the time domain, was correct
for analysis and provided a challenge. With the help of Dr. Barney Oliver at Hewlett
Packard, who had just developed the sampling oscilloscope, and the generation of very
short pulses using avalanche transistors and tunnel diodes, the UWB technology started
to evaluate. The former Sperry Research Centre Sudbury then continued the work, in
1965 where this writer formed a group of very talented engineers to help with the
further development of this technology. Dr. J. Lamar Allen expanded the analysis of
linear and non-reciprocal microwave networks and antennas to ferrite devices. Dr.
CHAPTER 1 SUMMARY
33
Harry Cronson later extended the work to time domain metrology where the frequency
domain properties of passive microwave networks were found via their impulse
response and Fourier transforms (FT). Both the US Air Force at Rome Labs and the US
Army in Huntsville, Alabama supported this work. At this time, Drs. David Lamensdorf
and Leon Susman started the analysis of antennas using time domain techniques.
The final task that needed to be developed before real system development
began was the threshold receiver. In the early 1970's both avalanche transistor and
tunnel diode detectors were constructed in an attempt to detect these very short duration
signals. Dr. A. Murray Nicolson of the tunnel diode constant false alarm rate receiver
improved this work in the development. This improved version of this receiver detector
is still in use today. With all the system blocks in place, a short-range radar sensor was
developed as a pre-collision sensor for the airbag and used later in cars (1972). The
range of this sensor was about 8 feet. Later improvements in power generation
techniques resulted in a space docking radar (25-30 feet) and an aircraft runway traffic
sensor with a range of 300 feet. Many systems that require different range requirements
were developed, including a new class of altimeters. In the metrology area (1970-1980),
this writer together with Dr. Nicolson developed a narrow base band pulse fixture to
measure the properties of microwave absorbing materials directly from a single pulse
measurement. Most of the development of those stealthy materials done at Wright
Patterson AFB used this approach until the Hewlett Packard network analyzer became
available. This was used to develop an anti-collision system for unmanned vehicles in
work and later this technique was expanded to measure liquid levels in a tank.
Work in radar continued in the 1990's with the development of synchronized
arrays of short pulse sources. Peak powers in the order of 100 kW (peak base band
power) were achieved using low cost sources designed to radiate and scan in space
microwave pulse packets having pulse durations on the order of 1-3 ns. These systems
were used for the detection applications.
In 1978, efforts turned toward the communication of these signals. Voice signals
were transmitted reliably over hundreds of feet without the need for synchronization and
demonstrated to the government. In 1979, data signals were communicated over much
SUMMARY CHAPTER 1
34
greater ranges using the 19 kHz sub carrier from classical music frequency modulated
stations in urban areas.
During the period 1984-1994, the work in communications was considerably
expanded working together with Dr. Robert J. Fontana.
Until now, over 200 papers were published in accredited IEEE journals and
more than 100 patents were issued on topics related to ultra wideband technology. Due
to the reach area of applications, the business interests for UWB technology are growing
exponentially.
1.3. Features and Applications of UWB
Since the duration of used monopulses is extremely short, there are many
features of the UWB system, summarized as follows:
• High data rate performance
This is important for communications where UWB pulses can be used to provide
extremely high data rate performance in multi-user network applications.
• Fine range resolution and precision distance
This fact allows quality for radar applications [35], [36].
• Multipath resistance
Consequently, UWB systems are well suited for high-speed, mobile wireless
applications. Multipath cancellation occurs when a strong reflected wave arrives
out of phase with the direct path signal, producing a reduced amplitude response
in the receiver. With very short pulses, the direct path has come and gone before
the reflected path arrives avoiding the cancellation. In addition, implementation
of the RAKE receiver improves multipath resistance [36], [38].
• Low interference with other systems
This fact is significant for both military and commercial applications, since this
low energy density translates into a low probability of detection (LPD) RF
signature. An LPD signature is of particular interest for military applications
(e.g., for covert communications and radar); however, an LPD signature also
CHAPTER 1 SUMMARY
35
produces minimal interference to proximity systems and minimal RF health
hazards as it was shown in [39], [40].
• Low system complexity and low cost
UWB systems can be made nearly "all-digital", with minimal RF or microwave
electronics. Due to the inherent RF simplicity of UWB designs, these systems
are highly frequency adaptive, enabling them to be positioned anywhere within
the RF spectrum. According to [39], this feature avoids interference to existing
services, while fully utilizing the available spectrum.
• The UWB system always occupies a wide bandwidth (order of GHz)This
insures a high capacity multiple access and ultra high-speed transmission (<
Several hundreds of Mbps). According to the classification of [41], applications
of the UWB system can be divided on military and civil. In the military and
government marketplace, these applications include:
• Tactical Handheld & Network LPI/D Radios
• Non-LOS LPI/D Ground wave Communications
• LPI/D Altimeter/Obstacle Avoidance Radar
• Tags (facility and personal security, logistics)
• Intrusion Detection Radars
• Precision Geolocation Systems
• Unmanned Aerial Vehicle (UAV) and Unmanned Ground Vehicle (UGV)
• Data links
• LPI/D Wireless Intercom Systems
While civil applications include:
• High Speed (20+ Mb/s) LAN/WANs
• Altimeter/Obstacle Avoidance Radars (commercial aviation) Collision
Avoidance Sensors
• Tags (Intelligent Transportation Systems, Electronic Signs)
• Intrusion Detection Radars
• Precision Geolocation Systems
• Industrial RF Monitoring Systems
SUMMARY CHAPTER 1
36
As for the commercial marketplace, however, there are currently no "approved"
applications within the United States, since the frequency approval for UWB operation
has yet to be acted upon by the Federal Communications Commission (FCC).
1.4. UWB Signal Definition
In order to define an UWB signal, the following definition for the fractional
bandwidth is employed:
2 H Lf
H L
f fB
f f
−=
+
(1.1)
where L
f and H
f represent the lower and upper frequencies (3 dB points) of the signal
spectrum, respectively. Thus, as it was defined in [41] and [42], UWB signals are
signals that have a fractional bandwidth greater than 25% in contrast to narrowband
signals with fractional bandwidth less than 1%. Figure 1.1 presents the comparison of
the Fractional Bandwidth of a Narrowband and Ultra wideband communications
systems.
1.4.1. Types of UWB Signals
There are two forms of UWB. First is IR-UWB, based on transmitting
information sending a very short duration pulses and the second is MC-UWB, based on
using multiple simultaneous carriers.
1.4.1.1. IR-UWB Versus MC-UWB
The relative advantages and disadvantages of those two types of signal are
controversial issues and have been discussed extensively in the standards bodies.
CHAPTER 1 SUMMARY
37
One of the issues is minimizing interference transmitted by, and received by the
UWB system. In MC-UWB it is possible to choose carrier frequencies to avoid
narrowband interference or from narrowband system. Therefore, it might be considered
Figure 1.1 Comparison of the Fractional Bandwidth of a Narrowband and Ultra
Wideband Communication System
that MC-UWB is well suited for avoiding interference. The most common form of
multicarrier modulation, OFDM, has become the leading modulation for high data rate
systems.
In addition, MC-UWB vs. IR-UWB is more flexible and scalable, but requires
an extra layer of control in the physical layer. However, for both types of UWB signals,
IR-UWB and MC-UWB spread spectrum techniques can be applied in order to reduce
the impact of interference of UWB system.
SUMMARY CHAPTER 1
38
IR-UWB signals need fast switching time for the transmitter and receiver and
very high precise synchronization between them. Since IR-UWB has a high
instantaneous power during the very short interval of the pulse, it can better avoid
interference to UWB systems, but, on the other hand, this high instantaneous power
increases the possibility of interference from UWB to narrowband systems. In addition,
IR-UWB are very low-cost systems since they can be made nearly "all-digital", with
minimal RF or microwave electronics.
Figure 1.2. Spectrum of a Gaussian Monocycle- Based Impulse UWB Signal (Data
taken from [48])
On the other hand, MC-UWB systems have a number of advantages over their
single carrier counterparts [44], [45]. They include better spectrum utilization and
CHAPTER 1 SUMMARY
39
therefore higher bit communications. In addition, MC-UWB has simpler channel
synchronizations, which leads to low-cost transceiver implementation and has the
continuous variations in power over a very wide bandwidth. Therefore, implementing a
MC-UWB front end can be challenging. This might be particularly challenging for the
power amplifier. UWB-OFDM is a novel MC-UWB system that uses a frequency
hopping scheme for reliable high bit rate communication over multi-path fading
channels [46]. The main advantage of UWB-OFDM system over normal OFDM is its
fine time resolution and ability to resolve multipath. Changing a frequency selective to
several parallel flat fading channels, OFDM system has not such high multipath
resistance [47].
Figure 1.2 and Figure 1.3 illustrates a comparison of the spectrum of IR-UWB
and MC-UWB, respectively.
Figure 1.3. Spectrum of an OFDM based MC-UWB Signal (Data taken from [48])
SUMMARY CHAPTER 1
40
1.5. UWB Compatibility with Other Services
UWB technology offers simultaneously high data rate communication and high
accuracy positioning capabilities as it was mentioned before. These systems can utilize
low transmitted signal power level with extremely wide bandwidth. Due to the very low
PSD, UWB systems can co-exist with the other radio systems.
The FCC recently approved the deployment of UWB on an unlicensed basis in
the 3.1–10.6 GHz band [49]. The essence of this ruling is to limit the PSD measured in a
MHz bandwidth. UWB spectral mask and FCC part 15 limits are shown in Figure 1.4.
Figure 1.4. UWB Spectral Mask and FCC Part 15 Limits. (Data taken from [49])
The spectral mask allows UWB enabled devices to overlay existing systems
while ensuring sufficient attenuation to limit adjacent channel interference. Additional
PSD limits have been placed below 2 GHz to protect critical applications such as GPS.
CHAPTER 1 SUMMARY
41
The first consequence of this spectral mask imposed by the FCC is to express the use of
base band pulse shapes without additional transmit filtering.
Figure 1.5. WPAN, WLAN, and Cellular Networks: Typical Link Ranges. (Data taken
from [49])
In summary, UWB communications are allowed at a very low average transmit
power compared to more conventional (narrowband) systems that effectively restricts
UWB to short ranges [50]. UWB is thus, a candidate physical layer mechanism for
IEEE 802.15 WPAN for short-range high-rate connectivity that complements other
wireless technologies in terms of link ranges. Typical Link Ranges limits of WPAN,
WLAN, and Cellular Networks is shown in Figure 1.5. One of the main problems,
according to the compatibility, is interference caused by UWB signals to other various
radio systems, as well as the performance degradation of UWB systems in the presence
of narrowband interference and pulsed jamming. An UWB system suffers most from
PAN LAN WAN
Short-Range
Range
0-10m 0-100m 0-1
km
Short-Range
SUMMARY CHAPTER 1
42
narrowband systems if the narrowband interference and the nominal centre frequency of
the UWB signal are overlapping. This is proved in [41] by BER simulations in an
AWGN channel with interference at global system for GSM and UMTS/WCDMA
frequencies. In the in-band interference study, the victim radio systems are
UMTS/WCDMA, GSM900, and GPS. It is shown that better results are achieved with
proper selection of UWB pulse waveform and their width for spectral planning. Using
short pulses, interference in the observed frequency bands is the smallest if the pulse
waveform is based on higher order Gaussian waveforms.
When the UWB system degradation is studied in the presence of an interfering
and jamming radio system, results show that the system performance suffers most if the
interference and the nominal centre frequency of the UWB system are overlapping.
Thus, the UWB performance depends on the pulse waveform and on the pulse width. It
is shown that for high data rates, short pulses should be used. Additionally, it is shown
that the third derivative of the Gaussian pulse performs better than the first derivative.
On the other hand, if the data rate demands are not so high, and long pulses can be used,
then lower order waveforms perform better.
1.6. UWB Problems
As with any technology, there are always applications that may be better served
by other approaches. Therefore, there are still some problems related to UWB systems.
• In order to process ultra-wideband signals, it is necessary to have an
extremely large sampling rate.
As it was mentioned in the abstract, in a straightforward approach, with the constant
sampling rate, the length of the array that contains the bit samples can be very large,
depending on the relationship between the duty cycle and a bit rate. Since this array
should pass through the chain of blocks that model the channel and receiver responses,
it is obvious that a large number of convolutions should be done. Thus, even in very fast
workstations, the total computing time in order to estimate BER can be very high. This
fact significantly reduces the efficiency of the simulator. Furthermore, as mentioned in
CHAPTER 1 SUMMARY
43
this thesis, applying direct/quadrature signal decomposition to UWB signals, which is
fundamental technique used to shorten the required simulation runtime, it is not possible
to mitigate a large sampling frequency.
According to [41] UWB disadvantages are:
• Potential interference by transmissions with other licensed bands in the
frequency domain due to the wideband nature of the emissions
UWB is an RF wireless technology, and as such is still subject to the same laws of
physics as every other RF technology. Thus, there are obvious tradeoffs to be made in
SNR versus bandwidth, range versus peak and average power levels, etc.
• Need for further standards participation to develop approaches for
coexistence within operational scenarios important for the industry
• The existing cellular and personal communications services will probably
not be replaced due to the inability over long distances
As with any technology, there are always applications that may be better served by
other approaches. For example, for extremely high data rate (10’s of Gigabits/second
and higher), point-to-point or point-to-multipoint applications, it is difficult today for
UWB systems to compete with high capacity optical fibre or optical wireless
communications systems. Of course, the high cost associated with optical fibre
installation and the inability of an optical wireless signal to penetrate a wall,
dramatically limits the applicability of optically based systems for in-home or in-
building applications. In addition, optical wireless systems have extremely precise
pointing requirements, obviating their use in mobile environments. However, UWB
could provide a complementary bandwidth option inside buildings and homes.
1.7. Conclusion
The first mentioned problem for designing UWB systems, i.e. mandatory large
sampling rate, was used for the further development of this thesis where a complete
Pulse Position Modulation (PPM) TH-UWB system is simulated using the very high-
speed system simulator. This method takes advantage of some of the properties of TH-
UWB systems in order to improve all previous designs several orders of magnitude,
SUMMARY CHAPTER 1
44
independently on the sampling rate. Comparing to previous simulators, sampling
frequency can be as high as needed, since the simulation run-time in order to calculate
BER curve does not depend on it. Transmitted signal is stored in the Transmitted
Distorted Received (TDR) waveform vector; therefore it is not necessary to operate with
the signal samples in every simulation. The only influence of the sampling rate is on the
length of the TDR waveform vector. Relying on this approach, the complexity of the
algorithm needed to evaluate the TH-UWB system is reduced. Additionally, the
algorithm complexity is linear with the number of users, frames, multipath components,
and RAKE fingers. Thus, it is possible to process a large number of samples and to
accurately estimate low BER in a short time application.
CHAPTER 2 UWB SYSTEM MODEL
45
Chapter 2
2. UWB System Model
2.1. Introduction
In order to design a real TH-UWB system, many aspects should be taken into
careful consideration, such as modulation schemes, waveforms design, time-hopping
codes, receiver architecture, decision schemes, or channel models.
This chapter gives an overview of MA TH-IR-UWB system design and notation
convention that I will use throughout this thesis, including a transmitter design; two
statistical models for UWB channel are presented based on data collected from
extensive UWB propagation measurements. Saleh-Valenzuela and based on Saleh-
Valenzuela, model proposed by Intel that will be employed for the purposes of this
thesis.
This chapter provides a description of a single user and multiuser receiver
structure, assuming perfect synchronization and perfect channel estimation. As an
optimum single user receiver, selective RAKE receiver is used for the purposes of this
thesis.
In addition, as a one part of the contribution of this thesis low complexity
method for synchronization is presented. Thanks to this approach, a low complexity for
real time implementation and the good performance in terms of BER versus Signal to
Noise Ratio (SNR) are achieved.
UWB SYSTEM MODEL CHAPTER 2
46
2.2. Multiple Access IR-UWB Signal Structure and Signal Model
In this thesis is considered the MA TH-IR-UWB system composed by Nu
different links (corresponding to different real users or links).The transmitted signal in
one direction of one of the links consists of a series of pulses whose frame structure can
be seen in Figure 2.1. A single bit is subdivided in Nf frames, each of them with period
Tf. Each of the frames is composed of Nh chips of duration Tc. In one of the chips the
monocycle ( )tr
w t is transmitted (one monocycle per chip), whose position (the number
of the chip) is given by a pseudorandom TH sequence.
Figure 2.1. Frame Structure for TH Signals
According to [55], the transmitted signal through the kth
link might be expressed as
( ) ( ) ( )( ) ( ) ( )k k k
j tr f j c j
j
s t A t w t jT c T d λ
∞
=−∞
= − − −∑ (2.1)
The meaning of the terms is explained in the following points:
CHAPTER 2 UWB SYSTEM MODEL
47
2.2.1. Pulse Shapes
( )tr
w t represents the transmitted monocycle with duration Tp<<Tf. Some possible
waveforms for the UWB monocycle have been proposed in [56] and [57], such as first,
second and third derivatives of the Gaussian, Laplacian, rectangle or even one period of
a sine wave pulse. However, ( )tr
w t can be baseband, as proposed in [4], high pass or
modulated, to comply with FCC regulation. In Figure 2.2 and Figure 2.3 are shown
simple, first, second and third derivatives of the Gaussian pulse and they frequency
spectrum, respectively.
Figure 2.2. Example UWB Pulses
UWB SYSTEM MODEL CHAPTER 2
48
Figure 2.3. PSD of the Different UWB Pulses
Specifically in this thesis, the pulse choice for the UWB signal is a baseband
pulse that is shaped as the second derivative of the Gaussian pulse defined as
224 ( / )
( ) (1 ( / ) ) exp23
tr
tw t t
σσ
σ π
= − −
(2.2)
The factor 4
3σ π
ensures that the signal is normalized to have the unit energy, i.e., it
is considered
( 1)
2
( 1)
2 ( ) ( ) ( )
0
( )
( ) 1,
f
f
f
f
j T
tr
jT
j T
k k k
tr f j c j
jT
w t dt
w t jT c T d dt
+
+
=
− − − − =
∫
∫ λ τ
(2.3)
for j=1, 2…, Nf and k=1, 2,…, Nu.
CHAPTER 2 UWB SYSTEM MODEL
49
The scale factorσ determines the effective time width of the pulse shape and
will be considered as Tc/11, resulting in an effective width of the order of one
nanosecond.
2.2.2. Modulation Schemes
IR-UWB systems might have two modulation schemes, either PPM or PAM.
The transmitted signal in the case of PAM is represented by
( ) ( )( ) ( ) ( )k k
j tr f j c
j
s t A t w t jT c T∞
=−∞
= − −∑ (2.4)
where
• ( ) ( )k
j jA d t= for k=1, 2… Nu, represents the amplitude of the jth
pulse, which is
dependent on the data ( ) ( )k
jd t and the specific modulation scheme.
The transmitted signal in the case of PPM is represented by
( ) ( ) ( )( ) ( )k k k
j tr f j c j
j
s t A w t jT c T d λ
∞
=−∞
= − − −∑ (2.5)
where
• ( ) 0,1k
jd ∈ represents a sequence of time-shifts in a PPM modulation. In [58] is
presented a complete analysis of an UWB system based on M-ary PPM
modulation, where M different time shifts are applied to the signals. However,
even with the advantages derived of the use of modulation with M bigger than
two, the receiver complexity to handle the severe timing requirements can make it
completely unsuitable in the practice. This could be the reason why most of the
work regarding UWB considers just a binary PPM modulation. Therefore, the
choice for this thesis is also a binary PPM modulation, i.e. M=2. Additionally, the
symbols are scaled by the constant amplitude A, where 2A is the energy per
UWB SYSTEM MODEL CHAPTER 2
50
symbol. For the purposes of this thesis, it is considered that every user in the
system has equal power, i.e. ( )kA A= for k=1, 2… Nu.. Figure 2.4 and Figure 2.5
illustrates an example of PPM modulated UWB signal and PAM modulated UWB
signal using the data sequence 1 -1, respectively.
• λ represents a delay constant in the PPM modulation. In this paper, it is assumed
that constant λ is adequately taken, i.e. ( )tr
w t
and ( )tr
w t λ− are orthogonal
monopulses [55].
2.2.3. TH Sequences
( ) 0,1,..., 1k
j hc N∈ −
represents a TH code, where Nh is the integer number
that denotes the position within the frame where the monocycle should be transmitted in
order to mitigate MUI. In Figure 2.1 is shown an example when two users are active and
(1)
1c = 1, (1)
2c =Nf, (2)
1c =2 and (2)
2c =1. In [59]an algorithm to easy design these sequences
can be founded, and in [60]and [61], there are complete analyses of the influence of the
codes on the PSD of the signal. For the purposes of this work, pseudorandom TH codes
are used.
Figure 2.4. Example of a PPM Modulate UWB Signal Using the Data Sequence
1 -1
CHAPTER 2 UWB SYSTEM MODEL
51
Figure 2.5. Example of a PAM Modulate UWB Signal Using the Data Sequence
1 -1
2.3. The MC-UWB System Model
2.3.1. Overview of the MC-UWB System
Although MC-UWB system will not be considered in this thesis, in this section a
brief overview of MC-UWB and its special case OFDM UWB will be given.
MC-UWB has produced many research interests in the last years. The
transmitted MC-UWB signal has the following complex baseband form:
0
1
( ) ( ) exp( 2 ( ))S
r
n tr p p
c s
s t A b w t rT j nf t rTπ
=
= − −∑∑
(2.6)
where N represents the number of subcarriers, r
nb represents the symbol that is
transmitted in the rth
transmission interval over the nth
subcarrier. A is a constant that is
in charge of controlling the transmitted PSD and determines the energy per bit.
0
1
p
fT
= represents the fundamental frequency.
UWB SYSTEM MODEL CHAPTER 2
52
2.3.2. OFDM UWB
Multi-band OFDM as a standard system has been proposed for WPAN physical
layer in [62]. It is a promising technology for UWB transmission because it represents a
special case of MC transmission that permits subcarriers to overlap in frequency without
mutual interference. Therefore, the hence spectral efficiency is increased. Allocating
each user a group of subcarriers, multiple users might be supported. OFDM-UWB uses
a frequency coded pulse train as a shaping signal.
The frequency coded pulse train is defined as
1
( ) ( ) exp( 2 ( ) / )N
tr c
n
w t s t nT j c n Tπ
=
= − −∑ (2.7)
where s(t) represents an elementary pulse with unit energy and duration Ts<T, and wtr(t)
has duration Tp=NT. Each pulse is modulated with a frequency ( )
n
c
c nf
T= where c(n) is
a permutation of the integers 1,2,…,N. In [48] is shown that the set
0( ) ( )exp( 2 )k tr
p t w t j kf tπ= is orthogonal for k=1, 2… N.
2.4. UWB Multipath Channel
2.4.1. Introduction
Key to wireless receiver design is a channel knowledge that is often obtained via
estimation [63]-[70]. Usually it is necessary to take accurate measurements of the
channel prior to develop a complete mathematical channel model as in [71]-[76]. The
development of channel models for UWB communication systems requires extensive
data on UWB signal propagation. Both experimental and simulation techniques can be
used to investigate the propagation of UWB signals in indoor and indoor-outdoor
environments. The advantage of experimental techniques is that all system and channel
affecting the propagation are accounted for without presumptions. Unfortunately, those
methods are usually expensive; consume a lot of time, and limited by the characteristics
CHAPTER 2 UWB MULTIPATH CHANNEL
53
of available equipment, such as bandwidth, sensitivity, attenuation and the dispersion of
the connecting cables. On the other hand, less time consuming and cheaper simulation
techniques are free from the limitations of experimental approaches. The accuracy of
simulation results depends on the amount of details included in the simulation model.
However, more details require more complex computer programs. Therefore, a
compromise between the required accuracy and the available computational resources
should be done in designing simulators for UWB communication systems.
In narrowband wireless communication systems, the information signal
modulates a very high frequency sinusoidal carrier. Therefore, along each propagation
path the signal suffers very little distortion because the system elements, i.e. antennas,
reflecting walls, diffracting object in the channel have essentially constant
electromagnetic properties over the narrow bandwidth of the radiated signal. The only
signal degradation is provoked by multipath components. On the other hand, in UWB
systems, the information signal might be distorted due to the transmitting/receiving
antennas not meeting the necessary bandwidth requirements, and also due to the
dispersive behaviour of building materials in the propagation channel. Although
multipath components are also present in UWB channels, unlike narrowband signals,
UWB signals do not suffer fading due to the destructive interference of multipath
components.
In this section, two statistical models for UWB channel are presented based on
data collected from extensive UWB propagation measurements. Saleh-Valenzuela and
based on Saleh-Valenzuela, model proposed by Intel that will be employed for the
purposes of this thesis are described.
2.4.2. Saleh-Valenzuela Model
A common model for the urban, indoor and radio channel environment was the
model introduced in [71]. That was a clustering model, known as Saleh-Valenzuela.
This model was based upon observations from experimental data where it was noted
that rays tended to arrive in closely spaced groups, or in clusters. It was concluded that
the inter-arrival times of the rays within a cluster are exponentially distributed and the
UWB MULTIPATH CHANNEL CHAPTER 2
54
inter-arrival times of the clusters have Poisson distribution. The amplitude of each ray
can be either positive or negative with Rayleigh distribution and a mean square value
that decays with increasing ray and cluster arrival time. The mathematical expression
for this model is
, ,
0 0
( ) ( )k l l k l
l k
h t t Tα δ τ
∞ ∞
= =
= − −∑∑ (2.8)
where
lT represents the delay of the l
th cluster, while lk ,τ represents the delay of the k
th
multipath component relative to the lth
cluster arrival time lT .
By definition, 0,l lTτ = . The distribution of cluster arrival time and the ray arrival time
are given by
1( )
1( ) , 0l lT T
l lf T T e l−−Λ −
−= Λ > (2.9)
, , 1( )
1( ) , 0k l k l
l lf e kλ τ τ
τ τ λ−
− −
−= > (2.10)
Channel impulse response is shown in Figure 2.6 and the double exponential
model in Figure 3.2.
CHAPTER 2 UWB MULTIPATH CHANNEL
55
Figure 2.6. Channel Impulse Response
lk ,α represents the amplitude of the kth
multipath component of the lth
cluster.
This variable is the product of an equally likely random 1± and the Rayleigh random
variablekl
β , which has the mean square variable defined as
, //2 2
, 0,0( ) ( ) k llT
k lE E e eτ γ
β β−− Γ
= (2.11)
2
0,0( )E β represents the mean square value of the first ray of the first cluster,
determined by the path loss between the transmitter and receiver. The distance between
transmitter and receiver is denoted with d. In order to compute 0,0τ and 0,0β , the distance
between transmitter and receiver d should be given, or due to the periodic nature of the
signal 0,0τ is uniformly distributed between 0 andc f
N T .
UWB MULTIPATH CHANNEL CHAPTER 2
56
Figure 2.7. Exponential Decay of Mean Cluster Power and Ray Power Within
clusters (taken from [76])
According to [72], path loss might be presented as
( ) ( ) 0 10 0 ( )( ) ( ) 10 ( / )dB dB dB
P d P d d dβ ε= − + (2.12)
where β represents the path loss exponent, 2β = . It determines the rate at which the
received signal amplitude in free space decreases with distance. The path loss exponent
was determined in [74] to be approximately 1.75. In majority of the papers in a dealing
with a channel modelling, is adopted that the typically reference distance in indoor
environment is 0d =1m. ( )dB
ε represents a zero mean, Gaussian random variable (in dB)
that represents measurement error in the path loss and arises due to the shadowing.
CHAPTER 2 UWB MULTIPATH CHANNEL
57
2.4.2.1. Proposed Model Based on Intel Measurements
Based on this clustering phenomenon observed in the measurements, in [76] is
proposed UWB channel model derived from the Saleh-Valenuela model. This channel
model was made with one slight modification since the observations have shown that
the lognormal distribution better fits the measurement data. Thus, the multipath model
consists on the following, discrete time impulse response:
, ,
0 0
( ) ( )L K
k l l k l
l k
h t t Tα δ τ
= =
= − −∑∑ (2.13)
where as in Saleh- Valenzuela model
lk ,α represents the multipath gain coefficient,
lT represents the delay of the lth
cluster, and
lk ,τ represents the delay of the kth
multipath component relative to the lth
cluster
arrival time lT
lk ,α might be ether real or complex (with a magnitude and phase term)
Some considerations are following:
1. If real coefficients are adopted, then the channel coefficients could be defined as
, , ,k l k l k lpα β=
(2.14)
where
lkp , is equally likely +1 or -1, and
lk ,β is the lognormal fading term
The term lkp , is used to account for the random pulse inversion that can occur
due to reflections, as observed in the measurements. Then, the real impulse
response of the channel could be convolved with the real UWB transmitted
waveform.
UWB MULTIPATH CHANNEL CHAPTER 2
58
2. If complex coefficients were adopted, the complex, baseband channel model
would need to be convolved with the complex, baseband representation of the
transmitted waveform. For UWB pulsed systems, the meaning of phase are bit
ambiguous since it is not necessarily carrier based. The phase is directly related
to delay for a given centre frequency. Since the distribution of the phase term is
not characterized, it is suggested that a uniformly distributed phase in [ ]π2,0
could be an adequate model, based on Saleh-Valenzuela channel model.
In this case, the channel coefficients can be modelled as
,
, ,k lj
k l k leφ
α β−
= (2.15)
where
lk ,φ is the random phase term, uniformly distributed in [ ]π2,0 , and lk ,β is the
lognormal fading term.
3. Due to the simplicity of the real channel coefficients, and in order to avoid the
ambiguity of phase for an UWB waveform, it is assumed that
, , ,k l k l k lpα β= (2.16)
where lkp , and lk ,β have already been defined above.
This model uses the similar definitions as the Saleh-Valenzuela:
lT represents the arrival time of the first path of the lth
cluster,
τk,l represents the delay of the kth
path within the lth
cluster relative to the first
path arrival time lT ,
Λ represents the cluster arrival rate,
and λ represents the ray arrival rate, i.e. the arrival rate of path within each
cluster.
By definition, it is taken that 0,l lTτ = . The distribution of cluster arrival time and the ray
arrival time are given by:
1( )
1( ) , 0l lT T
l lf T T e l−−Λ −
−= Λ > (2.17)
CHAPTER 2 UWB MULTIPATH CHANNEL
59
, , 1( )
1( ) , 0k l k l
l lf e kλ τ τ
τ τ λ−
− −
−= >
(2.18)
The channel coefficients are defined as follows:
, , ,k l k l k lpα β=
(2.19)
where
),(Normal)(10log20 2
,, σµβ lklk ∝ , or equivalently 20/
, 10n
lk =β , ),Normal( 2σµ ln ∝ ,
, //
, 0[ ] k llT
k lE e eτ γ
β−Γ
= Ω
(2.20)
Tl represents the excess delay of bin l,
0Ω is the mean power of the first path of the first cluster,
lkp , is equal likely +1 or -1, and the parameter µl is given by
20
)10ln(
)10ln(
/10/10)ln(10 2,0 σγτ
µ −
−Γ−Ω
=lkl
l
T
(2.21)
The measurements from Intel include both LOS and NLOS channels with
antenna separation 1-20 meters. In the Table 3.1, the mean excess delay, rms delay, and
the mean path number generated by the model are presented. They well fit the
measurements including LOS and NLOS. Also from Table 2.2 and Table 3.3, it is
obviate that the model fit both mean excess delay and rms delay at the same time for
either LOS or NLOS channel.
UWB MULTIPATH CHANNEL CHAPTER 2
60
The results from the corresponding Figure 2.8 and Figure 3.4 to the Table 2.2 and Table
2.3 (respectively) show that the proposed model fits the measurements taken in the
home environment for both LOS and NLOS. Of course, this only represents a small set
of channel data, and other environments should be considered. Therefore, it was
estimated how the model could be adopted to represent other possible channel
conditions that might be appropriate for the consideration. As shown above, five key
parameters define the model:
Λ represents the cluster arrival rate,
λ represents the ray arrival rate, i.e., the arrival rate of the path within each cluster,
Γ represents the cluster decay factor,
γ represents the ray decay factor, and
σ represents the standard deviation of the lognormal fading term (dB).
Mean excess delay (ns) ( mτ ) 13.69
RMS delay (ns) ( rmsτ ) 13.80 Simulated
Mean NP10dB 33
Mean excess delay (ns) ( mτ ) 13.59
RMS delay (ns) ( rmsτ ) 12.94 Measured
Mean NP10dB 33
Mean excess delay (ns) ( mτ ) 4.70
RMS delay (ns) ( rmsτ ) 8.81 Simulated
Mean NP10dB 7
Mean excess delay (ns) ( mτ ) 4.01
RMS delay (ns) ( rmsτ ) 8.88 Measured
Mean NP10dB 7
Table 2.1.
Simulated and Measured Results for
Intel Model Evaluation using Intel’s
Results. Simulation Results are
Generated from Intel Model with
Γ=13 ns, γ=6 ns, Λ=1/13 ns,
λ=1/0.23 ns, σ =4.8 dB Both LOS
and NLOS Channels with Antenna
Table 2.2.
Simulated and Measured Results for
LOS UWB Channels using Intel’s
Model. Simulation Results are
Generated from Intel Model with
Γ=16 ns, γ=1.6 ns, Λ=1/60 ns,
λ=1/0.5 ns, σ =4.8 dB.
CHAPTER 2 UWB MULTIPATH CHANNEL
61
Figure 2.8. One LOS Channel Realization Generated From Intel Model Using the Same
Parameter as the Ones in Table 2.2. (Experimental Data taken from [76])
Mean excess delay (ns) ( mτ ) 17.22
RMS delay (ns) ( rmsτ ) 15.59 Simulated
Mean NP10dB 35
Mean excess delay (ns) ( mτ ) 17.36
RMS delay (ns) ( rmsτ ) 14.53 Measured
Mean NP10dB 35
Table 2.3. Simulated and Measured Results for NLOS UWB Channels Using Intel’s
Model. Simulation Results are Generated from Intel Model with Γ=16 ns, γ=8.5 ns,
Λ=1/11 ns, λ=1/0.35 ns, σ =4.8 dB. (Experimental data taken from [76])
UWB MULTIPATH CHANNEL CHAPTER 2
62
These model parameters were found using a brute force search to match different
channel characteristics, considering mean excess delay ( mτ ), RMS delay ( rmsτ ), and
number of significant paths that cross a 10 dB threshold (NP10dB).Table 2.4 provides
the results of this search.
Figure 2.9. One NLOS Channel Realization Generated from Intel Model Using the
Same Parameter as the Ones in Table 3.3. (Experimental data taken from [76])
The above channel characteristics were chosen since they seem to represent
reasonable extensions. For the purposes of this work parameters from Table 2.4 for
NLOS model from Intel measurements will be used.
The double-exponential decay model seems to provide enough degrees of
freedom to easily match the channel measurements, and can be used to match the NLOS
and LOS channel characteristics separately. Assuming there are Nu active users, the
CHAPTER 2 UWB MULTIPATH CHANNEL
63
transmitted signal of the kth
user through the multipath channel has the following
structure:
Channel Characteristics NLOS* NLOS# NLOS
#
LOS# LOS*
Mean excess delay (ns) ( mτ ) 17 22 27 3 4
RMS delay (ns) ( rmsτ ) 15 20 25 5 9
NP10dB 35 40 45 4 7
Model Parameters
Λ (1/ns) 1/11 1/14 1/15 1/22 1/60
λ (1/ns) 1/0.35 1/0.33 1/0.32 1/0.94 1/0.5
Γ 16 22 30 7.6 16
γ 8.5 10 10 0.94 1.6
σ (dB) 4.8 4.8 4.8 4.8 4.8
* Based on Intel measurements.
# Example of other possible channel characteristics to test
Table 2.4. Example Multipath Channel Characteristics and Corresponding Model
Parameters (Experimental data taken from [76]).
( ) ( )
1
( ) [ ( )* ( )] ( )uN
k k
k
r t s t h t n t=
= +∑ (2.22)
where * denotes convolution, ( ) ( )kh t is the normalized channel response from (2.13) for
the kth
user and ( )n t represents the AWGN with mean zero and a double-sided power
spectral density 2 / 2n
σ . The impulse response from the equation (2.13) can also be
presented as a single summation by one-to-one mapping of the amplitude coefficients
lk ,α into a new set of coefficientsl
β . In addition, the arrival time ,l k lT τ+
can be
UWB MULTIPATH CHANNEL CHAPTER 2
64
mapped into a new arrival timel
τ . Thus, channel response from (2.13) can be presented
as
0
( ) ( )l l
l
h t tβ δ τ
∞
=
= −∑ (2.23)
Then, signal from (2.22) can be written as
( ) ( ) ( ) ( )
1 1
( ) [ ( )] ( ),uN L
k k k k
l rec j f j c l
k l j
r t A w t d jT c T n tβ λ τ
∞
= = =−∞
= − − − − +∑∑∑ (2.24)
where ( )rec
w t represents the received pulse of the kth
user after the multipath
propagation. Received pulse can be presented as a convolution between the transmitted
monocycle and the distorted channel response ( )dist
h t as
( ) ( ) * ( ).
rec tr distw t w t h t=
(2.25)
In addition, it is assumed, in order to simplify the system model, in this sum of many
scaled and time-shifted versions of the transmitted pulses, there is no pulse waveform
distortion. Channel models that consider pulse waveform distortion due to diffraction of
the electromagnetic waves around objects are more realistic, but also more complex
[74], [75].
CHAPTER 2 SINGLE USER RECEIVER STRUCTURE
65
2.5. Single User Receiver Structure
2.5.1. Introduction
IR-UWB radio communications with pulses of very short duration, typically on
the order of a few nanoseconds, are spreading the energy of the radio signal from near 0
to several GHz. Therefore, IR-UWB might accommodate a large number of
simultaneous users. Regulatory consideration over such a broadband limit the radiated
power and very strict pulse shaping requirements to comply with FCC mask. Impulse
radios, operating in the highly populated lower range of the frequency band below 3.1
GHz, has to coexist with a variety of interfering signals, including self interference from
multipaths and multiuser interference. Additionally, UWB signals must not interfere
with narrowband radio systems operating in legacy systems. To fulfill those
requirements, spread spectrum techniques are often used. A simple means for spreading
the spectrum of low duty cycle pulse trains is time hopping, that will be used for the
purposes of this thesis, with pulse position modulations for data modulation at the rate
of many pulses per data bit. This signaling scheme is described as time hopped pulse
position modulation, or TH-UWB. Receivers for IR-UWB can be broadly categorized
as threshold or leading edge detectors (LED), correlation detectors (CD), and RAKE
receivers. Multiuser detectors (MUD) and hybrid RAKE/MUD-UWB receivers for
robust narrowband interference suppression are becoming popular.
The approach of single user receiver detects the user signal of interest by not
taking into account any information about MAI.
This section provides a description of a single user and multiuser receiver
structure, assuming perfect synchronization and perfect channel estimation. As an
optimum single user receiver, selective RAKE receiver is employed and as a multiuser
detector a MMSE RAKE is used for the purposes of this thesis.
In addition, as a one part of the contribution of this thesis low complexity
method for synchronization is presented. Thanks to this approach, a low complexity for
real time implementation and the good performance in terms of BER versus Signal to
Noise Ratio (SNR) are achieved.
SINGLE USER RECEIVER STRUCTURE CHAPTER 2
66
2.5.2. Selective RAKE Receiver
The single receiver structure, considered in this thesis, is RAKE receiver that
represents the optimum receiver structure in the presence of reach multipath
environment [79]. In order for such detector to be realizable, the number of paths
considered in the receiver must be limited to a finite number, say Lmax. In Figure 2.10 a
scheme of RAKE receiver structure of the qth
user for the ith
frame is shown.
This receiver correlates the received signal from (2.24) with the signal template
that should be previously synchronized. For the purposes of this thesis, the qth
receiver
link is considered as the desired signal, and the other links are considered as
interference. It is assumed that each finger of the RAKE is synchronized to a multipath
component. The output of each finger is coherently combined using MRC. Channel
estimation is required in the combining scheme and it is assumed perfect.
Assuming that all paths are resolvable, the statistic for the ith
frame on the qth
receiver is
( )
( )
( 1)
( ) ( )( ) ( ) ( )
qf i c
qf i c
i T c T
q q
i f i c
iT c T
t r t v t iT c T dtα
+ +
+
= × − −∫ (2.26)
where ( )( )qv t represents the template signal described as
max
( ) ( ) ( )
0
( ) ( ).L
q q q
m m
m
v t tβ ϕ τ
=
= −∑ (2.27)
The signal ϕ(t) depends on type of the employed modulation. Since this thesis applies
the binary PPM modulation, ϕ(t) is defined as
( ) ( ) ( ).
rec rect w t w tϕ λ= − − (2.28)
Lmax represents the number of RAKE fingers with the amplitudes ( )q
mβ and the
corresponding finger duration ( )q
mτ .
CHAPTER 2 SINGLE USER RECEIVER STRUCTURE
67
( )tϕ
( )
1
qτ
max
( )q
Lτ
( )
( )
( 1) qf i c
qf i c
i T c T
iT c T
dt
+ +
+
⋅∫
( )
( )
( 1) qf i c
qf i c
i T c T
iT c T
dt
+ +
+
⋅∫
iα
( )
1
qβ
max
( )q
Lβ
( )r t
.
.
.
.
.
.
.
.
.
.
.
.
Figure 2.10. RAKE Receiver Structure Scheme
Once the frame statistics has been calculated, a bit decision should be taken.
Supposing that ( )tr
w t and ( )tr
w t λ− are orthogonal, soft decision is obtained as
0, 0,decision
1, 0,
α
α
∀ ≥=
∀ < (2.29)
where the bit statistic for soft decision is presented as
1
.fN
i
i
α α
=
=∑ (2.30)
PERFORMANCE OF A PPM TH-UWB SYSTEM EMPLOYING RAKE RECEIVER CHAPTER 2
68
2.5.2.1. Performance of a PPM TH-UWB System employing RAKE Receiver
This section describes performance of the RAKE receiver in PPM TH-UWB
data detection technique for the system downlink. Results are compared in order to
show the influence of the number of RAKE fingers on the system performance.
Equation (2.32) presents a theoretical analysis of the performance of a PPM TH-UWB
systems under certain restrictions, based on the one presented in [55]. Under the
assumptions of independent links and random sequence selections (with Cmax < Nh/2),
the MUI can be modelled as Gaussian, and the BER can be expressed as
( )u
BER Q SNR N = (2.31)
where
22( )
2 (1)2
1( )
1 1( ) ( )
(1)( ) ( )
u
uN k
rec
k
f f rec
SNR N
Aw t s t dt ds
SNR AN T w t t dt
ϕ
ϕ
∞ ∞
∞= −∞ −∞
−∞
=
+ −
∑ ∫ ∫∫
(2.32)
and
2
21
( )2
y
x
Q x e dyπ
∞
−
= ∫ (2.33)
This analysis does not take into consideration explicitly neither the multipath
characteristics of the channel nor the RAKE structure, only the signal distortion (where
the multipath could be embedded). The expression from (2.32) can be extended to the
multipath case just by modelling the L paths of each link as (Nu – 1) L independent
sources, with amplitudes ( )k
lβ . On the other hand, in order to assume the influence of the
RAKE receiver, the template waveform changes from ϕ(t) tomax
( ) ( )
1
( )L
q q
m m
m
tβ ϕ τ
=
−∑ .
Then, SNR can be calculated as
CHAPTER 2 PERFORMANCE OF A PPM TH-UWB SYSTEM EMPLOYING RAKE RECEIVER
69
2 22
( )
22
2
max
1( )
1( ) ( )
(1)( ) ( )
uu N
rake channel k
krec
f f rake rec
SNR N
L
w t s t dt dsSNR
N T L w t t dt
β η
ϕ
η ϕ
∞ ∞
=
∞
−∞ −∞
−∞
=
+ −
∑∫ ∫
∫
(2.34)
where η2
channel(k) represents the mean square value of the amplitude coefficients of the
kth
channel impulse response and rake
β and η2
rake are the mean and the mean square
values of the RAKE coefficients of the qth
link receiver, respectively.
SNR (1) represents the Signal to Noise Ratio in the single user case (without MUI). In
Figure 2.11 it can be seen how the assumption of a Gaussian distribution of the MUI is
valid under the assumption of no multipath response.
Figure 2.11 Histogram of the distribution of the MUI for a PPM TH-UWB system with
Tc=1 ns, Nh= 1024 slots, Nu=900 links, λ = 180 ps, Nf =64 and no multipath. The
number of simulations is 330.503. It can be noticed the Gaussian distribution of the
interference. (Data taken from [83])
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.60
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000Histogram of the Multi User Interference
Num
ber
of occurr
ences
Amplitude
PERFORMANCE OF A PPM TH-UWB SYSTEM EMPLOYING RAKE RECEIVER CHAPTER 2
70
If no statistical channel description is available, these values can be easily estimated as
( )2
2 ( )
( )
1
1ˆ
Lk
channel k l
lLη β
=
= ∑ (2.35)
max
( )
1max
1ˆL
q
rake m
mLβ β
=
= ∑ (2.36)
( )
max 22 ( )
1max
1ˆ
Lq
rake m
mLη β
=
= ∑ (2.37)
Figure 2.12. Theoretical BER Performance versus SNR of a PPM TH-UWB System
Downlink Employing RAKE Receiver in a Multipath Channel; L=100, Nf=64; Nh=128
Since the single user detector is not able to handle multipath signal neither for two users
as will be shown later in this thesis, just in order to see the number of RAKE Fingers
CHAPTER 2 MULTIUSER DETECTION (MUD) RECEIVERS
71
impact on the system performance, in Figure 2.12 tapped delay line channel was used
with L=100 multipath components. The theoretically calculated BER of a PPM TH-
UWB system employing RAKE receiver is presented. BER is shown as a function of the
RAKE fingers for the number of users Nu equal to 2, and 64. It is demonstrated that
RAKE receiver outperforms the matched filter, i.e. the case when Lmax=1. It is
demonstrated that is inefficient to use a simple matched filter receiver where the
template is matched to the transmit pulse. The energy capture of such receiver is very
low, and performance is unacceptable. In addition, it is demonstrated that RAKE
receiver is able to completely resolve the L strongest channel paths. However, it is
shown that degradation of the performance in the case when employing RAKE receiver
with 30 fingers comparing to the performance when RAKE receiver with Lmax=100
fingers is presented, is only 1 dB for BER=10-3
. Moreover, when number of RAKE
fingers has maximum value, i.e. Lmax=L=100, there is no difference in the performance
when number of users Nu is changed from 2 to 64. This can be explained as follows: As
it was shown in [48], the energy capture is relatively low for a moderate number of
fingers when Gaussian pulses are used, a typical NLOS channel can have up to ∼ 70
resolvable dominant multipath components. Even, if number of RAKE fingers Lmax can
reach that number, it would only be able to capture the part of the signal energy.
2.6. Multiuser Detection (MUD) Receivers
In many papers, it is shown that multiuser detection is a critical task for
successful operation of UWB systems. Many papers also show that MMSE receiver has
the best performance in terms of SINR at the expense of high computational complexity
since it requires the matrix inversion every time the spreading sequence changes.
In this section it is described a RAKE MUD UWB receiver. In order to implement any
multiuser detector, it is necessary to have a multiuser signal model.
Defining ( ) ( )1 2k kb d= − , the frame statistic q
iα on the q
th receiver can be presented on the
other way as
MULTIUSER DETECTION (MUD) RECEIVERS CHAPTER 2
72
,q n= +
qα R Ab α (2.38)
where
1 2[ , ,..., ] ,f
q T
Nα α α=α
[ , ,..., ] ,f
n n n n T
Να α α
1 2=α
1 2diag( , ,..., ),uN
A A A=A
1 2[ , ,..., ] ,u
T
Nb b b=b and
( , )(1, ) (2, )
1 1 1
( , )(1, ) (2, )
2 2 2
( , )(1, ) (2, )
u
u
u
f f f
N qq q
N qq q
N qq q
N N N
u u u
u u u
u u u
=
qR
(2.39)
where for all k and i
( ) ( )
( , )
( ) ( )
1 if
0 if
k q
i ik q
fi
k q
i i
c cNu
c c
=
=
≠
(2.40)
where assuming a random TH sequences
( ) ( ) 1( )k q
r i i
h
P c cN
= = , for k q≠ (2.41)
From (2.3) and the orthogonallity of ( )tr
w t and ( )tr
w t λ− , assuming perfect signal
and channel estimation, it can be shown that noise power on the output of the receiver is
CHAPTER 2 MULTIUSER DETECTION (MUD) RECEIVERS
73
( )
( )
( )
( )
( 1)2, 2 ( ) ( ) 2
( 1)
2 2
2
[( ) ] ( ( ))2
( )
.
q
f i c
q
f i c
qf i c
qf i c
i T c T
n q q qni f i c
iT c T
i T c T
n tr
iT c T
n
E t iT c T dt
w t dt
σα ν
σ
σ
+ +
+
+ +
+
= − − =
=
∫
∫ (2.42)
It implies the following:
2(( ) ) .T
nE σ=
n,q n,qα )(α I (2.43)
Equation (2.38) will play a key role for implementation of any multiuser detector into
TH-UWB systems. Depending how the matrixq
M is selected, different receivers can be
implemented as
( ) 1 .q
q
−
=b A M α (2.44)
for the case of MMSE receiver, matrixq
M is defined as
2arg min .
qE = − M
M Mα Ab (2.45)
Using the principle of orthogonallity from [92], i.e. the fact that [( ) ] 0TE − =Mα Ab α ,
from (45) can be obtained
1( ) ( [ ]) ,T T T
q E−
=qM AA R αα (2.46)
where [ ]TE αα represents the covariance matrix ofα , given as
MULTIUSER DETECTION (MUD) RECEIVERS CHAPTER 2
74
2
[ ] [ ( ) ] [( )( ) ] ( ) [ ] [( )( ) ]
( ) ( ) .
T T T T T T T T T
T T
n
E E E E E= + = +
= +
q q n n q q n n
q q
αα AA R bb R α α R AA R bb α α
R AA R Iσ
(2.47)
2.6.1. Performance of a PPM TH-UWB System employing MMSE RAKE
Receiver
From(2.45),(2.46) and [93], it can be demonstrated that the SINR of the MMSE
detector is given as
2 2 1( ) ( ) ( ( ) )T T T
q qSNR q A σ−
= +(k) q q (k)i iu R D R I u (2.48)
where (k)iu represents the k
th column of the matrix qR , i.e.:
qΩ is the sub matrix of Ω derived by deleting the q
th column vector, and qD is the
diagonal matrix given as
2diag( ,..., , ,... ),
u
2 2 2
q 1 q-1 q+1 NA A A A=D (2.49)
Therefore, BER can be calculated as
( ( ))BER Q SNR q= (2.50)
The pulse shaper is selected to be the second derivative of the Gaussian function that
has been normalized to have unit energy.
In Figure 2.13 is demonstrated theoretical BER Performance of a PPM TH-UWB
System Employing RAKE Receiver vs. BER Performance of a PPM TH-UWB System
Employing MMSE Receiver in a AWGN Channel for Nf=8; Nh=4 and Nu=5. It is shown
that single user receivers are incapable of effectively rejecting heavily loaded wideband
interference.
CHAPTER 2 SYNCHRONIZATION AND CHANNEL ESTIMATION
75
0 5 10 15 20 25 3010
-3
10-2
10-1
100
SNR[dB]
BE
R
MMSE detector
single user receiver
Figure 2.13. Theoretical BER Performance of a PPM TH-UWB System Employing
RAKE Receiver vs. BER Performance of a PPM TH-UWB System Employing MMSE
Receiver in AWGN Channel; Nf=8; Nh=4; Nu=5
2.6.2. Synchronization and Channel Estimation
Channel estimation and synchronization are very important tasks for the
performance of UWB systems. There are many papers dealing with those topics, [63]-
[69]. As it was mentioned, the first part of the contribution of this thesis is a low
complexity synchronization.
In [63] both data-aided and non-data aided (blind) methods are considered, and
due to their requirement of multi-dimensional search to maximize the log-likelihood
function, those methods have high complexity. Low-complexity timing acquisition and
tracking are considered in [64], based on the second-order cyclostationarity without
considering channel estimation.
SYNCHRONIZATION AND CHANNEL ESTIMATION CHAPTER 2
76
In [65] synchronization and channel estimation are carried out via two different
approaches: a Least Squared (LS) method that ignores a channel structure and a
subspace technique that exploits this structure for channel estimation. The disadvantage
of the first approach is a large number of frames needed for achieving good estimation
accuracy. Subspace method requires fewer frames and yields better performance at the
expense of complexity.
In [69] symbol timing is obtained to a precision that is enough for symbol
demodulation. This approach is based on a completely blind channel estimation
technique where first-order cyclostationarity is used. This method might be hardly
achievable in practice due to the requirement of several FFT operations. This leads that
the received signal must be sampled at a much higher rate than the symbol rate.
In this thesis a joint symbol, frame and chip synchronization method for UWB
system from [70] is proposed. It is assumed that the channel is estimated using Pilot
Waveform Assisted Modulation (PWAM), and that synchronization is achieved by
maximizing the energy of the estimated multipath channel. Based on this method for
synchronization in a combination with PWAM method for channel estimation, FFT
operations that are used in many works are avoided and the algorithm has very low
complexity. Additionally, in order to even more increase the speed of the simulation
process, this method is implemented in the enhanced time algorithm that will later be
described in details. Therefore, the algorithm can deal with channels with a large
number of taps that are difficult to estimate using existing algorithms. Implementation
of this method in the enhanced time algorithm was not an easy task since the transmitted
waveform is “hidden” in the TDR, as this thesis explains. Thanks to this approach, low
complexity for real time implementation and the good performance in terms of BER
versus SNR are achieved. This chapter describes the procedure from [70] used to
estimate ( )k
lβ and ( )k
lτ parameters of the multipath channel response.
Since the PWAM method subsumes the TR as a special case, in this chapter, the
TR will be briefly described.
CHAPTER 2 SYNCHRONIZATION AND CHANNEL ESTIMATION
77
2.6.3. Transmitted Reference UWB Receiver
TR systems were first proposed in [66]. In a typical TR system, a pair of
unmodulated and modulated signals is transmitted, and the former is employed to
demodulate the latter. Figure 2.14 illustrates TR of the symbol with PAM, i.e. the
monocycle ( )w t transmitted and modulated as
( ) ( ) ( )f
v t w t b p t T= + ⋅ − (2.51)
where b = ±1,
After multipath propagation, the received waveform is given by
( ) ( ) ( )f
r t h t b h t T= + ⋅ − (2.52)
Then, the receiver correlates r(t ) with its delayed version r(t − Tf ) in order to yield the
symbol estimate :
2ˆ ( ) ( ) ( )
fb sign r t r t T dt sign b h t dt b= − = =∫ ∫ (2.53)
linkth
q
Figure 2.14. Block Scheme of the Receiver (with Channel Estimation and Joint
Synchronization)
SYNCHRONIZATION AND CHANNEL ESTIMATION CHAPTER 2
78
fT
( ) ( ) ( ), 1, 1f
v t w t b w t T b= + ⋅ − ∈ − +
( ) ( ) ( ), 1, 1fr t h t b h t T b= + ⋅ − ∈ − +
2ˆ ( ) ( ) ( )
fb sign r t r t T dt sign b h t dt b
= − = =
∫ ∫
Figure 2.15. Illustration of the Transmitted Reference System
The TR system described in [66] employs a binary PPM modulation. The transmitted
signals consist of Np UWB pulses (pilot waveforms), ( )tr
w t with energy Ep. Pilot
waveforms are divided into Np/2 unmodulated interleaved with Np/2 PPM modulated
waveforms.
Assuming(2.1), the transmitted pilot signal of the kth
user is presented as
12
( ) ( ) ( )
0
( ) ( )
( ) [ ( 2 )
( 2( 1) )]
pN
k k k
p p tr f j c j
j
k k
tr f j c j
s t E w t jT c T d
w t j T c T d
λ
λ
−
=
= − − −
+ − + − −
∑ (2.54)
TR receiver produced many research interests, since it can capture the entire signal
energy for a slowly varying channel without requiring channel estimation. Another
potentially attractive feature of UWB autocorrelation receivers is their relative
CHAPTER 2 SYNCHRONIZATION AND CHANNEL ESTIMATION
79
robustness to synchronization problems. However, fundamental system drawbacks, such
as bandwidth inefficiency and high noise vulnerability, coupled with the advent of
stored reference and matched filter implementations in the 1950s and 1960s largely
mitigated research interest in TR schemes [80].
2.6.4. Channel Estimation using Pilot Waveform Assisted Modulation
(PWAM)
PWAM method subsumes TR as a special case. Figure 2.16 shows how the
signal is obtained at the receiver by simply averaging over several received pilot
waveforms.
fT
ˆ( )h t
Figure 2.16. Illustration of the PWAM Scheme
SYNCHRONIZATION AND CHANNEL ESTIMATION CHAPTER 2
80
This method is explained in [68], where a general PWAM scheme and obtained
conditions for which the scheme operates optimally is described. In this method,
minimum channel MSE and maximum average capacity are the two optimally
measures. Under the optimally conditions, this transmitter design thereby achieves
Cramer-Row lower bound.
In PWAM, the channel is assumed static over burst duration of fNT . Each burst includes
up to / fN N N= symbols that are either pilot or information bearing. Pilot waveforms
are used at the receiver in order to form a channel estimate. During each burst,
sN distinct information symbols are sent, corresponding to s s fN N N= waveforms.
Therefore, the number of pilot waveforms is p sN N N= − .
The power of the th
pn pilot waveform is denoted by ( )p p
nε ; and the power of the
th
dn data waveform is denoted by ( )
d dnε . Thus, the total pilot energy is
1
0
( )p
p
N
p p p
n
nε ε
−
=
= ∑ ,
and the total data energy is1
0
( )s
s
N
d d d
n
nε ε
−
=
= ∑ . The received waveform corresponding to
the th
pn pilot waveform is
)( ) ( ) ( ) ( ), 0,p pn p p n f
r t n h t n t t Tε = + ∈ (2.55)
where ( )pn
n t represents the AWGN in the frame containing th
pn pilot waveform and
double-sided power spectral density 2 / 2σ .
In order to limit the noise power at the output of the receiver, it is assumed that
the receiver front-end is modelled as an ideal band pass filter with double-sided
bandwidth B (>>1/Tf) and centre frequency f0. Therefore, the AWGN has
autocorrelation function
2
0( ) : [ ( ) ( )] sin ( ) cos(2 )pn p p
R t E n t n t B c B fτ σ τ π τ= + = (2.56)
CHAPTER 2 SYNCHRONIZATION AND CHANNEL ESTIMATION
81
where sinc( ) : sin( ) /( ).t t tπ π=
pN received pilot waveforms are summed up to form the channel estimate
1 1
0 0
ˆ( ) ( ) ( ) ( ) ( )p p
p p
p p
N N
n p p n
n n
h t r t n h t n tβ β ε
− −
= =
= = + ∑ ∑ (2.57)
for )0,f
t T∈ where
11
0
: ( )p
p
N
p p
n
nβ ε
−−
=
= ∑ .The sum is multiplied by a constant β in
order to guarantee the unbiased ness of the channel estimate ˆ( )h t . According to [68], the
following constraints must be observed in order to ensure that the system is optimal:
1. For a known total number of pilot waveforms per burst, pN and the total energy
assigned to pilot waveformsp
ε , equi-probable pilot power waveforms minimize the
channel MSE.
2. If the total data energyd
ε and the total pilot energyp
ε are known, equi-powered
information symbols maximizes the average capacity C.
3. If the total data energy d
ε , the total pilot energy p
ε , and the number of waveforms
per burst N are known, the number of pilot waveforms that maximizes the average
capacity is given by: * *( )p s f
N N N N= − ,
where *
1if is an integer
otherwise
f f
s
f
N N
N NN
N
N
−
=
4. With fixed burst size N, number of information symbols per burst s
N , and total
transmission energy d p
ε ε ε= + , the optimal energy allocation factor is
2
2
1,
2
,1
s
s
N
N
N
ε
σα
ε
σ
=
+
(2.58)
SYNCHRONIZATION AND CHANNEL ESTIMATION CHAPTER 2
82
As it was mentioned before, PWAM method subsumes TR as a special case. It can be
noted for N=2, in order to achieve optimal PWAM, number of information bearing
symbols, number of pilots and α should be Nf=1, Np=1 and1
2α = , respectively.
Therefore, this resulting PWAM represents a TR autocorrelation system described in
[66].
A theoretical expression for an N pilot-based receiver (Figure 2.17) was
developed in The Mobile and Portable Radio Research Group (MPRG), both for
biphase and PPM modulation.
( )h t
( )h t
∫
1
0
1 N
n
n
REFN
−
=
∑
( )n t
( )n t
Figure 2.17. Pilot Based Receiver
2.6.5. Synchronization
In timing offset estimation, the receiver is not able to distinguish two time delays
that are separated by multiple symbol durations, e.g. 0τ and 0 kTτ + . Thus, this thesis
resolves timing offset estimation only within one symbol duration. And presents the
first arrival time as
0 0 0
( ) ( ) ( ) ( )
0
k k k k
frames f chips cN T N Tτ τ τ
τ µ= + + (2.59)
CHAPTER 2 SYNCHRONIZATION AND CHANNEL ESTIMATION
83
where 0 0 0
( ) ( ) ( )[0, 1], [0, 1] and [0, )k k k
frames f chips h cN N N N Tτ τ τ
µ∈ − ∈ − ∈ .
Accordingly, other path delays, as a delay respect to the beginning of the frame for the
first path of the kth
link can be described by
( )
,0
( ) ( )
0: ,k
l
k k
lkϕ τ τ= − ∀ (2.60)
that represents the timing offset over a rich multipath environment (Figure 2.18).
With these definitions, the received signal from (2.24) might be predefined as
0 0 0
( ) ( ) ( ) ( ) ( ) ( ) ( )
,0
1 1
( ) [ ( ( ) )] ( )uN L
k k k k k k k
l rec c frames f chips c l
k l
r t A w t d c T N T N T n tτ τ τ
β λ µ ϕ
= =
= − − − + + − +∑∑
(2.61)
Taking advantage of the previous estimated channel, the timing offset estimation can be
achieved maximizing the energy of the estimated multipath channel as
0
00
2
00
ˆˆ arg max [ ( )]
T
T
h t dt
τ
ττ
τ
+
≤ ≤
= ∫
(2.62)
Substituting (2.57) in(2.62), it is obtained the final expression for 0τ . The symbol
synchronization requires estimation of all the three components; frame synchronization
requires estimation of the pair0 0
( ) ( )( , )k k
chipsN
ϕ ϕµ , while estimating only the parameter
0
( )k
ϕµ
chip synchronization can be achieved. Other path delays, as a delay respect to the
beginning of the frame for the first path of the kth
link are straightforward from(2.60).
SYNCHRONIZATION AND CHANNEL ESTIMATION CHAPTER 2
84
Figure 2.18. Timing Offset Presentation
2.6.6. Conclusion
This thesis considers an MA TH-IR-UWB system composed by Nu different
links. These links can correspond to a different real users transmitting and receiving
through different terminals or to different links established between two terminals in
order to achieve a higher aggregate bit rate. No further assumptions about the symmetry
of these links will be made, so they can be symmetric or asymmetric depending on the
system functionality (file downloading, video streaming, videoconference,
telemetry…). In the case of different terminals, they can be static or mobile (with low
speed, like a person walking) and they can be close one to another or relatively far
away, taking into account that so far the main applications of this kind of systems are
indoor communications, where distances cannot be too large. One of the links consists
of a series of pulses whose frame structure can be seen in Figure 2.1. A single bit is
CHAPTER 2 SYNCHRONIZATION AND CHANNEL ESTIMATION
85
composed of Nf frames, each of them with period Tf. Each one of the chips is
subdivided in Nh slots of length Tc, in one of the monocycle is transmitted (one
monocycle per chip), whose position (the number of the slot) is given them by a
pseudorandom TH sequence. The data modulation in the monocycles for the purposes
of this thesis is in time shift, and the slot length Tc should be large enough to contain
the different monocycles. The bit rate is 1/TfNf or equivalently 1/TcNhNf.
For the multipath channel case, the random NLOS channel model is generated
according to [76], where rays within an observation window arrive in several clusters.
The magnitude of each arriving ray is a lognormal distributed random variable with
exponentially decaying mean square value with parameters Γ and γ . The cluster arrival
times are modelled as Poisson variables with cluster arrival rate Λ . Rays within each
cluster arrive according to a Poisson process with ray arrival rate λ . Multipath channel
model parameters are selected to be Γ =16 γ =8.5, 1/ Λ =11 ns, 1/ λ =0.35 ns, L=400,
Lmax=400 or, Γ =33, γ =5, 1/ Λ =2 ns, 1/ λ =0. 5 ns, L=400, Lmax=400. In the case of
AWGN channel, i.e. considering L=1, Lmax=1, noise variance is2
1n =σ . For the
multipath channel case, results show .the ensemble performance of 100 realizations.
As a single user detector a selective RAKE with Lmax fingers is selected. It is
shown that degradation of the performance in the case when employing RAKE receiver
with 30 fingers comparing to the performance when RAKE receiver with Lmax=100
fingers is presented, is only 1 dB for BER=10-3
. Moreover, when number of RAKE
fingers has maximum value, i.e. Lmax=L=100, there is no difference in the performance
when number of users Nu is changed from 2 to 64. This can be explained as follows: As
it was shown in [48], the energy capture is relatively low for a moderate number of
fingers when Gaussian pulses are used, a typical NLOS channel can have up to ∼ 70
resolvable dominant multipath components. Even, if number of RAKE fingers Lmax can
reach that number, it would only be able to capture the part of the signal energy.
Since it is shown that RAKE receivers are incapable of effectively rejecting
heavily loaded wideband interference, as a multiuser detector, for the purposes of this
thesis MMSE RAKE receiver is proposed. It known that MMSE receiver has the best
performance in terms of SINR at the expense of high computational complexity.
SYNCHRONIZATION AND CHANNEL ESTIMATION CHAPTER 2
86
Based on the method for synchronization in a combination with PWAM method
for channel estimation used in this thesis, FFT operations that are used in many works
are avoided and the algorithm has very low complexity. Additionally, in order to even
more increase the speed of the simulation process, this method is implemented in the
enhanced time algorithm. Therefore, the algorithm can deal with channels with a large
number of taps that are difficult to estimate using the existing algorithms. Furthermore,
as it is shown on Figure 5.12, simulation time per bit is independent on the sampling
frequency. Therefore, increasing the sampling frequency as much as needed, a very high
accuracy can be achieved without prolonging the simulation time.
Thus, this algorithm outperforms all the previous designs by several orders of
magnitude, independently on the sampling rate, in terms of a very straightforward and
fast processing. Thanks to this approach, low complexity for real time implementation
and the good performance in terms of BER versus SNR are achieved
CHAPTER 3 THE SLOWNESS OF SIMULATING TH-UWB SYSTEM
87
Chapter 3
3. The Slowness of Simulating
TH-UWB System
3.1. Introduction
There are a large number of literatures dealing with the simulation as applied to
the design and the analysis of communication system, e.g. [81] and [82].
Simulation of any communication system might be a very difficult issue due to two
reasons. First, since many solutions exist, a development of the simulator is both, art
and science. Second, simulation considers a deep knowledge of a large number of fields
and the appropriate models must be available. In addition, the assumptions used in the
model development must be known and their impact on the accuracy of the resulting
simulation must be evaluated. Further, development of the simulator requires
knowledge of the computer language and software management principles as well as
grounding in digital signal processing.
Particularly, UWB system requires taking a second look at simulation
methodology. Design of the UWB system model was explained in the previous chapters
of the thesis, while, this chapter covers the following tasks:
• Differences between UWB and traditional narrowband systems and difficulties in
model development.
• A brief review of the fundamental simulation methodologies.
• New IR-TH-UWB system simulator that is the innovation of our research group and
will be used for the purposes of this thesis.
THE SLOWNESS OF SIMULATING TH-UWB SYSTEM CHAPTER 3
88
3.2. Differences between UWB and Traditional Narrowband Systems
As it was mentioned before, UWB system requires taking a second look at
simulation methodology. In the following research, it will bee seen that
direct/quadrature signal decomposition, which is a fundamental technique used to
shorten the required simulation runtime, when applied to UWB signals it is not possible
to mitigate large sampling frequency. Thus, direct/quadrature signal decomposition no
longer provides simulation time savings. Therefore, in order to process UWB signals a
large computational time is needed. Furthermore, since the wide bandwidth required for
UWB channel sounding gravely complicates the process, data collection for UWB
channel model development is complicate task. In addition, component modelling and
simulation development presents challenges, specific for the UWB signal environment.
3.2.1. Large Sampling Frequency
In order to process UWB signals, is necessary to have an extremely large
sampling rate. For the case of narrowband system, simulation model can be based on
signals with relatively small bandwidth. Since using the direct/quadrature
decomposition of the modulated carrier, the carrier is usually translated to zero
frequency. For example, if a band pass signal has centre frequency f0 and bandwidth B,
it can be presented as
0 0( ) ( ) cos 2 ( )sin 2d q
x t x t f t x t f tπ π= − (3.1)
where ( )d
x t and ( )q
x t are the direct and the quadrature channel signals, respectively.
Both have bandwidth B/2. Therefore, this insures requirement of the lower simulation
sampling frequency, which will be deserving reason for a large time saving [81].
Now it will be shown that using of direct /quadrature decomposition in UWB
signals does not help to increase simulation-sampling frequency.
CHAPTER 3 THE SLOWNESS OF SIMULATING TH-UWB SYSTEM
89
In Figure 3.1 is shown the spectrum of a bandpass signal that has a carrier
frequency f0 Hz and a bandwidth of B Hz. It is obvious that the highest frequency in the
bandpass signal is
02
h
Bf f= + (3.2)
Without application of direct /quadrature decomposition, i.e. considering
baseband signal and satisfying the Nyquist criterium, a minimum sampling frequency is
, 02 2s BB h
f f f B= = + (3.3)
On the other hand, using direct/quadrature decomposition, i.e. considering
narrowband signal, both components, the direct and the quadrature has bandwidth B/2,
and each of them achieves minimum sampling frequency B Hz. Therefore, the minimum
sampling frequency for narrowband signal is
, 2s NB
f B= (3.4)
Now, in order to see the performance of direct /quadrature decomposition in
narrowband and UWB system, it would be useful to define the relation between
sampling frequencies when direct /quadrature decomposition is applied and when it is
not. This relation is defined as
, 0
,
1
2
s BB
s NB
f fR
f B= = + (3.5)
Large values of R indicate that a large saving simulation runtime is achieved
using direct /quadrature decomposition, while low values of R indicate that direct
/quadrature decomposition doesn’t help a lot in runtime saving.
THE SLOWNESS OF SIMULATING TH-UWB SYSTEM CHAPTER 3
90
In order to analyze the role of the ratio R, both narrowband and UWB will be compared.
• Narrowband Signal
Figure 3.1. Wideband Signal Spectrum
Assuming that narrowband signal has a carrier frequency f0=1000 MHz and a
bandwidth B=1 MHz, the ratio R has value
1000 11000.5
1 2R = + = (3.6)
and the minimum sampling frequency is
, 2 2s NB
f B MHz= =
(3.7)
• UWB Signal
Assuming that UWB signal extends from 3 GHz (3000 MHz) to 10 GHz (10000
MHz), the centre frequency f0= (10-3)/2 GHz=3500 MHz and a bandwidth B=10-3=7
GHz (7000 MHz). Therefore, the ratio R has value
CHAPTER 3 THE SLOWNESS OF SIMULATING TH-UWB SYSTEM
91
3500 11
7000 2R = + = (3.8)
This value shows that there is no sense to use direct /quadrature decomposition of UWB
signals. Therefore, in order to process UWB signals, is necessary to have an extremely
large sampling rate. In a straightforward approach, with the constant sampling rate, the
length of the array that contains the bit samples can be very large, depending on the
relationship between the duty cycle and bit rate. Since this array should pass through the
chain of blocks that model the channel and receiver responses, it is obvious that a large
number of convolutions should be done. Thus, even in very fast workstations, the total
computing time in order to estimate BER can be very high. This fact significantly
reduces the efficiency of the simulator.
3.2.2. Difficulties in Model Development
In order to develop a simulator, it is necessary to define attributes of the physical
device being modelled that affect the required simulation product. For narrowband
systems, a large body of well-understood models has been developed. Therefore,
development of a model is usually easily and quickly accomplished.
Unfortunately, the model development might be a difficult task due to following
reasons:
• Although UWB communication systems were in introduced in the early 1970's
[28]-[31], the community of interest in UWB system is relatively recent. Thus,
until now, there is no handful of well-established models.
• Additionally, poor library of tested and validated models is not widely available.
• The actual number of channel models is also limited. While, there is a
comprehensive library of channel models developed for narrowband systems,
most suitable models for UWB system are Saleh-Valenzuela small scale model
[71] and the 802.15.3a model [76]. Investigating other aspects of a UWB
system, such as amplification, signal recovery and data conversion, some
drawbacks in standard models might be founded. For instance, it is observed
A BRIEF REVIEW OF BER ESTIMATION TECHNIQUES CHAPTER 3
92
from the experimental data that the multipath amplitudes of the multipath channel
components do not correspond to a Rayleigh or Ricean distribution as the traditional
channel models. Concerning many measurements, multipath amplitudes of the
UWB channel tend to follow Nakagami-m distribution, which exceeds additional
parameterization (the value of parameter m) to model a channel. Therefore, in order
to simulate UWB systems, sometimes is better to develop a new model from
experimental data then simply extracting some previously developed from the
existing library.
• Since the UWB system deals with phase response, in order to have accurate
pulse transmissions, after the multipath propagation, the amplitude responses of
the pulses must be constant and their phase responses must be linear over the
bandwidth of interest. This condition is very difficult to achieve in such wide
bandwidth, so equalization is also a big problem in UWB systems.
• While modelling concept for narrowband system is the assumption of steady
state operation, a modelling concept for UWB system becomes more complicate.
Since an UWB system has a small duty cycle, the transmitter components are
assumed to return to a relaxed state between pulses. The transmitter is
consequently operating in a transient mode; therefore, models have to be based
on the solution of differential equations. Certainly, this is significantly more
complicated process.
3.3. A Brief Review of BER Estimation Techniques
This section of the thesis describes the three basic simulation techniques: Monte
Carlo, modification of Monte Carlo technique, known as semi-analytic and discrete
event simulation. Additionally, a high-speed algorithm designed for a TH system is
presented that was used for the purposes of this thesis. It is assumed that those
techniques are used to estimate BER.
CHAPTER 3 A BRIEF REVIEW OF BER ESTIMATION TECHNIQUES
93
3.3.1. Monte Carlo Simulation Techniques
The Monte Carlo simulation technique is very simple and flexible that can be
applied to a wide variety of systems, where the signal processing operations defined by
every functional in the system block diagram are known. In order to apply this method,
it is necessary to synchronize the system. In Figure 3.2 is presented a system block that
represents an implementation of Monte Carlo estimation procedure.
In general, Monte Carlo simulations are implementations of a random
experiment designed to estimate the probability of a particular event happening. This is
realized using two counters in the simulation algorithm. The first counter is known as
the replication counter, and is incremented by one every time the random experiment is
repeated. The second counter is known as event counter since it is incremented by one
every time the event of interest is observed. Then, the estimated probability of the event
of interest occurring is
ˆ E
Np
N= (3.9)
where E
N and N represent the values in the event and replication counters at the end
of the simulation run, respectively.
Relating to communications case, assuming that a simulation is being performed
in order to calculate BER, random experiment is the bit processing through the
communication system. Bit processing through the communication system is random
process since the channel noise; multiuser and other system interferences may, or may
not destroy the transmitted bit and cause an error. Therefore, in the case if E
N
represents the number of the bit errors occurred during the transmission of N bits, the
BER might be calculate from (3.9) as
ˆlimN
BER p→∞
= (3.10)
A BRIEF REVIEW OF BER ESTIMATION TECHNIQUES CHAPTER 3
94
Thus, in order to have hundred percent accurately estimated BER, number of
random experiment has to be a finite number. Unfortunately, in a real system, it is
impossible to achieve. Additionally, in order to achieve a high accuracy of the
simulation; the length of the transmitted bits should be at least two orders of magnitude
greater than the inverse of BER [82]. This means that for e.g. 107
bits has to be
processed in order to estimate BER~10-5
. Therefore, the disadvantage of the Monte
Carlo method is the very long simulation run time. This time might be especially long in
UWB systems since in order to accurately model pulse transmission, UWB signals has
to be sampled at rates much higher than the Niquist rate. Thus, a comprehensive low-
level simulation that models all aspects of the UWB system would be expected to run
for weeks.
Figure 3.2. Schematic Representation of Implementation of Monte Carlo Method
3.3.2. Importance Sampling Technique
Importance sampling, as it is described in [82], permits a considerable saving
time by reducing the number of experiments necessary to calculate single a BER. In
order to apply this method under optimum conditions, the experiments should be
independent and the noise dimensionality should be closed to one. In Figure 3.3 the
CHAPTER 3 A BRIEF REVIEW OF BER ESTIMATION TECHNIQUES
95
Importance Sampling proces is ilustrated.The input proces is the signal plus noise vector
from (2.30),i.e. 1 2[ , ,..., ]fN
α α α=α . g(.) represents a transfer function and *α represents
the
Signal Samples sα
nαNoise Samples
System g (*)Output
(To decision device)
*α
. . . . . .
α
Nf samples
Figure 3.3. Importance Sampling Illustration
output of the system. For simplicity, it is assumed that samples of *α and α are
synchronized. It is assumed that the system has a single AWGN source with
variance 2σ , i.e. 2(0, )
nf Nα
σ∈ . Usually the biased density function can diferr from the
original just modufying the variance emphazizing it by factor 2γ . Acording to [82], the
optimum value for γ is 4. Therefore, the biased density function becomes
*
2
*(0, )nf Nα
σ∈ , where 2 2 2
*n nσ γ σ= . This scheme represents the conventional importance
sampling.
Then the BER of a binary system can be computed as
A BRIEF REVIEW OF BER ESTIMATION TECHNIQUES CHAPTER 3
96
1
N
e
eBERN
ψ
=
=
∑ (3.11)
where
0 if no error ocurred in the experiment,
if an error ocurred in the experiment,e
ewψ
=
Since this “artificial” increase in number of errors is done in a known way, it can be
easily corrected on the end of the simulation run choosing the value
2 2 2*(1 1/ )( ) / 2n
e n
ew e
γ α σ
γ−
= (3.12)
Importance sampling method appears to be theoretically one of the best
extrapolation methods in the sense of a short simulation run time. Nevertheless,
implementation of this method is dependent on the system. The reason for this is that it
is usually necessary to “enter” the system in order to emphasize the noise, and
generally, it is necessary to identify the system between each noise source and the
system input.
3.3.3. Semi-Analytic Simulation Technique
Semi-Analytic simulation technique is “hybrid” since it combines both
simulation and analysis techniques. The analysis contribution to the algorithm is BER
calculation. The simulation algorithm generates a noiseless monopulse at the receiver.
Assuming that the noise is AGN with known PDF, BER can be calculated using
formula. Comparing to Monte Carlo method, the advantage of the Semi–Analytic
technique is a time saving. This is achieved because it is not necessary to wait for errors
to occur.
In order to illustrate this technique, a binary PPM UWB system is considered
and the multipath can be modeled using a tapped delay line filter. In addition, it is
CHAPTER 3 A BRIEF REVIEW OF BER ESTIMATION TECHNIQUES
97
assumed that all system components are operating in a linear region, and the only noise
source is the thermal noise. In Figure 3.4 is shown a diagram of Semi-Analytic BER
estimation for BPSK. Relaying on the fact from digital communications theory that the
BER is a function of a signal space separation and noise power, BER for this system is
given by:
0 0 1 0 1 1 0 1( ) ( ) ( ) ( )BER P S P S D S P S P S D S= ∈ + ∈ (3.13)
Figure 3.4. Diagram of a Semi-Analytic BER Calculation for
BPSK
where S0 and S1 represent transmitted signals “0” and “1”, respectively. It is considered
that the probabilities that S0 and S1 are equal, i.e. 0 1( ) ( ) 1/ 2P S P S= = .
D0 and D1 are decision regions for “0” and “1”, respectively.
HIGH SPEED SYSTEM SIMULATOR CHAPTER 3
98
0S and 1S represent received signals “0” and “1”, respectively, and 0 1 0( )P S D S∈ and
1 0 1( )P S D S∈ are the probabilities of error given that S0 and S1 are transmitted,
respectively.
Therefore, assuming noise as an AGN, with variancen
σ , it is considered
21
2
0 1
( )
2
0 1 0
1( )
2
n
n S
S D n
P S D S e dnσ
πσ
−
∈
∈ = ∫
(3.14)
20
2
1 0
( )
2
1 0 1
1( )
2
n
n S
S D n
P S D S e dnσ
πσ
−
∈
∈ = ∫
(3.15)
Certainly, it might be useful to implement Semi-Analytic method in any
simulations, due to the following reasons; in linear channels, it can rapidly provide the
correct answer and it measures the accuracy of the other simulations methods under the
same conditions. In addition, this technique is easy to implement, although the
“analytical” part, which relates the simulated waveform to the bit error rate, depends on
the modulation method.
However, implementation of this technique is very problem specific and can not
be set up in advance in order to solve some general problems.
3.4. High Speed System Simulator
In [83] is presented a new method to design a TH-UWB (or in general TH)
communication system simulator. The method takes advantage of some of the properties
of this kind of systems in order to provide a very straightforward and fast processing
that improves all the previous designs by several orders of magnitude, independently on
the sampling rate. Comparing to previous simulators, sampling frequency can be as high
as wished, since the simulation run time does not depend on it.
CHAPTER 3 HIGH SPEED SYSTEM SIMULATOR
99
3.4.1. Signal and noise separation. Signal processing
To apply this algorithm, the first step should be the separation between the
signal and the noise component of every frame statistic. Then, a frame statistic of the ith
frame on the qth
receiver is described as
s n
i i iα α α= +
(3.16)
where assuming (2.24) and (2.26), the signal component can be presented as
dtTciTttr c
q
i
TcTi
TciT
f
qss
i
cq
if
cq
if
)()( )(
)1(
)(
)(
)(
−−×= ∫++
+
να (3.17)
with
( ) ( )
1
( ) ( ) ( )uN
s k k
k
r t s t h t=
= ∗ ∑ (3.18)
and
dtTciTttn c
q
i
TcTi
TciT
f
qn
i
cq
if
cq
if
)()( )(
)1(
)(
)(
)(
−−×= ∫++
+
να (3.19)
represents the noise part of the ith
frame statistic on the qth
receiver.
For a simplified analysis, it is useful to extract the effect related to the waveform
distortion from those related to the delay. It is known that given two functions ψ(t) and
ξ(x), with ξ(x) zero out of the interval [0, T] fulfil the following expression:
( ) ( ) ( ) ( ( )) ( ) ( )
t T
t T
t T t T
t T t x T t x dx x x dx
τ
τ
ττ
ψ ξ ψ ξ ψ ξ τ
+
= +
− = +
∗ − = − − = −∫ ∫
(3.20)
HIGH SPEED SYSTEM SIMULATOR CHAPTER 3
100
that can be applied to (3.17) as
( )
( ) ( ) ( )
( 1)1
( )* ( ) * ( )u
qf i c
N
s k k q
i f i T c Tk
s t h t T tα ν+ +
=
= − ∑ (3.21)
where ( ) ( )qv t is equal to zero out of the interval [0, Tf] as ( )
max
q
L fTτ < .
Alternatively, equivalently, applying(2.24), the signal component is
( )
( ) ( ) ( ) ( )
1 1
( )
( 1)
( )
( )* ( )
u
qf i c
N Ls k k k k
i l f j c j l
k j l
q
rec f i T c T
A t jT c T d
w t v T t
α β δ λ τ
∞
= =−∞ =
+ +
= − − − −
∗ −
∑∑∑ (3.22)
The noise component can be expressed equivalently as
( ) ( )( ) ( ) .f
n q q
i f f i c Tn t v T t iT c Tα = ∗ − − − (3.23)
Considering(2.27), after some trivial operations, the last term in (3.22) can be expanded
as
max
( ) ( ) ( )
0
( ) ( ) ( ) ( ).L
q q q
f m m f
m
v T t t t t Tϕ β δ τ δ
=
− = − ∗ + ∗ +∑
(3.24)
Thus, if it is defined the TDR, Ω(t), as
( ) ( ) ( )rec
t w t tϕΩ = − ∗ (3.25)
the signal component from (3.22) can be rewritten as
max
( ) ( ) ( ) ( ) ( ) ( )
1 1 0
* ( ( ))uN LL
s k q k k k q
i l m f j c j l m
k j l m
t jT c T dα Αβ β λ τ τ
∞
= =−∞ = =
= δ − − − − −∑∑∑∑
CHAPTER 3 HIGH SPEED SYSTEM SIMULATOR
101
( )( 1)
( ) .q
i T c Tf ci
fT t
+ +
∗Ω − (3.26)
Ω(t) is very interesting to analyze. If it is considered no channel distortion and perfect
signal estimation, Ω(t) for PPM becomes
( ) ( ) ( ) ( ) ( ),tr tr tr tr
t w t w t w t w t λΩ = − ∗ − − ∗ − (3.27)
that is the subtraction of the autocorrelation and its replica shifted by λ. In the case of
channel distortion, if the channel impulse response hdist(t) has a duration η, the TDR will
be nonzero in the interval [-Tc-η, Tc +η +λ]. This way, only positions of signals are
saved.
After the reciprocal change of(3.20), if it is defined
( ) ( ) ( ) ( ) ( )
, , , ( ) ( ) ( ),k k q k q
i j l m f j i c l mj i T c c Tε τ τ= − + − + − (3.28)
the signal component on the qth
receiver can be expressed as
( ) ( ) ( ) ( )
, , ,
, , , 0
( ) ( ) .
fT
s k q k k
i l m i j l m j
j k l m
t d t dtα Αβ β δ ε λ= − − Ω∑ ∫
(3.29)
This integral will be nonzero only for the values that satisfy
( ) ( ) ( )
, , ,
k k k
j c i j l m c jd T T dλ η ε λ η λ− − − < < + + − (3.30)
It can also be expressed with independence of the PPM transmitted data. Therefore, for
i = 1…Nf, let j, k, l, m∈Γ to be the set of values that satisfies the condition
( )
, , , .k
i j l m cTε η λ< + + (3.31)
Then, αis can be obtained as
HIGH SPEED SYSTEM SIMULATOR CHAPTER 3
102
( ) ( ) ( ) ( )
, , ,
, , ,
( ).s k q k k
i l m i j l m j
j k l m
A dα β β ε λ
∈Γ
= Ω +∑ (3.32)
Thus, the signal component of the bit statistic after the soft decision detection can be
expressed as
( ) ( ) ( ) ( )
, , ,
1 , , ,
( ).fN
s k q k k
l m i j l m j
i j k l m
A dα β β ε λ
= ∈Γ
= Ω +∑ ∑ (3.33)
therefore, the component αs is the sum of both. It is important to notice how the
sampling rate fs only determines the size of Ω(t), so it has a little impact on the total
computing time.
In the case of different links, i.e. when the distortion is different for every link, signal
can be presented as
( )
( ) ( ) ( ) ( ) ( )
, , ,
1 1 , ,
( ).f u
k
N Ns k q k k k
l m i j l m j
i k j l m
A dα β β ε λ
= = ∈Γ
= Ω +∑∑ ∑ (3.34)
A is in charge of controlling the Signal to Noise Ratio (SNR). Thus, for a given
waveform Ω(t), A can be defined as
max
( ) 2
1
,
(0) ( )
nLq
m
m
SNRA σ
β
=
=
Ω ∑ (3.35)
where σn represents the noise standard deviation.
CHAPTER 3 HIGH SPEED SYSTEM SIMULATOR
103
Link (q)Sequence
generator
( )q
j cc T
Template
generator
Channel
( )r t
Correlator
Decision
iα
Figure 3.5. Conceptual Model of the UWB Receiver for the qth
User
From the evaluation of this simulator, a large time saving can be obtained from the
following features:
• Since )(
,,,
k
mljiε is independent on the data, it can be computed only once for a whole
sequence of transmitted bits, thus the number of simulations will be reduced in
order to evaluate(3.33). Figure 3.6 shows signal processing flowchart.
• Transmitted waveform is stored in the TDR, thus it is not necessary to operate
with the signal samples in every simulation. The only influence of the sampling
rate is the length of the TDR. Since this vector is accessed at a particular position
given by λε)()(
,,,
k
j
k
mlji d+ , i.e. positions of the lth
echo of the jth
frame of the kth
link, an
increase in length could make the access slower. In the next section, it will be
shown that this effect is disregard. Therefore, it can be considered that the
simulation speed is approximately independent on the sampling rate.
HIGH SPEED SYSTEM SIMULATOR CHAPTER 3
104
• The algorithm complexity is linear with the number of users, frames, multipath
components, and RAKE fingers. In [83] importance sampling method is
implemented in order to even more make the error vector calculation faster. In this
thesis this method is avoided in order to permit the system to be no-linear and in
order to simplify the algorithm. However, with this algorithm is possible to reduce
the complexity of previous algorithms several orders of magnitude.
Figure 3.6. Signal Processing Flowchart
CHAPTER 3 CONCLUSION
105
3.5. Conclusion
In the previous sections of this thesis, has been presented an analytical model of
a whole multi-user UWB communication system. In order to simulate it, a very
straightforward structure could be based on a Monte Carlo simulation method, where a
vector of bits is generated and transmitted through a given link. The vector of bits
received after decision is compared with the original one and the Bit Error Probability
is estimated as the average number of errors between the length of the vector (number
of bits transmitted). In order to have a good estimation, this length should be at least
two orders of magnitude the inverse of the BER. Thus, hundreds of millions of bits
should be processed for a BER =10-6
.
The main problem is the length of vectors. For instance, a binary PPM TH-
UWB system with a bit rate of 100 kbps and 1 nanosecond pulses has ten thousands
possible chip slots per bit. The necessary sampling rate to avoid aliasing can be higher
than 10 Gigasamples per second, depending on the waveform, so every bit is
represented by at least one hundred thousand samples. In order to simulate the different
system blocks, several operations should be applied on these vectors (convolutions,
windowing…), so the total computing time in order to estimate a single BER value for a
given set of conditions can be very high, which reduces the simulator utility.
Speaking about time performance of the enhanced time-hopping simulator
algorithm, three facts should be remarked:
1. Computational time linearly grows with the number of users, the number of
chips, the channel length and the number of RAKE fingers.
2. Computational time is independent on the sampling frequency.
3. Computational time is at least two orders of magnitude lower than those from
previous TH simulators presented in the literature
106
CHAPTER 4 A NOVEL APPROACH OF MULTIUSER SIGNAL MODEL FOR SIMULATIONS
107
Chapter 4
4. A Novel Approach of Multiuser
Signal Model for Simulation
Purposes
4.1. Introduction
It is known that MMSE receiver has the best performance in terms of SINR at
the expense of high computational complexity. In addition, in order to process ultra-
wideband signals, an extremely large sampling rate is mandatory. Therefore, in order to
compute BER curves, simulation time can be very long.
Implementation of any multiuser detector in this algorithm might be a difficult
issue, since a signal is masked by TDR and a typical multiuser structure with correlation
matrix does not exist. Therefore, applying this method, in this thesis, a new approach of
multiuser detection is achieved. With this approach, it is possible to reduce the
simulation process significantly by avoiding any convolution operation, which is the
most time-consuming. This algorithm takes advantage of some of the properties of IR-
TH-UWB systems in order to improve all the previous designs by several orders of
magnitude, independently on the sampling rate, in terms of a very straightforward and
fast processing. Relaying on this approach, number of simulation operations needed to
evaluate MMSE receiver matrix are reduced. Thus, it is possible to process a large
number of samples and to accurately estimate low BER in a short time application.
Assuming all the features of the algorithm, numerical results show three main
time performances of this algorithm. First, simulation time linearly grows with the
number of users and the number of frames. Second, simulation time does not depend on
A NOVEL APPROACH OF MULTIUSER SIGNAL MODEL FOR AWGN CHANNEL CHAPTER 4
108
the sampling frequency and simulation time per bit is order of ns. Third, the number of
simulation operations in order to calculate any multiuser detector is reduced.
This chapter presents one part of the contribution of this thesis.
4.2. A Novel Approach of Multiuser Signal Model for AWGN
Channel
In this section, based on the high-speed simulation algorithm, it is presented the
novel multiuser signal model for the AWGN channel [84]. AWGN channel is applied
by specifying parameters in (3.26) and (3.33) as ( ) ( ) 0k q
l mτ = τ = , L=Lmax=1
and ( ) ( ) 1k q
l mβ β= = .
It is supposed that all Nu transmitters are active and all the transmissions from
the active transmitters are synchronized.
Therefore, only one symbol interval can be considered. Then from(3.33), the signal
component on the qth
receiver can be presented as
( ) ( )
1
( ) .uN
q k k n
i i i
k
A dα ε λ α
=
= Ω + +∑ (4.1)
The noise contribution to the frame statisticsi
α on the qth
receiver can be presented as
, ( ) ( )( ) ( ) .f
n q q q
i f f i c Tn t v T t iT c Tα = ∗ − − − (4.2)
Then, frame statistics might be represented as
( ) ( )
1
( ) .uN
q k k n
i i i
k
A dα ε λ α
=
= Ω + +∑ (4.3)
CHAPTER 4 A NOVEL APPROACH OF MULTIUSER SIGNAL MODEL FOR AWGN CHANNEL
109
Defining ( ) ( )1 2k kb d= − , the frame statistic s
iα on the q
th receiver can be presented on the
other way as
, ( ) ( )
1
( ) .uN
s q k k n
i i i
k
b Aα ε α
=
= Ω +∑ (4.4)
From (4.4), the signal vector on the qth
receiver can be rewritten in matrix form as
,q n= +
qα R Ab α (4.5)
where
1 2[ , ,..., ] ,f
q T
Nα α α=α
[ , ,..., ] ,f
n n n n T
Να α α
1 2=α
1 2diag( , ,..., ),uN
A A A=A
1 2[ , ,..., ] ,u
T
Nb b b=b and
( )(1) (2)
1 1 1
( )(1) (2)
2 2 2
( )(1) (2)
( ) ( ) ( )
( ) ( ) ( ).
( ) ( ) ( )
u
u
u
f f f
N
N
N
N N N
ε ε ε
ε ε ε
ε ε ε
Ω Ω Ω
Ω Ω Ω
= Ω Ω Ω
qR
(4.6)
From (2.3) and the orthogonallity of ( )tr
w t and ( )tr
w t λ− , assuming perfect signal
and channel estimation, it can be shown that noise power on the output of the receiver is
( )
( )
( )
( )
( 1)2, 2 ( ) ( ) 2
( 1)
2 2
2
[( ) ] ( ( ))2
( )
.
q
f i c
q
f i c
qf i c
qf i c
i T c T
n q q qni f i c
iT c T
i T c T
n tr
iT c T
n
E t iT c T dt
w t dt
σα ν
σ
σ
+ +
+
+ +
+
= − − =
=
∫
∫ (4.7)
A NOVEL APPROACH OF MULTIUSER SIGNAL MODEL FOR AWGN CHANNEL CHAPTER 4
110
It implicates the following
2(( ) ) .T
nE σ=
n,q n,qα )(α I (4.8)
From (4.6) it can be seen that this is not a typical correlation matrix from [85]defined as
( , )(1, ) (2, )
1 1 1
( , )(1, ) (2, )
2 2 2
( , )(1, ) (2, )
u
u
u
f f f
N qq q
N qq q
N qq q
N N N
u u u
u u u
u u u
=
qR
(4.9)
where for all k and i
( ) ( )
( , )
( ) ( )
1 if
0 if
k q
i ik q
fi
k q
i i
c cNu
c c
=
=
≠
(4.10)
where assuming a random TH sequences, we have
( ) ( ) 1( )k q
r i i
h
P c cN
= = , for k q≠ (4.11)
Thus, comparing those correlation matrices from (4.6) and (4.9), it is obvious that in
order to calculate matrix from (4.6)it is not necessary to operate with the signal sample
every time when the TH sequence change. Since )(
,,,
k
mljiε is independent on the data, it
might be computed only once for a whole sequence of transmitted bits, only when the
channel conditions change.
MMSE RAKE RECEIVER IMPLEMENTATION CHAPTER 4
111
4.3. A Novel Approach of Multiuser Signal Model for Synchronous
Channel
This section describes a novel approach of multiuser signal model for
synchronous multipath channel [88]. There are no many literatures dealing with this
topic. In the case of multipath propagation, size of the matrix qR will beu
Q N× , where
Q is the number of components of the largest column. Q depends on the channel and
RAKE structure and its average value is in general smaller than max2
f
u
LL N
N .The
elements of qR are values that fulfils (3.31). In the case of no overlapping of the RAKE
windows, this value is smaller than2
f
u
LN
N. The columns whose length is less then Q
are completed with zeros. In addition, in the presence of multipath environment, beside
the valid values of ( )
, , ,
k
i j l mε , their corresponding amplitudes ( ) ( )k q
l mβ β would be stored.
Therefore, the correlation matrix on the lth
echo on the mth
RAKE finger is
( ) ( )(1) ( ) (1) (2) ( ) (2) ( )
1, , 1, , 1, ,
( ) ( )(1) ( ) (1) (2) ( ) (2) ( )
2, , 2, , 2, ,
,
( )(1) ( ) (1) (2) ( ) (2)
, , , ,
( ) ( ) ( )
( ) ( ) ( )
( ) ( )
u u
u u
u
N Nq q q
l m l m l m l m l m l m
N Nq q q
l m l m l m l m l m l m
l m
Nq q
l m Q l m l m Q l m l
β β ε β β ε β β ε
β β ε β β ε β β ε
β β ε β β ε β β
Ω Ω Ω
Ω Ω Ω
=
Ω Ω
qR
( )( )
, ,( )uNq
m Q l mε
Ω
(4.12)
Thus, the correlation matrix will be
max
,
1 1
.LL
l m
l m= =
=∑∑q qR R (4.13)
Multipath propagation has influence on the length of the TDR. However, matrix
Ω should be recalculated only when the channel conditions change. Depending on the
channel coherence time and the bit rate, it is possible to find the number of bits that can
MMSE RAKE RECEIVER IMPLEMENTATION CHAPTER 4
112
be simulated without alerting qR . Simulation results for multipath channel have been
validated in [89] and [90].
4.4. MMSE RAKE Receiver Implementation
Equation (4.5) will play a key role for implementation of any multiuser detector into
TH-UWB systems. Depending how the matrix q
M is selected, different receivers can
be implemented as
( ) 1q
q
−
=b A M α (4.14)
In [91], for the case of MMSE receiver, matrixq
M is defined as
α
( )
, , ,
k
i j l mε
Figure 4.1. Signal Processing Flowchart (as in [83])
2arg min .
qE = − M
M Mα Ab (4.15)
CHAPTER 4 MMSE RAKE RECEIVER IMPLEMENTATION
113
Using the principle of orthogonallity from [92], i.e. the fact that [( ) ] 0TE − =Mα Ab α ,
from (4.15) can be obtained
1( ) ( [ ]) ,T T T
q E−
=qM AA R αα (4.16)
where [ ]TE αα represents the covariance matrix ofα , given as
2
[ ] [ ( ) ] [( )( ) ]
( ) [ ] [( )( ) ]
( ) ( ) .
T T T T T
T T T T
T T
n
E E E
E E
σ
= + =
+ =
+
q q n n
q q n n
q q
αα AA R bb R α α
R AA R bb α α
R AA R I
(4.17)
As it was mentioned before, since )(
,,,
k
mljiε is independent on the data, it needs to be
calculated only once for the whole sequence of the transmitted bits as Figure 4.1
illustrates. This means that reduced number of operations will be needed in order to
calculate matrix qR , i.e. to calculate matrixq
M . In Figure 4.2 is shown error vector
calculation flowchart, and in
Figure 4.3 a complete simulator flowchart is presented.
It should be noticed ho the algorithm complexity is linear with number of users,
frames, multipath components and RAKE fingers. It can be seen how the values stored
in the matrix qR , defined as
( )(1) (2)
1 1 1
( )(1) (2)
2 2 2
( )(1) (2)
( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( )
u
u
u
f f f
N
N
N
N N N
ε ε ε
ε ε ε
ε ε ε
Ω Ω Ω
Ω Ω Ω
= Ω Ω Ω
qR
(4.18)
MMSE RAKE RECEIVER IMPLEMENTATION CHAPTER 4
114
which represent time positions in the TDR waveform are multiplied by their amplitudes
and the transmitted data and used to generate MMSE receiver matrix.
As we mentioned before, since )(
,,,
k
mljiε is independent on the data, it needs to be calculated
only once for the whole sequence of the transmitted bits. This means that the reduced
number of operations will be needed in order to calculate matrix qR , i.e. to calculate
matrixq
M .
qM ...1
Vector
transmitted
0
K
Accumulator
DecisionLink (q)
0
Vector received0 0 0 1
...
0 1 0 0...X-OR0 1
K
K
×
A White Gaussian Noise
uN
0
( )qb
×
+×
TAA
×
Amplitudes
βl(k)
βm(q)
Positions in
the TDR
waveform (k)iu
(q) T(R )
2
nσ I
]TE[αα
× +1
0
uN
1( )−
⋅
Ω
Figure 4.2. Error Vector Calculation Flowchart
CHAPTER 4 MMSE RAKE RECEIVER IMPLEMENTATION
115
Figure 4.3. Simulator Flowchart
In Figure 4.4 is shown how positions of signals are calculated.
Matrix T represents the chip positions
(1) (1) (1) (1)
1 0 0
( ) ( ) ( ) ( )
1 0 0
f
u u u u
f
c f N c f f
N N N N
c f N c f f
c T T c T N T
c T T c T N T
τ τ
τ τ
+ + + +
=
+ + + +
T
(4.19)
and P represents the channel delay
(1) (1)
1
( ) ( )
1u u
L
N N
L
τ τ
τ τ
=
P
(4.20)
In order to compute ( )
, , ,
k
i j l mε an element tkj of T and another pkl of P should be chosen, (for
1..k..Nu, for 1..j..Nf, and 1..l..L), and added. The result is the position of the lth
received
echo of jth
chip of the kth
link. Then, position in the first link frame i can be calculated
as (tkj + pkl )/Tf where · denotes ‘the maximum integer smaller than ·’. This chip
affects both to the ith
and to the (i-1)th
receiver windows (due to the RAKE length) .
Vector received
Multiuser
Interference
TH-UWB
Transmitter
TH-UWB
Channel
MMSE RAKE
Receiver
0 0 1 0 ...
0 1 1 0 ... 0 1 0 0 ... X-OR
Vector transmitted
Noise Vector
THEORETICAL PERFORMANCE OF THE MMSE RECEIVER (NOVEL APPROACH) CHAPTER 4
116
Thus, the two possible relative positions will be ζ(k)
r = (tkj + pkl ) – c(k)
(i+r)Tc- (i+r)Tf , r =
-1, 0 . These positions affect the decision if (3.31) is verified, therefore all the values
that satisfy that )(
,,,
k
mljri+ε = ζ(k)
r-τ(1)
m <Tc + η , 1..m,..Lmax, r = -1, 0 can be computed
and they can be stored in the row vector e(k), with a length inferior to 2LmaxLNf.
Figure 4.4. Position Vector Calculation Flowchart
4.5. Theoretical Performance of the MMSE Receiver-Based on the
Novel Approach
From(4.15), (4.16) and [93], it can be demonstrated that the SINR of the MMSE detector
is given as
2 2 1( ) ( ) ( ( ) )T T T
q qSNR q A σ−
= +(k) q q (k)i iu R D R I u (4.21)
where (k)iu represents the k
th column of the matrix qR , i.e.:
+
T
P
tkj
pkl
L
Nu
Nu
Nf
Tf
ζ-1
ζ0
i Lmax
τ(q)
m
+ Is
ζ(k)r -τ
(q)m <Tc+η?
r
Store positions
CHAPTER 4 THEORETICAL PERFORMANCE OF THE MMSE RECEIVER (NOVEL APPROACH)
117
max
max
max
( )
1
( )
2
( )
( ) ( ) ( )
1, ,
1 1
( ) ( ) ( )
2, ,
1 1
( ) ( ) ( )
, ,
1 1
( )
( ) for the AWGN case
( )
( )
( ) for the
( )
f
k
k
k
N
LLk q k
l m l m
l m
LLk q k
l m l m
l m
LLk q k
l m Q l m
l m
ε
ε
ε
β β ε
β β ε
β β ε
= =
= =
= =
Ω
Ω Ω
Ω =
Ω
Ω
∑∑
∑∑
∑∑
(k)iu
multipath channel case
(4.22)
qΩ is the sub matrix of Ω derived by deleting the q
th column vector, and qD is the
diagonal matrix given as
2diag( ,..., , ,... ),
u
2 2 2
q 1 q-1 q+1 NA A A A=D (4.23)
Therefore, BER can be calculated as
( ( ))BER Q SNR q= (4.24)
For the multipath channel case, the random channel model is generated according to
[76], where rays within an observation window arrive in several clusters. The magnitude
of each arriving ray is a lognormal distributed random variable with exponentially
decaying mean square value with parameters Γ and γ . The cluster arrival times are
modelled as Poisson variables with cluster arrival rate Λ . Rays within each cluster
arrive according to a Poisson process with ray arrival rate λ . Channel model parameters
are as before selected to be Γ =16 γ =8.5, 1/ Λ =11 ns, 1/ λ =0.35 ns, L=400, Lmax=400.
In the case of AWGN channel, i.e. considering L=1, Lmax=1, noise variance is2
1n =σ .
The pulse shaper is selected to be the second derivative of the Gaussian function that
has been normalized to have unit energy. For the multipath channel case, results show
the ensemble performance of 100 realizations.
CONCLUSION CHAPTER 4
118
10 11 12 13 14 15 16 17 18 19 20 2110
-5
10-4
10-3
10-2
10-1
Eb/N0
BE
R
theoretical MMSE receiver performance in AWGN channel
simulated MMSE receiver performance in AWGN channel
theoretical MMSE receiver performance in NLOS channel
simulated MMSE receiver performance in NLOS channel
Figure 4.5.Comparison Between the Theoretical and Results Obtained with New
Approach for AWGN and NLOS Channel; Γ =16 γ =8.5, 1/ Λ =11 ns, 1/ λ =0.35 ns,
L=400, Lmax=400;Nu=5; Nf=8; Nh=4
4.6. Conclusion
Consequently, the presented numerical results show the following time
performance of this algorithm:
1. There is no dependence between the sampling frequency and simulation time.
Therefore, increasing the sampling frequency as much as needed, a very high
accuracy can be achieved without prolonging the simulation time;
2. Simulation time linearly grows with the number of users, frames and multipath
components;
CHAPTER 4 CONCLUSION
119
3. Comparing MMSE correlation matrices from (4.9)and (4.12), it can be seen that
in order to calculate matrix from (4.12)it is not necessary to operate with the signal
sample and to calculate MMSE matrix inversion every time when the TH sequence
change. This fact significantly reduces the complexity of this algorithm.
Complexity of this algorithm is O(Nu*Nf*L*Lmax), while using Monte Carlo
method complexity is Nh times higher. Therefore, assuming a large spreading
factor of the UWB signals and a high computational complexity of MMSE
receiver matrix, this algorithm yields a large saving of simulation time comparing
to the previous designs.
With this accurate flexible simulation model; we might analyze the
influence of the MMSE receiver on different factors of TH-UWB systems (the
number of users, waveform design time-hopping codes, channel models…) and
achieve a low BER in a real time application even in the presence of reach
multipath environment.
120
CHAPTER 5 SIMULATION RESULTS
121
Chapter 5
5. Simulation Results
5.1. Introduction
Since an accurate and flexible simulation model is obtained; this chapter
analyzes the influence of different factors (number of users, number of chips, waveform
designs, sampling frequency, receiver architectures, channel models…).
Those results under different scenarios have already been presented in many
works until now, but using this algorithm is possible to reach BER order of 10-6
for such
system loading (the number of transmitters with different pairs (Nh, Nf)) in a short time
application. The results will be divided in two groups. On one side is system
performance employing single user receiver, and on the other, the system performance
when multiuser MMSE receiver is implemented.
Two channel models are employed. First one is AWGN channel with noise
variance is 2 1n
=σ . Second one is generated according to [76]. The magnitude of each
arriving ray is a lognormal distributed random variable with exponentially decaying
mean square value with parameters Γ and γ . The cluster arrival times are modelled as
Poisson variables with cluster arrival rate Λ . Rays within each cluster arrive according
to a Poisson process with ray arrival rate λ . In the second one, channel model
parameters are selected to be Γ =16, γ =8.5ns, 1/ Λ =11 ns, 1/ λ =0.35 ns. It is
considered the system with the chip duration Tc= 2 ns, and PPM time shift λ =180 ps.
SIMULATION RESULTS CHAPTER 5
122
5.2. Single User Receiver
5.2.1. Number of Users Influence on BER Performance in AWGN Channel
5 6 7 8 9 10 11 12 13 1410
-7
10-6
10-5
10-4
10-3
10-2
10-1
SNR
BE
R
Nu=2
Nu=16
Nu=64
Nu=128
Figure 5.1. Number of Users Influence on BER performance employing Single User
Receiver; Second Derivative of the Gaussian Monopulse; AWGN channel ; Nf=32,
Nh=64, fs=200/Tc
In Figure 5.1, the BER performance in terms of system loading (i. e. the number
of users Nu) is presented. It is assumed that pseudorandom time hopping codes are used
with Nf=32, Nh=64 in the presence of AWGN channel. As the number of users
increases, there are more interfering signals. Hence, the performance becomes worse as
shown in Figure 5.1. For example, with normalized system loading L= Nu/ (Nf*Nh)
=0.000976 is possible to reach BER=10-5
for SNR=12.5 dB. It can be seen how single
CHAPTER 5 SIMULATION RESULTS
123
user receiver performance breaks down dramatically as more users are added to the
system. With a reasonable load of Nu=64 users, a 3-dB penalty is seen at BER=10-3
comparing to the case when only one interferer is presented.
5.2.2. Number of Chips Influence on BER Performance in AWGN Channel
5 6 7 8 9 10 11 12 13 1410
-5
10-4
10-3
10-2
10-1
100
SNR
BE
R
Nh=2
Nh=16
Nh=32
Nh=64
Figure 5.2. Number of Chips Influence on BER performance employing Single User
Receiver; Second Derivative of the Gaussian Monopulse; AWGN channel; Nu=64,
Nf=64, fs=200/Tc,
In order to see the impact of (Nf, Nh) for a fixed Nf=64 and Nu =64, the following
cases are considered Nh =2, 16, 32 and 64. In Figure 5.2 it can be seen how the
performance of the single user detector can be improved as Nh increases, as expected.
SIMULATION RESULTS CHAPTER 5
124
For example, the loss of 4-dB when Nu=2* Nh is seen at BER=2*10-3
comparing to the
case when the number of user is equal to the number of chips.
5.2.3. Type of the Monocycle Influence on BER Performance in AWGN
Channel
5 6 7 8 9 10 11 12 13 1410
-3
10-2
10-1
SNR
BE
R
Second Derivative of the Gaussian Monocycle
Rayleigh Monocycle
Cubic Monocycle
Figure 5.3. Monocycle Shape Influence on BER performance employing Single User
Receiver; AWGN channel ; Nu=64, Nh=64, Nf=8, fs=200/Tc,
To see the impact of monopulse shape in the presence of AWGN channel, 3
types of monocycles are used: second derivative of the Gaussian, Rayleigh and Cubic
monocycle with the same duration for Nu=64, Nh=64, Nf=8. In Figure 5.3 is shown that
those monocycles have similar BER performance. From the point of view of
CHAPTER 5 SIMULATION RESULTS
125
interference, in [41] is described the in-band interference study, where the victim radio
systems are UMTS/WCDMA, GSM900, and GPS. It is shown that better results are
achieved with proper selection of UWB pulse waveform and their width for spectral
planning. Using short pulses, interference in the observed frequency bands is the
smallest if the pulse waveform is based on higher order Gaussian waveforms.
In addition, some possible waveforms for the UWB monocycle have been proposed in
[56] and [57].
5.2.4. Sampling Frequency Influence on BER Performance in AWGN
Channel
5 6 7 8 9 10 11 12 13 1410
-6
10-5
10-4
10-3
10-2
10-1
100
Eb/N0
BE
R
fs=10/Tc
fs=40/Tc
fs=200/Tc
Figure 5.4. Sampling Frequency Influence on BER performance employing Single User
Receiver; Second Derivative of the Gaussian Monopulse; AWGN channel; Nu=64,
Nh=64, Nf=8, Nh=4
SIMULATION RESULTS CHAPTER 5
126
The effect of the sampling frequency on BER performance employing single
user receiver in the presence of AWGN channel can be seen in Figure 5.4. It can be
noticed how the performance of single user detector can be improved as fs increases, as
expected. For example, the performance of 1-dB when fs =200/Tc is seen at BER=10-5
comparing to the case when the sampling frequency is 5 times lower. It is shown that
the low sampling frequency as fs=10/Tc will seriously affect BER performance.
As it will be shown how there is no dependence between the bit simulation time
and the sampling frequency, a very high accuracy can be obtained without affecting the
simulation time, which is a very important feature of the algorithm.
5.2.5. Influence of Different Parameters on BER Performance in the
Multipath Channel
Since the single user detector is not able to handle multipath signal neither
for two users, as it is shown in Figure 5.5, in this thesis previous analysis of the system
performance in the presence of multipath channel will not be done.
5 6 7 8 9 10 11 12 13 14
10-0.7
10-0.6
10-0.5
SNR
BER
Nu=2;Nh=64;Nf=32
Figure 5.5. BER performance employing Single User Receiver; Second Derivative of
the Gaussian Monopulse; Multipath Channel L=400, Nu=2, Nh=64, Nf=32, fs=200/Tc
CHAPTER 5 SIMULATION RESULTS
127
5.2.6. Synchronization and Channel Estimation
In this section, simulation results for two cases under the consideration are
discussed. It is presented how the synchronization increases the system performance in
downlink which block scheme is presented in Figure 5.6, and after that, for the same
scenario, in uplink shown in Figure 5.7.
In order to see this method performance, all results are obtained in the presence
of NLOS channel from Table 2.4 based on Intel measurements, just with 20 multipath
components, since the single user detector is not able to handle multipath signal neither
for two users as it is shown in Figure 5.5. In the simulations is considered system with
13 users where chip duration is Tc=2 ns, sampling frequency fs=200/Tc, Nf=8 and
Nh=256. Additionally, in order to gather multipath energy, the performance of the
system is examined using RAKE correlation receivers.
( )n t
receiverth
q( )
( )k
h t
(1)( )s t
(2)( )s t
( )( )uN
s t
Figure 5.6. UWB Downlink System Model
( )n t
receiverthq
(1) ( )s t
(2) ( )s t
( )( )uN
s t
(1)( )h t
(2)( )h t
( )( )uN
h t
Figure 5.7. UWB Uplink System Model
SIMULATION RESULTS CHAPTER 5
128
5 6 7 8 9 10 11 12 13 14 1510
-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
SNR
BE
R
known channel
10000 pilots
100 pilots
Figure 5.8. Channel Estimation Performance in the PPM TH-UWB System Downlink
employing RAKE Receiver in NLOS Multipath Channel based on Intel Measurements
from Figure 3.4; Lmax=18, Nu=13, Nf=32, Nh=128, fs=200/Tc, Perfect Synchronization
SNR 9 10 11 12 13 14
BER(known channel) 0.003
0.0011 0.0003 0.00006 0.00001 0.000001
BER (100 pilots) 0.01 0.0045 0.0022 0.0005 0.0001 0.00002
BER(10000 pilots) 0.02 0.009 0.004 0.0012 0.0035 0.00007
Table 5.1 Channel Estimation Performance in the PPM TH-UWB System Downlink
employing RAKE Receiver in NLOS Multipath Channel based on Intel Measurements
from Figure 3.4; Lmax=18, Nu=13, Nf=32, Nh=128, fs=200/Tc, Perfect Synchronization
CHAPTER 5 SIMULATION RESULTS
129
5 6 7 8 9 10 11 12 13 1410
-6
10-5
10-4
10-3
10-2
10-1
100
SNR
BE
R
known channel
10000 pilots
100 pilots
10 pilots
1 pilot; TR case
Figure 5.9. Channel Estimation Performance in the PPM TH-UWB System Uplink
employing RAKE Receiver in NLOS Multipath Channel from Figure 3.4 based on Intel
Measurements; Nu=13, Nf=32, Nh=128, fs=200/Tc, Perfect Synchronization
SNR 9 10 11 12 13 14
BER(known channel) 0.003
0.0012 0.0004 0.00012 0.000013 0.00000001
BER (10000 pilots) 0.01 0.005 0.0018 0.0005 0.0001 0.00002
BER(100 pilots) 0.02 0.007 0.0035 0.0012 0.0004 0.00006
BER(10 pilots) 0.05 0.03 0.02 0.01 0.007 0.003
BER(1 pilot) 0.5 0.5 0.5 0.5 0.5 0.5
Table 5.2 Channel Estimation Performance in the PPM TH-UWB System Uplink
employing RAKE Receiver in NLOS Multipath Channel from Figure 3.4 based on Intel
Measurements; Nu=13, Nf=32, Nh=128, Perfect Synchronization
SIMULATION RESULTS CHAPTER 5
130
5 6 7 8 9 10 11 12 13 1410
-7
10-6
10-5
10-4
10-3
10-2
10-1
100
SNR
BE
R
perfect synchronization
synchronization
asynchronized system
Figure 5.10. BER Performance versus SNR of a PPM TH-UWB System Downlink
employing RAKE Receiver in NLOS Multipath Channel from Figure 3.4 based on Intel
Measurements; Lmax=18, Nu=13, Nf=32, Nh=128, Np=10000, fs=200/Tc
SNR 9 10 11 12 13 14
BER(synchronized) 0.002
0.0007 0.0004 0.00012 0.000013 0.000001
BER (perfect timing) 0.15 0.007 0.025 0.0008 0.0002 0.000035
BER(asynchronized) 0.5 0.5 0.5 0.5 0.5 0.5
Table 5.3. BER Performance versus SNR of a PPM TH-UWB System Downlink
employing RAKE Receiver in NLOS Multipath Channel from Figure 3.4 based on Intel
Measurements; L=400; Lmax=18; Nu=13; Nf=32; Nh=128; Np=10000
CHAPTER 5 SIMULATION RESULTS
131
5 6 7 8 9 10 11 12 13 1410
-7
10-6
10-5
10-4
10-3
10-2
10-1
100
SNR
BE
R
perfect synchronization
synchronization
asynchronized system
Figure 5.11. BER Performance versus SNR of a PPM TH-UWB System Uplink
Employing RAKE Receiver in a NLOS Multipath Channel from Figure3.4 based on
Intel Measurements; Nu=13, Nf=32, Nh=128, Np=10000, fs=200/Tc
SNR 9 10 11 12 13 14
BER(synchronized) 0.002
0.0007 0.0004 0.00012 0.000013 0.000001
BER (perfect timing) 0.15 0.007 0.025 0.0008 0.0002 0.000035
BER(asynchronized) 0.5 0.5 0.5 0.5 0.5 0.5
Table 5.4. BER Performance versus SNR of a PPM TH-UWB System Uplink
employing RAKE Receiver in NLOS Multipath Channel from Figure 3.4 based on Intel
Measurements; Lmax=18, Nu=13, Nf=32, Nh=128, Np=10000, fs=200/Tc
Figure 5.8 (Table 5.1) and Figure 5.9 (Table 5.2) displays the performance of a
pilot-based receiver in system downlink and uplink, respectively. It should be noted that
SIMULATION RESULTS CHAPTER 5
132
the BER curve gets arbitrary closer to the lower bound as the number of pilots increases.
Figure 5.11 shows the influence of the joint synchronization on the system performance
in downlink and uplink, respectively. It is shown that timing offset will seriously affect
BER performance, while degradation in the case when synchronization is applied
comparing to perfect timing is only 2 dB for BER=10-4
.
5.3. Time Performance and Complexities of the algorithm
This section presents some of the time performances of this method. As it is
shown in Figure 5.12, simulation time per bit is independent on the sampling frequency.
Therefore, increasing the sampling frequency as much as needed, a very high accuracy
can be reached without prolonging the simulation time. Figure 5.13 demonstrates that
simulation time of the applied method is linearly dependent on the number of multipath
components.
Table 5.5 demonstrates the difference in complexity of this and Monte Carlo
algorithm. Implementation of the synchronization in the enhanced time algorithm is
described in Appendix A. It is shown that complexity of this algorithm is
O(Nu*Nf*L*Lmax), while using Monte Carlo method complexity is Nh times higher.
Thus, considering a large spreading factor of the UWB signals, this algorithm causes a
large saving of computational time comparing to the previous designs.
Figure 5.12. Relation between the Sampling Frequency and the Simulation Time per Bit
for a PPM-TH-UWB System with PWAM assuming Synchronization; SNR=5dB, Np=1,
fs=200/Tc
CHAPTER 5 SIMULATION RESULTS
133
Figure 5.13. Effect of the Number of Multipath Components on the Simulation Time
per Bit for a PPM-TH-UWB System with PWAM assuming Perfect Synchronization;
SNR=5dB, Np=1, fs=200/Tc
Table 5.5. Comparison of the Algorithms Complexities
Algorithm Complexity of the
Algorithm
Perfect timing in downlink O(Nu*Nf*L*Lmax)
Synchronization in downlink O(Nu*Nf*L*Lmax)
Perfect timing in uplink O(Nu*Nf*L*Lmax)
Synchronization in uplink O(Nu*Nf*L*Lmax)
Monte Carlo simulator
with fixed rate
O(Nh*Nu*Nf*L*Lmax)
SIMULATION RESULTS CHAPTER 5
134
5.4. Multiuser Receiver
In order to validate this thesis approach for MUD in TH-UWB system, Figure
5.14 presents comparison between the theoretical results from [88] and the simulation
results based on this new approach. As a reference case, the theoretical curves for the
case of conventional TH-UWB with employed multiuser MMSE detector and single
user detector are repeated from [88]. It is obvious that the results obtained with a new
approach are the same as in [88]. The system with five users is considered in the
presence of AWGN channel ( 2 1n
σ = ), where Tc= 2 ns, fs=200/Tc, PPM λ = 180 ps, Nf =8
and Nh =4. The pulse shaper has been selected to be the second derivative of the
Gaussian function and has been normalized to have unit energy. All simulations have
been done in Mathlab with a Pentium IV, on 3 GHz with 512 MHz RAM, running under
Windows XP.
0 5 10 15 20 25 3010
-4
10-3
10-2
10-1
100
Eb/N0
BE
R
theoretical conventional MMSEsingle user detector using our algorithmconventional MMSE using our algorithmtheoretical single user detector
Figure 5.14.Comparison Between Results from [85] and Results Obtained with a
New Approach; L=1 (AWGN); Nu=5, Nf=8, Nh=4, fs=200/Tc
CHAPTER 5 SIMULATION RESULTS
135
In this section, results are obtained employing MMSE RAKE receiver. Three
channel models are considered. First one is AWGN channel with noise variance 2 1n =σ .
Second and third has 400 paths and is generated according to [76].
The magnitude of each arriving ray is a lognormal distributed random variable
with exponentially decaying mean square value with parameters Γ and γ . The cluster
arrival times are modelled as Poisson variables with cluster arrival rate Λ . Rays within
each cluster arrive according to a Poisson process with ray arrival rate λ . In the second
one, (Channel 2), channel model parameters are selected to be Γ =16, γ =8.5ns,
1/ Λ =11 ns, 1/ λ =0.35 ns. In the third one, (Channel 3), the parameters are selected to
be Γ =33, γ =5 ns, 1/ Λ =2 ns, 1/ λ =0.5 ns. In all simulations, system with Tc= 2 ns, and
λ = 180 ps is considered.
5.4.1. Number of Users Influence on BER Performance in the AWGN
Channel Employing MMSE RAKE Receiver
12 13 14 15 16 17 18 19 20 2110
-5
10-4
10-3
10-2
10-1
Eb/N0
BER
Nu=2
Nu=5
Nu=10
Nu=20
Figure 5.15. Effect of the Number of Users on BER Performance for a PPM-TH-UWB
System with MMSE Receiver; Nh=4, Nf=8, Tc=2 ns, fs=200/Tc, L=1
SIMULATION RESULTS CHAPTER 5
136
In Figure 5.15, the BER performance in terms of system loading L= Nu/ (Nf*Nh) (i. e.
the number of users Nu) is presented. It is assumed that pseudorandom time hopping
codes are used with Nf=8, Nh=4 in the presence of AWGN channel. In all simulations,
MMSE receiver as a MUD is employed. As the number of users increases, there are
more interfering signals. Therefore, the performance becomes worse as shown in Figure
5.15 and with normalized system loading of L= Nu/ (Nf*Nh) =0.0625 is possible to reach
BER=10-5
for Eb/N0=21dB.
It can be seen how MMSE receiver performance not breaks down dramatically
as single user detector (Figure 5.1) as more users are added to the system. With a load
of Nu=20 users=5*Nh, only 2-dB penalty is seen at BER=10-3
comparing to the case
when only one interferer is presented.
5.4.2. Number of Chips Influence on BER Performance in AWGN Channel
employing MMSE Receiver
12 13 14 15 16 17 18 19 20 2110
-6
10-5
10-4
10-3
10-2
10-1
Eb/N0
BE
R
Nh=2
Nh=4
Nh=8
Nh=16
Figure 5.16. Effect of the Number of Chips on BER Performance for a PPM-TH-UWB
System with MMSE Receiver; Nu=5, Nf=8, Tc=2 ns, fs=200/Tc, L=1
CHAPTER 5 SIMULATION RESULTS
137
In order to see the influence of (Nf, Nh) for a fixed Nf=8 and Nu =5 on BER performance,
the following cases are considered Nh =2, 4, 8, 16. In Figure 5.16 it can be seen how the
performance of the MMSE detector can be improved as Nh increases, as expected. For
example, the loss of 3-dB is seen at BER=10-3
when Nh=2< Nu comparing to the case
when Nh=16>3* Nu.
5.4.3. Sampling Frequency Influence on BER Performance in AWGN
Channel employing MMSE Receiver
10 12 14 16 18 20 2210
-5
10-4
10-3
10-2
10-1
Eb/N0
BE
R
fs=10/Tc
fs=20/Tc
fs=40/Tc
fs=200/Tc
Figure 5.17. Sampling Frequency Influence on BER performance employing MMSE
Receiver; Second Derivative of the Gaussian Monopulse; AWGN channel; Nu=64,
Nh=64, Nf=8, Nh=4
The impact of the sampling frequency on BER performance employing MMSE receiver
in the presence of AWGN channel can be seen in Figure 5.17. It can be seen how the
SIMULATION RESULTS CHAPTER 5
138
performance of MMSE detector can be improved as fs increases, as expected. It should
be noted that the BER curve gets arbitrary closer to the lower bound as the sampling
frequency increases. For example, the performance of 3-dB when fs =200/Tc is seen at
BER=10-3
comparing to the case when the sampling frequency is 10 times lower. It is
shown that low sampling frequency as fs=10/Tc will seriously affect BER performance.
Additionally, BER performance is the same when fs=200/Tc and fs=40/Tc.
As it will be shown how there is no dependence between the bit simulation
time and the sampling frequency, a very high accuracy can be obtained without
affecting the simulation time, which is a very important feature of the algorithm.
5.4.4. Number of Users Influence on the BER Performance in the Channel2
Employing MMSE RAKE Receiver
10 12 14 16 18 20 22 24 26 2810
-6
10-5
10-4
10-3
10-2
10-1
Eb/N0
BE
R
Nu=2
Nu=5
Nu=10
Figure 5.18. Effect of the Number of Users on BER Performance for a PPM-TH-UWB
System with MMSE Receiver; Nh=4, Nf=8, Tc=2 ns, fs=200/Tc, Γ =16, γ =8.5, 1/ Λ =11
ns, 1/ λ =0.35 ns, L=400, Lmax=400 (Channel2)
CHAPTER 5 SIMULATION RESULTS
139
In Figure 5.18, the BER performance in terms of system loading (i.e. the number
of users Nu) is presented. It is assumed that the system with pseudorandom time hopping
codes are used (Nf=8, Nh=4) in the presence of reach multipath environment (Channel2).
MMSE RAKE receiver as a MUD is employed. It is demonstrated, as the number of
users increases, there are more interfering signals. Therefore, the performance becomes
worse as shown in Figure 5.18 and with normalized system loading of L= Nu/ (Nf*Nh) =
0. 156 is possible to reach BER=10-5
for Eb/N0=28dB.
It can be seen how MMSE receiver performance does not breaks down
dramatically as more users are added to the system. With a load of Nu=10 users, only 1-
dB loss is seen at BER=10-4
comparing to the case when only one interferer is presented.
5.4.5. Number of Chips Influence on BER Performance in the Channel2
Employing MMSE RAKE Receiver
10 15 20 2510
-5
10-4
10-3
10-2
10-1
Eb/N0
BE
R
Nh=4
Nh=8
Nh=2
Figure 5.19. Effect of the Number of Chips on the BER Performance for a PPM-TH-
UWB System with MMSE Receiver; Nu=5, Nf=8, Tc=2 ns, fs=200/Tc, Γ =16, γ =8.5,
1/ Λ =11 ns, 1/ λ =0.35 ns, L=400, Lmax=400 (Channel2)
SIMULATION RESULTS CHAPTER 5
140
In order to see the influence of (Nf, Nh) for a fixed Nf=8 and Nu =5 on BER
performance, the following cases are considered Nh =2, 4, 8. In Figure 5.19 it can be
seen how the performance of MMSE RAKE detector employed in the system in the
presence of Channel 2 can be improved as Nh increases, as expected. For example, the
loss of 1-dB is seen at BER=10-3
when Nh=4<Nu comparing to the case when Nh=8>Nu.
Additionally, it is shown that MMSE RAKE receiver when Nh=2<Nu/2 is incapable of
effectively rejecting heavily loaded wideband interference.
5.4.6. Sampling Frequency Influence on BER Performance in the Channel 2
employing MMSE Receiver
10 12 14 16 18 20 2210
-4
10-3
10-2
10-1
Eb/N0
BE
R
fs=200/Tc
fs=20/Tc
fs=10/Tc
Figure 5.20. Sampling Frequency Influence on BER performance employing MMSE
RAKE Receiver; Second Derivative of the Gaussian Monopulse; Channel 2; Nu=5,
Nh=4, Nf=8
CHAPTER 5 SIMULATION RESULTS
141
The effect of the sampling frequency on BER performance employing single user
receiver in the presence of Channel 2 can be seen in Figure 5.20. It can be noticed how
the performance of MMSE RAKE detector can be improved as fs increases, as expected.
For example, the loss of 4-dB when fs =200/Tc is seen at BER=10-2
comparing to the
case when sampling frequency is 10 times lower. It is shown that low sampling
frequency as fs=10/Tc will seriously affect BER performance.
As it will be shown how there is no dependence between the bit simulation
time and the sampling frequency, a very high accuracy can be obtained without
affecting the simulation time, which is a very important feature of the algorithm.
5.4.7. Number of Users Influence on BER Performance in the Channel 3
Employing MMSE RAKE Receiver
10 12 14 16 18 20 22 24 26 2810
-6
10-5
10-4
10-3
10-2
10-1
Eb/N0
BE
R
Nu=2
Nu=5
Nu=10
Figure 5.21. Effect of the Number of Users on BER Performance for a PPM-TH-UWB
System with MMSE Receiver; Nh=4, Nf=8, Tc=2 ns, fs=200/Tc, Γ =33, γ =5, 1/ Λ =2 ns,
1/ λ =0. 5 ns, L=400, Lmax=400 (Channel3)
SIMULATION RESULTS CHAPTER 5
142
In order to see the impact of the number of users on the system performance in
the presence of Channel 3, in Figure 5.21, the BER performance in terms of system
loading (i. e. the number of users Nu) is shown. As in Figure 5.18, system with
pseudorandom time hopping codes are used (Nf=8, Nh=4). MMSE RAKE receiver as a
MUD is employed. It is demonstrated, as the number of users increases, there are more
interfering signals. Therefore, the performance becomes worse as shown in Figure 5.21
and with normalized system loading of L= Nu/ (Nf*Nh) = 0.3125 is possible to reach
BER=10-5
for Eb/N0=28dB.
It can be seen how MMSE receiver performance does not breaks down
dramatically as more users are added to the system. With a load of Nu=10 users, only 1-
dB loss is seen at BER=10-4
comparing to the case when only one interferer is presented.
5.4.8. Number of Chips Influence on BER Performance in the Channel 3
Employing MMSE RAKE Receiver
10 12 14 16 18 20 22 2410
-7
10-6
10-5
10-4
10-3
10-2
10-1
Eb/N0
BE
R
Nh=16
Nh=4
Nh=2
Figure 5.22. Effect of the Number of Chips on BER Performance for a PPM-TH-UWB
System with MMSE Receiver with Nh=4, Nf=8, Tc=2 ns, fs=200/Tc, Γ =33, γ =5, 1/ Λ =2
ns, 1/ λ =0. 5 ns, L=400, Lmax=400 (Channel3)
CHAPTER 5 SIMULATION RESULTS
143
In order to see the influence of (Nf, Nh) for a fixed Nf=8 and Nu =4 on BER
performance, the following cases are considered Nh =2, 4, 16. Comparing Figure 5.21
and Figure 5.22 it can be seen how the performance of MMSE RAKE detector
employed in the system in the presence of Channel 3 can be improved as Nh increases,
much more comparing to the performance of the system in the presence of Channel 2.
For example, the loss of 3-dB is seen at BER=10-3
when Nh = 4<Nu comparing to the
case when Nh=16>2* Nu. Equivalently, it is shown that MMSE RAKE receiver when
Nh=2 is incapable of effectively rejecting heavily loaded wideband interference.
10 15 20 2510
-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
Eb/N0
BE
R
Nu=2;AWGN
Nu=5;AWGN
Nu=10;AWGN
Nu=20;AWGN
Nu=2;L=400
Nu=5;L=400
Nu=10;L=400
Figure 5.23. Effect of the Number of Users on the BER Performance for a PPM-TH-
UWB System with MMSE Receiver in the presence of AWGN channel vs. BER
Performance for a PPM-TH-UWB System in the presence of Channel 2; Nh=8, Nf=8,
Tc=2 ns, fs=200/Tc, L=400, Lmax=400
SIMULATION RESULTS CHAPTER 5
144
In order to compare the impact of the number users on system performance in
the presence of Channel 2 and AWGN, results are repeated from Figure 5.15 and Figure
5.18. It can be seen that for the same system loading, the loss of the system performance
in the presence of multipath channel is same for all cases comparing to the system
performance in the presence of AWGN channel. For example, the loss in system
performance in the presence of multipath channel of 3.5-dB is seen at BER=10-3
for
Nu=2, 5, 10 comparing to the system performance in the presence of AWGN channel.
10 15 20 2510
-10
10-8
10-6
10-4
10-2
100
Eb/N0
BE
R
Nh=2;AWGN
Nh=4;AWGN
Nh=8;AWGN
Nh=16;AWGN
Nh=8;L=400
Nh=4;L=400
Nh=2;L=400
Figure 5.24. Effect of the Number of Chips on BER Performance for a PPM-TH-UWB
System with MMSE Receiver in the presence of AWGN channel vs. BER Performance
for a PPM-TH-UWB System with MMSE Receiver in the presence of Channel 2; Nu=8,
Nf=8, Tc=2 ns, fs=200/Tc, L=400, Lmax=400
CHAPTER 5 SIMULATION RESULTS
145
In order to compare the impact of the number chips on system performance in
the presence of Channel 2 and AWGN, results are repeated from Figure 5.16 and Figure
5.19. It can be seen that for the same system loading, the loss of the system performance
in the presence of multipath channel is same for all cases comparing to the system
performance in the presence of AWGN channel. For example, the loss in system
performance in the presence of multipath channel of 5-dB is seen at BER=10-4
for Nh =2,
4, 8 comparing to the system performance in the presence of AWGN channel. It is
interesting to notice that the system performance in the presence of multipath channel
when Nh=8> Nu is same as system performance in the presence of AWGN channel when
Nh=2<Nu/2.
5.4.9. Number of RAKE Fingers Influence on BER Performance in the
Channel 2 Employing MMSE RAKE Receiver
10 15 20 2510
-5
10-4
10-3
10-2
10-1
Eb/N0
BE
R
Lmax=L=400
Lmax=370
Lmax=350
Lmax=300
Lmax=1
Figure 5.25. Effect of the Number of RAKE Fingers on BER Performance for a PPM-
TH-UWB System with MMSE Receiver in the presence of Channel 2; Nu=8, Nf=8,
Nh=4, Tc=2 ns, fs=200/Tc, L=400
SIMULATION RESULTS CHAPTER 5
146
In order to collect multipath energy, a RAKE receiver can be implemented with Lmax<L
fingers. This RAKE must be able to capture a large number of different multipath
components (fingers) and combine them to improve the SNR. Each one of its Lmax
fingers is adapted to a different propagation path and the Lmax strongest multipath
components are chosen.
In Figure 5.25 the impact of the number of RAKE fingers on the BER
performance is presented. It is shown that for Lmax =L system has the best performance
and it is possible to achieve BER=5*10-5
at SNR=25 dB; while employment of the
RAKE receivers with Lmax<L=300, 350 or370 fingers leads to saturation at SNR=22 dB
and it is not possible to achieve BER lower than BER=10-3
.
In addition it is shown that the energy capture of MMSE receiver without RAKE
receiver (i.e. Lmax=1) is very low, and performance is unacceptable.
5.4.10. Effect of the Synchronization on BER Performance for a PPM-TH-
UWB System with MMSE Receiver in the presence of Channel 2
In Figure 5.26 effect of the synchronization on the BER performance of a PPM-
TH-UWB System employing MMSE receiver in the presence of multipath channel is
presented. In addition it is shown that degradation in the case when synchronization is
applied comparing to perfect timing is only 2.5 dB for BER=10-4
.
Therefore, a complete Pulse Position Modulation (PPM) TH-UWB system is
simulated using a high-speed system simulator and it is shown that algorithm that this
thesis proposes can deal with channels with a large number of taps and reach low BER
in a real time application.
CHAPTER 5 SIMULATION RESULTS
147
10 15 20 2510
-12
10-10
10-8
10-6
10-4
10-2
100
Eb/N0
BE
R
L=400; perfect synchronization
AWGN
L=400;synchronization
Figure 5.26. Effect of the Synchronization on BER Performance for a PPM-TH-UWB
System with MMSE Receiver in the presence of Multipath Channel (Channel2) Nu=13,
Nf=8, Nh=8, Tc=2 ns, fs=200/Tc, L=400, Lmax=400.
5.5. Time Performance and Complexities of the Algorithm
The following numerical results show the time performance of this algorithm.
Figure 5.27 presents the relation between simulation time and the sampling frequency.
As was explained before, there is no dependence between them. Thus, increasing the
sampling frequency, a very high accuracy can be achieved without prolonging the
simulation time.
In Figure 5.28, Figure 5.29 and Figure 5.30, is demonstrated that the simulation
time linearly grows with the number of users, number of frames and the number of
multipath components, respectively. Comparing MMSE correlation matrices from (4.9)
and (4.12) , it can be seen that in order to calculate matrix from (4.12) it is not necessary
SIMULATION RESULTS CHAPTER 5
148
to operate with the signal sample and to calculate MMSE matrix inversion every time
when the TH sequence change. This is illustrated in Figure 5.31.This fact significantly
reduces the complexity of this algorithm. Complexity of this algorithm is
O(Nu*Nf*L*Lmax), while using Monte Carlo method complexity is Nh times higher.
Illustration of this comparison is shown in Figure 5.31. Therefore, assuming a large
spreading factor of the UWB signals and a high computational complexity of MMSE
receiver matrix, this algorithm yields a large saving of simulation time comparing to the
previous designs.
With this accurate flexible simulation model; we might analyze the influence of
MMSE RAKE receiver on different factors of TH-UWB systems (the number of users,
waveform design time-hopping codes, channel models…) and achieve a very low BER
performance in a real time application.
Figure 5.27. Relation between the Sampling Frequency and the Simulation Time per Bit
for a PPM-TH-UWB System employing MMSE RAKE Receiver; Nu=5, Tc=2 ns,
fs=200/Tc, Nf=8, Nh =4, L=400, Lmax=100.
50 100 150 2000.3
0.35
0.4
0.45
0.5
0.55
Number of samples per chip
Sim
ula
tion t
ime p
er
bit
CHAPTER 5 SIMULATION RESULTS
149
10 15 20 25 30 35 40 45 500.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
Number of users
Sim
ula
tio
n t
ime
pe
r b
it
Figure 5.28. Effect of the Number of Users on the Simulation Time per Bit for a
PPM-TH- UWB System employing MMSE RAKE Receiver; Tc=2 ns, fs=200/Tc, Nf=8
Nh=4, L=400, Lmax=100.
1 2 3 4 5 6 7 8 9 100.125
0.13
0.135
0.14
0.145
0.15
0.155
0.16
0.165
0.17
0.175
Number of multipath components
Sim
ula
tio
n t
ime
pe
r b
it
Figure 5.29. Effect of the Number of Multipath Components on the Simulation time per
Bit for a PPM-TH- UWB System with MMSE Receiver; Nu=5, Tc=2 ns, fs=200/Tc, Nf=8,
Nh =4, Lmax=L.
SIMULATION RESULTS CHAPTER 5
150
5 10 15 20 25 30 35
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Number of frames
Sim
ula
tion t
ime p
er
bit
Figure 5.30. Effect of the Number of Frames on the Simulation Time per Bit for a PPM-
TH- UWB System with MMSE Receiver; Nu=5, Tc=2 ns, fs=200/Tc, Nh =4, L=400,
Lmax=100.
Chip position calculation
( )
, , ,
k
i j l mε
MMSE matrix calculation
Data (fast variation)
Channel conditions (slow variation)
Chip position calculation +
MMSE matrix calculation
Data (fast variation)*channel conditions variation*length of the pseudorandom
time hopping sequence
MMSE matrix calculation flowchart using our algorithm-O(Nu*N
f*L*L
max)
MMSE matrix calculation flowchart using Monte Carlo algorithm-O(Nh*Nu*N
f*L*L
max)
Figure 5.31. MMSE Matrix Calculation Flowchart using our Algorithm vs. MMSE
Matrix Calculation Flowchart using Monte Carlo Method.
CHAPTER 5 SIMULATION RESULTS
151
Algorithm Complexity of the
algorithm
MMSE using speed simulator Figure 5.1 O(Nu*Nf)
Previous simulator Monte Carlo with
fixed rate Figure 5.1
O(Nh*Nu*Nf)
MMSE using speed simulator Figure 5.2 O(Nu*Nf)
Previous simulator Monte Carlo with
fixed rate Figure 5.2
O(Nh*Nu*Nf)
MMSE using speed simulator Figure 5.3 O(Nu*Nf)
Previous simulator Monte Carlo with
fixed rate Figure 5.3
O(Nh*Nu*Nf)
MMSE using speed simulator Figure 5.4 O(Nu*Nf)
Previous simulator Monte Carlo with
fixed rate Figure 5.4
O(Nh*Nu*Nf)
MMSE using speed simulator Figure 5.5 O(Nu*Nf*L*Lmax)
Previous simulator Monte Carlo with
fixed rate Figure 5.5
O(Nh*Nu*Nf*L*Lmax)
Table 5.6 Comparisons of the Algorithms Complexities in Single User Receiver
SIMULATION RESULTS CHAPTER 5
152
Algorithm Complexity of the
algorithm
MMSE using speed simulator Figure 5.1 O(Nu*Nf)
Previous simulator Monte Carlo with
fixed rate Figure 5.1
O(Nh*Nu*Nf)
MMSE using speed simulator Figure 5.2 O(Nu*Nf)
Previous simulator Monte Carlo with
fixed rate Figure 5.2
O(Nh*Nu*Nf)
MMSE using speed simulator Figure 5.3 O(Nu*Nf)
Previous simulator Monte Carlo with
fixed rate Figure 5.3
O(Nh*Nu*Nf)
MMSE using speed simulator Figure 5.4 O(Nu*Nf)
Previous simulator Monte Carlo with
fixed rate Figure 5.4
O(Nh*Nu*Nf)
MMSE using speed simulator Figure 5.5 O(Nu*Nf*L*Lmax)
Previous simulator Monte Carlo with
fixed rate Figure 5.5
O(Nh*Nu*Nf*L*Lmax)
Table 5.7 Comparisons of the Algorithms Complexities in Multiuser Receiver
Therefore, this algorithm takes advantage of some of the properties of TH-UWB
systems in order to improve all the previous designs by several orders of magnitude,
independently on the sampling rate, in terms of a very straightforward and fast
processing. Relying on this approach, the number of simulation operations needed to
evaluate MMSE receiver matrix are reduced.
CHAPTER 6 SUMMARY OF THE CONTRIBUTIONS
153
Chapter 6
6. Conclusions
6.1. Thesis Summary
In this thesis, a complete Pulse Position Modulation (PPM) TH-UWB system is
simulated using a high-speed system simulator, which is the innovation of our research
group. This algorithm takes advantage of some of the properties of this kind of systems
in order to provide a very straightforward and fast processing that improves all the
previous designs several orders of magnitude, independently on the sampling rate.
Comparing to previous simulators, sampling frequency can be as high as needed, since
the simulation run-time does not depend on it. Transmitted signal is stored in the
Transmitted Distorted Received (TDR) waveform vector, thus it is not necessary to
operate with the signal samples in every simulation. The only influence of the sampling
rate is on the length of the TDR waveform vector. The algorithm complexity is linear
with the number of users, frames, multipath components, and RAKE fingers.
In order to develop the simulation code, an important task in every simulation
process is definition of the attributes of the physical device that affect the required
simulation products, i.e. Bit Error Rate (BER). One of those attributes in IR-TH-UWB
systems is synchronization that produces alignment of transmitter and receiver clocks,
so information can be accurately exchanged. Particularly with PPM, synchronization is
very important to correct demodulation of the received signals because information is
conveyed in the time position of the pulse. Another critical task for successful operation
of UWB systems is a multiuser detection. Some papers show that MMSE receiver has
the best performance in terms of SINR at the expense of high computational complexity
since it requires the matrix inversion every time the spreading sequence changes.
SUMMARY OF THE CONTRIBUTIONS CHAPTER 6
154
Therefore, there are no many papers dealing with this topic, especially not in UWB
systems in the presence of real multipath environment.
Unfortunately, since the transmitted signal is stored in the TDR waveform
vector, it is very difficult to extract it. Thus, implementation of those tasks
(synchronization, channel estimation and multiuser detection) might be a big problem
for system simulation.
In the first chapter of this thesis, the fundamentals of UWB system are
overviewed. Within the following sections, topics covered are UWB history, features
and applications of UWB system, types of UWB signals, UWB spectrum and
regulations and some of the possible problems of this system.
The second chapter gives an overview of MA UWB system design, including a
transmitter design. Additionally, this chapter presents the overall system model and
notation convention that I have used throughout this thesis.
In addition, two statistical models for UWB channel are presented based on data
collected from extensive UWB propagation measurements. Saleh-Valenzuela and based
on Saleh-Valenzuela, model proposed by Intel that will be employed for the purposes of
this thesis are described. This channel model was made with one slight modification
since the observations have shown that the lognormal distribution better fits the
measurement data.
Additionally, the second chapter provides a description of a single user and
multiuser receiver structure, assuming perfect synchronization and perfect channel
estimation. As an optimum single user receiver, selective RAKE receiver is used for the
purposes of this thesis and as a multiuser receiver, MMSE RAKE is employed.
In addition, as a one part of the contribution of this thesis low complexity
method for synchronization is presented. With this approach, a low complexity for real
time implementation and the good performance in terms of BER versus SNR are
achieved.
Since the UWB system requires taking a second look at simulation
methodology, the chapter three covers the following tasks:
• Differences between UWB and traditional narrowband systems and difficulties
in model development
CHAPTER 6 SUMMARY OF THE CONTRIBUTIONS
155
• A brief review of the fundamental simulation methodologies.
• New IR-TH-UWB system simulator that is the innovation of our research group
and will be used for the purposes of this thesis.
In Chapter four, I implemented a MMSE RAKE receiver for Ultra-Wideband
(UWB) system using a new time-hopping system simulator, achieving a novel approach
of MUD. With this approach, it is possible to reduce the simulation time significantly by
avoiding any convolution operation, which is the most time-consuming. Relaying on
this approach, number of simulation operations needed to evaluate MMSE receiver
matrix are reduced. Complexity of this algorithm is O(Nu*Nf*L*Lmax), while using
Monte Carlo method complexity is Nh times higher. Thus, for systems with a very large
spreading factor, as UWB is, this provides a large computational time saving.
Additionally, I have derived a theoretical formula of the performance of MMSE
RAKE receiver detector for PPM IR-TH-UWB based on this new approach and some
previous researches.
In chapter five, simulation results are provided in order to validate this approach.
And it is shown that is possible to achieve very low BER for a certain system loading.
6.2. Summary of the Contributions
As it was commented in abstract, this thesis has two main parts. In the first part
of the thesis, a joint symbol, frame and chip synchronization method for PPM IR-TH-
UWB system in the presence of dense multipath environment is proposed. It is assumed
that the channel is estimated using Pilot Waveform Assisted Modulation (PWAM), and
that synchronization is achieved by maximizing the energy of the estimated multipath
channel. Based on this method for synchronization in combination with PWAM method
for channel estimation, FFT operations that are used in many works are avoided and the
algorithm has a very low complexity. Additionally, in order to even more increase the
speed of simulation process; this method is implemented in the enhanced time
algorithm. Therefore, algorithm that this thesis proposes can deal with channels with a
large number of taps that are difficult to estimate using the existing algorithms. It is
shown that the complexity of this algorithm is O(Nu*Nf*L*Lmax), while using Monte
SUMMARY OF THE CONTRIBUTIONS CHAPTER 6
156
Carlo method complexity is Nh times higher. Therefore, assuming a large spreading
factor of the UWB signals, this algorithm yields a large saving of computational time
comparing to the previous designs. Additionally, simulation time is independent on the
sampling rate. Thanks to this approach, low complexity for real time implementation
and the good performance in terms of BER versus Signal to Noise Ratio (SNR) are
achieved. Simulation shows that this synchronization system helps to mitigate the
negative effects of timing offset.
In the second part of the thesis, MMSE receiver for PPM IR-TH-UWB systems
using a high-speed system simulator is implemented. Implementation of any multiuser
detector in this algorithm was a difficult issue since a transmitted signal is ‘hidden’ in
TDR and there is no typical multiuser structure. Therefore, applying this method, in this
thesis, a new approach of multiuser detection is achieved. Since the transmitted
waveform is stored in the TDR, it is not necessary to operate with the signal samples in
every simulation. Thus, correlation matrix should be recalculated only when the channel
conditions change. Depending on the channel coherence time and the bit rate, it is
possible to find the number of bits that can be simulated without alerting the correlation
matrix. The only influence of the sampling rate is the length of the TDR. Derived results
show that this effect is disregarded. Therefore, it can be considered that the simulation
speed is approximately independent on the sampling rate. As for synchronization and
channel estimation, complexity of this algorithm with MMSE included is
O(Nu*Nf*L*Lmax), i.e. Nh times lower comparing to Monte Carlo method. Additional
advantage of this approach is that the complexity of the algorithm is linear with the
number of users, frames, multipath components, and RAKE fingers.
Furthermore, with this approach, it is possible to reduce the simulation process
significantly by avoiding any convolution operation, which is the most time-consuming.
Relaying on this approach, the number of simulation operations needed to evaluate
MMSE receiver matrix are reduced. Thus, it is possible to process a large number of
samples and to accurately estimate low BER in a short time application. In addition, I
derived a theoretical formula of the performance of the MMSE detector for PPM IR-
TH-UWB based on this new approach. This new formula is validated by comparing
results to some other results based on some previous researches.
CHAPTER 6 SUMMARY OF THE CONTRIBUTIONS
157
Both tasks, synchronization and the new approach of multiuser detection
proposed in this thesis, give a good performance in terms of low complexity, fast
processing and BER versus Signal to Noise Ratio (SNR) performance.
All results are evaluated using the proposed algorithm and simulations are
provided in order to validate this implementation. They demonstrate that the simulation
time linearly grows with the number of users and the number of frames. The main gain
of this thesis is that the complexity of the algorithm in order to calculate the complete
PPM IR-TH-UWB system is Nh times lower comparing to previous methods, where Nh
is a number of chips in those systems. Therefore, assuming a large spreading factor of
the UWB signals, this algorithm yields a large saving of computational time comparing
to the previous designs and is possible to achieve a very low BER in a real time
application. With this accurate flexible simulation model; in this thesis the performance
of the TH-UWB system and the impact of different factors of TH-UWB systems (the
number of users, waveform design time-hopping codes, channel models, receivers…)
are analyzed and a low BER in a real time application even in the presence of reach
multipath environment is achieved.
( )q
j cc T( )q
jdλ
( ) ( )ks t
Figure 6.1. Conceptual Model of the UWB Signal Generation
SUMMARY OF THE CONTRIBUTIONS CHAPTER 6
158
Link (q)Sequence
generator
( )q
j cc T
Template
generator
Channel
( )r t
Correlator
MMSE
iα
Decision
Channel
estimation
and
synchronizati
on
( )r t
Figure 6.2. Conceptual Model of the UWB Receiver for the qth
User
6.3. Future Research
Although in this thesis a complete Pulse Position Modulation (PPM) TH-UWB
system is simulated using the high-speed system simulator, adaptive solutions, in
particular, have the potential of providing the anticipated multiuser detection
performance gains with a complexity that would be manageable for UWB systems.
The main characteristic of the adaptive system is its time-varying, self-adjusting
performance. The requirement for such performance might be considered as a need of
the designer to foresee all possible input conditions, at least statistically, and to know
CHAPTER 6 FUTURE RESEARCH
159
how the system would behave under these conditions. The designer has then chosen a
specific criterion whereby performance is to be judged, such as the amount of error
between the outputs of “real” and “ideal” system. Finally, the designer has chosen the
system that appears best according to the performance criterion selected, generally
choosing this system from an apriori restricted class of designs (such as linear systems).
However, in many instances, the complete range of input conditions may not be
exactly known, or might change from time to time. In such occasions, an adaptive
system that continually seeks the optimum within an allowed class of possibilities, using
an orderly search process, would give superior performance compared with a system of
fixed design.
By their natural properties, adaptive systems must be time varying and
nonlinear. Their characteristics depend, among other things, on their input signals.
The future work of this thesis might be incorporation of such technique in
previous in order to cope better with channel variations.
In order to make an introduction of the future work, an optimum combining
RAKE receiver will be briefly described. Figure 6.3 illustrates the implementation of
the optimum combining UWB RAKE receiver. The MMSE filter parameters are varied
such that the mean squared error (MMSE) criterion intends to find a weight vector that
will minimize the mean squared error (MSE) between the combined signal and some
desired or reference signal. The error signal can be defined as
( ) ( ) ( )q q H q
e b= − w α (6.1)
where ( )qb is the reference signal. The weight vectors are estimated from a training
sequence that is known to the receiver. The MSE is given by
2 2 2( ) ( ) ( ) ( )q q H q q H H H
b bJ E e E b b
α α αα
= = − = − − +
w α w r r w w R w
(6.2)
FUTURE RESEARCH CHAPTER 6
160
where αα
R = ( ) ( )( )q q HE α α is the covariance matrix of the received signal, and
bαr = ( ) ( ) *( )q qE α α is the cross-correlation vector between the received signal. The
MSE J is minimized when the gradient vector defined by
*
( )J
J∂
∇ =
∂w (6.3)
is equal to the null vector. Therefore, the optimum vectorMMSE
w , and the following
relation using (6.2) and (6.3)
( ) 0MMSE
MMSE b
J
αα α
∇ =
=
w
R w r (6.4)
Equation (6.4) is well known as the Weiner solution, given by
1
MMSE b
−
αα α=w R r
(6.5)
Therefore the error vector calculation flowchart is presented in Figure 6.4 is the
same as in Figure 4.2, with only difference that amplitudes of the conventional RAKE
receiver fingers ( )q
mβ replaced with their optimum coefficients ( )q
mw .
In practice, the matrix αα
R is estimated from a block of training symbols. The
maximum likelihood estimate is given by the sample covariance matrix
1( ) ( )
0
1ˆ ( )N
q q T
qN
−
αα
=
= ∑R α α
(6.6)
where N is the block size. Because training is an overhead function that consumes
recourses, it is of interest to develop techniques that can work with short training sets. It
is well-known that the number of vector samples required in estimating a L L×
correlation matrix within 3 dB of its true value is 2L [94]. For a dispersive channel
CHAPTER 6 FUTURE RESEARCH
161
resulting in a large number of nonzero taps L, a large number of samples are required to
train MMSE.
( )tϕ
( )
1
qτ
max
( )q
Lτ
( )
( )
( 1)q
f i c
qf i c
i T c T
iT c T
dt
+ +
+
⋅∫
( )
( )
( 1)q
f i c
qf i c
i T c T
iT c T
dt
+ +
+
⋅∫
α
( )
1
qβ
max
( )q
Lβ
( )r t
1w
maxLw
∑y
Figure 6.3 Optimum Combining UWB RAKE Receiver for IR-TH-UWB
qM ...1
Vector
transmitted
0
K
Accumulator
DecisionLink (q)
0
Vector received0 0 0 1
...
0 1 0 0...X-OR0 1
K
K
×
A White Gaussian Noise
uN
0
( )qb
×
+×
TAA
×
Amplitudes
βl(k)wm
(q)
Positions in
the TDR
waveform (k)iu
(q) T(R )
2
nσ I
]TE[αα
× +1
0
uN
1( )−
⋅
Ω
Figure 6.4. Error Vector Calculation Flowchart when Optimum RAKE Receiver is
employed
162
APPENDIX
163
Appendix A
Synchronization using a High
Speed System Simulator
To apply this algorithm, the first step should be the separation between the
signal and the noise component of every frame statistic. Then, a frame statistic of the ith
frame on the qth
receiver is described as
s n
i i iα α α= +
(7.1)
where assuming (2.24) and (2.26), the signal component after channel estimation and
synchronization can be presented as
( )
( )
( 1)
( ) ( )( ) ( )
qf i c
qf i c
i T c T
s s q q
i f i c
iT c T
r t t iT c T dtα ν
+ +
+
= × − −∫ (7.2)
with
( ) ( )
1
ˆ( ) [ ( )* ( )]uN
s k k
k
r t s t h t=
= ∑ (7.3)
where ( )ˆ ( )kh t represent the estimated channel response
and
APPENDIX
164
( )
( )
( 1)
( ) ( )( ) ( )
qf i c
qf i c
i T c T
n q q
i f i c
iT c T
n t t iT c T dtα ν
+ +
+
= × − −∫ (7.4)
represents the noise part of the ith
frame statistic on the qth
receiver.
For a simplified analysis, it is useful to extract the effect related to the waveform
distortion from those related to the delay. It is known that given two functions ψ(t) and
ξ(x), with ξ(x) zero out of the interval [0, T] fulfil the following expression:
( ) ( ) ( ) ( ( )) ( ) ( )
t T
t T
t T t T
t T t x T t x dx x x dx
τ
τ
ττ
ψ ξ ψ ξ ψ ξ τ
+
= +
− = +
∗ − = − − = −∫ ∫
(7.5)
that can be applied to (3.17) as
( )
( ) ( ) ( )
( 1)1
( )* ( ) * ( )u
qf i c
N
s k k q
i f i T c Tk
s t h t T tα ν+ +
=
= − ∑ (7.6)
where ( ) ( )qv t is equal to zero out of the interval [0, Tf] as ( )
max
q
L fTτ < .
Alternatively, equivalently, applying(2.24), the signal component is
( )
( ) ( ) ( ) ( )
1 1
( )
( 1)
( )
( )* ( )
u
qf i c
N Ls k k k k
i l f j c j l
k j l
q
rec f i T c T
A t jT c T d
w t v T t
α β δ λ τ
∞
= =−∞ =
+ +
= − − − −
∗ −
∑∑∑ (7.7)
The noise component can be expressed equivalently as
( ) ( )( ) ( ) .f
n q q
i f f i c Tn t v T t iT c Tα = ∗ − − − (7.8)
APPENDIX
165
Considering(2.27), after some trivial operations, the last term in (7.8)can be
expanded as
max
( ) ( ) ( )
0
ˆ ˆ( ) ( )* ( )* ( )L
q q q
f m m f
m
T t t t t Tν ϕ β δ τ δ
=
− = − + +∑
(7.9)
where ( )ˆ ˆq
m lτ τ= and ( )ˆ ˆ( ) q
mh t β= are multipath arrival times and magnitude of the
estimated channel respectively. Thus, if it is defined the TDR Ω(t) as
( ) ( ) ( )rec
t w t tϕΩ = − ∗ (7.10)
the signal component from (3.22) can be rewritten as
max
( ) ( ) ( ) ( ) ( ) ( )
1 1 0
ˆ ˆ* ( ( ))uN LL
s k q k k k q
i l m f j c j l m
k j l m
A t jT c T dα β β δ τ τ
∞
= =−∞ = =
= − − − − −∑∑∑∑
( )( 1)
( ) .q
i T c Tf ci
fT t
+ +
∗Ω − (7.11)
Ω(t) is very interesting to analyze. If it is considered no channel distortion and perfect
signal estimation, Ω(t) for PPM becomes
( ) ( ) ( ) ( ) ( ),tr tr tr tr
t w t w t w t w t λΩ = − ∗ − − ∗ − (7.12)
that is the subtraction of the autocorrelation and its replica shifted by λ. In the case of
channel distortion, if the channel impulse response hdist(t) has a duration η, the TDR will
be nonzero in the interval [-Tc-η, Tc +η +λ]. After the reciprocal change of(3.20), if it is
defined
( ) ( ) ( ) ( ) ( )
, , ,ˆ( ) ( ) ( )k k q k q
i j l m f j i c l mj i T c c Tε τ τ= − + − + − (7.13)
APPENDIX
166
the signal component on the qth
receiver can be expressed as
( ) ( ) ( ) ( )
, , ,
, , , 0
ˆ ( ) ( )
fT
s k q k k
i l m i j l m j
j k l m
A t d t dtα β β δ ε λ= − − Ω∑ ∫
(7.14)
This integral will be nonzero only for the values that satisfy
( ) ( ) ( )
, , ,
k k k
j c i j l m c jd T T dλ η ε λ η λ− − − < < + + − (7.15)
It can also be expressed with independence of the PPM transmitted data.
Therefore, for i = 1…Nf, let j, k, l, m∈Γ to be the set of values that satisfies
( )
, , ,.k
i j l m cTε η λ< + + (7.16)
Then, αis can be obtained as
( ) ( ) ( ) ( )
, , ,
, , ,
ˆ ( ).s k q k k
i l m i j l m j
j k l m
A dα β β ε λ
∈Γ
= Ω +∑ (7.17)
Thus, the signal component of the bit statistic after the soft decision detection,
can be expressed as
( ) ( ) ( ) ( )
, , ,
1 , , ,
ˆ ( ).fN
s k q k k
i l m i j l m j
i j k l m
A dα β β ε λ
= ∈Γ
= Ω +∑ ∑ (7.18)
In the case of different links, i.e. when the distortion is different for every link,
signal can be presented as
( ) ( ) ( ) ( ) ( )
, , ,
1 , , ,
ˆ ( ).fN
s k q k k k
i l m i j l m j
i j k l m
A dα β β ε λ
= ∈Γ
= Ω +∑ ∑ (7.19)
APPENDIX
167
A is in charge of controlling the Signal to Noise Ratio (SNR). Thus, for a given
waveform Ω(t), A can be defined as
max
( ) 2
1
,ˆ(0) ( )
Lq
m
m
SNRA
β
=
=
Ω ∑ (7.20)
where σn represents the noise standard deviation. From the evaluation of this simulator,
a large time saving can be obtained from the following features:
Since )(
,,,
k
mljiε is independent on the data, it can be computed only once for a whole
sequence of transmitted bits, thus the simulations will be reduced in order to
evaluate(3.33).
Transmitted waveform is stored in the TDR, thus it is not necessary to operate
with the signal samples in every simulation. The only influence of the sampling rate is
the length of the TDR. Since this vector is accessed at a particular position given
by λε)()(
,,,
k
j
k
mlji d+ , i.e. positions of the lth
echo of the jth
frame of the kth
link, an increase in
length could make the access slower. The algorithm complexity is linear with the
number of users, frames, multipath components, and RAKE fingers.
168
BIBLIOGRAPHY
169
Bibliography
[1] Win M. Z., Ju J., Quiu X., Li V. O. K. and Scholtz R. A., ATM based Ultra-Wide
Bandwidth Multiple-Access Radio Networks for Multimedia PCS, IEEE 4th
Annual Networld+Interop Conference, pp. 101–108, May, 1997.
[2] C. Falsi, D. Dardari, L. Mucchi, and M. Z. Win, “Time of Arrival Estimation for
UWB Localizers in Realistic Environments,” EURASIP Journal on Applied
Signal Processing, vol. 2006, Article ID 32082, 13 pages, 2006.
doi:10.1155/ASP/2006/32082
[3] D. Dardari, “Pseudo-Random Active UWB Reflectors for Accurate Ranging”,
IEEE Communications Letters, vol 8 , Issue: 10 , pp 608 – 610, Oct. 2004.
[4] Scholtz R. A. and Win M.Z., “Impulse Radio, How it works,” IEEE
Communication Letters, vol. 2, pp. 36–38, February, 1998.
[5] Astanin, L. Yu. and Kostylev, A.A., Principles of Ultra Wideband Radar
Measurements (in Russian). Radio i Svjas, Moscow, 1989.
[6] Barrett, T.W., Impulse (Time-Domain) Radar Technology Assessment
Colloquium. 16 -17 March, 1988, W. J. Schafer Associates.
[7] Barrett, T.W., Noel, B., et (Ed.), Ultra-Wideband Radar: Proceedings of the
First Los Alamos Symposium, CRC Press, Boca Raton, FL, 1991.
[8] Baum, Carl E., Carin, Lawrence and Stone, Alexander P., Editors, Ultra–
Wideband Short–Pulse Electromagnetics 3, Plenum Press, New York, 1997.
[9] Bennett, C.L., Ross, G.F., Time-Domain Electromagnetics and its Application,
Proceedings. IEEE 66, 299-318, 1978.
[10] Bertoni, Henry L., Carin, Lawrence and Felsen, Leopold B., Editors, Ultra–
Wideband Short–Pulse Electromagnetics, Plenum Press, New York, 1993.
[11] Carin, Lawrence and Felsen, Leopold B., Editors, Ultra–Wideband Short–Pulse
Electromagnetics 2, Plenum Press, New York, 1995.
BIBLIOGRAPHY
170
[12] Glebovich, G.V., Andriyanov, A.V., Vvedenskij, V., Kovalev, I.P., Krylov, V.V.
& Ryabinin, A., Study of Objects Using Picosecond Pulses, Moscow, Radio i
Svyaz’, 1984
[13] Harmuth, Henning F., Transmission of Information by Orthogonal Functions,
First Edition, Springer New York, 1969.
[14] Harmuth, Henning F., Transmission of Information by Orthogonal Functions,
Second Edition, Springer–Verlag, Berlin, 1972.
[15] Harmuth. Henning F., “Range-Doppler Resolution of Electromagnetic Walsh
Waves in Radar,” IEEE Transactions on Electromagnetic Compatibility, EMC-
17, 106-111, 1975.
[16] Harmuth, Henning F., “Selective Reception of Periodic Electromagnetic Waves
with General Time Variation,” IEEE Transactions on Electromagnetic
Compatibility, Vol. 19, No. 3, pp. 137–144, August 1977.
[17] Harmuth, Henning F., Sequence Theory, Academic Press, New York 1977.
[18] Harmuth, Henning F., Nonsinusoidal Waves for Radar and Radio
communication, Academic Press, New York, 1981.
[19] Harmuth, Henning F., Antennas and Waveguides for Nonsinusoidal Waves,
Academic, New York, 1984.
[20] Kostylev, A.A., Astanin, L. Yu., Zinov’ev, J.S. & Pasmurov, A. Ya., Radar
Characteristics of Aircraft, CRC Press, Boca Raton, LA, 1994.
[21] Mc Ewan, T.E., Ultra-Wideband Radar Motion Sensor. US Patent 5,361,070
dated November 1, 1994.
[22] Meleshko, E.A., Nanosecond Electronics in Experimental Physics,
Ehnergoatomizdat Press, Moscow, 1987.
[23] Miller, Edmund K. and Landt, Jeremy A., “Direct Time–Domain Techniques for
Transient Radiation and Scattering from Wires,” Proceedings of the IEEE, Vol.
68. No. 11, pp. 1396–1423, November 1980
[24] Morey, R.M., “Geophysical survey system employing electromagnetic
impulses,” US Patent 3, 806, 795, 1974.
[25] Noel, Bruce, Editor, Ultra–wideband Radar: Proceedings of the First Lost
Alamos Symposium, CRC Press, 1991.
BIBLIOGRAPHY
171
[26] Papoulis, A., The Fourier Integral and Its Applications, McGraw-Hill, New
York, Chapter 5 1962.
[27] Robbins, K., “Short Base-Band Pulse Receiver,” U.S. Patent No. 3, 662, 316,
1972.
[28] Ross, G.F., “The transient analysis of multiple beam feed networks for array
systems,” Ph.D. dissertation, Polytechnic Institute of Brooklyn, Brooklyn, NY
1963.
[29] Ross, G.F., “The transient analysis of certain TEM mode four-port networks,”
IEEE Transaction on Microwave Theory and Technology, vol. MTT-14, No. 11,
pp. 528-547, 1966.
[30] Ross, G.F., “Transmission and reception system for generating and receiving
base-band duration pulse signals for short base-band pulse communication
system,” U.S. Patent 3,728,632. 1973.
[31] Ross, G.F., “A time domain criterion for the design of wideband radiating
elements,” IEEE Transactions on Antennas Propagation, vol. 16, No. 3, pp. 355,
1968.
[32] Taylor, J.D. “Ultra-Wideband Radar Overview,” in Introduction to Ultra–
Wideband Radar Technology (J.D.Taylor ed.), 1-10, CRC Press, Boca Raton, FL,
1995.
[33] Tektronix, Inc., S.W. Millikan Way, P.O. Box 500, Beaverton, Oregon 97005:
Instruction Manual: Type S-2 Sampling Head, 1968.
[34] Varganov, M.E., Zinov’ev, Yu.S., Astanin, L.Ya., Kostylev, A.A., Sarychev,
V.A., Siezkinskij, S.K., Dmitriev, B.D. Radar Response of Flight Vehicles,
Moscow, Radio I Svyaz’, 1985.
[35] Fontana R. J., Recent Applications of UWB Radar and Communications Systems.
MultiSpectral Solutions, Inc. 2000
[36] Scholtz R. A., “Ultra-Wide Bandwidth Signal Propagation for Indoor Wireless
Communications,” Proceedings IEEE International Conference On
Communications, June 1997.
[37] J. D. Taylor, Ultra-wideband Radar Technology, Boca Raton , FL:CRC,2001.
BIBLIOGRAPHY
172
[38] Foerster J, Ultra-Wide Band Technology for Short- or Medium-Range Wireless
Communications, Intel Technology Journal Q2, 2001.
[39] Petroff A., Time Modulated Ultra-Wideband (TM-UWB) Overview, Time
Domain Corporation, 2000.
[40] Zhao L., “Performance of Ultra- WideBand Communications in the Presence of
Interference,” IEEE Proceedings. vol. 12 no 7, 2001.
[41] http://www.safecomprogram.gov/NR/rdonlyres/E63F70B1-40A1-4E7E-B3FC-
27DD36449F38/0/Ultra_Wideband_Communications.pdf
[42] Cramer J-M. R.; Win M.Z.; Scholtz R.A., Evaluation of the Multipath
Characteristics of the Impulse Radio Channel, Personal, Indoor and Mobile
Radio Communications, 1998. The Ninth IEEE International, PIMRC'98,
Symposium on, vol. 2, pp. 864 -868, 1998.
[43] Tobjorn C., Analysis of UWB for Indoor Geolocation, Master Thesis at Chalmer
University 2000.
[44] IEEE 802.15 WPAN high bit rate alternative PHY task group 3a (TG3a)
Web site: http://www.ieee802.org/15/pub/TG3a.html
[45] Saberinia E. and Tewfik A.H. Single and Multi-carrier UWB Communications,
IEEE ISSPA 2003, July 2003.
[46] Tewfik A.H. and Saberinia E., High Bit Rate Ultra-Wideband OFDM, IEEE
GLOBECOM 2002, vol.3, pp. 2260-2264, Nov. 2002.
[47] Wang Z. and Giannakis G. B. “ Wireless Multicarrier Communications: Where
Fourier Meets Shannon”, IEEE Signal Processing Magazine, vol. 17, no. 3, pp.
29-48, May 2000.
[48] H. Jeffrey Reed, An Introduction to Ultra Wideband Communication Systems;
Prentice Hall, 2005.
[49] Revision of part 15 of the Commission’s Rules Regarding Ultra-Wideband
Transmission Systems, First note and Order, Federal Communications
Commission, ET-Docket 98-153, Adopted February 14, 2002, released April 22,
2002.Available:http://www.fcc.gov/ Bureaus/ Engineering Technology/ Orders/
2002/ fcc02048.pdf.
[50] http://www.pswn.gov/library/pdf/Emerging_Wireless_Technologies-Part4.pdf.
BIBLIOGRAPHY
173
[51] Matti H., Veikko H., Raffaello T., Jari H. J. I., and Matti L., “On the UWB
System Coexistence With GSM900, UMTS/WCDMA, and GPS,” IEEE Journal
on Selected Areas in Communications vol. 20, no. 9, December 2002.
[52] M. Z. Win, P. C. Pinto, A. Giorgetti, M. Chiani, and L. A. Shepp, "Error
performance of Ultrawideband systems in a Poisson Field of narrowband
interferers," IEEE International Symposium on Spread Spectrum Techniques &
Applications (ISSSTA), Manaus, Brazil, Aug. 2006, Invited Paper.
[53] A. Giorgetti, M. Chiani, and D. Dardari, "Coexistence issues in cognitive radios
based on ultra-wide bandwidth systems," IEEE International Conference on
Cognitive Radio Oriented Wireless Net. and Comm. (CROWNCOM), Mykonos,
GREECE, June 2006.
[54] A. Giorgetti, M. Chiani, and M. Z. Win, Ultra-Wide Bandwidth Rake Reception
in the presence of Narrowband Interferers "IEEE Vehicular Technology
Conference (VTC 2004-Spring), pp. 1659-1663, Milan, May 2004.
[55] Win M. Z. and Scholtz R. A., “Ultra-Wide Bandwidth Time-Hopping Spread-
Spectrum Impulse Radio for Wireless Multiple-Access Communications,” IEEE
Transactions on Communications, vol. 48, no. 4, pp. 679-891, April 1997.
[56] Conroy J. T., Lo Cicero J. L. and UCCI D. R., Communication Techniques Using
Monopulse Waveforms,” IEEE Military Communications Conference
Proceedings 1999, MILCOM 1999, vol. 2, pp. 1181-1185, Nov. 1999.
[57] Chen X., Kiaei S., Monocycle Shapes for Ultra Wideband Systems, IEEE
International Symposium on Circuits and Systems 2002, ISCAS 2002, vol. 1, pp.
I-597 – I-600, May 2002.
[58] Win M. Z., “On the Power Spectral Density of Digital Pulse Streams Generated
by M-ary Cyclostationary Sequences in the Presence of Stationary Timing Jitter,”
IEEE Transactions on Communications, vol. 46, no. 9, pp. 1135-1145, Sept.
1998.
[59] Ramírez-Mireles F., “Performance of Ultrawideband SSMA Using Time
Hopping and M-ary PPM,” IEEE Journal on Selected Areas in Communications,
vol. 19, no. 6, pp. 1186-1196, June 2001.
BIBLIOGRAPHY
174
[60] Iacobucci M. S., Di Benedetto M. G., Time Hopping Codes in Impulse Radio
Multiple Access Communication Systems, International Symposium on 3rd
Generation Infrastructure Services, Athens, July 2001.
[61] Rome J., Piazzo L., On the Power Spectral Density of Time-Hopping Impulse
Radio, IEEE Conference on Ultra Wideband Systems and Technologies 2002,
UWBST 2002, pp. 241-245, May 2002.
[62] IEEE P802.15 Working Group for Wireless Personal Area Network, Multi-band
OFDM Physical Layer Proposal for IEEE 802.15 Task Group 3a, September
2003.
[63] Lottici V., Andrea A.D’, and Mengali U., “Channel estimation for ultra-
wideband communications,” IEEE J. Selected Areas on Communications, vol.20,
pp. 1638-1645, Dec. 2002.
[64] Tian Z., Yang L., and Giannakis G. B., “Non-data aided timing-offset estimation
for ultra-wideband transmissions using cyclostationarity,” IEEE Transaction on
Communications, vol.4. pp. 121-124, Mar. 2003.
[65] Carobonelli C., Mengali U., and Mitra U., Synchronization and channel
estimation for UWB signals, GLOBECOM 2003, pp. 764-768.
[66] Choi, J.D.; Stark, W.E.; “Performance of ultra-wideband communications with
suboptimal receivers in multipath channels,” IEEE Journal on Selected Areas in
Communications. Volume: 20, Issue: 9, Dec. 2002 Pages: 1754 – 1766.
[67] D. Dardari, A. Giorgetti, M. Chiani, T. Q. S. Quek, and M. Z. Win, A Stop-and-
Go Transmitted-Reference UWB receiver, ICUWB 2006, The 2006 IEEE
International Conference on Ultra-Wideband, Waltham, Massachusetts, USA,
September, 2006.
[68] Yang L., Giannakis G. B., “Optimal Pilot Waveform Assisted Modulation for
Ultra wideband Communications,” IEEE Transactions on Wireless
Communications, vol.3, pp. 1236-1249, 2004.
[69] Wang Z. and Yang X., Ultra wide-band communications with blind channel
estimation based on first-order statistics, pp.529-532 ICASSP, 2004.
[70] Marjanovic M., Páez Borrallo J. M., Analysis of Timing Offset Estimation
Schemes in UWB, pp.116, EUSIPCO, September, 2005.
BIBLIOGRAPHY
175
[71] Saleh A. and Valenzuela R., “A Statistical Model for Indoor Multipath
Propagation,” IEEE JSAC, vol. SAC-5, no. 2, February 1987, pp. 128–137.
[72] Stuber G. L. Principles of Mobile Communication. Kluwer Academic Publishers,
1996.
[73] Hashemi H., “Impulse Response Modelling of Indoor Radio Propagation
Channels,” IEEE JSAC, vol. 11, no. 7, September 1993, pp. 967–978.
[74] Jean-Marc Cramer R. An Evaluation of Ultra-Wideband Propagation Channels.
PhD thesis, University of Southern California, Los Angeles, CA, December
2000.
[75] Foerster J. Channel modelling sub-committee report final. IEEE 802.15.SG3a
Study Group, December 2002.
[76] Foerster J., Li Q., UWB channel modelling contribution from Intel, IEEE
P802.15-02/279r0-SG3a, June 2002.
[77] Homer E. A. Synchronization of Ultra-Wideband signals in the Dense Multipath
Channel .PhD thesis, University of Southern California, Los Angeles, CA,
December 2004.
[78] Win M. Z., Ultra-Wide Bandwidth Spread-Spectrum Techniques for Wireless
Multiple-Access Communications. PhD thesis, University of Southern California,
Los Angeles, CA, May 1998.
[79] Price R. and Green P.E. “A communication technique for the multipath channel,”
Proceedings of the IRE, pp 555-570, March 1958.
[80] Simon, Marvin K., Omura, Jim K., et al, Spread Spectrum Communications, vol.
1, Computer Science Press, 1985.
[81] Tranter W. H., Shanmugan K. S., Rappaport T. S., and Kosbar K. L., Principles
of Communication Systems Simulation with Wireless Applications, Upper Saddle
River, New Yersey: Prentice Hall PTR, 2004.
[82] Jeruchim M. C., Balaban P., and Shanmugan K.S., Simulation of Communication
Systems, 2nd
ed., New York: Kluwe Academic/Plenum Publishers, 2000.
BIBLIOGRAPHY
176
[83] Barrau G. N., Páez Borrallo J. M., “A New Time-Hopping Multiple Access
Communication System Simulator Time Hopping: Application to Ultra
Wideband,” EURASIP JASP, Special Issue of UWB-State of the Art, pp. 346–
358, 2005.
[84] Marjanovic M., Páez Borrallo J. M., A Low Complexity Simulation Algorithm for
TH-UWB MMSE RAKE Receiver, ISSPIT 2006, The 6th
IEEE International
Symposium on Signal Processing and Information Technology, Vancouver,
Canada, August, 2006.
[85] Choi J., “Random Sign Repetition Time-Hopping UWB with Multiuser
Detection,” EURASIP JASP, Special Issue of UWB State of the Art, pp. 590-598,
2005.
[86] Giancola G., Di Benedetto G., “A Novel Approach for Estimating Multi User
Interference in Impulse Radio UWB Networks: the Pulse Collision Model”
Special Issue on Signal Processing in UWB Communications, Eurasip Journal
on Signal Processing, Elsevier Publishers, 2005.
[87] De Nardis and Di Benedetto M. G. “Medium Access Control Design for UWB
Communications Systems: Review and Trends”, Journal of Communications and
Networks, vol. 5, num. 4, pp. 386-393, December 2003.
[88] Marjanovic M., Páez Borrallo J. M., A New Approach of MUD in UWB Systems,
ICUWB 2006, The 2006 IEEE International Conference on Ultra-Wideband,
Waltham, Massachusetts, USA, September, 2006.
[89] Marjanovic M., Páez Borrallo J. M., A Low Complexity Simulation Algorithm for
TH-UWB MMSE RAKE Receiver in NLOS Channel, ICECS 2006, 13th
IEEE
International Conference on Electronics, Circuits and Systems, Nice, France,
December, 2006.
[90] Marjanovic M., Páez Borrallo J. M., “On the Development of a Very Fast
Simulator for TH-UWB System,” IEEE Transactions on Wireless
Communications, submitted, November, 2006.
[91] Verdu S., Multiuser Detection, Cambridge University Press, 1998.
[92] Haykin S., Adaptive Filter Theory; Prentice Hall, 1991.
[93] Tse D.N.C. and Hanly S.V., “Linear Multiuser Receivers: effective interference,
BIBLIOGRAPHY
177
effective bandwidth and user capacity,” IEEE Transactions on Information
Theory, vol. 45, no.2, pp. 641-657, 1999.
[94] Monzingo R. A. and Miller T. W., Introduction to Adaptive Arrays, New York:
John Wiley and Sons, 1980.
[95] Bernard W., Samuel D. S., Adaptive Signal Processing; Prentice Hall, 1985.