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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



TELECOMUNICACIÓN

DEPARTAMENTO DE SEÑALES, SISTEMAS Y RADIOCOMUNICACIONES

TESIS DOCTORAL


los Sistemas TH-UWB



Madrid, Mayo de 2007



TELECOMUNICACIÓN


TESIS DOCTORAL


los Sistemas TH-UWB



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



TELECOMUNICACIÓN


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.

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


5.4.4. Number of Users Influence on the BER Performance in the Channel2


5.4.5. Number of Chips Influence on BER Performance in the Channel2


5.4.6. Sampling Frequency Influence on BER Performance in the Channel 2


5.4.7. Number of Users Influence on BER Performance in the Channel 3


5.4.8. Number of Chips Influence on BER Performance in the Channel 3


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

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


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


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



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



Γ =33, γ =5, 1/ Λ =2 ns, 1/ λ =0. 5 ns, L=400, Lmax=400 (Channel3)........141


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


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


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


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


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


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.


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:


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


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.


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


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


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.


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.


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 .


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.


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.


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)


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.


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


RMS delay (ns) ( rmsτ ) 12.94 Measured

Mean NP10dB 33



Mean NP10dB 7



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.


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 NP10dB 35



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])


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


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


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.


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.


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)


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


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


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)


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)


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)


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).


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


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.


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.


• 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.


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


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)


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


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


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


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)


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 − − − − −∑∑∑∑


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


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.


103

Link (q)Sequence

generator

( )q

j cc T

Template

generator

Channel

( )r t

Correlator

Decision

iα


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.


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

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


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


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)


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.

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


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 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.


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


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


Nh=64, Nf=8, Nh=4


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


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


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


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


Measurements; Nu=13, Nf=32, Nh=128, Perfect Synchronization


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


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


Measurements; L=400; Lmax=18; Nu=13; Nf=32; Nh=128; Np=10000


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


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


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


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)


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


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


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.


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


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


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


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


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)


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


5.4.5. Number of Chips Influence on BER Performance in the Channel2


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)


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


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


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


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)


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


5.4.8. Number of Chips Influence on BER Performance in the Channel 3


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


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)


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


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


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


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


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.


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


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


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.


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.


151


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)




O(Nh*Nu*Nf)




O(Nh*Nu*Nf)




O(Nh*Nu*Nf)

MMSE using speed simulator Figure 5.5 O(Nu*Nf*L*Lmax)



O(Nh*Nu*Nf*L*Lmax)

Table 5.6 Comparisons of the Algorithms Complexities in Single User Receiver


152


algorithm




O(Nh*Nu*Nf)




O(Nh*Nu*Nf)




O(Nh*Nu*Nf)




O(Nh*Nu*Nf)

MMSE using speed simulator Figure 5.5 O(Nu*Nf*L*Lmax)



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.


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


155


• 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


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.


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


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


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

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


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.

BIBLIOGRAPHY

169

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