The Multipath Fading and the Frequency Response of the Channel in an Indoor Radiating Cable System

The Multipath Fading and the Frequency

Response of the Channel in an Indoor Radiating Cable System

M.C. Jorge Alberto Seseña Osorio

Thesis submitted in partial fulfillment of the

requirements for the degree of Doctor in Science

with specialty in Electronics

Instituto Nacional de Astrofísica, Óptica y

Electrónica

Supervised by:

Dr. Ignacio Enrique Zaldívar Huerta, INAOE

Dr. Alejandro Aragón Zavala, ITESM campus Querétaro

The author hereby grants to INAOE permission

to reproduce and to distribute copies of this

thesis document in whole or in part

The Multipath Fading and the Frequency

Response of the Channel in an Indoor Radiating Cable System

M.C. Jorge Alberto Seseña Osorio

Thesis submitted in partial fulfillment of the

requirements for the degree of Doctor in Science

with specialty in Electronics

Instituto Nacional de Astrofísica, Óptica y

Electrónica

Supervised by:

Dr. Ignacio Enrique Zaldívar Huerta, INAOE

Dr. Alejandro Aragón Zavala, ITESM campus Querétaro

The author hereby grants to INAOE permission

to reproduce and to distribute copies of this

thesis document in whole or in part

Abstract

The use of wireless handheld devices has increased in recent years, at the same time; the data transmission rate rises exponentially. This trend has led to a greater concentration of mobile devices in specific locations, such as office buildings, shopping centers, airports, sports stadiums, etc. In this context, the next generation of wireless services must be able to develop ubiquitous ultra-broadband speeds. Hence, solutions are required for overcoming the hurdles present at these locations in order to satisfy the user requirements. In this regard, dedicated systems are an alternative for providing wireless services at indoor environments, while also allowing performance improvement and the possibility of offering tailored services for specific environments. In this context, radiating cables have been used as alternative distribution systems for indoor environments where distributed antenna systems have limitations giving full coverage due to obstacles (walls, doors, furniture, etc.) between the receiver and transmitter. Such scenarios generate challenges on the study and design of these radiating cable systems – for example, issues involved in the wireless communication channel.

This work presents the multipath fading and the frequency response of the channel of a radiating cable system. These topics are essential in the planning and research of any wireless system. In this context, there are a few simple propagation models for radiating cables which are somewhat restricted to radiating cables placed along a straight line. Furthermore, little attention has been paid to the frequency response of such systems. In this work, the radiating cable is installed in different paths in order to analyze experimentally the behavior of the channel, different paths of radiating cable allow shaping the coverage area for demanding scenarios. An exhaustive modeling of the multipath fading as well as the frequency response of the channel is carried by using statistical and autoregressive models, respectively.

iii

The proposed modeling considers the first wall reflection, penetration loss, cable termination, and radiating cable paths. The use of different empirical coefficients allows consideration of the mentioned propagation mechanisms. The coefficients of the proposed modeling were obtained empirically; this allows modeling different propagation mechanisms without knowing the construction material characteristics. These situations have not been considered by the current propagation models for radiating cable systems. The proposed modeling is carried out using three different propagation models and has been experimentally validated by sets of measurements. Measurements were performed in a university building in the frequency range from 900 MHz to 2.1 GHz. A careful selection of the data sets validates the robustness of the proposed modeling. The results show an averaged error of less than 1 dB. Thus, the large-scale fading showed a standard deviation between 2.5 dB and 3.7 dB for the distributions with the best fitting, and the small-scale fading was fitted to various probability distributions.

The coherence bandwidth and the rms delay spread (rms) were obtained by measuring the frequency response of the channel and it was demonstrated that there is dependence between rms and the receiver position along the cable length. This dependence must be taken into account in the design and study of broadband systems with mobility. On the other hand, simulations of small-scale fading were carried out too. First, the Rayleigh fading simulator was used and subsequently the Rician and Weibull fading were obtained. Simulations showed a better fit with theoretical distributions, compared with experimental distributions, and the maximum absolute error between measurements and simulations was 1.71 dB.

iv plane. This better-defined behavior showed the variation of delay along the cable length. The magnitude of Pole 1 was almost constant, and its angle rotates counterclockwise, which represents the variation of the delay with receiver positions along the cable length. At the same time, Pole 2 displayed a reduction in its magnitude and minimum variations on its angle. This describes the reduction of the rms as the receiver moved away from the cable feeder in a direction parallel to the cable.

Resumen

El uso de dispositivos inalámbricos portátiles se ha incrementado en los últimos años, al mismo tiempo las velocidades de transmisión de datos crece exponencialmente. Esta tendencia ha generado una mayor concentración de dispositivos móviles en lugares específicos, por ejemplo en edificios con oficinas, centros comerciales, terminales aéreas, estadios deportivos, etc. En este contexto, la próxima generación de servicios inalámbricos debe ser capaz de desarrollar altas velocidades de transmisión en cualquier lugar. Por consiguiente, soluciones son requeridas para superar los obstáculos presentes en estos lugares con el fin de satisfacer los requerimientos del usuario. A este respecto, los sistemas dedicados son una alternativa para proveer servicios inalámbricos en interiores, ya que permiten mejorar el desempeño y dan la posibilidad de ofrecer servicios a la medida para lugares específicos. En este sentido, los cables radiantes han sido utilizados como sistemas de distribución para interiores donde los sistemas con antenas distribuidas tienen limitaciones para dar cobertura completa debido a obstáculos (paredes, puertas, muebles, etc.) entre receptor y transmisor. Tales escenarios generan retos en el estudio y diseño de estos sistemas con cable radiante - por ejemplo, los temas relacionados con el canal inalámbrico de comunicación.

Este trabajo presenta el desvanecimiento por trayectos múltiples y la respuesta de frecuencia del canal en un sistema de cable radiante. Estos temas son esenciales en la planificación y la investigación de cualquier sistema inalámbrico. En este contexto, hay pocos modelos de propagación para cable radiante que están de alguna forma restringidos a un cable radiante colocado en línea recta. Además, poca atención se ha puesto en el modelado de la respuesta de frecuencia de tales sistemas con cable radiante. En este trabajo, el cable radiante fue instalado a lo largo de diferentes rutas con el fin de analizar experimentalmente el comportamiento

vii del canal, diferentes rutas de cable radiante permiten la conformación de la zona de cobertura para escenarios exigentes. Un modelado exhaustivo de los desvanecimientos por trayectorias múltiples, así como la respuesta de frecuencia del canal fue realizado mediante el uso de modelos estadísticos y auto regresivos respectivamente.

El modelado propuesto considera la reflexión en paredes, pérdidas por penetración, la terminación del cable y las rutas del cable radiante instalado. El uso de diferentes coeficientes empíricos permite considerar los mecanismos de propagación mencionados. Los coeficientes del modelado propuestos fueron obtenidos empíricamente; esto permite modelar los diferentes mecanismos de propagación sin conocer las características de los materiales de construcción. Estas situaciones no han sido consideradas por los modelos actuales de propagación para cable radiante. El modelado propuesto es realizado usando tres modelos de propagación y ha sido experimentalmente validado mediante mediciones. Las mediciones son desarrolladas en un edificio universitario en el rango de frecuencia de 900 MHz a 2.1 GHz. Una selección cuidadosa de los datos valida la robustez del modelado propuesto. Los resultados muestran un error promedio menor a 1 dB. Así, los desvanecimientos de gran escala mostraron una desviación estándar entre 2.5 y 3.7 dB para las distribuciones con el mejor ajuste.

El ancho de banda coherente y la dispersión del retardo rms fueron obtenidos midiendo la respuesta de frecuencia del canal, y fue demostrado que hay una dependencia entre la dispersión del retardo y la posición a lo largo de la longitud del cable. Esta dependencia debe ser tomada en cuenta en el diseño y estudio de sistemas de banda ancha con movilidad. Por otro lado, las simulaciones de los desvanecimientos de pequeña escala fueron realizadas también. Primero, el simulador de los desvanecimientos Rayleigh fue usado, y posteriormente los desvanecimientos Rayleigh y Weibull fueron obtenidos. Las simulaciones mostraron un mejor ajuste con las distribuciones

viii teóricas, comparadas con las distribuciones experimentales, y el máximo error absoluto entre las mediciones y simulaciones fue de 1.71 dB.

También, un modelo auto regresivo para la respuesta de frecuencia fue llevado acabo. Los resultados mostraron que un modelo AR de quinto orden da un mejor ajuste del ancho de banda coherente; sin embargo los polos del modelo AR de segundo orden mostraron un comportamiento mejor definido en el plano complejo. Este comportamiento mejor definido mostró la variación del retardo a lo largo de la longitud del cable. La magnitud del polo 1 fue casi contante, y su ángulo rotó en sentido horario, lo cual representa la variación del retardo en el receptor a lo largo de la longitud del cable. Al mismo tiempo, el polo 2 mostró una reducción en su magnitud y una mínima variación en su ángulo. Esto describe la reducción de la dispersión del retardo a medida que el receptor se mueve lejos del alimentador del cable en una dirección paralela al cable.

Agradecimientos

A los Doctores Ignacio E. Zaldívar Huerta y Alejandro Aragón Zavala, por haber supervisado mi trabajo de tesis y darme la oportunidad de utilizar diferentes instalaciones, equipos y dispositivos para el proyecto.

Al INAOE, por ser mí segunda casa durante la Maestría y el Doctorado.

Al Tecnológico de Monterrey Campus Querétaro, por permitirme utilizar sus instalaciones y equipos.

Al CONACyT, por el apoyo económico otorgado mediante la beca de Doctorado (34612) así como por el apoyo parcial del proyecto de Ciencia básica CONACyT número 154691.

A los Doctores Rogerio Enríquez Caldera, Roberto S. Murphy Arteaga, Reydezel Torres Torres, José Alejandro Díaz Méndez y Dr. Miguel Ángel Gutiérrez de Anda, por el apoyo y comentarios constructivos que me dieron al inicio de este proyecto.

A los integrantes de mi jurado de examen doctoral, Dr. Juan Manuel Ramírez Cortés, Dr. José Alejandro Díaz Méndez, Dra. Josefina Castañeda Camacho, Dr. Gerardo Antonio Castañón Ávila y Dr. Jaime Martínez Castillo, por los comentarios ofrecidos para el mejoramiento de la tesis.

A mis amigos que me han mostrado su apoyo, en especial a Jesús Huerta Chua y su familia por el apoyo y compañía que me dieron durante mi estancia en Querétaro.

A mi esposa Rosalba, por el amor, paciencia y apoyo que me brinda.

A mis padres y hermano, por el amor, ejemplo y apoyo que siempre me muestran.

A Dios, por permitirme conservar la fe en los momentos más difíciles.

xii

DEDICATORIA

A mi amada y linda esposa Rosalba

A aquel ser que aún no llega, pero sé que llegará y nos hará más felices

A mis padres y hermano

xiii

xiv

Contents Abstract …………………………………………………………………….……...ii

Resumen …………………………………………………………………….……..iii

Agradecimientos ………………………………………………………………….v

Dedicatorias …………………………………………………………………….vi

1 General Introduction

1.1 Wireless communications today ……………………………….……... 1

1.2 Wireless Channel …………………………………………………….…... 3

1.3 Multipath fading ………………………………………………………...... 3

1.4 Propagation in radiating cable systems ……………………….…..... 4

1.5 Purpose of this Thesis ……………………………………………...... 6

1.6 Outline …………………………………………………………………...... 6

2 Theoretical Foundations

2.1 Introduction ………………………………………………………….…..... 9

2.2 Characteristics of a wireless channel ………………………….…...... 9

2.2.1 Large-Scale Fading …………………………………………... 13

2.2.2 Small-Scale Fading …………………………………………...... 15

2.3 Effects of fading channel manifestations on wireless systems design ………………………………………...... 20

2.4 Radiating Cable ……………………………………………………..…... 28

2.4.1 Factors affecting radio propagation from radiating cables …………………………………………...... 29

2.4.2 Longitudinal attenuation ……………………………………… 30

2.4.3 Coupling loss ………………………………………………...... 30

2.4.4 Propagation mechanisms …………………………………...... 32

2.4.5 Radiating cable models ……………………………………….. 32

3 Measurements and Procedures

3.1 Introduction …………………………………………………………..….. 35

3.2 Description of the radiating cable system …………….………….... 36

3.3 Narrowband measurements ………………………………………….. 37

3.3.1 Narrowband measurements in the radiating cable system ………………………………...... …...... 39

3.3.2 Large-scale fading in the radiating cable system ...... 40

3.3.3 Model calibration....………….…………..……………...... 42

3.3.4 Modeling of propagation mechanisms in the radiating cable system....……….…………..….…………..……………...... 44

3.4 Wideband Measurements ……………………………………………... 49

3.4.1 Wideband measurements in the radiating cable system .. 51

3.4.2 Small-scale fading in the radiating cable system ...... 53

4 Modeling and Simulation

4.1 Introduction …………………………………………………………….... 55

4.2 Results of narrowband measurements ………………………..…… 55

xvi

4.2.1 Large-scale fading ……………………………………….....….. 55

4.2.2 Small-scale fading …………………………………………...... 58

4.2.3 Doppler Spread of the channel …………………………….... 61

4.3 Results of wideband measurements ……………………………..…. 61

4.3.1 The rms delay spread ………………………………………..… 61

4.3.2 The Coherence Bandwidth BC …………………………….… 65

4.4 Frequency Domain Channel Modeling ……………………….…….. 67

4.4.1 Autoregressive Modeling ………………………………..……. 68

4.5 Simulations ………………………………………………………….…... 74

4.5.1 Simulations of narrowband channel ……………………..…. 74

4.5.2 Simulations of the frequency response of the channel .... 79

5 Conclusions and Future work

5.1 General Conclusions …………………………………………………... 83

5.2 Recommendations for future research and applications …….... 86

Appendix: List of Publications…………………………………... 89

List of Figures…………………………………………………………….... 119

List of Tables…………………………………………………………….... 123

Bibliography…………………………………………………………….... 125

xvii

xviii

CHAPTER 1

General Introduction

1.1 Wireless communications today The use of wireless handheld devices has increased in recent years [1]; in 2011 the number of global mobile cellular subscriptions was nearly six billion and should have exceeded that number by 2013. This trend has led to a greater concentration of mobile devices in specific locations, such as office buildings, shopping centers, airports, sports stadiums, etc. At the same time, the data transmission rates rise exponentially [2]. In this context, the next generation of wireless services must be able to develop ubiquitous ultrabroadband speeds. Hence, solutions are required for overcoming the hurdles present at these locations in order to satisfy the user requirements. In this regard, dedicated systems are an alternative for providing wireless services at indoor environments, while also allowing performance improvement and the possibility of offering tailored services for specific environments. Thus, the concept of distributed antenna systems has been proposed and consists of splitting the transmitted power between several antenna elements in order to provide coverage in the area of interest [3, 4, 5, 6, 7]. In this context, radiating cables have been used as alternative distribution systems for indoor environments where distributed antenna systems have limitations giving full coverage due to obstacles (walls, doors, furniture, etc.) between the receiver and transmitter. For example, Figure 1.1 shows how the coverage of signal is improved in an indoor environment by exploiting the characteristics of a radiating cable. Such scenarios generate challenges on the study and design of these radiating cable systems – for example, issues involved in the wireless communication channel.

Indoor Environment

Regions with Regions with

signal coverage signal coverage

Radiating

Antenna Cable Distributed Antenna System Radiating Cable System

Figure 1.1: Improvement of signal coverage by using a radiating cable

Radiating cables were originally conceived to provide subterranean radio propagation, for example, in railway tunnels and underground mining [8, 9]. However, its implementation has gained even more strength when applied toward a wide variety of needs for underground and enclosed radio communications, for instance mobile communication in buildings, car parks, large buildings, road tunnels, emergency services, etc. [10].

In summary, radiating cables are used to distribute radio waves in sites where common antennas fail, besides being used as part of wireless systems such as in radio detection and indoor positioning systems [11, 12, 13, 14]. The constant increase in its use has made the current propagation models unable to fulfill the requirements in the prediction of received power. In this context, there are a few simple propagation models for radiating cables which are somewhat restricted to radiating cables placed along a straight line. Furthermore, little attention has been paid to the frequency response of such systems.

According to previous discussion, the behavior of the wireless channel must be comprehended. Special attention must be paid to variations of the received power, also known as multipath fading, because it allows

2 understanding the operation, design and analysis of specific radiating cable systems.

1.2 Wireless Channel In general, a wireless system is composed of a transmitter, a receiver and a wireless channel. There is relative control of transmitter and receiver performance due to the different signal-processing schemes that can be used to improve the wireless system performance. In contrast, there is no control on the wireless channel due to its strong dependence on the environment, making its modeling extremely complex. Figure 1.2 shows a schematic diagram of a wireless system.

Information

Source Channel Multiplex Modulate Multiple RF and Coding Coding Access Antennas

Transmitter Wireless Channel

Receiver

Source Channel De- De- Multiple Antennas Decoding Decoding multiplex modulate Access and RF

Information

Figure 1.2: Schematic diagram of a wireless system [15].

1.3 Multipath fading Figure 1.3 depicts a wireless channel from a typical environment. In this case, the signal travels from the transmitter to the receiver by multipath; thus, the multipath waves arrive at the receiver from different directions, producing constructive and destructive interferences (multipath fading). As the receiver

3 is displaced, even in short distances, the interferences are stronger, thus generating the loss of the signal temporarily. The strengths of paths depend on propagation mechanisms, such as reflection, diffraction, scattering and refraction, and its deterministic analysis is limited to simpler cases. In complex cases, a statistical analysis is more useful and more common. In statistical modeling, the channel parameters are collected from measurements.

Reflection Diffraction Receiver Transmitter Antenna RX Antenna TX

Wireless

Channel

Scattering Refraction

Figure 1.3: Multipath channel.

1.4 Propagation in radiating cable systems In the case of propagation modeling in radiating cable systems, some attempts have been reported with either low accuracy or impractical implementation. For instance, if a physical approach is considered, there is a model that allows the prediction of radio coverage using ray tracing [16]. The disadvantage of this approach is that the description of building materials, its accurate geometry, and clutter of furniture must be known; moreover, an excessive computational time is required. On the other hand, semi-empirical approaches to compute the radiated field of a radiating cable at indoor environments are reported in [17]. In [17], the authors describe a parametric study in the frequency domain in order to characterize the transmission

4 channel in terms of field amplitude variation. To validate this study, a straight length of a radiating cable was installed in a tunnel and a series of measurements in the frequency range of 420-925 MHz was taken. In [18], the author presents the derivation of an empirical model for the mean propagation loss for a distributed antenna system. A series of experiments was carried out in a single-story office building considering a straight length of radiating cable. In [19], the author assumes simple geometries in the installation of cables.

Usually, an empirical radio propagation model for a radiating cable system considers that the cable is laid in a straight line, where the received power is expressed by a similar equation to that used for conventional antennas, which considers the main parameters of the radiating cable system (line loss and coupling loss), but neglects other effects that could modify the predicted signal strength. For example, in a system where the radiating cable is laid with different routes [20], the received power increases along the cable length in contrast to a typical propagation model that predicts a reduction of the signal level. Figure 1.4 shows such a situation.

Corridor route distance Figure 1.4: Received power in a corridor along the cable length [20]

1.5 Purpose of this Thesis The aim of this thesis is to present novel contributions to the study and development of future radiating cable systems in indoor environments. This goal is carried out by modeling and simulating multipath fading and response frequency of the channel for a specific radiating cable system installed in different paths. This set-up can be used to develop different applications, since it allows shaping the coverage area for demanding scenarios. The modeling, and the simulations of multipath fading and the frequency response of the channel, were carried out in the frequency range of 900-2100 MHz. The results were compared with the measurements through probability functions. The propagation modeling takes into consideration propagation mechanisms such as reflections, penetration loss and the cable termination particular to the environment, as well as specific cable paths. These situations have not been considered by other propagation models for radiating cable systems. Moreover, the modeling of frequency response of the channel is carried out by means an autoregressive model, which has not been reported before for a radiating cable system. Finally, simulations of measurements are given, which may be used in the research and design of specific systems, or even in simulation tools.

1.6 Outline Chapter 2 presents a brief summary of the concepts related to channel characteristics and its effects on wireless system designs, and the radiating cable. Chapter 3 gives a description of the radiating cable system and the measurement systems as well as the procedure carried out in this work. Chapter 4 presents the results of the modeling and simulations of multipath fading, encompassing some channel characteristics and the comparison of models by calculating the quadratic error of cumulative distributions of measurements and the modeling. Moreover, the modeling of frequency

6 response is carried out by using an autoregressive model; its results are presented and used to calculate the coherence bandwidth of the channel. This channel characteristic is compared with that measured at the site. Finally, Chapter 5 presents a summary of the results, the conclusions, and some guidelines for future work.

CHAPTER 2

Theoretical Foundations

2.1 Introduction

In this chapter the characteristics of a general wireless channel are presented. Later, some effects of wireless channel characteristics on networks design are given, and, finally a general summary of the radiating cable is presented.

2.2 Characteristics of a wireless channel

A communication channel is the physical medium that the signal uses to travel from the transmitter to receiver. During its path, different propagation mechanisms which may modify the signal in some degree occur. There are three basic mechanisms: reflection, diffraction and scattering. Reflection occurs when the signal impinges on smooth surfaces (medium 2) and which have large dimensions compared with the signal wavelength; thus, an amount of the signal energy is reflected and other is propagated toward the medium 2. Diffraction takes place when the signal path is obstructed by large obstacles which do not allow the signal arrives to the receiver, however, secondary waves are formed and which reach the receiver (shadowing). Finally, scattering is generated when the signal impinges on either rough surfaces or small objects compared with the signal wavelength, in such case the signal is spread out in all directions.

The combination of the above mentioned mechanisms generate a phenomenon known as multipath propagation, which makes reference to all different paths what a signal may take from the transmitter to receiver. This

9 phenomenon generates fluctuations in the received signal, due the diversity of paths which have different amplitudes, phases and angles of arrival. In a multipath fading environment the received power variations can be determined as the product of two effects; and is given by [21]

r  mr0 (2.1)

Where m is known as the large scale fading (shadowing) and r0 as the small scale fading. Figure 2.1 shows a simulation of the received power variations along a travelled distance. The simulation was obtained by a Susuki series generator [22].

Figure 2.1: Variations of the received power

(Large-scale fading and small-scale fading)

Figure 2.2 shows a summary of the fading manifestations in a wireless channel [23]. The two fading effects that characterize wireless communications are the large-scale fading and small scale fading, blocks 1 and 4, respectively. The large-scale fading is manifested when the distance between the transmitter and receiver is increased in long distances compared with the signal wavelength (block 2) and the variations around the mean (block 3). On the other hand, the small-scale fading (block 4) occurs when there are small changes in position (block 5) and time variances of the channel (block 6). The manifestations of small-scale fading can be described in two domains and they are represented by blocks 7, 10, 13, and 16. Finally the types of signal degradation, due to small-scale fading, are listed in blocks 8, 9, 11, 12, 14, 15, 17 and 18. The following sections give a brief description of the fading manifestation with the help of the blocks in figure 2.2.

Fading Channel

Manifestations

1 4

Large-scale fading due to motion Small-scale fading due to small over large areas changes in position

2 3 5 6

Mean signal-attenuation Variations Time spreading of Time variance of the vs distance aboutthe mean the signal channel (Moving (Multipath) object)

7 10 13 16

Time-delay Frequency-domain Time-domain Doppler-shift domain description description description Domain description

8 9 14 15

Frequency Flat fading Fast Slow selective fading fading

fading TmTs Tm>Ts

11 12 17 18

Frequency Flat fading Fast Slow selective f0>W fading fading fading Wfd f0

Tsis the symbol time. Tsis the symbol time. Tm is the excess delay time. T0 is the coherence time. f0 is the coherence bandwidth. fd is the frequency shift. W is the signal bandwidth. W is the signal bandwidth.

Figure 2.2: Wireless channel fading [23].

2.2.1 Large-Scale Fading

Large-scale fading are slow signal variations, when there are movements on large areas (blocks 2 and 3). Usually its estimation is obtained by measuring length intervals in the range of 10 to 40 wavelengths [21, 24] of the received power, and then the samples are averaged inside each interval in order to remove the small-scale fading. This large scale fading is caused by the scattering of large and distant objects, and is modeled statistically by a lognormal distribution.

The large-scale fading is obtained by removing the dependence on distance of measurements. This dependence on distance or attenuation is represented by the path loss; free-space loss is a model used to represent the attenuation and is given (in decibel units) [25] by

Lfs dB  32.4 10log10 f MHz 20log10 dkm (2.2)

Where f is the signal frequency and d is the distance between transmitter and receiver. Usually the propagation models predict the mean and the standard deviation of the path loss within large areas. A general model is given by [26]

Lp ddB  LS d0 dB10nlog10d d0  X dB (2.3)

Where d0 is the reference distance, LS is the path loss at the reference distance, n is the exponent that gives the increasing rate of the attenuation,

X is a zero-mean Gaussian random variable that represents the variations around the mean path loss and  is its standard deviation. Estimated values of  and n can be found in [26, 27], which were obtained in different indoor environments. In this context, another path-loss model for indoor

13 environments is a modification of Eq. (2.3) [28], that considers losses due to the walls and floors between transmitter and receiver and is given by

n  d  P Q   Ld dB  10log10   WAFp  FAF q (2.4)  d0  p1 q1

Where P and Q are the number of walls and floors between the transmitter and receiver, WAF(p), FAF(q) and n are wall and floor attenuation factors and the path loss exponent respectively. They are determined by best fitting model given by Eq. (2.4) applied to measurement data. Nevertheless, it has been observed that the total floor loss is a non-linear function of the number of penetrated floors; therefore the COST231 multi-wall model has been proposed [29] and is given by

W n f 2 n f 1b LT  LF  Lc  Lwinwi  L f n f (2.5) i1

Where LF is the path loss in the free space, W is the number of walls, Lwi is the attenuation due to the wall wi, of type i, nf is the number of floors and Lf is the loss per floor. Lf and nf are empirically parameters.

Since the area between the transmitter and receiver is often not homogeneous, path loss model with multiple gradients has been used, for example in [30] the path loss was modeled with four different gradients, and is given by

 20log10 d, 1 d  10 m  d 20  30log10 , 10  d  20 m  10 L  L  d (2.6) p 0 29  60log , 20  d  40 m  10 20  d  47 120log , d  40 m  10 40

An empirical model to use at WLAN [31] frequencies has the general form of

LdB  k1  k2 log10 f  k3 log10 d  nw k4P1  k5P2  k6mf (2.7)

Where f and d represent the signal frequency and the distance between transmitter and receiver, P1 and P2 are associated with the angle of incidence in a wall, nw and mf are the number of walls and floors respectively. Minimum least square error is used to obtain the coefficients ki.

At this point, all models presented in this section have been empirical models. However, physical models can also be used to predict the indoor propagation. The most common physical models are the ray-tracing models [32, 33] and the finite-difference time-domain approach (FDTD) [34, 35]. Nevertheless enough detail about building layout and construction materials must be known in order to carry out these physical models. Due their complexity these physical models are rarely used for practical planning of systems [25].

2.2.2 Small –Scale Fading

The small scale fading is characterized by rapid variations of the received power in short distances; these distances are less than a wavelength . These rapid variations are mainly caused by the scattering of nearby objects

15 to the receiver; typically the small scale fading is modeled statistically with a Rayleigh distribution when there is no direct path (line-of-sight). In the other hand, a Rician distribution is used when there is a direct path between transmitter and receiver. In order to understand the effects in the signal when small scale fading is presented in the channel, Figure 2.2 is used. The time spreading of the signal and block 5 can be explained with the help of Figure 2.3 (a). This figure shows the multipath intensity profile S() which is a representation of the signal arrivals when the time increases. It shows the signal intensity with different delays; from this graphic the maximum excess delay Tm can be obtained and which is a measuring of the time between the first and the last received component. Usually the last received component is established at 10 dB or 20 dB below the level of the strongest component.

The maximum excess delay (Tm) affects the behavior of the channel. For example, if Tm is greater than the symbol time Ts, the channel shows frequency-selective fading, block 8. In the case Tm

A similar description can be given from point of view of the frequency domain, block 10. Figure 2.3 (c) shows the absolute value of the spaced-frequency correlation function |R(f)| which can be obtained with the Fourier transform of the multipath intensity profile S(). R(f) represents the correlation between the channel responses when two signals are applied with different frequencies f1 and f2, respectively. The x-axis is the difference between the frequencies f=f1-f2, In other words, the spaced-frequency correlation function shows the range of frequencies which the channel passes with roughly equal gain and linear phase (coherence bandwidth f0). Considering that W is the signal bandwidth, the channel shows frequency-nonselective or flat fading

16 when f0>W, otherwise frequency-selective occurs. The upper limit on the transmission rate is established by the channel-coherence bandwidth f0 without an equalizer in the receiver.

Tm is not always the best indicator of the system behavior when the signal propagates through the channel, because different channels may have the same maximum excess delay but different multipath intensity profiles.

Therefore, the root mean square (rms) delay spread is used, rms, which is the second central moment of the multipath intensity profile. It is given by

2 2  rms      (2.8)

2 Where  is the mean excess delay and  is the second moment given by

L n 2  i i n i1   L n  1,2 (2.9) 2  i i1

Where i represents the amplitude of the ith path and i is its delay.

S()

S()

f fc+fd 0  fc-fd c

Tm Maximun excess fd Spectral broadenig

Multipath intensity profile Doppler power spectrum (a) (b)

|R(f)) |R(t))

t 0 0 f

T0 = 1/fd Coherence Time f0 = 1/Tm Coherence bandwidth

Space-frequency correlation Space-time correlation function function (c) (d) Figure 2.3. Channel correlation functions and power density functions.

The time variance of the channel is caused by movements of the transmitter, receiver or objects within the channel, block 6, and generates changes on propagation-path. The channel’s time variance characteristics can be found by using the spaced-time correlation function. Figure 2.3 (d) shows the spaced-time correlation function which is the correlation between the channel responses when one signal is applied twice at time t1 and t2. The x-axis is t=t2-t1. In other words, the spaced-time correlation function gives the time when the channel remains without changes or the coherence time

T0. When time symbol Ts is greater than the coherence time T0, the channel is described with the term fast fading, block 14, otherwise the term slow fading is used, block 15.

In the case of fast fading, several changes during the time of the symbols generate a distortion in the baseband pulse shape. Conversely, in slow fading the transmission symbol stays unchanged.

The time variance also can be characterized in the Doppler-frequency shift domain, block 16. Figure 2.3 (b) shows the Doppler power spectrum S() as a function of Doppler-frequency shift . The Doppler power spectrum estimates the spectral broadening due to the rate of changes in the channel. In multipath environment, the signal travels by different paths and each path can be affected by the movement of different objects, therefore different Doppler shifts are generated and a Doppler spreading of the transmitted signal will be presented. Also the width of the Doppler power spectrum fd is known as Doppler spread, fading rate, fading bandwidth, or spectral broadening. The

Doppler spread fd and the coherence time T0 are related with the approximationT0 1 fd . Defining T0 as the time over which the channel’s response have a correlation of at least 0.5, T0 is given in [23] by

9 T0  (2.10) 16fd

When the signal bandwidth W, is less than the Doppler spread fd, the channel is known as fast fading (W

(W>fd). Fast fading generates distortion in the signal; therefore slow fading must be ensured making the symbol time be less than the coherence time.

2.3 Effects of fading channel manifestations on wireless systems design

The large-scale fading has a direct impact on the estimated coverage of a wireless system. In this context, there is a minimum received power level Pmin which guarantees a reliable performance of the system. In other words, if the received power is below Pmin, then the wireless system will have a poor performance. Thus the outage probability pout(Pmin ,d) is defined as the probability that a received power, Pr(d), falls below Pmin at the distance d, and is given by [36]

 P  P d   min r  poutPmin ,d   pPr d   Pmin   1Q  (2.11)   L 

Where Pr(d) is the received power estimated with an appropriate propagation model, L is the standard deviation of the large-scale fading, and the Q function is the probability that a Gaussian random variable x with mean zero and variance one is bigger than z. This is given by

 1  y2  Qx  px  z   exp dy (2.12) z 2  2 

In this way, due to the variations (large-scale fading) around the mean received power, the coverage won’t form a circular shape; as in the case where path loss is only considered. Figure 2.4 shows this situation, where the base station antenna has a horizontal omnidirectional radiation pattern for a specific distance D; the received power will have variations which generate regions with Pr below the Pmin. Figure 2.5 shows that as the distance di is reduced, the percentages of locations, which fulfill the specified coverage quality, are increased. Thus coverage area is the percentage of locations within a specific area, where the received signal will be above of a minimum required threshold. The coverage area is obtained by taking an increment on area dA at a distance r from the base station and which is multiplied by PA.

Where PA is the probability that a received power Pr(r) is greater than and a specific threshold Pmin, PA=p(Pr(r)>Pmin). For a circular coverage area with radius R from a base station, the coverage area is given by

1 1 2 R C  PAdA  PArdrd (2.13) R2 cell.area R2 0 0

Where PA is calculated with Eq. (2.11), considering the propagation model

Eq. (2.3) for Pr(d), C is obtained as follows:

1 2 R C  pPr r  Pmin rdrd R2 0 0 (2.14) 1 2 R  P  P  L d 10n log r d  C  Q min t S 0 10 0 rdrd 2 0 0   R   L 

Where Pt is the transmitted power.

Base Station Path loss only

D Path loss and Variations (Large-scale fading)

Figure 2.4. The received power takes into account the path loss and variations at the service area edge.

50% 90% Tx 95%

Figure 2.5. Coverage contours for 50%, 90% and 95% for locations which fulfill with the specified coverage quality.

P  P  L d 10nlog R d  10nlog e Letting a  min t S 0 10 0 andb  10 , we have  L  L

2 R   r  C  rQa  blog dr (2.15) 2 0 R   R  The solution of this integral is given by [37]

 2  ab   2  ab  C  Qa exp Q  (2.16)  b2   b  The effects of large scale fading in the coverage planning can be shown by using Eq. (2.16). Figure 2.6 shows the percentage of coverage area for different L-values by using values reported in [27] for Eq. (2.3) (n=3.54,

LS(d0)=31.7 dB) and assuming Pmin=-105dBm and Pt=15dBm. It is observed when L is reduced, the coverage area is increased; for example for a 95% of locations adequately covered, the distances from the transmitter are approximately 111 m, 149 m, 198 m and 257 m for L= 12.8, L= 9.8, L=6.8 and L=3.8 dB respectively. This fact notices that a wrong estimation of the large-scale fading creates errors in the initial planning of a wireless network. In this sense, the dimensioning of a wireless network consists of determining its coverage and capacity; later modifying network parameters in order to reach the required coverage and to avoid interferences. The wireless network functions, the power control, handoff and channel access, are also affected by local mean variations [38]. For example in CDMA systems, all mobiles must receive the same power and adjust the transmit power to maximize the system capacity; this process is developed by the power control function which is dependent on the local mean variations. Furthermore, local mean variations also impact on the co-channel interference. Systems are designed with sufficient frequency and reuse distances between base stations to avoid co-channel interferences; however, an error of local mean variation generates an incorrect reuse of the distance between base stations.

Figure 2.6. Effects of large-scale fading on the estimating of the coverage area.

The effects of the small-scale fading are observed on ISI distortion, pulse mutilation, irreducible BER and loss in SNR. The rms delay spread, Eq. (2.8), is a measure of this phenomenon and it allows calculating data rates for unequalized channels. For example according to [39], the ratio of the rms delay spread to symbol duration must be below 0.2 in order to have a tolerable interference.

On the other hand, the bit error rate (BER) is affected by small-scale fading as follows. When the transmitted signal is affected only by an additive white Gaussian noise (AWGN channel), the simplest case of a channel is been considered. In this case, the transmitter and receiver are not in motion, and

24 the signal bandwidth is small in comparison with the channel bandwidth. Thus the BER performance of binary shift keying (BPSK) is given by

Pe  Q 2  (2.17) Where Q is the complementary cumulative normal distribution and  is the signal-to-noise ratio SNR which is considered as constant. Figure 2.7 shows the BER in the AWGN channel case; nevertheless in practical environments, the SNR is not constant due to the channel fading. Thus, the mean SNR must be considered to obtain the average BER; which is given by

 Pe  Pe p d (2.18) 0

Where Pe is the BER for a specific digital modulation and p() is the pdf of small-scale fading that represents the specific environment. In the case of a Rayleigh fading environment and substituting Eq. (2.17) in Eq. (2.18), the average BER is given by

1    Pe  1  (2.19) 2  1  

Where  is the average SNR. Figure 2.7 shows the bit error rate in a Rayleigh fading by using Eq. (2.19).

Figure 2.7. AWGN and Rayleigh channel BER for BPSK.

As it has been described, the received amplitude of the signal has fluctuations due to the multipath of the signal and movement of objects. In this context, the received signal decreases below the threshold level for acceptable performance of the receiver, thus the statistics of fading rate and the duration of the fade are important parameters in the wireless network design. Figure 2.8 shows a fading simulation which was generated by using two filtered Gaussian noise generators in quadrature [22], the parameters related to the fading rate and its duration are indicated.

Figure 2.8. Level-crossing and fade-duration statistics

For a Rayleigh fading enveloped distribution, the average number of down crossings of a threshold level A per second is given by [40]

2 N  2 f M  exp   (2.20)

Where  = A/Arms is the ratio of the threshold level to the rms signal amplitude, and fm is the maximum Doppler spread of the signal. The average fade duration for Rayleigh fading is given by

exp 2 1     (2.21) 2 f M

Where and fM were defined in Eq. (2.20).

2.4 Radiating Cable

An antenna is one of the main components of a wireless system; its characteristics affect directly the system performance. In this context, the functioning of a radiating cable can be understood with an analogy of the irrigation of water in a garden as it is explained in [41]. Omnidirectional or directional antennas function as a sprinkler send out equal amounts of water in every directions or a water stream in a smaller area, respectively. A third alternative is the use of holey hoses, which irrigate water along its length, likewise the radiating cable works as a continuous antenna, allowing radiation to occur along the cable length for uniform coverage. Recently radiating cables have been extensively used as part of wireless systems which operate in the frequency range of UHF, such as in distributed antenna systems for in- building cellular scenarios, radio detection systems and wireless indoor positioning systems [11, 12, 13, 14]. Because most users congregate inside buildings and stay there longer, wireless service providers are becoming more interested in delivering their services in these places. This has motivated researchers to focus their efforts on obtaining optimal coverage levels inside buildings. It is well-known that for indoor wireless communications, constructive and destructive interference have a crucial effect on the signal being transmitted. Consequently, developing accurate propagation models is a hard task. One way to distribute the signal effectively inside buildings and, as a result minimize multipath effects is to use distribution antenna systems [42, 25]. However, there are some places such as long corridors, tunnels, airport piers, areas inside sports stadiums or underground stations, in which a uniform coverage cannot easily be achieved by using such systems. This makes radiating cable systems a good technological alternative [27, 43, 44].

A radiating cable or leaky feeder is a coaxial cable where the outer conductor has been slotted allowing radiation to occur along the cable length for uniform

28 coverage, Figure 2.9. In the field of wireless communications, a radiating cable can be used as a passive distribution system, improving coverage in any underground or closed environment [45, 46]. When it is used in combination with a dedicated indoor cell, such as picocell or microcell, capacity is not sacrificed and coverage can be smoothly distributed within the premises.

Slotted copper Dielectric Innerconductor outer conductor Outer jacket

Figure 2.9. Radiating cable

2.4.1 Factors affecting radio propagation from radiating cables

A coaxial cable acts as a radiating cable, if periodic apertures are slotted on its outer conductor along the cable. These apertures allow the generation of cylindrical wave fronts that will be propagated in a radial direction outside the cable. Depending on the position of the apertures, the cables can be classified as couple-mode and radiating-mode. In both cases, common characteristics for these types of cables are the so-called longitudinal attenuation and coupling loss [25]. Generally, these parameters are supplied by the manufacturer and must be taken into account at the moment of establishing a propagation model. Beyond these effects, other propagation

29 mechanisms such as reflection and transmissions must be taken into account.

2.4.2. Longitudinal attenuation

Longitudinal attenuation is related to cable construction, conductor size and dielectric material. This parameter allows the evaluation of the signal loss in the cable and is expressed in decibels per meter (dB/m) at a specific frequency. For a given size, the value of the longitudinal attenuation increases as the frequency of operation is also increased. Table 1 shows two types of cable manufactured by RFS World [47] which shows this dependence. Figure 2.10 illustrates the dependence of longitudinal attenuation with a physical length.

2.4.3. Coupling loss

Coupling loss describes the propagation loss between the cable and a test receiver placed at a particular radial distance from the cable. In practice, coupling loss depends on several factors such as the mounting environment, cable mounting positions, the kind of mobile antenna as well as the operating frequency [16]. As for the previous case, this parameter is supplied by the manufacturer in terms of a median value, as illustrated in Table 2.1. Figure 2.10 shows the characteristics of a RCF 12-50J cable, size=1/2”, having a coupling loss of 69 dB at 1900 MHz, that must be taken into account for radio planning purposes.

Table 2.1. Longitudinal attenuation and coupling loss of two different cables of RFS [47]

RCF 12-50J RCF 78-50JA Size=1/2” Size=7/8” Frequency Longitudinal Coupling Longitudinal Coupling (MHz) Attenuation Loss Attenuation Loss (dB/100 m) (dB) (dB/100 m) (dB) 450 5.70 67 3.05 75 900 8.40 66 4.4 73 1900 13.6 69 7 70 2200 14.7 70 7.8 70 2600 15.9 70 8.8 68

0 Longitudinal Atennuation -13.6

Power inside -35 the cable Coupling Loss

Signal Level (dBm) Level Signal Received power -69

-82.6 -90 0 20 40 60 80 100 120 Radiating cable length (m)

Figure 2.10: System loss that must be take into account in the planning of a radiating cable system, longitudinal attenuation = 13.6 dB/100 m and coupling loss = 69 dB.

2.4.4. Propagation mechanisms

In a practical environment, propagation mechanisms such as reflection and diffraction due to interfering objects, the so-called waveguiding effect, attenuation due to floor and wall penetration, etc. must be considered. As the signal propagates in space, objects with greater dimensions than the signal wavelength cause reflections. The waveguiding effect is generated when the radiating cable is near and perpendicular to corridors, thus producing multiple reflections that enhance the signal due to adding interference effects. Penetration loss should be considered when the signal travels through walls and floors made of different materials. Diffraction can be caused by sharp edges, windows and doors through the signal travels.

The modeling of all these effects must consider that a radiating cable differs from a conventional antenna and it can require sophisticated and complex algorithms. Therefore in this work, a simple modeling that incorporates effects such as the reflection, penetration loss and the cable termination is established to obtain the large scale fading of the channel.

2.4.5 Radiating cable models

The wave propagation from a radiating cable can be modeled as the radio propagation from a conventional antenna considering the transmitted power, the distance between antennas, and a particular distance considered as a reference. In this sense, the model proposed in [19] considers the main characteristics of a radiating cable system such as the longitudinal attenuation, the coupling loss and a loss factor due to blockages. Therefore, the radio propagation is determined in linear scale as:

Pt Pr  n (2.22) zalclbd

Where Pr is the received power, Pt is the transmitted power, za is the longitudinal attenuation, lc is the coupling loss, lb is a loss factor, d is the radial distance between the cable axis and receiver, and n is the loss exponent.

On the other hand, in [18] is proposed a radio propagation model that considers the radiating cable as a line source and the waves are spread in a cylindrical surface. A straight section of the cable is taken into account and it is ended with an antenna. In the near field and considering a mono pole antenna in the receiver, the radio propagation is modeled in linear scale as

32 P  P (2.23) r t 8 2zadL

Where Pr is the received power, Pt is the transmit power,  is the signal wavelength, za is the longitudinal attenuation, d is the radial distance between the cable axis and receiver in meters and L is the radiating cable length in meters.

Finally the Friis transmission equation can be also used to model wave propagation from the radiation cable. Thus, considering the longitudinal attenuation; the received power in linear scale is

2 P  P (2.24) r t 4d 2 za Where the receive antenna and transmit antenna gains were assumed as 1, Pr is the received power,  is the signal wavelength, za is the longitudinal attenuation and d is the radial distance between the cable axis and receiver in meters.

It is important to remark that Eqs. (2.22) and (2.23) are valid only for the case when one straight segment of radiating cable is considered. For those cases where there is more than one straight segment or path, the use of the

33 expressions is not reliable. On the other hand, no information is provided for cable terminations.

Small-scale fading measurements have been reported in [19], which are carried out by measuring the time dispersion. The measurements were carried out in an indoor environment and it was obtained a maximum value of 60.6 ns for the rms delay spread, therefore according to [39], the system can support the data rate up to 3.3 Mb/s without equalization.

CHAPTER 3

Measurements and Procedures

3.1 Introduction

In order to characterize the multipath fading of a radio channel, different measurements must be carried out. The channel characteristics allow determining the most important issues involved in the designing of a wireless communication system. For example: the achievable signal coverage, maximum data rate, BER and irreducible BER. All these issues are related to the fading channel manifestations which were described in chapter 2, section 2.2. In this context, the achievable coverage (the area or range of operation for a specific system) can be determined knowing the large-scale fading, as it was explained in section 2.3. On the other hand, the maximum data rate, the BER and irreducible BER in the channel are determined by knowing the small-scale fading. Thus, according to the fading channel manifestations, there are two sorts of measurements which are: narrowband measurements and wideband measurements.

The narrowband measurements are focused on determining the distance power gradient or the attenuation versus the distance and variations about the mean of the received power. However these measurements do not provide any information regarding to the time delay of a signal. On the other hand, wideband measurements are focused on determining information of the multipath delay spread as well as the frequency selectivity of the channel. In both cases, calibration of the measurement system is essential in order to obtain reliable results according to recommendations given in [25]. It also provides a guide of how to implement these measurements. In this work the narrowband and wideband measurements were carried out. In the following

35 sections a description of the radiating cable system as well as the measurements and procedures are explained.

3.2 Description of the radiating cable system

The radiating cable system is located inside a university building which has classrooms, laboratories, offices and a warehouse. This building is a five- story structure where the interior and exterior walls were built with drywall and block, respectively. Ceilings were built of steel decks and metallic beams, while the floors were built of ceramic tile. Ceilings are 4 meters high with false ceilings of 3 meters high. Figure 3.1 shows the building.

Figure 3.1: Engineering and Electronic Centre, Building no. 2.

The radiating cable was placed over the false ceiling of the second level and it was laid in three paths. The first path of the radiating cable was located over the communication laboratory. The second path was positioned along the corridor and the third path was placed over the warehouse. Figure 3.2 shows the layout of the second level indicating the placement of the radiating cable as well as the coordinate system used in this experiment.

20 room 2203 First

Path room Warehouse Communication 2204 WC Third Laboratory Path Second 15 Path y(m)

Room 10 Room Room 2207 2201 2202

5 Radiating Generator Matched Cable Load

0 0 5 10 15 20 25 30 35

x(m)

Figure 3.2: Layout of the second floor that indicates the radiating cable position on a coordinate system.

3.3 Narrowband measurements

The basic narrowband measurement system is showed in Figure 3.3 and it is composed of two stages. The first one is the transmitter stage which consists of an antenna and a source that generates an unmodulated carrier signal. An unmodulated signal or constant signal provides assurance that the variations of the received signal level are only produced by the signal multiple paths generated in the channel, in contrast to the use of a specific modulation scheme which generates additional variations in the received signal level. The receiver stage is composed by an antenna connected to the receiver in this case a data acquisition system is necessary in order to control the

37 receiver and to store measurements and also receiver positions. Thus, the measurements are collected while the receiver is moved through the area.

Unmodulated Propagation Receiver Carrier Signal Channel

Data Acquisition System

Figure 3.3: Narrowband measurement system.

The first step is to obtain the local mean power because the path loss modeling is the main issue involved in narrowband measurements. The local mean power is found by averaging the received power around a specific area. Usually, the estimation of the local mean power is obtained by measuring length intervals in the range of 20 to 40 wavelengths [24], then, the samples are averaged inside each interval. In indoor environments [48, 49], small areas and subintervals of around 10 wavelengths have been selected in order to remove the rapidly varying signal (small-scale fading) without affecting the slowly varying signal (large-scale fading). And, at least two samples per signal wavelength are required [25]. The procedure is feasible for measurement in straight routes, however, in cases where the measurement routes are composed by different ways; this approach leads us to obtain some inaccuracies. Two intervals can be close together, producing two averaged values rather than one. Therefore, it is suggested that samples are averaged inside a square area [25] this will be explained in section 3.3.1; which is devoted to the development of the narrowband measurements of the wireless system under study.

3.3.1 Narrowband measurements in the radiating cable system

RF signals were supplied by the use of a Rohde and Schwarz Signal Generator, model SMB100A [50]. Measurement frequencies were selected at 900, 1700, 1900 and 2100 MHz. and in each case the electrical powers were 20, 20, 10, and 20 dBm, respectively. The radiating cable was the RCF model 12-50J fabricated by RADIAFLEX® RFS [51]. The use of a matched load of 50 ohms at the end of the link avoided unwanted electrical reflections. The receiver stage was composed by different omnidirectional monopole antennas plugged in to a Rhode and Schwarz Vector Network Analyzer (VNA) [50], model ZVL6 equipped with the electrical spectrum analyzer (option that allows achieving the measurements at 1700 and 2100 MHz). The experimental setup and measurement equipment used for this experiment are illustrated in Figure 3.4. Also, a portable SeeGull Lx dual-band radio scanner, 900/1900 MHZ, from PCTEL [52], was used to achieve measurements at 900 and 1900 MHz. The software InSite v3.1.0.19 from PCTEL allows controlling the scanner. In all these cases the receiver antenna was placed at 1.5 meters high.

RADIATING CABLE

OMNIDIRECTIONAL OMNIDIRECTIONAL MONOPOLE Spectrum MONOPOLE Radio ANTENNA Analyzer ANTENNA Scanner (VNA ZVL-6) (SeeGull Lx)

PC PC

Figure 3.4: Narrowband measurements for radiating cable system.

3.3.2 Large-scale fading in the radiating cable system

As a first step, the in-site measurement data were collected by using different trajectories (walk routes), and recorded by means of the radio scanner as well as using the spectrum analyzer option of the VNA. At the second level, the walk routes traveled at a constant speed in most of the rooms. Sample locations were recorded with the software InSite v3.1.0.19, from PCTEL, and with a special program developed in Matlab for the radio scanner and the spectrum analyzer, respectively. The entire layout from Figure 3.2 was segmented in a grid of 4x4 squares, as illustrated in Fig.3.5. All samples inside each square were averaged and represented by measurement spots (Figure 3.5). This procedure allows the recording of variations of the large- scale fading, and consequently, eliminates small-fading effects [25].

Figure 3.5: Grid used to divide the layout from Figure 3.2.

Figure 3.6 (a) and 3.6 (b) show experimental results corresponding to the received power and averaged power, respectively. In both cases, the example corresponds to 1900 MHz. The fast-fading effect was removed by [25].

n Pri  1 10  Pr  10log10 10  (3.1)  n i1 

Where Pri is the received power in dBm, and n is the number of samples inside a square of the grid.

Figure 3.6: Raw and averaged measurements.

In order to obtain only the large-scale fading and its variations, it is necessary to extract the dependence on distance of the averaged measurements, in other words the path loss must be eliminated. This can be carried out by using some propagation models for radiating cables as those ones from section 2.4.5 in chapter 2. Therefore the averaged measurements were used to obtain the parameters of the models and the variations of the large-scale fading according to the following procedure.

The measurement spot set was divided into two groups, which were used for model tuning and model validation (or obtaining of large-scale fading variations). The corresponding measurement spots for model tuning were selected for corridor and the rooms. In the first case, measurement locations

41 were selected everywhere along the corridor. For the second case, measurement locations were chosen considering only the corners and the middle of the rooms. Figure 3.7 shows measurement spot locations for model tuning and model validation at 1900 MHz. In this case, 40% of measurement spots were used for model tuning. On the other hand, to have confidence in the results of this experiment, 60 % of the samples were used for model validation.

22 Measurement spots for model validation Measurement spots for model tuning 20

Position y (m) Position 12

6 0 5 10 15 20 25 30 Position x (m)

Figure 3.7: 40% of measurement spots were used for model tuning (1900 MHz).

3.3.3 Model calibration

An initial calibration of propagation models (section 2.2) is necessary in order to reduce errors in the results. The environment is divided by zones, and inside each zone there are representative propagation mechanisms nearby radiating cable paths. Figure 3.8 shows second floor layout with different

42 zones. The model calibration is carried out in zone no. 2, because there are no obstacles that could generate reflections or penetration loss, and only one cable segment is near the receiver (direct path between source and receiver).

Radiating Cable

2204 L/T Zone 72104 L/T Zone 6

Zone 1 Zone 2 Zone 3

Zone 4 Zone 5 2201 L/T 2207 L/T

Figure 3.8: Second floor layout and zone distribution for propagation modeling.

The following procedure is applied to equations (2.22), (2.23) and (2.24), but only the calibration of eq. (2.17) is shown. In zone no. 2, the main contribution to the received power is a direct ray between radiating cable and receiver. Thus, the received power is calculated with eq. (2.17) in a logarithmic scale which is

PR  PT Z  LC  LB 10nlog10d (3.2)

Where PR is the received power, PT is the transmitted power, aZ is the longitudinal loss, LC is the coupling loss, d is the distance between the cable and the receiver, and n is the attenuation exponent, which is assumed equal

43 to 1. A calibration factor is found by the mean value of the difference between calculated values with Eq. (3.2) and measurement values. Thus, Eq. (3.2) is

PR  PT Z  LC  LB 10nlog10d CF (3.3)

Where CF is the calibration factor.

Finally, the calibrated Eq. (2.17) is

Pt Pr  n (3.4) zalcb l d cf Where cf is the calibration factor in linear scale. Eqs. (3.5) and (3.6) are obtained in a similar way using Eq. (2.18) and Eq. (2.19), respectively. In this procedure, the floor and ceiling reflections are included.

3 2 PP (3.5) rt8cf 2zadL  2 PPrt (3.6) 4d2 za cf

3.3.4 Modeling of propagation mechanisms in the radiating cable system

The modeling of all propagation mechanisms that are present in a practical indoor environment is a difficult task, if not impossible. However, in order to keep the modeling simple, and at the same time considering situations that have not been taken into account by other models, only the reflected rays, penetration loss, radiating cable paths and the cable termination are considered. In particular, first reflected rays and transmission losses are calculated with empirical coefficients, which are not dependent on the wall constitutive parameters or the incident angle.

Figure 3.9 illustrates a radiating cable installed along a corridor. Assuming that the radiating cable only generates rays that are perpendicular to cable axis, there are three main paths through the signal travels. Two paths are generated due to the first reflection of the signal on walls. The distances of reflected signals in walls W1 and W2 are d1 and d2 respectively. Meanwhile, there is a direct ray that travels from the radiating cable to the receiver, where its distance is d0. Thus, the received power is composed by the addition of three paths and is determined by

Prrrr Total01 P 1 d P 2 d 2  R P d R (3.7)

Where Pr can be calculated with Eqs. (3.4), (3.5) or (3.6), and R1 and R2 are empirical coefficients.

Wall W2 Radiating Wall W1 Cable

d0 d2 d1

Receiver Antenna

Figure 3.9: Multi-path generated by reflected and direct rays.

Figure 3.10 illustrates the penetration loss generated when there is a wall between the radiating cable and the receiver antenna. In this case, the

45 distance between the radiating cable and the receiver antenna is d1. Furthermore, the received power is

PPrr Total1 d T 1   (3.8)

Where Pr can be calculated with Eqs. (3.4), (3.5) or (3.6), and T1 is an empirical coefficient.

Radiating Wall W1 Cable

Receiver Antenna

Figure 3.10: Transmission loss generated by a wall.

Figure 3.11 shows two paths or segments of radiating cable, which are close to the receiver position. Each segment generates a ray that reaches the receiver, however, these rays are affected by the walls W1 and W2 (penetration loss). Thus, the received power is

Pr Total P r d 1 T 1 P r  d 2 T 2 (3.9)

Where Pr can be calculated with Eqs. (3.4), (3.5) or (3.6), and T1 and T2 are empirical coefficients.

Wall W2 Radiating Cable Receiver Antenna d2

Wall W1

Figure 3.11: Two radiating cable segments which contribute to the received signal, each ray is affected by penetration loss (Top View).

Finally, Figure 3.12 shows a situation where there are two radiating cable segments. The received power is the sum of two rays generated by cable segments. And the horizontal segment produces a ray that hits the wall W1 (penetration loss), while the ray launched by the vertical segment does not find any wall. However, as a special case, an empirical coefficient K is added in order to incorporate the effect of the cable termination, because this segment is terminated with a matched load. Thus, the received power is

Pr Total P r d 1 T 1 P r  d 2  K (3.10)

Where Pr can be calculated with Eqs. (3.4), (3.5) or (3.6), meanwhile T1 and K are empirical coefficients.

ManchedMatched LoadLoad Receiver Antenna d2

Radiating Cable Wall W1

Figure 3.12: Two radiating cable segments that contribute to the received signal (Top View).

Table 3.1 shows a summary of the equations used to model the indoor radio propagation with their corresponding zones. Where Pr Total Meas is the averaged measurements of the received power, Pr Theo is the received power calculated with Eqs. (3.4), (3.5) or (3.6); d0, d1 and d2 are the distances traveled by the direct ray and those reflected or transmitted rays through walls. Finally, R1, R2,

T1, T2 and K are empirical coefficients.

Table 3.1: Equations used in every environment zones.

Number of Equations in linear scale Zone

Pr Total Meas P r Theo d 0 P r Theo d 1 R 1 1 and 3  Pr Theo d 2 R 2

4 and 5 Prr Total Meas P Theo d 1 T 1

6 Pr Total Meas P r Theo d 1 T 1 P r Theo d 2 T 2

7 Pr Total Meas P r Theo d 0 K P r Theo d 1 T 1

To obtain reflection and transmission coefficients for walls, it is necessary to know, for example, the complex permittivity of wall materials , wall thickness, the incident angle, polarization, etc., At the same time, other assumptions must be considered, such as homogeneous walls and smooth surfaces. But all this information is usually not available in multipath environments; therefore the prediction of the signal level is not reliable. Thus, the empirical coefficients were obtained numerically using the data reserved for model tuning.

3.4 Wideband Measurements

There are various wideband measurements procedures which can be carried out either in the time domain or in the frequency domain. In the time domain case, the impulse response of the channel is measured. While in the frequency domain case, the frequency response of the channel is measured.

The impulse response of the channel can be measured either by transmitting a short pulse or transmitting a wideband spread-spectrum signal. In the short duration pulse case, the received signal is sampled which is the convolution of the pulse with the channels impulse response. And the ratio of peak to average power must be high in order to detect low power multipath. Additionally, in the wideband spread-spectrum signal case, the signal is modulated by a pseudo-random sequence and the receiver signal is correlated with the original signal. In this case, the duration of the signal must be short compared with the channel coherence time.

In the frequency domain case, the frequency response of the channel is measured directly. Figure 3.13 shows the measurement system which uses as a main component a network analyzer. Thus, it is possible to obtain the channel impulse response by using Fourier transform techniques.

Antenna Tx Antenna Rx

Network Analyzer

f0 +Nf f0 f f0 f f0 +Nf 0 0

Figure 3.13: Measurement system for the frequency domain case.

In the transmitter antenna which is plugged to one port of the network analyzer, a set of discrete frequencies fk is swept; where fk=f0+kf and 0

L H k  H f   exp  j2f exp  j     f kf  i  i   i  f kf i1 L (3.11)    i exp j2kf i exp ji , 0  k  N i1

Where i, i and i represent the magnitude, arrival time and phase respectively, of the L individual paths. Because the measurement system is limited band, the system measures windowed frequency characteristics of the channel. Therefore, the measured frequency response is given by

L Hmeas k  Wki exp j2kfi exp ji , 0  k  N (3.12) i1

Where W(k) are the effects of filtering in the frequency domain.

The baseband impulse response of the channel can be obtained by the inverse discrete Fourier transform of the measured samples Hmeas(k), and is given by

1 N 1 ht   H meas kexp j2tkf  (3.13) N k 0

Where t is the sample of time. The frequency-domain measurement system can measure a span of time of Tm=1/f. And the time resolution t is obtained by using the inverse of the bandwidth of the measurements

1 t  N (3.14)  fk k 1

Where N is the number of complex samples.

3.4.1 Wideband measurements in the radiating cable system

The measurements were carried out with the Rhode and Schwarz Vector Network Analyzer (model ZVL6), and the measurement system was the same as shown in Figure 3.14., but with some modifications. For example, the antenna Tx was replaced by the radiating cable which has already been described in previous sections. Around 30 meters of flexible low loss coax cable (LMR-400 from Times Microwave Systems) were used to connect the receiver antenna with Port 2 of the network analyzer. A low noise amplifier

(ZRL-2400 from Mini-Circuits) was used between the wideband omnidirectional antenna of the receiver and the flexible low loss coax cable. Figure 3.14 illustrates the wideband measurement system used in the experiment. The measurements were made with a set of discrete frequencies fk=f0+kf, where f0 =1300 MHz which is the lowest frequency, and f= 0.5 MHz. The frequency response consists of 1000 complex samples, which were recollected at approximately 250 ms. Additionally, the receiver antenna was placed at 1.5 meters high on a trolley which carried the power source for the low noise amplifier.

Antenna Rx Channel

Radiating Cable

Low Power Noise Source Amplifier ZLR-2400 Mini-Circuits

Network Analyzer ZVL6 Cable LMR-400 Times Microwave Systems

Figure 3.14: Wideband measurements for radiating cable system.

3.4.2 Small-scale fading in the radiating cable system

The frequency response measurements were collected inside each room at the second floor of the building 2. In each room around 120 frequency responses were measured and recorded, and the separation between the frequency response samples was 10 cm. These samples were distributed throughout the test area. Then, in the corridor case, samples were collected along three parallel paths to the second segment of the radiating cable. Figure 3.15 shows an example of an impulse response obtained in a room. In order to obtain the small scale characteristics, the multipath intensity profile must be obtained. The last received component is established at 20 dB below the level of the strongest component, thus, the rms delay spread was obtained by using Eq. (2.8). The surrounding environment is kept stationary during the measurements by avoiding object movements.

Figure 3.15: An impulse response obtained in the room 2201.

The coherence bandwidth (c) is a measure of the grade of similarity or coherence of the channel in the frequency domain. Bc can be obtained with the 3-dB width of the magnitude of complex autocorrelation function of the frequency response which is given by [40]

N k 1  RH k  H  fi H fik , k  0 (3.15) N i1

Where H(fi) is the frequency response at fi. Bc is inversely proportional to the delay spread of the channel rms. A relationship between the 3-dB width of the frequency correlation function and the rms delay of the channel can be found by a linear regression of logarithms, the relationship is given by

 Bc  C rms (3.16) Where C and  are empirical coefficients.

In the next chapter, the results of the measurements described here will be presented.

CHAPTER 4

Modeling and Simulation

4.1 Introduction

The channel modeling can be carried out from two perspectives, narrowband channel modeling and wideband channel modeling. And each one is utilized for different applications and specific objectives. Narrowband channel modeling is mainly focused on the behavior of the received signal strength. On the other hand, wideband channel modeling is focused on the multipath delay spread as well as the frequency selectivity of the channel. Thus, this chapter is devoted to the presentation of the channel characteristics obtained from measurements taken at the site, which were described in chapter 3, as well as the narrowband and wideband channel modeling. Furthermore, simulations for the narrowband modeling and the frequency response of the channel are carried out. Finally, the comparison between the measurements, results of the modeling and simulations is also given.

4.2 Results of narrowband measurements

4.2.1 Large-scale fading

Table 4.1 shows the standard deviation of large-scale fading for the second level. The large-scale fading was obtained by the difference between averaged measurement values and calculated values; it allows removing the signal-level distance dependence. The calculated values were computed using equations from Table 3.1 and the coefficients obtained by the tuning of models. There are three cases which correspond to the usage of the propagation models presented in the chapter 3. The results show an averaged error less than 1 dB.

Table 4.1: Standard deviation of the large-scale fading.

Equation Equation Equation (3.4) (3.5) (3.6) Frequency Standard Standard Standard (MHz) Deviation Deviation Deviation (dB) (dB) (dB) 900 3.53 3.74 4.29 1700 2.38 2.58 3.07 1900 3.15 2.91 3.63 2100 2.52 2.77 2.89

From these results, the standard deviation of the large-scale fading shows similar values among models used, however the results from (3.6) are the larger ones. Because the large-scale fading follows a normal distribution [25, 40], the normal distributions were fitted to large-scale fading results. Figure 4.1 illustrates the normal distribution fitted by the probability-probability plot at 1700 MHz corresponding to the three cases described in chapter 3. And when both the theoretical and the estimated distribution coincide, the result is a straight line. Therefore, departures from the straight line mean departures from the specified distribution (normal distribution).

Fig. 4.1: Probability-Probability plot of large scale fading at 1700 MHz.

The fitting between an experimental distribution EDs(si) and a theoretical distribution TDs(si) can also be evaluated by calculating the quadratic error [53] which is given by

qe  ED s TD s 2  S i S i (4.1)

Where si is the x-axis of the cumulative distribution functions either experimental or theoretical. The quadratic error (qe) is shown for each fitting of Figure 4.1. Table 4.2 presents a summary of the quadratic error obtained for all cases.

Table 4.2: Quadratic error between estimated and theoretical normal distribution function for large-scale fading.

Quadratic Error (qe) Frequency Eq. (3.4) Eq. (3.5) Eq. (3.6) (MHz) 900 0.3453 0.1698 0.5204 1700 0.0783 0.0563 0.1367 1900 0.1343 0.1676 0.1245 2100 0.1617 0.2079 0.1739

Eq. (3.5) shows the best fit at 900 and 1700 MHz, while Eq. (3.6) corresponds to 1900 MHz. Finally Eq. (3.4) gives the best fit at 2100 MHz.

4.2.2 Small-scale fading

The small-scale fading was obtained by the difference between the measurements and its local mean power [54]. These results were fitted to four probability distributions functions and the quadratic error was calculated in order to find the best fitting among them. These probability distributions functions were Lognormal, Rayleigh, Rician and Weibull, because they are often used in the modeling of the wireless channel fading [25, 40]. Table 4.3 shows the probability distribution functions. The fitting of the measurements in every room was calculated and Table 4.4 shows the quadratic error between the theoretical probability distributions and the experimental distributions for each room.

Table 4.3: The probability distribution functions used for modeling the small- scale fading.

Lognormal Rician

2 2 1 logxx 2 x x2  A2  2 2  Ax  px x  e p x x  e I 0   x 2  2  2  0  x   0  x   A  0 x is the received signal envelope x is the received signal envelope voltage r (volts) voltage r (volts) 2 is the variance of the random 2 is the variance of the random multipath multipath A is the direct path amplitude (volts).

I0 is the Modified Bessel function of first kind and zero-order.

Rayleigh Weibull

2 2 b1 x x 2 b b  x  x a px x  e 2 px x    e  a  a  0  x   0  x  

is the received signal envelope x x is the received signal envelope voltage (volts) r voltage r (volts) 2  is the variance of the random b is the shape parameter multipath a is the scale parameter

Table 4.4: Quadratic error of fitted probability distributions in every room.

Frequency Room Lognormal Rayleigh Rician Weibull Distribution Distribution Distribution Distribution 900 MHz 2201 3.0403 3.1925 0.1058 0.1827 2202 2.0556 0.7964 0.1263 0.1905 2203 1.2550 1.8279 0.3117 0.3070 2204 1.3358 0.4355 0.4378 0.4013 2207 3.3154 2.1367 0.2264 0.3138 Warehouse 2.5173 1.3097 0.1481 0.2071 Corridor 0.9817 0.0322 0.0332 0.0324 Entire Floor 1.6962 0.5394 0.0524 0.0501 1700 MHz 2201 1.1197 0.0479 0.0123 0.0123 2202 1.3550 0.9517 0.0492 0.0341 2203 0.9277 0.1444 0.1471 0.1541 2204 1.9109 0.1311 0.1311 0.0974 2207 0.8426 0.1014 0.1025 0.0777 Warehouse 1.0747 0.0180 0.0129 0.0128 Corridor 1.1985 0.1687 0.0103 0.0033 Entire Floor 1.0636 0.0398 0.0070 0.0028 1900 MHz 2201 1.4926 0.7228 0.0987 0.0735 2202 3.0604 0.2247 0.2174 0.2350 2203 1.8629 1.2486 0.1816 0.2199 2204 1.3180 0.2456 0.1148 0.1069 2207 2.2868 1.0749 0.0858 0.1258 Warehouse 1.5195 1.1461 0.1692 0.1470 Corridor 3.0133 2.0596 0.2240 0.3509 Entire Floor 2.1435 0.9875 0.0824 0.1363 2100 MHz 2201 1.0541 0.0191 0.0196 0.0180 2202 0.7823 0.7136 0.0998 0.0515 2203 2.4445 2.6638 0.1867 0.2474 2204 0.7918 0.0805 0.0816 0.0898 2207 1.5657 0.0170 0.0173 0.0165 Warehouse 0.7918 0.0155 0.0134 0.0159 Corridor 0.9103 0.0316 0.0219 0.0191 Entire Floor 0.7807 0.0350 0.0166 0.0094

Results show that the Weibull distribution gives the best fitting at 900, 1700 and 2100 MHz in the entire floor, while the Rician distribution gives the best fitting at 1900 MHz.

4.2.3 Doppler Spread of the channel

To determine the Doppler spread of the channel it is necessary a measurement system capable of sampling the small-scale fading of the signal. The system must measure the amplitude and phase of the received signal at the Nyquist rate, which is associated with the highest Doppler shift. However the maximum Doppler shift at 1700, 1900 and 2100 MHz, can be obtained with

v f f  m c (4.2) M c

Where vm is the velocity of objects in the environment fc is the signal frequency and c is 3x108 m/s.

4.3 Results of wideband measurements

4.3.1 The rms delay spread

The rms delay spread of channel is important in wireless system design because it limits the symbol transmission rate R. Figure 4.2 depicts the obtained cumulative distribution of rms delay spread for all measurements. From this figure, it is observed that the maximum value of the rms delay spread is 54.4 ns and the minimum value is 10.25 ns. The rms delay spread values are less than 34.4 ns 50 % of the time.

Figure 4.2: CDF of the rms delay spread obtained from wideband measurements.

As can be observed in the results, the cumulative distribution does not follow any particular distribution and the range of rms delay spread values are closely similar to [19]. On the other hand, the cumulative distribution functions of the delay spread for every room have a smaller range of variations and different averaged values as shown in Figure 4.3.

Figure 4.3: CDF of the rms delay spread for every room of the second floor.

From the results of Figure 4.3, it is observed that the mean of the delay spread in a particular area depends on its location with respect to the length of the radiating cable. For example, Figure 4.4 corresponds to the normalized impulse responses which were obtained along a parallel route to the radiating cable in the corridor. Also, Figure 4.4 illustrates how the impulse response starts with different delays, in the case of x=5 m and y=14 m (according to Figure 3.2), the impulse response starts around 15.5 ns, on the contrary, for x=25 m and y=14 m (according to Figure 3.2), the impulse response starts around 108 ns. Furthermore, the impulse responses finish in a similar time, this fact explains the different mean values obtained from the rms delay spread for every room, Figure 4.3. The former case corresponds to the area of the radiating cable which is near to the feeder; and the latter case corresponds to the opposite situation.

Figure 4.4: Normalized impulse responses along the corridor.

Figure 4.5 shows the dependence between the rms delay spread and the length of the radiating cable as well as its fitted line. Thus, the relationship between rms delay spread and the length of the radiating cable along the corridor is given by

3   50  x (4.3) rms 2

Where x is the position of the receiver along corridor given in meters, and rms is given in ns.

Figure 4.5: A scatter plot of rms delay spread rms versus x position along the corridor. Also the line fitted to data is shown.

4.3.2 The Coherence Bandwidth BC

The coherence bandwidth determines the range of frequencies over which the channel can be considered flat (frequencies with comparable amplitude fading). It can be obtained experimentally using Eq. (3.14). Figure 4.6 corresponds to the complementary cumulative distribution function of 3-dB width of the correlation function of the frequency response.

0.9

0.8

0.7

0.6

0.5

0.4

Probability Abscissa >

0.3

0.2

0.1

0 5 10 15 20 25 30 3dB Width (MHz)

Figure 4.6: The complementary cumulative distribution function of 3-dB width of the frequency correlation function.

Frequently, there is an inverse relationship between the rms delay spread and the coherence bandwidth of the channel, Eq. (3.15). The coefficients of the inverse relationship are calculated by a linear regression (on logarithmic scales) between the rms delay spread and the 3-dB width of the correlation function of the frequency response. Figure 4.7 shows the width (3 dB) of the frequency correlation function versus its corresponding rms delay spread and the best-fit line. Thus, the inverse relationship is given by

1 Bc  (4.4)  rms

Where Bc is the coherence bandwidth and rms is the rms delay spread.

Figure 4.7: Relationship between the 3-dB width of the frequency correlation function and the rms delay spread and the best-fit line.

In the next sections, the obtained results will be used to model and simulate the wireless channel.

4.4 Frequency Domain Channel Modeling

The channel modeling in the frequency domain allows the direct use of the measured frequency responses which were described in chapter 3. In this context, an autoregressive (AR) model in the frequency domain for indoor radio propagation has been reported in different works [55, 56, 57, 58]. However these works were based on wireless systems where the receiver

67 and transmitter used conventional antennas, in contrast the results of this work are for a wireless system which uses a radiating cable.

4.4.1 Autoregressive Modeling

The measured frequency response can be understood as a random process; therefore, an AR model can map the frequency response samples into a limited number of filter poles representing an AR process. An AR process of order p is given by

H fn , x ai H fni , x V  fn  (4.5) i1

th Where H(fn,x) is the n sample of the measured frequency response at location x, V(fn) is a complex white noise process and the complex constants ai are the parameters of the model. Taking the z-transform of eq. (4.5), the AR process can be depicted as the output of a linear filter with a transfer function driven by a zero-mean white noise. The transfer function is given by

1 p 1 Gz  p   1 1 i1 1 pi z (4.6) 1 ai z i1

th where pi is the i pole of the transfer function. The N measurement samples are described by the locations of the p poles of G(z), where typically N>>p.

And the ai parameters are the solution for Yule-Walker equations [56]:

R l ai Ri  l  0, l  0 (4.7) i1

In which R(k) is the frequency correlation function defined in eq. (3.14), and

R(-l)=R(l). The variance of the zero-mean white noise process V(fn) is the minimum mean-square of the predictor output, which is given by

p 2  v  R0 ai Ri (4.8) i1

In general, the order of the model depends on the measured site; however the fifth-order process has been used as an upper bound [56, 58, 40].

Conventionally a pole close to the unit circle denotes significant power at the frequency related to the angle of the pole. However, in the case of the autoregressive (AR) frequency domain model, a pole close to the unit circle means that there is significant power at the delay related to the pole angle. The delay is calculated as

    (4.9) 2f s

Where  is the angle of the pole, and fs is the frequency step (0.5 MHz).

After various series of measurements, the corridor was found as the main site where the general characteristics of the channel can be determined. Therefore the results of Figure 4.8 show the scatter plots of the poles for models of 2nd, 3rd, 4th and 5th order at the corridor.

Figure 4.8: Scatter diagrams of the locations of the poles for the AR models of 2nd, 3rd, 4th and 5th order.

These results show that for all cases, there are two poles close to the unit circle with averaged angles of -0.3403 rad and -0.5394 rad which correspond to delays 108.32 ns and 171.7 ns respectively. According to the work reported in [56], two significant poles can be interpreted as two significant clusters of multipath arrivals.

Figure 4.9 shows the complementary cumulative distribution functions of the 3-dB width of the correlation function for the measurements and data generated with AR models of 2nd and 5th order. The statistic of the AR model

70 of 5th order fits more closely to the original measurements; however the particular case of 2nd order will be used to understand the relationship between the model poles and the behavior of the channel.

Figure 4.9: Complementary cumulative distribution functions of the frequency correlation function for measurements and the AR models.

Second order model

Figure 4.10 depicts the enlarged scatter plot of poles for the second order model, poles show a shifting which corresponds to the position change of the receiver along the corridor. The arrow marks the direction of the shifting when the receiver is moved along positive x-axis from x=5 m to x=25 m at y=14 m (according to layout of Figure 3.2). The clockwise shifting of the pole 1 marks an increase of the delay of the first cluster of multipath arrivals. The pole 2 has almost null change of the angle but a reduction of the magnitude is

71 manifested. It means a reduction of the span of the impulse response or the power delay profile along the corridor, and in consequence the rms delay spread is reduced. This situation has been already shown in Figure 4.4 from section 4.3.1 which was presented as a point of view of the impulse response.

Figure 4.10: Enlarged scatter plot of poles for the second order model.

Table 4.5 shows the statistics of poles for the AR model of second order, and for all places of the experiment. The averaged magnitude of pole 1 remains above of 0.95 and its variations are small. On the other hand, the magnitude of pole 2 is less than that of the pole 1 and its variations are

72 greater than that of the pole 1. Conversely, the angle of pole 1 has more variations than that of the pole 2. These results will be used to simulate the channel frequency response by generating poles of the AR model.

Table 4.5: Statistics of poles for the AR model of 2nd order.

Stan. average Minimum maximum Dev. Magnitude Polo 1 0.9605 0.0111 0.9204 0.9864 Angle Polo 1 (Rad.) 0.3054 0.034 0.2145 0.3872 room 2201 Magnitude Polo 2 0.8073 0.0648 0.5644 0.9198 Angle Polo 2 (Rad.) 0.6217 0.0322 0.5203 0.7005 Magnitude Polo 1 0.9514 0.0083 0.9285 0.9822 Angle Polo 1 (Rad.) 0.3329 0.0379 0.2006 0.4064 room 2202 Magnitude Polo 2 0.6422 0.0611 0.4932 0.8946 Angle Polo 2 (Rad.) 0.6533 0.0382 0.5615 0.7445 Magnitude Polo 1 0.971 0.0072 0.9505 0.9857 room 2203 Angle Polo 1 (Rad.) 0.1551 0.026 0.0695 0.204 Magnitude Polo 2 0.7638 0.07 0.5367 0.8813 Angle Polo 2 (Rad.) 0.4902 0.035 0.4031 0.5843 Magnitude Polo 1 0.967 0.0073 0.941 0.9846 room 2204 Angle Polo 1 (Rad.) 0.2084 0.0285 0.1448 0.2858 Magnitude Polo 2 0.8044 0.0659 0.5751 0.9188 Angle Polo 2 (Rad.) 0.5086 0.0279 0.4296 0.5747 Magnitude Polo 1 0.9852 0.0037 0.9776 0.9915 room 2207 Angle Polo 1 (Rad.) 0.4233 0.0247 0.3908 0.4743 Magnitude Polo 2 0.6087 0.108 0.3905 0.7649 Angle Polo 2 (Rad.) 0.6154 0.0336 0.5354 0.6798 Magnitude Polo 1 0.9823 0.0041 0.9716 0.9915 Warehouse Angle Polo 1 (Rad.) 0.4779 0.0126 0.4304 0.4995 Magnitude Polo 2 0.5958 0.1146 0.3607 0.7918 Angle Polo 2 (Rad.) 0.6264 0.0213 0.5743 0.6712 Magnitude Polo 1 0.974 0.014 0.9202 0.9951 Corridor Angle Polo 1 (Rad.) 0.3403 0.0765 0.18882 0.4548 Magnitude Polo 2 0.6959 0.1714 0.1966 0.9559 Angle Polo 2 (Rad.) 0.5394 0.0405 0.4125 0.6765

4.5 Simulations

4.5.1 Simulations of narrowband channel

According to Table 4.4, the Rician and Weibull fading provided the best description of the small-scale fading; however first it was necessary to generate the Rayleigh fading as following [60]: Considering the scenario given in Figure 4.11, the signal multipath components arrive around the receiver antenna and the received voltage is the sum of all the possible multipath components. Thus the received voltage is given by

N vr  an cos0t  n  4.10 n1

Where an are random amplitudes, n are random phases and 0 is the angular frequency. Simplifying Eq. (4.10) and using a simple trigonometric identity [60], the received voltage can be expressed as

vr  X cos0tY sin0t  rcos0t  4.11

N Where X  a cos  n1 n  n 

N Y  a sin  n1 n  n 

r  X 2 Y 2  envelope

 Y    tan1    X  As N  , the Central Limit Theorem dictates that the random variables X and Y follow a Gaussian distribution, whereas that r follows a Rayleigh distribution.

N Multipath Components

Receiver Antenna

Figure 4.11: Multipath Propagation

Thus, simulations of narrowband channel were developed by filtering Gaussian noise and Figure 4.12 corresponds to a schematic diagram of the Rayleigh and Rician simulator. The fading phenomenon is band-limited by the width of the Doppler spectrum, therefore the Rayleigh fading was filtered using a Butterworth filter [22]. This method generates the Rayleigh fading, also a complemented step was necessary in order to obtain the Weibull or Rician fading. The Rician fading is generated by adding a constant value a to the Rayleigh fading, while the Weibull fading was obtained by using the relationship between Rayleigh fading and Weibull fading, and is given in [59] by

1  r2 n  r n    R  4.12 W    2   2 c  Where  is the scale parameter and  is the shape parameter of the Weibull 2 pdf, and c is the variance of Rayleigh fading.

I Gaussian random rR number generator G(0,1)

c

Rayleigh Gaussian random Q fading jrR rR’ number generator Doppler spread G(0,1)

rR Rician fading j

Figure 4.12: Schematic diagram of the Rayleigh and Rician simulator.

Figures 4.13 to 4.16 show the cumulative distribution functions of the small scale fading of measurements, the modeling and simulations. The probability of very low signal levels is indicated by the left tail of the cumulative distribution. For example, in the case of 1% of probability, the absolute errors between the measurements and fitted distributions are 0.17, 1.14, 0.58 and 1.48 dB at 900, 1700, 1900 and 2100 MHz, respectively. While the absolute errors between measurements and simulations are 0.38, 0.65, 0.80 and 1.71 dB. The absolute error rises as the signal frequency increases, and it is greater in the simulations. However, an exception occurs in the fitted distribution at 1700 MHz.

100%

10%

Probability that Signal Level <= AbscissaLevel Signal that Probability

Measurements Weibull distribution Simulation 1% -20 -15 -10 -5 0 5 10 Signal Level (dB about median)

Figure 4.13: Cumulative distribution of small-scale fading in the entire floor at 900 MHz.

100%

10%

Probability that Signal Abscissa Level <=

Measurements Weibull distribution Simulation 1% -20 -15 -10 -5 0 5 10 15 Signal Level (dB about median)

Figure 4.14: Cumulative distribution of small-scale fading in the entire floor at 1700 MHz.

100%

10%

Probability that Signal Abscissa Level <=

Measurements Rician distribution Simulation 1% -20 -15 -10 -5 0 5 10 15 Signal Level (dB about median)

Figure 4.15: Cumulative distribution of small-scale fading in the entire floor at 1900 MHz.

100%

10%

Probability that Signal Abscissa Level <=

Measurements Weibull distribution Simulation 1% -20 -15 -10 -5 0 5 10 15 Signal Level (dB about median)

Figure 4.16: Cumulative distribution of small-scale fading in the entire floor at 2100 MHz.

4.5.2 Simulations of the frequency response of the channel

In order to simulate the frequency response of the channel, a random generation of poles of the AR model was carried out. The second order model is easier to perform because the scatter plot is better defined, Figure 4.8. Thus, the poles were obtained by Gaussian noise sources which used data from Table 4.5 The variance of the white noise is set to an arbitrary value [56], and the result can be scaled to the desired signal level. Figure 4.17 shows the complementary cumulative distribution functions of 3-dB width of the frequency correlation function of measurements, the AR model and its simulation. The simulation follows the AR model from 100 % until 40% of probability, although as the x-axis increases the separation with measurements also rises. In the particular case of 90% of probability, there are an absolute error of 1 MHz for the AR model and simulations. From point view of a designer, the worst case might be the one of most interest; therefore, the left tails of both distributions should fit to measurements.

Figure 4.17: Complementary cumulative distribution function of 3-dB width of the correlation function of the frequency response (AR model of 2nd order).

A second simulation was carried out for the fourth order model which is shown in Figure 4.18. In this case, the CDF of the AR model is closer to measurements than in previous case, but there is no improvement in the results of simulations. One of the main reasons is that the generation of the poles is less accurate because the location of the poles is not well defined as it is shown in Figure 4.8.

Figure 4.18: Complementary cumulative distribution function of 3-dB width of the correlation function of the frequency response (AR model of 4th order).

The modeling of frequency response of the channel by an autoregressive process was presented. Although, there are other related works, the particular case of a radiating cable system has not been reported yet. These results show that the AR model of second order can be used to describe the frequency response of the channel. As mentioned above, the rms delay spread and the coherence bandwidth depend on the receiver position with respect to the radiating cable length. Such situation was described by the position of the poles on the scatter plots. Subsequently simulations of channel fading were carried out in order that they can be used

80 to test systems with defined characteristics (modulation, coding, equalization, etc.).

CHAPTER 5

Conclusions and Future Work

5.1 General Conclusions

At the beginning of this work, it was pointed out that the radiating cable can be used as part of wireless systems as in distributed antenna systems, for in- building cellular scenarios, radio detection systems and wireless indoor positioning systems. In this context, the study and design of any wireless system needs to know the multipath fading behavior of the channel in order to obtain an optimal performance of the system. Therefore, the measurements, modeling and simulations of channel fading in a radiating cable system have been presented in this work. Due to the particular characteristics of the cable installation, some results contrasted with other works reported in the literature. Furthermore, the rms delay spread and the frequency selectivity of the channel showed dependence on the receiver position along the cable length. This dependence must be taken into account in the design of broadband systems with mobility. At the same time, it can be exploited in applications like indoor positioning systems.

It was observed that the models used in other works for a radiating cable system did not fit completely to measurements used in this work. Usually, the propagation models estimate a negative relationship between the received power and the receiver position when the receiver is moved away from the cable feeder in a direction parallel to the cable; however, the measurements showed a positive relationship. Hence, the modeling of the received power was conducted in a more detailed manner. The proposed modeling considers the first wall reflection, penetration loss, cable termination, and radiating cable paths. The use of different empirical coefficients allows consideration of the mentioned propagation mechanisms.

The coefficients of the proposed modeling were obtained empirically; this allows modeling different propagation mechanisms without knowing the construction material characteristics.

In summary, the proposed propagation modeling will allow the planning of radiating cable systems in indoor environments. By means of an appropriate routing of the radiating cable inside a building and taking into account the main propagation mechanisms, coverage areas could fulfill the requirements of the users. These situations have not been considered by the current propagation models for radiating cable systems. The proposed modeling is carried out using three different propagation models and has been experimentally validated by sets of measurements performed in a university building in the frequency range from 900 MHz to 2.1 GHz. A careful selection of the data sets validates the robustness of the proposed modeling. The results show an averaged error of less than 1 dB. Thus, the large-scale fading showed a standard deviation between 2.5 dB and 3.7 dB for the distributions with the best fitting, and the small-scale fading was fitted to various probability distributions. The Rician distribution gave the best fitting at 1900 MHz for the entire floor, while the Weibull distribution gave the best fitting for other frequencies (900 MHz, 1700 MHz, 2100 MHz). This will be useful for estimating the coverage and the co-channel interference.

The coherence bandwidth and the rms delay spread (rms) were obtained by measuring the frequency response of the channel and it was demonstrated that there is dependence between rms and the receiver position along the cable length. This dependence must be taken into account in the design and study of broadband systems with mobility. For example, it was shown in [39] that without diversity or equalization, the ratio of the rms delay spread to symbol duration in a digital transmission must be kept below 0.2 to have a tolerable intersymbol interference. Thus, assuming this criterion, in Room

2202 the maximum value of rms was 54.4 ns, and so, the channel was able to

84 support a data rate up to 3.6 Mb/s. Meanwhile, in Room 2207 the maximum value of rms was 28.5 ns, and hence, the channel was able to support a data rate up to 7 Mb/s.

Also, an autoregressive (AR) model for the frequency response was carried out. Results showed that a fifth order AR model gives the best fitting at the 3-dB width of the frequency correlation function; however the poles of the second order AR model showed a better-defined behavior in the complex plane. This better-defined behavior showed the variation of delay along the cable length. The magnitude of Pole 1 was almost constant, and its angle rotates counterclockwise, which represents the variation of the delay in receiver positions along the cable length. At the same time, Pole 2 displayed a reduction in its magnitude and minimum variations on its angle. This describes the reduction of the rms as the receiver moved away from the cable feeder in a direction parallel to the cable.

On the other hand, simulations of small-scale fading were carried out too. First, the Rayleigh fading simulator was used and subsequently the Rician and Weibull fading were obtained. Simulations showed a better fit with theoretical distributions compared with experimental distributions, and the maximum absolute error between measurements and simulations was 1.71 dB.

The simulation of the frequency response was carried out by an AR process. The poles were generated by a random numbers generator with normal distribution. The statistics were specified in Table 4.5. In the case of an AR model of the second order, its results were fitted to the simulations from 100 % to 40 %, however, as expected, a deviation occurred with the measurements when the axes increased. A second simulation for an AR model of the fourth order was also performed, but there was no improvement in the simulation results. Therefore, the simulations were not fully consistent

85 with the measurements, because the poles of the AR model were scattered over large areas of the complex plane.

The areas with the best fittings were placed in the left tails of the distributions, thus, simulations can be used as the worst case that may occur in a system. The worst case is the situation that designers want to know. Besides, it should be noted that the modeling of the frequency response with an AR model of the second order is a useful tool to describe the behavior of delays of significant paths in a channel.

5.2 Recommendations for future research and applications

This work can be expanded from various aspects such as:

(1) Connecting the RF supply on the other end of the radiating cable and performing again the work described herein, in order to verify the dependence of results with the environment. Also in this context, to carry out the same study but in different environments and with different cable routes. (2) Using developed simulations for the evaluation of specific systems, which can be defined under different modulation schemas, coding and equalization. (3) Designing a simulation tool which allows evaluating a specific system.

(4) Finally, a possible application of rms dependence with the receiver position along the cable length that can be focused on indoor positioning. There are many techniques for indoor positioning whose explanation and study is outside the scope of this work, and a brief introduction can be found in [61]. Nevertheless, a sketch is given as follows. Suppose another radiating cable system with different orientation is set up in such a way that each radiating cable is perpendicular to each other. The axes of a coordinate system are thus formed by the radiating cables, and the coordinates (x, y) can be

86 obtained by measuring or calculating the rms delay spread (rms) and by using Eq. (4.3). Obviously, its implementation requires more than just obtaining the rms delay spread and using Eq. (4.3); therefore, a full investigation would be necessary.

Appendix: Publications

1. Jorge A. Sesena-Osorio, Alejandro Aragón Zavala, Jorge Rodríguez- Asomoza, Ignacio E. Zaldívar-Huerta, and José Luis Cuevas-Ruíz, ”Indoor propagation measurements for radiating cable in the UHF band 800 MHz- 2500 MHz”, 21st International Conference on Electrical Communications and Computers, San Andres Cholula, (CONIELECOMP), 299-303, February 2011.

2. J. A. Sesena-Osorio, A. Aragon-Zavala, I. E. Zaldivar-Huerta, and G. Castanon, "Indoor propagation modeling for radiating cable systems in the frequency range of 900-2500 MHz," Progress In Electromagnetics Research B, Vol. 47, pp. 241-262, 2013.

3. Seseña-Osorio J. A., Aragón-Zavala A., Zaldívar-Huerta I. E., ”Experimental Estimation of The Large-Scale Fading in an Indoor Environment and Ist Impact on the Planning of Wireless Networks”, 2013 SBMO/IEEE MTT-S International Microwave & Optoelectronics Conference (IMOC), Rio de Janeiro, Brazil, pp. 1-5, August 2013.

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List of Figures

1.1 Improvement of signal coverage by using a radiating cable…………. 2

1.2 Schematic diagram of a wireless system [14]……………………………. 3

1.3 Multipath channel…………………………………………………………… 4

1.4 Received power in a corridor along the cable length [19]……………. 5

2.1 Variations of the received power(Large-scale fading and small-scale fading)…………………………………………………………………………….. 10

2.2 Wireless channel fading [22]……………………………………………… 12

2.3 Channel correlation functions and power density functions. (a) Multipath intensity profile, (b) Doppler power spectrum, (c) Space-frequency correlation function, and (d) Space-time correlation function……………………………………………………...... 18

2.4 The received power takes into account the path loss and variations at the service area edge………………………………………………………………. 22

2.5 Coverage contours for 50%, 90% and 95% for locations which fulfill with the specified coverage quality………………………………………………….. 22

2.6 Effects of large-scale fading on the estimating of the coverage area………………………………………………………………………..…...….. 24

2.7 AWGN and Rayleigh channel BER for BPSK…………………………… 26

2.8 Level-crossing and fade-duration statistics………………….……….…. 27

2.9 Radiating cable…………………………………………………….……..… 29

2.10 System losses that must be take into account in the planning of a radiating cable system,longitudinal attenuation = 13.6 dB/100 m and coupling loss = 69 dB…………………………………………………………………….... 31

3.1 Engineering and Electronic Centre, Building no. 2……………………..… 36

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3.2 Layout of the second floor that indicates the radiating cable position on a coordinate system………………………………………………………………. 37

3.3 Narrowband measurement system…………………………………...….. 38

3.4 Narrowband measurements for radiating cable system………………… 39

3.5 Grid used to divide the layout from fig. 3.2…………………………...... 40

3.6 Raw and averaged measurements……………………………………... 41

3.7 40% of measurement spots were used for model tuning (1900

MHz)…………………………………………………………………...…………... 42

3.8 Second floor layout and zone distribution for propagation modeling…………………………………………………………………………... 43

3.9 Multi-path generated by reflected and direct rays…………………….... 45

3.10 Transmission loss generated by a wall…………….……………….... 46

3.11 Two radiating cable segments which contribute to the received signal, each ray is affected by penetration loss (Top View)…………………………. 47

3.12 Two radiating cable segments that contribute to the received signal (Top

View)……………………………………………………………………………..... 48

3.13 Measurement system for the frequency domain case……………...... 50

3.14 Wideband measurements for radiating cable system……………...... 52

3.15 An impulse response obtained in the room 2201……………………... 53

4.1 Probability-Probability plot of large scale fading at 1700 MHz………… 57

4.2 CDF of the rms delay spread obtained from wideband measurements.. 62

4.3 CDF of the rms delay spread for every room of the second floor……. 63

4.4 Normalized impulse responses along the corridor………………………. 64

4.5 A scatter plot of rms delay spread rms versus x positionalong the corridor.

Also the line fitted to data is shown………………………...... …. 65

4.6 The complementary cumulative distribution function of 3-dB width of the

120 frequency correlation function………………...... 66

4.7 Relationship between the 3-dB width of the frequency correlation function and the rms delay spread and the best-fit line………………………………... 67

4.8 Scatter diagrams of the locations of the poles for the AR models of 2nd,

3rd, 4th and 5th order.……………………………………………………..... 70

4.9 Complementary cumulative distribution functions of the frequency correlation function for measurements and the AR models…………………. 71

4.10 Enlarged scatter plot of poles for the second order model……….... 72

4.11 Multipath Propagation …………………………………………….... 75

4.12 Schematic diagram of the Rayleigh and Rician simulator………….... 76

4.13 Cumulative distribution of small-scale fading in the entire floor at 900

MHz……………………...... ………………………………... 77

4.14 Cumulative distribution of small-scale fading in the entire floor at 1700

MHz……………………………………………………..………………...……….. 77

4.15 Cumulative distribution of small-scale fading in the entire floor at 1900

MHz………………………………………………………………..………………. 78

4.16 Cumulative distribution of small-scale fading in the entire floor at 2100

MHz…………………………………………………………..……………………. 78

4.17 Complementary cumulative distribution function of 3-dB width of the correlation function of the frequency response (AR model of 2nd orderl)……………………………………………..…………………………... 79

4.18 Figure 4.18: Complementary cumulative distribution function of 3-dB width of the correlation function of the frequency response (AR model of 4th order).…………………………………………..………………………………... 80

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List of Tables

2.1 Longitudinal attenuation and coupling loss of two different cables of RFS [46]………………………………………………………………………...... 31

3.1 Equations used in every environment zones………………………..…… 48

4.1 Standard deviation of the large-scale fading…………………………… 56

4.2 Quadratic error between estimated and theoretical normal distribution function for large-scale fading………………………………………….. 58

4.3 The probability distribution functions used for modeling the small-scale fading. ……………………………………………………………………………….. 59

4.4 Quadratic error of fitted probability distribution in every room……...…. 60

4.5 Statistics of poles for the AR model of 2nd order…………………. 73

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Bibliography

[1] ITU World Telecommunication (2013). ICT Indicators database [Online]. Available: http://www.itu.int/ITU-D/ict/statistics [2] S. Cherry, “Edholm’s law of bandwidth,” IEEE Spectrum., vol.41, p. 50, July 2004. [3] Dudley, S. E. M., T. J. Quinlan and S. D. Walker, “Ultrabroadband Wireless-Optical Transmission Links Using Axial Slot Leaky Feeders and Optical Fiber for Underground Transport Topologies”, IEEE Transactions on Vehicular Technology, Vol. 57, No. 6, 3471-3476, November 2008. [4] Feng, L., X. Yang, Z Wang and Y. Li, “The Application of Leaky Coaxial Cable in Road Vehicle Communication System”, in Proceedings of 9th International Symposium on Antennas Propagation and EM Theory, 1015-1018, 2010. [5] A. A. M Saleh, A. J. Rustako, Jr. and R. S. Roman, “Distributed antennas for indoor communication”, IEEE Transactions on Communications, vol. com-35, No. 12 December 1987. [6] P. Chow, A. Karim, V. Fung and C. Dietrich, “Performance advantages of distributed antennas in indoor wireless communication systems, Proc. of IEEE 44th Vehicular Technology Conference, Vol. 3. pp. 1522-1526, June 1994. [7] K.J. Bye, “Leaky feeders for cordless communication in the office”, Proc. European Conference on Electrotechnics (Eurocon ’88), pp. 387–90, Stockholm, June 1988. [8] N. Monk and H.S. Wingbier, “Communications with moving trains in tunnels”, IRE Transactions on Vehicular Communications, 7, pp .21- 28, 1956. [9] J. C. Cawley, “An Assessment of Leaky Feeder Radio Systems in Underground Mines,” in Proc. Fifth WVU Conference on Coal Mine Electrotechnology, Morgantown, West Virginia, U.S.A., 1-15, Aug. 1980. [10] EUPEN AG Cable, URL: http://www.eupen.com/cable/rf/radiating/index.html [11] Higashino, T., K. Tsukamoto, and D. Komaki, “Radio on Leaky Coaxial Cable (RoLCX) System and Its Applications”, in Proceedings of PIERS, 40-41, Beijing, China, March, 2009.

125

[12] Higashino, T., K. Tsukamoto, and D. Komaki, “Radio on LCX as Universal Radio Platform and Its Application”, in Proceedings of Progress In Electromagnetics Research Symposium, 773-776, Xi`an, China, March, 2010. [13] Nishikawa, K., T. Higashino, K. Tsukamoto and S. Komaki, “A new position detection method using leaky coaxial cable”, IEICE Electronics Express, Vol. 5, No. 8, 285-290, April 2008. [14] Weber, M., U. Birkel, R. Collmann and J. Engelbrecht, “Comparison of Various Methods for Indoor RF Fingerprinting using Leaky Feeder Cable”, in Proceedings of 7th Workshop on Positioning Navigation and Communication (WPNC), 291-298, 2010. [15] G. D. Durgin, “Space-Time Wireless Channels,” Prentice Hall, First Ed. 2003. [16] Morgan, S. P., “Prediction of Indoor Wireless Coverage by Leaky Coaxial Cable Using Ray Tracing”, IEEE Transaction on Vehicular Technology, Vol. 48, No. 6, 2005-2014, November 1999. [17] Liénard, M., Ph. Mariage, J. Vandamme and P. Degauque, “Radiowave retransmission in confined areas using radiating cable: Theoretical and experimental study”, in Proceedings of IEEE 44th Vehicular Technology Conference, 938-941, 1994. [18] Carter, K., “Prediction Propagation Loss from Leaky Coaxial Cable Terminated with an Indoor Antenna”, in Proceedings of 8th Virginia Tech/MPRG Symposium Wireless Communications, pp. 71-82, 1998. [19] Zhang, Y. P., “Indoor Radiated-Mode Leaky Feeder Propagation at 2.0 GHz”, IEEE Transactions on Vehicular Technology, vol. 50, no. 2, pp. 536-545, March 2001. [20] Seseña-Osorio J. A., Aragón-Zavala A., J, Rodriguez-Asomoza, Zaldívar-Huerta I. E., ”Indoor propagation measurements for radiating cable in the UHF band 800 MHz-2500 MHz”, 21st International Conference on Electrical Communications and Computers, San Andres Cholula, (CONIELECOMP), 299-303, February 2011. [21] W. C. Y. Lee, Mobile communications design fundamentals, 2nd edition, John Wiley & Sons, 1993. [22] F. P. Fontán and P. M. Espiñeira, Modeling the Wireless Propagation Channel, John Wiley & Sons, 2008. [23] B. Skar, “Rayleigh fading channels in mobile digital communication systems Part I: Characterization”, IEEE Communications Magazine, vol. 35, pp. 90-100, July 1997.

126

[24] W. C. Y. Lee, “Estimate of local average power of a mobile radio signal,” IEEE Trans. On Vehicular Technology, VT-34, No. 1, pp. 22- 27, 1985. [25] S. R. Saunders and A. Aragón-Zavala, Antennas and propagation for wireless communication systems, 2nd edition, John Wiley & Sons, 2007. [26] T. S. Rappaport, Wireless communications: principles and practice, 2nd edition, Prentice Hall, 2002. [27] S. Y. Seidel and T. S. Rappaport, “914 MHz Path loss prediction models for indoor wireless communications in multifloored buildings”, IEEE Transactions on antennas and propagation, pp. 207-217, February 1992. [28] K. W. Cheung, J. H. M. Sau, and R. D. Murch, “A new empirical model for indoor propagation prediction”, IEEE Transactions on vehicular technology, pp. 996-1001, August 1998. [29] Cost231 final report, CAST Action 231, Digital Mobile Radio Towards Future Generation Systems, European Commission/COST Telecommunications, Brussels, Belgium, 1999. [30] D. Akerberg, “Properties of a TDMA pico cellular office communication system”, Proc: IEEE Globecom, vol. 3, pp. 1343-1349, December 1988. [31] S. C. Tuan, J. C. Chen, H. T. Chou and H. H. Chou, “Optimization of propagation models for the radio performance evaluation of wireless local area networks”, IEEE Antennas and propagation society international symposium, vol. 2, pp. 146-149, 2003. [32] Z. Ji, B. H. Li, H. X. Wang, H. Y. Chen, and T. K. Sarkar, “Efficient ray- tracing methods for propagation prediction for indoor wireless communications”, IEEE Antennas and propagation magazine, 43, pp. 41-49, April 2001. [33] W. M. O´Brien, E. M. Kenny, and P. J. Cullen, “An efficient implementation of a three-dimensioanel microcell propagation tool for indoor and outdoor urban environments”, IEEE Transactions on vehicular technology, pp. 622-630, March 2000. [34] Y. Wang, S. Safavi-Naeini, and S. K. Chaudhuri, “A hybrid technique based on combining ray tracing and FDTD methods for site-specific modeling of indoor radio wave propagation”, IEEE transactions on antennas and propagation, vol. 48, no. 5, May 2000.

127

[35] J. W. H. Lee, A. K. Y. Lai, “FDTD Analysis of indoor radio propagation”, IEEE Antennas and Propagation Society International Symposium, vol. 3, 1664-1667, June 1998. [36] A. Goldsmith, Wireless communications, First edition, Cambridge University Press, 2005. [37] W. C. Jakes, Microwave mobile communications, First edition, IEEE Press, 1974. [38] L.-C. Wang and C.-W. Chang, “Probability of false power control command in CDMA systems subject to measurement errors,” IEEE Commun. Lett., vol. 9, no. 4, pp. 298-300, April 2005. [39] J. C. I. Chuang, “The effects of time delay spread on portable radio communications channels with digital modulation”, IEEE Journal on selected areas in communications, vol. Sac-5, no. 5, pp. 879-899, June 1987. [40] K. Pahlavan, and A. H. Levesque, “Wireless Information Networks”, 2nd Ed., Wiley & Sons, 2005. [41] Jim Ralston, Gary Enstad, Radiating cables can solve tricky wireless communication August 2013 [online]. Available: http://www.controleng.com/single-article/radiating-cables-can-solve- tricky-wireless-com. [42] Hua-Min, Ch. and Ming Chen, “Capacity of the Distributed Antenna Systems over Shadowed Fading Channels”, in Proceedings of IEEE 69th Vehicular Technology Conference, 1-4, 2009. [43] Zhou, S., M. Zhao, X. Xu, J. Wang and Y. Yao, “Distributed Wireless Communication System: A New Architecture for Future Public Wireless Access”, IEEE Communications Magazine, 108-113, March 2003. [44] Stamopoulos, I., A. Aragón and S. R. Saunders, “Performance Comparison of Distributed Antenna and Radiating Cable Systems for Cellular Indoor Environments in the DCS Band”, in Proceedings of Twelfth International Conference on Antennas and Propagation, 771- 774, 2003. [45] Dudley, S. E. M., T. J. Quinlan and S. D. Walker, “Ultrabroadband Wireless-Optical Transmission Links Using Axial Slot Leaky Feeders and Optical Fiber for Underground Transport Topologies”, IEEE Transactions on Vehicular Technology, Vol. 57, No. 6, 3471-3476, November 2008. [46] Feng, L., X. Yang, Z Wang and Y. Li, “The Application of Leaky Coaxial Cable in Road Vehicle Communication System”, in

128

Proceedings of 9th International Symposium on Antennas Propagation and EM Theory, 1015-1018, 2010. [47] Online Available: http://www.rfsworld.com/dataxpress/Datasheets/pdf/?q=RCF12-50JFL [48] W. Honcharenko, H. L. Bertoni and J. L. Dailing, “Bilateral averaging over receiving and transmitting areas for accurate measurements of sector average signal strength inside buildings,” IEEE Transactions on antennas and propagation, vol. 43, No. 5, pp. 508- 512, May 1995. [49] R. A. Valenzuela, O. Landron, and D. L. Jacobs, “Estimating local mean signal strength of indoor multipath propagation,” IEEE Transactions on vehicular technology, vol. 46, No. 1, pp. 203-212, February 1997. [50] Rohde & Schwarz, URL: http://www2.rohde-schwarz.com [51] RFS, URL: http://www.rfsworld.com [52] PCTEL, URL: http://www.pctel.com [53] M. Lecours, J. Chouinard, G. Y. Delisle, and J. Roy, “Statistical modeling of the received signal envelope in a mobile radio channel,” IEEE Transactions on vehicular technology, Vol. 37, No. 4, pp. 204- 212, November 1988. [54] G. Tzeremes and C. G. Christodoulou, “Use of Weibull distribution for describing outdoor multipath fading,” IEEE Antennas and Propagation Society International Symposium, Vol. 1, pp. 232-235, 2002. [55] W. Turin et al. “Autoregressive modeling of an indoor UWB channel”, Conference on Ultra Wideband Systems and Technologies, Baltimore, MD, USA, pp.71-74, 2002. [56] S. J. Howard and K. Pahlavan, “Autoregressive Modeling of Wide- Band Indoor Radio Propagation”, IEEE Trans. Commun., vol. 40, no. 9, pp. 1540-1552, September 1992. [57] G. D. Morrison et al. “Statistical analysis and autoregressive modeling of the indoor radio propagation channel”, 1st International Conference on Universal Personal Communications, Dalla, TX., USA, pp. 97-101, 1992. [58] S. J. Howard and K. Pahlavan, “Autoregressive Modeling of an indoor radio channel” IEEE Commun. Lett. vol. 26, no. 12, pp. 816-817, 1990. [59] P. Huang, D. Rajan, and J. Camp, “Weibull and Suzuki Fading Channel Generator Design to Reduce Hardware Resources”, Wireless Communications and Networking Conference WCNC, Shanghai, China, p. 3443-3448, April 2013.

129

[60] F. Gross, Smart Antennas for Wireless Communications With Matlab, First edition, MacGraw-Hill, 2005 [61] D. Schneider. (2013, Nov. 20). New Indoor Navigation Technologies Work Where GPS Can´t [Online]. Available: http://spectrum.ieee.org/telecom/wireless/new-indoor-navigation- technologies-work-where-gps-cant.

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