The Multipath Fading and the Frequency
Response of the Channel in an
Indoor Radiating Cable System
By
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 at
Instituto Nacional de Astrofísica, Óptica y Electrónica
Supervised by:
Dr. Ignacio Enrique Zaldívar Huerta, INAOE Dr. Alejandro Aragón Zavala, ITESM campus Querétaro
© INAOE 2014
The author hereby grants to INAOE permission to reproduce and to distribute copies of this
i
The Multipath Fading and the Frequency
Response of the Channel in an
Indoor Radiating Cable System
By
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 at
Instituto Nacional de Astrofísica, Óptica y Electrónica
Supervised by:
Dr. Ignacio Enrique Zaldívar Huerta, INAOE Dr. Alejandro Aragón Zavala, ITESM campus Querétaro
© INAOE 2014
The author hereby grants to INAOE permission to reproduce and to distribute copies of this
iii
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.
iv
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.
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
v
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
vii
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
viii
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
ix
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.
xi
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.
xiii
DEDICATORIA
A mi amada y linda esposa Rosalba
A aquel ser que aún no llega, pero sé que llegará y nos hará más
felices
xv
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
xvi
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
xvii
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
1
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 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. 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.
2
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
Antenna
Distributed Antenna System
Indoor Environment
Radiating Cable
Radiating Cable System
Regions with signal coverage
Regions with signal coverage
3
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.
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
Source Coding
Channel Coding
Multiplex Modulate Multiple Access RF and Antennas Source Decoding Channel Decoding De-multiplex De-modulate Multiple Access Antennas and RF Wireless Channel Transmitter Receiver Information Information
4
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.
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
Receiver
Antenna RX Transmitter
Antenna TX
Reflection Diffraction
Scattering
Refraction
Wireless Channel
5
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.
Figure 1.4: Received power in a corridor along the cable length [20]
Corridor route distance
6
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
7
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.
9
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
10
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]
0 mr
r (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)
11
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.
12
Figure 2.2: Wireless channel fading [23].
Large-scale fading due to motion over large areas
Small-scale fading due to small changes in position
Mean signal-attenuation vs distance
Variations aboutthe mean
Time spreading of the signal (Multipath)
Time variance of the channel (Moving
object) Frequency-domain description Time-delay Domain description Time-domain description Doppler-shift domain description Frequency selective fading Tm>Ts
Flat fading Tm<Ts
Frequency selective fading
f0<W
Flat fading
f0>W
Fast fading T0<Ts
Slow fading T0>Ts
Fast fading
W<fd
Slow fading W>fd
Tsis the symbol time.
Tm is the excess delay time.
f0 is the coherence bandwidth.
W is the signal bandwidth.
Tsis the symbol time.
T0 is the coherence time.
fd is the frequency shift.
W is the signal bandwidth.
1
2 3
4
5 6
7 9 8 12 14 11
13 16
18 17 15 10 Fading Channel Manifestations
13
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 log-normal 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
dB f
MHz
d
kmLfs 32.410log10 20log10 (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]
d dB L
d dB n
d d
X
dBLp S 0 10 log10 0 (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
14
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
WAF
p FAF
qd d dB d L Q q P p n
1 1 0 10 log 10 (2.4)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 i b n n f f wi wi c F T f f n L n L L L L 1 1 2 (2.5)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
15 m d d m d d m d d m d d L Lp 40 , 40 log 120 47 40 20 , 20 log 60 29 20 10 , 10 log 30 20 10 1 , log 20 10 10 10 10 0 (2.6)
An empirical model to use at WLAN [31] frequencies has the general form of
dB k k f k d nw
k P k P
k mfL 1 2log10 3log10 4 1 5 2 6 (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
16
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<Ts, block 9, the channel
shows frequency nonselective or flat fading. The frequency selective fading is presented when the signal is distorted because the multipath components continue after symbol time Ts. Thus the receiver cannot distinguish between
neighbor symbols.
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
17
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
22
rms (2.8)
Where
is the mean excess delay and 2 is the second moment given by2 , 1 1 2 1 2
n L i i L i i n i n (2.9)18
Multipath intensity profile (a)
Doppler power spectrum (b)
Space-frequency correlation function
(c)
Space-time correlation function
(d)
Figure 2.3. Channel correlation functions and power density functions. |R(t))
0 t
T0 = 1/fd Coherence Time
f |R(f))
f0 = 1/Tm Coherence bandwidth
0
S()
fc-fd fc fc+fd
fd Spectral broadenig
Tm Maximun excess
0 S()
19
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
approximationT01 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
d f T
16 9
20
When the signal bandwidth W, is less than the Doppler spread fd, the channel
is known as fast fading (W<fd), otherwise it is referred to as slow fading
(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]
L r r out d P P Q P d P p d P p min minmin, 1 (2.11)
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
x p x z
y dyQ z
2 exp 2 1 2 (2.12)21
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
area cell R AA P rdrd
R dA P R C . 2 0 0 2 2 1 1 (2.13)
Where PA is calculated with Eq. (2.11), considering the propagation model
Eq. (2.3) for Pr(d), C is obtained as follows:
2 0 0 0 10 0 min 2 20 0 min
2 log 10 1 1 R L S t R r rdrd d r n d L P P Q R C rdrd P r P p R C (2.14)
22
Figure 2.4. The received power takes into account the path loss and variations at the service area edge.
Figure 2.5. Coverage contours for 50%, 90% and 95% for locations which fulfill with the specified coverage quality.
Letting
L S
t L d n R d
P P a
10 0
0
min 10 log
and
L e n b 10 log 10
, we have
Tx 95% 90% 50% d1
d2
d3
Path loss only
Path loss and Variations (Large-scale fading) Base Station
23
R dr R r b a rQ R C 0 2 log 2 (2.15)The solution of this integral is given by [37]
b ab Q b ab a QC exp 2 2 2 (2.16)
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.
24
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
25
the signal bandwidth is small in comparison with the channel bandwidth. Thus the BER performance of binary shift keying (BPSK) is given by
2
Q
Pe (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
d
p P Pe
e0 (2.18)
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 1 2 1 e P (2.19)
Where is the average SNR. Figure 2.7 shows the bit error rate in a Rayleigh fading by using Eq. (2.19).
26
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.
27
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]
2exp
2
fM
N (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
M f
2 1 exp 2
(2.21)
28
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
29
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.
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
Slotted copper outer conductor Outer
jacket
30
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.
31
Table 2.1. Longitudinal attenuation and coupling loss of two different cables of RFS [47]
RCF 12-50J Size=1/2” RCF 78-50JA Size=7/8” Frequency (MHz) Longitudinal Attenuation (dB/100 m) Coupling Loss (dB) Longitudinal Attenuation (dB/100 m) Coupling Loss (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
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.
0 20 40 60 80 100 120
-90 -82.6 -69 -35 -13.6 0 10
Radiating cable length (m)
Si g n a l L e ve l (d Bm) Coupling Loss Longitudinal Atennuation Received power Power inside the cable
32
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:
n b c t r d l zal P
33
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
zadL P
Pr t 2
2 8 3
(2.23)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
d
za PPr t 2
2
4
(2.24)
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
34
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.
35
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
36
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.
37
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
Communication Laboratory Warehouse 25 20 15 10 5 0
0 5 10 15 20 25 30 35
x(m) y(m) First Path Second Path Third Path Radiating Cable Generator Matched Load Room 2202 room 2203 room 2204 WC Room 2201 Room 2207
38
receiver and to store measurements and also receiver positions. Thus, the measurements are collected while the receiver is moved through the area.
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.
Unmodulated Carrier
Signal
Propagation
Channel
Receiver
Data Acquisition
