Graphical Interface for propagation models in urban ...€¦ · João Pedro Apolinário Instituto...
Transcript of Graphical Interface for propagation models in urban ...€¦ · João Pedro Apolinário Instituto...
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Graphical Interface for propagation models in urban
environments
João Pedro Apolinário
Instituto de telecomunicações, Instituto Superior Técnico
Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal
Abstract – This work consists on the development
of a graphical application that allows simulating
and demonstrating some of the aspects related to
the propagation of electromagnetic waves in
presence of the Earth within mobile communication
systems. This application was developed using
MATLAB® and includes the following features:
Representation of the field interference pattern due
to ground reflection, ray tracing in an atmosphere
with a given refraction index profile horizontally
stratified with or without obstacles, visualization of
the effects caused by the inversion of the refraction
index (mirages), representation of the electrical
field close to obstacles and evolution of the
electrical field in the presence of multiple buildings
in an urban environment (mobile communication
scenario).
I. INTRODUCTION
Radio propagation is the behaviour of radio waves
when they are transmitted, or propagated from one
point on the Earth to another, or into various parts of the
atmosphere. As a form of electromagnetic radiation,
radio waves are affected by the phenomena of
reflection, refraction, diffraction, absorption, polarization
and scattering [1].
The studies of all this phenomena are of great
relevance for the development of wireless and mobile
communications systems. Applications for education
purpose, allowing the visualization of the different
aspects of the propagation of electromagnetic-waves in
complex environments, find great application, not only
in education, but also in the design of mobile
communications systems and other radio wave
communication systems.
In recent years there has been a grown in the data
transferred through mobile terminals due to the
increased capacity and functionalities of these devices.
Some of the functionalities as video streaming, video
call, TV broadcast, high quality video games through
internet and others need a good binary rate and
efficiency from the systems. Therefor the mobile
communication and radio wave communication systems
need to be capable of satisfy all the requests and data
growth. This way, the radio propagation and mobile
communication models continue to have a very strong
interest in order to develop new and more sophisticated
systems.
In this paper is present a visualization tool developed
in MATLAB®
designed to allow the real-time
visualization of several phenomena related to the
propagation, reflection, refraction, and diffraction of
electromagnetic waves in an urban macro-cell
environment as well in long distance point-to-point
communication services.
This application is constituted by four modules. The
first module allows the representation of the field
strength in the presence of the ground, through a colour
graph reproducing different intensities, along a certain
distance and height for the reception antenna. The
influence of the frequency in the field is demonstrated
as well as the influence of an array of antennas and the
contribution of the polarization in the field maximums
and minimums. The second module corresponds to the
refraction module where the influence of the refraction
index of an atmosphere is demonstrated in the ray
tracing. Also is demonstrated the duct effect and the
distortion of images in super-refraction situations with
special attention to the mirage affect. The next module
is about diffraction, with the knife-edge model being
used to simulate an obstacle and the filed attenuation
due to obstacle. The influence of the frequency in de
model is demonstrated as well. A final module
simulates the field distribution in certain urban
environments, such as multi-path macro-cell based on
the Walfisch-Bertoni model as presented in [2]. In this
module is given special attention to the effect of the
reflection coefficient of the buildings and to the
frequency.
II. REFLECTION
This chapter shows the effect of the reflected ray in
the electrical field. The interference between the direct
ray and the reflected ray produces maximums and
minimums in the electrical field around a mean value
(free-space field). The polarization is another factor
analysed in this section as well as the frequency and
the use of an array of antennas as transmitter.
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The equation that represents the electrical field with
the reflected ray included is shown next
[ | | ( )]
where √
represents the free-space field, the
reflection coefficient of the ground and the phase
difference. The coefficient reflection depends of the
polarization. The polarization can be vertical or
horizontal as represented in Fig. 1.
Fig. 1 - Vertical and horizontal polarizations [3]
The reflection coefficients are given by
√
√
for horizontal polarization and
√
√
for vertical polarization. The phase difference is related
with the trajectory difference between the direct ray and
the reflected ray (Fig. 2). The phase difference is
represented by
{ }
with .
Fig. 2 - Representation of direct and reflected rays [3]
From the equation of the electrical field the maximums
and minimums are given by
(
) | |
(
) | |
and they occur when ( ) or ( ) ,
which results in
{ }
The first demonstration in this section is the variation
of the electrical field in a given distance. Using vertical
polarization is possible to get the evolution and the
visualization of the maximums and minimums of the
field.
Fig. 3 - Electrical field strength with distance using vertical
polarization
As seen in Fig. 3 is possible to distinguish the
maximums and minimums of the electrical field (blue
line) around the free-space field (red line) due to the
interference of the reflected ray with the direct ray. In
this figure the distance between antennas varies.
The electrical field presents maximums and minimums
with the variation of the distance between antennas.
The same behaviour also happens with the variation of
the height of the receiver antenna. In the next figure
(Fig. 4), that evolution is shown and from a certain point
it’s possible to see once again the maximums and
minimums of the field but this time both appear in
distance and height. From the Fig. 4 it is possible to see
that are combinations of the distance and height of the
receiver antenna that can have a better signal than
others.
10-1
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distance [m]
E [
V/m
]
Field Strenght variation with distance
Electrical Field
Free-Space Field
surrounding
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Fig. 4 - Evolution of the electrical field with ground
reflection
The next analysis consists on the influence of an array
of antennas in the electrical field. The antennas used
are half-wave dipoles and depending on the separation
between antennas and on the phase currents, the array
exhibits different behaviours as shown in Fig. 5.
Fig. 5 - Behaviour of the array with different configurations
The image in the upper left corner is the behaviour of
the array using only one antenna. In the upper right
corner the antennas are separated by with the
currents in phase. In the bottom, the antennas are
separated by but in the first the currents are in phase
and in the second they are lagged 45º. As we can see
changing the separation between the antennas change
the main lobe and that gets narrower and begins to
appear secondary lobes. The lagged in the current
change the inclination of the major lobes. Relatively to
the field, the array change the electrical field intensity
as represented in Fig. 6.
Fig. 6 - Electrical field with reflection using an array of 2 antennas separated by and with currents in phase
III. REFRACTION
The refraction index influences the ray trajectory.
Using the modified refraction index to describe different
atmospheres was possible to simulate the trajectory of
the rays and demonstrate the influence of the index in
them.
The modified refraction index is given by
where represents the refraction index, the height
and the Earth radius. The refractivity, , is given by
( )
with .
Using the last two equations is possible to obtain the
ray tracing. There are two cases to simulate. The case
where the standard atmosphere is used and the case
where special conditions occur, called duct.
To represent the trajectory an analytical model was
used, where
(√ √ )
√ and represents the height of the
transmitter.
The standard atmosphere is when the modified index
refraction is linear and doesn’t change. The next figures
represent the behaviour of the rays in that specific
atmosphere.
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Fig. 7 – Ray trajectory and , with ground
reflection
Fig. 8 – Ray trajectory for and
Fig. 9 – Ray trajectory for and
Fig. 10 – Ray trajectory for and
From the analysis of the figures it is possible to
conclude the influence of the modified refraction index
in the ray tracing. When the index is positive the rays
tend to rise and when the index is negative the rays
tend to sink.
When a special condition occurs, ducts may be
formed, where the rays can travel longer distances and
cause interferences in other systems. The duct takes
place when the atmosphere is constituted by two or
three layers. Each layer presents a different modified
refraction index, and in two consecutive layers the
signals of the indexes are opposite. The duct with two
layers is called surface duct and the duct with three
layers is called raised duct. The Fig. 11 and Fig. 12
demonstrate the effect of ducts on ray propagation.
Fig. 11 – Surface duct
Fig. 12 – Raised duct
From the observation of the figures we can conclude
that the rays are contained in the layer where the
modified refraction index is negative. Because of that,
the rays can travel longer distances contrary to normal
conditions. If the rays during propagation find an
obstacle, they can change trajectory backwards if they
collide sideways with the obstacle, or continue the
trajectory if they collide with the top of the obstacle. The
next figures represent the situation where a ray collides
sideway or in the top of the obstacle.
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Fig. 13 - Sideway reflection on an obstacle in a surface duct
Fig. 14 - Top reflection on an obstacle in a surface duct
Although is only represented the reflection in an
obstacle for the surface duct, in the others situations
(raised duct, and normal conditions) the rays exhibit the
same behaviour as shown in Fig. 13 and Fig. 14.
A consequence of the atmosphere with super-
refraction situations is the distortion of images captured
by the human eye, usually called mirages. This mirage
effect happens when the atmosphere presents different
modified refraction index in height. If the atmosphere is
stratified in two layers an upper mirage occur, if the
atmosphere is stratified in three layers a lower mirage
occur. The normal and distortion situation are
represented in Fig. 15 and Fig. 16.
Fig. 15 - Normal image captured by the human eye
Fig. 16 - Distortion of the image captured by human eye
due to super-refraction conditions
As we can see in Fig. 16 the rays have different
trajectories from the normal case and an image
captured by the human eye can be deformed due to
that fact.
To simulate the mirage effect, an image is divided in
equal vertical intervals, depending on the number of
lines in the image. Each line corresponds to a ray, and
after the ray tracing they arrive to a determined interval
in the image. The rays are numbered in an increasing
order of the departure angle. The arrived point is stored
in a matrix. The original image is then divided in two
halves. The superior half corresponds to the vertical
plan and the inferior half corresponds to the horizontal
plan. The Fig. 17 represents the image splitting.
Fig. 17 - Image splitting in two orthogonal planes
Now using the stored information in the previous
matrix, if a ray reaches the maximum distance he is in
the vertical plan, otherwise he is in the horizontal plan.
After defining where each ray belongs, the ray lengths
and heights are converted to a scale according with the
number of rays. These values are stored in a position
matrix and are converted in a new image.
An upper mirage is when the objects in the ground
level are copied to the sky. The Fig. 18 represents the
simulation of a upper mirage. In the image it is
represented the modified refraction index, with the
resulted ray tracing. The bottom left image is the
original image, and the bottom right image is the result
of the ray tracing due to the super-refraction situation.
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Fig. 18 – Upper mirage
For the lower mirage, the sky is copied to the ground
and is usually confused with a puddle. As represented
in Fig. 18, the lower mirage is shown in Fig. 19.
Fig. 19 - Lower mirage
IV. DIFRACTION
Usually in a long distance communication system the
path between the antennas isn’t flat, contrariwise. There
are mountains and other obstacles that create
additional attenuations on the signal. Several models
were created to study this effect. The one used in this
article is the knife-edge model.
The knife-edge model considers the obstacle as a
semi-infinite plan. The Fig. 20 represents the knife-edge
model geometry, where
̅
√
̅
Fig. 20 - Knife-edge geometry [4]
The attenuation is strongly dependent of the gap ( ̅)
between the ray and the top of the obstacle. The
attenuation is given by
( )
[
( )]
[
( )]
where ( ) and ( ) are the Fresnel integrals. The
Fig. 21 gives the attenuation as function of .
Fig. 21 - Knife-edge attenuation as function of the
penetration
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Imagem Original Atmosfera com M variável
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v
Knife-e
dge a
ttenuation,
A in d
B,
bellow
fre
e-s
pace
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As said before, the attenuation is strongly dependent of
the gap between the ray and the top of the obstacle.
The previous figure shows exactly that. As we can see
if the gap goes to negative the penetration ( ) goes
positive and the attenuation gets bigger. In the other
hand, if the gap is positive the penetration is negative
because the ray doesn’t pass throw the obstacle and
the attenuation is low or zero if the first Fresnel ellipsoid
is unobstructed.
After understanding the influence of the penetration
on the attenuation, it’s possible to describe how the
electrical field is calculated. Using the same expression
of the reflection section and adding the attenuation, we
get the follow equation
[ | | ( )
where and are the attenuation for the direct ray
and for the reflected ray. The Fig. 22 represents the
evolution of the electrical field as function of the height
and distance of the receiver antenna, using the
previous equation.
Fig. 22 - Knife-edge model at 300MHz
From the analysis of the figure, it is possible to see
the attenuation caused by the obstacle. This creates a
shadowing zone where the field presents very low
values.
Another very important factor that influences the knife-
edge model is the frequency. The higher the value of
the frequency the higher the attenuation caused by the
obstacle as shown in Fig. 23.
Fig. 23 - Knife-edge model at 1800MHz
As we can see, the field shows lower values after the
obstacle and the shadowing zone increases.
V. URBAN PROPAGATION MODELS
The urban environments are divided in cells. There
are three types of cells:
Macro-cell
Micro-cell
Pico-cell
The macro-cells are the coverage zones with
dimensions in the order of 2-3 km, where the base
stations are usually in the top of the buildings and the
mobile terminal are in the shadowing zone of the
obstacles.
One model to study the electrical field strength along
the cell is the Walfisch-Bertoni model. In this model, the
biggest contribution to the field is due to diffraction in
the top of the buildings. Two types of attenuation are
considered in this model:
The attenuation due to multiple obstacles that
interfere from the transmitter to the receiver
The attenuation associated to the diffraction
from the top of the building to the street.
The second attenuation is associated with the multi-
path effect caused by two buildings. The mobile
terminal is reached by several rays but only two have
preponderant contributions. Those are the direct ray
and the ray that reflects once in the front building. The
Fig. 24 represents the geometry of the multi-path.
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Fig. 24 - Multi-path geometry
Considering the buildings as semi-infinite plans and
the inclination ( ) of the wave relative to horizontal, the
attenuation ( ) is given by
| ( )| {
[
( )]
[
( )]
}
where ( ) and ( ) are the Fresnel integrals, and
are the equivalent height given by
√
[( )
]
√
( )[( ) ( )
]
The angle street ( ) is considered 90º because the
wave is in line with the buildings and is equal to
(
)
Lastly the electrical field is given by
| ( )|
| ( )|
| |
where is the direct ray, is the reflected ray and
| | is the reflection coefficient of the building.
The attenuation due to multiple buildings is only
applies when the buildings have all the same height and
the same spacing between them. In this situation, the
buildings are replaced by semi-infinite plans. The Fig.
25 shows the geometry used to calculate the
attenuation.
Fig. 25 Attenuation model for multi obstacles [1]
The attenuation ( ) induct by the multiple
obstacles is determined by the following expression
with given by
√
This expression used to calculate the attenuation
( ) can only be applied when and
where is the number of buildings and
{
}.
The total electrical field, after calculated all the
attenuations is given by
√
The last expression is the one used to calculate the
electrical field between the buildings.
To simulate the field at any distance and height, we
need to divide the figure in three zones. The first zone
is the one over the building, the second is the zone
between the buildings and the third is the zone after the
last building. Each zone has a different way to calculate
the electrical field. In the first zone is used the
expression of the free space field because there is no
interference from the reflected ray. The second zone
was calculated using the Walfisch-Bertoni model as
explain above. The third zone is calculated using the
knife-edge model without the reflected ray. The Fig. 26
represents the simulation of the Walfisch-Bertoni model
with the three zones represented.
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Fig. 26 - Walfisch-Bertoni Model
The previous figure was simulated using the following
specifications:
From the analysis of the Fig. 26 it is possible to see
that the electrical field decreases very quickly between
the buildings and is very low after the last building. The
blue line and red line represents the space where the
Walfisch-Bertoni model is valid.
The frequency influence the model in the same way
that influences the knife-edge model, which means that
the higher the frequency the higher the attenuation.
Furthermore the frequency influences the parameters
that validate the multi-obstacle attenuation. As we can
see from the expression of and , they depend on
the wavelength. The Fig. 27 shows the influence of the
frequency on the model.
Fig. 27 - Walfisch-Bertoni model at 500MHz
Other parameter of great influence is the reflection
coefficient of the buildings. If this parameter is zero, the
reflected ray does not contribute lowering the electrical
field. In this situation a shadowing zone appears next to
the previous building. This effect is represented in the
Fig. 28.
Fig. 28 - Walfisch-Bertoni model with
In the previous figure, the frequency used is 500MHz.
VI. CONCLUSIONS
This work aimed to create a didactic and project tool.
With this application is possible to demonstrate
graphically the theoretical models studied during the
course. In an academic context, permits to the students
analyse and understand how a parameter can influence
a model. The aspects addressed are the reflection,
diffraction, refraction and propagation models in
complex environments.
In the reflection topic, was represented graphically the
evolution of the electrical field with vertical polarization
considering the reflected ray in the ground. The
interference of the reflected ray with the direct ray was
demonstrated through the existence of maximums and
minimums of the electrical field. The influence of an
array of antennas was shown too. As conclusion, the
electrical field with ground reflection is influenced by the
frequency, by the distance and height of the receiver
antennas and by the polarization, all causing variations
of the field around a mean value.
In the refraction section the ray tracing was
demonstrated with a standard atmosphere and with
special conditions. When the modified refraction index
is negative, the ray goes down; otherwise, the ray goes
up. In special conditions, in a stratified atmosphere with
different refraction indexes a duct is formed and the
rays travel longer distances and are contained in the
layers where the index is negative. A special effect like
the mirages was demonstrated too. Due to the different
indexes in the atmosphere an image gets deformed in
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the human eye. If the atmosphere has two layers, a
superior mirage happens, if the atmosphere has three
layers an inferior mirage occurs.
The knife-edge model was the one chosen to
demonstrate the diffraction on obstacles. In this model,
the obstacle is substituted with a semi-finite plan and
the attenuation is calculated as function of the
penetration. The penetration is the difference between
the ray and the top of the building. If the penetration is
positive, which means the ray passes through the
obstacle, the attenuation is big. Otherwise, the
attenuation is low. The obstacle creates a shadowing
zone, where the electrical field is very low. The knife-
edge is influenced by the frequency. The higher the
frequency, higher the attenuation is.
The last topic is about the propagation models in
urban environments. In a macro-cell type scenario, the
Walfisch-Bertoni model was demonstrated. In this
model, two types of attenuations are considered. The
first attenuation is due to multiple obstacles and the
second is due to multi-path from the antenna to the
mobile terminal. In the multi-path attenuation, two rays
were considered to the calculations, the direct ray and
the reflected ray in the front building. The electrical field
gets lower and lower along the buildings and after the
last building the knife-edge model was used. The
frequency influences the Walfisch-Bertoni model the
same way as influences the knife-edge mode, in other
words, the higher the frequency higher the attenuation
gets. Another parameter analysed was the reflection
coefficient of the building. If the reflection is zero, the
field gets low and a shadowing zone appears.
VII. REFERENCES
[1] Wikipedia, Radio_propagation,
(http://en.wikipedia.org/wiki/Radio_propagation)
[2] J.Walfsich and H.Bertoni, ‘A theoretical mode of
UHF propagation in urban environments’ IEEE trans.
Antennas Propagat. Vol 36, Nº 12, pp. 1788.1796,
Dec.1988
[3] Figanier, J. Fernandes, C.A, ‘Aspectos de
Propagação na Atmosfera’, Secção de Propagação e
Radiação, IST-DEEC, 2002
[4] Fernandes, C.A, ‘Radiopropagação Mobile Radio
Communications’, Slides disciplina Radiopropagação,
IST-DEEC
http://en.wikipedia.org/wiki/Radio_propagation