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Propagation model based on ray tracing for the design of personal communication systems in indoor environments

01 Nov 2000-IEEE Transactions on Vehicular Technology (IEEE)-Vol. 49, Iss: 6, pp 2105-2112

TL;DR: A ray tracing technique to predict the propagation channel parameters in indoor scenarios is presented and some comparisons between predicted results and measurements are presented to validate the method.
Abstract: A ray tracing technique to predict the propagation channel parameters in indoor scenarios is presented. It is a deterministic technique, fully three-dimensional, based on geometrical optics (GO) and the uniform theory of diffraction (UTD). A model of plane facets is used for the geometrical description of the environment. The ray tracing is accelerated considerably by using the angular Z-buffer algorithm. Some comparisons between predicted results and measurements are presented to validate the method.

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 49, NO. 6, NOVEMBER 2000 2105
Propagation Model Based on Ray Tracing for the
Design of Personal Communication Systems in
Indoor Environments
Francisco Saez de Adana, Oscar Gutiérrez Blanco, Iván González Diego, Jesús Pérez Arriaga, and Manuel F. Cátedra
Abstract—In this paper, a ray-tracing technique to predict the
propagation channel parameters in indoor scenarios is presented.
It is a deterministic technique, fully three-dimensional, based on
geometrical optics (GO) and the uniform theory of diffraction
(UTD). A model of plane facets is used for the geometrical
description of the environment. The ray tracing is accelerated
considerably by using the Angular Z-Buffer algorithm. Some
comparisons between predicted results and measurements are
presented to validate the method.
I. INTRODUCTION
T
HE STUDY of the propagation in indoor environments
has increased enormously in recent years, the main reason
being the largeamountofcompetition that exists in mobile com-
munications at the moment. This makes it necessary to have a
way to predict the propagation in indoor environments in order
to carry out a prior analysis, which allows us to minimize the
number of base stations required to give an efficient service,
with the economical saving that it represents. Another factor
that in the future will be of great interest in the designs is the
limiting of the field level to a very restrictive low level in order
to comply with public health regulations.
It is very important to study how the different elements that
make up the buildings affect the propagation. The main problem
that appears is the fast fading [1] caused by multipath prop-
agation and the interference between the different paths. This
makes it very difficult to obtain good predictions at the received
power levels. However, due to its practical interest, in recent
years, many researchers have developed different models with
which to study indoor propagation.
Traditionally, statistical models have been used for this
problem [2]–[4]. For instance, the empirical model that predicts
the propagation path loss on the same floor or through different
floors is shown in [2]. A more sophisticated method that
considers the attenuation through individual walls and floors
is presented in [3]. A nonlinear function of the number of
penetrated floors is introduced in [4] to fit the measurements
better than in previous models.
At the moment, deterministic models are becoming more
popular [5]–[10]. For example, we can start by mentioning [5],
where a computer tool to predict path loss inside buildings
Manuscript received December 3, 1999; revised March 30, 2000. This work
was supported in part by Telefonica Moviles, Spain.
The authors are with Grupo de Servicios, Universidad de Alcalá, Alcalá de
Henares 28806 Spain (e-mail: felipe.catedra@alcala.es).
Publisher Item Identifier S 0018-9545(00)09179-9.
based on geometrical optics is reported. In [6], Valenzuela
estimates the local mean signal strength at a point as the sum
of the reflected and transmitted rays that reach that point. In
[7], results of hallway environments are shown using a method
that takes into account the material properties of the elements
of the building. Kajiwira shows the importance of polarization
in indoor propagation in [8], demonstrating that a circular
polarized wave can reduce the multipath fading. A theoretical
model for the analysis of corridor environments is presented in
[9]. A three-dimensional (3-D) propagation model, combined
with a patched-wall model, to predict radio losses in a corridor
environment is detailed in [10]. These models are based on the
ray tracing, determining the channel parameters taking into ac-
count the rays that, following different paths, reach the receiver
antenna. The main problem of ray tracing is the high amount of
CPU-time required to analyze the large amount of rays that can
reach a point after several reflections and transmissions.
In this work, a fully 3-D model based on geometrical optics
(GO) and the uniform theory of diffraction (UTD) is presented.
The geometrical representation of the elements in an indoor en-
vironment is based on plane facets. The influence of the electro-
magnetic properties of the material of each facet is included in
the expressions of GO and UTD and the transmission through
the walls is also included, as it has a very important effect on
this application.
As mentioned earlier, the problem with these ray-tracing
models is the high simulation time that they require. The reason
is the large amount of intersection tests needed to find out if
a ray hits a facet, as the number of facets used to represent a
building can be very high. In this paper, we describe a very
efficient ray-tracing technique for indoor environments, the
Angular Z-Buffer (AZB), which allows a reduction in the time
necessary to obtain the multipath propagation. The philosophy
behind this method consists in reducing the number of rigorous
tests that have to be made by reducing the number of facets that
each ray has to treat.
A code called FASPRI has been created using this electro-
magnetic method combined with the AZB. The efficiency of the
ray-tracing technique enables this code to be run on a PC. Some
results obtained with this code compared with measurements are
presented to show the accuracy of the method.
This paper is organized as follows. In Section II, the propa-
gation model is presented. In Section III, the geometrical model
used to represent the indoor environment is outlined. The AZB
applied to this case is described in Section IV. The validation
results compared with measurements are shown in Section V.
0018–9545/00$10.00 © 2000 IEEE

2106 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 49, NO. 6, NOVEMBER 2000
Finally, the conclusions of this work are presented at the end of
this paper.
II. P
ROPAGATION MODEL
The propagation model is based on GO and the UTD [11],
including the effects related to the transmission that is very im-
portant in these kinds of environments. These are asymptotic
high-frequency theories, which obtain the total electric field at
a point as the sum of the field associated with all the rays that
reach this point. The following effects, which are considered
enough to obtain good results in indoor propagation, are in-
cluded in this model:
1) direct field;
2) single-reflected field;
3) single-diffracted field;
4) transmitted field up to four transmissions
5) double-reflected field;
6) single-reflected single-diffracted and single- diffracted
single-reflected field;
7) single-reflected-transmitted and transmitted-single-re-
flected field, including up to three transmissions;
8) double-reflected-transmitted and transmitted-double-re-
flected field, including up to two transmissions.
In indoor environments, the elements of the geometry can be
composed of different materials. In this part, the method for ob-
taining the field associated to each effect including the charac-
teristics of the materials is presented.
A. Direct Field
The field contribution at the observation point (O) due to the
direct ray is given by
(1)
where
(2)
and
free-space wavenumber with being the wave-
length;
distance between the transmitter and the observa-
tion point;
free-space impedance;
power radiated by the transmitter;
Fig. 1. Axis system to apply the image theory.
gain of the transmitter antenna;
normalized radiation pattern of the transmitter
antenna;
and spherical coordinates of the observation point re-
ferred to the coordinate system associated with
the antenna.
B. Reflected Field
In this case, instead of the general expressions of GO, the
image theory is applied [12]. This theory, usually presented for
dipoles, can be generalized for other antennas defining an image
axissystem from the coordinate system of the antenna, as seen in
Fig. 1. This system is defined by a translation of the facet-fixed
axes, which are defined by making
parallel to the normal
vector of the facet,
parallel to one of the sides of the facet,
and
perpendicular to the other two axes [13].
Taking into account this new system and expressing the re-
flected field in its components parallel and perpendicular [11],
the reflected field can be expressed as
(3)
where
distance between the image and the observation
point;
,
parallel and perpendicular components of the
normalized radiation pattern of the transmitter
antenna referred to the facet-fixed system;
(4)
(5)

DE ADANA et al.: PROPAGATION MODEL BASED ON RAY TRACING 2107
and spherical coordinates of the observation point re-
ferred to the image coordinate system.
and are the parallel and perpendicular reflection co-
efficients given in [14] and [15], as seen in (4) and (5) at the
bottom of the page, where
incident angle at the facet;
facet thickness;
relative permittivity of the wall medium;
wave number of the wall medium
(6)
C. Transmitted Field
The expression for the transmitted field is very similar to that
used for the reflected field,but taking as its origin the transmitter
antenna instead of the image and taking into account the trans-
mission coefficients. The transmitted field is given by
(7)
where
distance between the transmitter antenna and
the observation point;
, parallel and perpendicular components of
the normalized radiation pattern of the trans-
mitter antenna;
and spherical coordinates of the observation point
referred to the coordinate system associated
with the antenna.
and are the parallel and perpendicular transmission
coefficients given in [14] and [15], as seen in (8) and (9) at the
bottom of the page.
D. Diffracted Field
To obtain the field diffracted by an edge, the general expres-
sions of the UTD are used [11], but including the influence of
the materials. Therefore, the diffraction coefficients [11] are as
follows:
(10)
Fig. 2. Bold line: facets that satisfy the normal vector criterion.
where
, ,
, and
components of the diffraction coefficients given
in [11];
reflection coefficients given by (4) and (5).
E. Multiple Effects
The second and higher order effects are computed as a com-
bination of the previous effects [11].
III. G
EOMETRICAL MODEL
A model of plane facets is used to describe the indoor geome-
tries. All the elements of an indoor emplacement such as walls,
columns, doors, etc., are represented by facets with three or four
vertices. In this model, the electric permittivity (
), the conduc-
tivity (
), and the thickness of each facet are introduced as input
data.
The number of facets necessary to model a complex environ-
ment with enough precision can be of several hundred facets.
Therefore, the number of intersection tests required to find the
ray paths can be very high, its computation taking a lot of CPU
time. So, a geometrical preprocessing has been chosen to reduce
this time. This process consists of computing the normal vectors
to the facets in order to introduce a criterion, which allows a re-
duction of approximately 50% of the number of facets that have
to be considered. This criterion only considers the facets facing
from the source, which are those that satisfy the criterion
(11)
where
normal vector to the facet;
(8)
(9)

2108 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 49, NO. 6, NOVEMBER 2000
Fig. 3. Regions of theta and phi that form a Z-buffer anxel.
vector that joins the source to one of the vertices of the
facet.
An example is depicted in Fig. 2. The facets that satisfy the
criterion are represented with a bold line.
But for a complicated model, this criterion is not enough for
an efficient analysis, other techniques to optimize the ray tracing
should be introduced.
IV. T
HE ANGULAR Z-BUFFER
In this method, the AZB algorithm [16] is used to speed up the
ray tracing. This algorithm is based on the light buffer technique
[17] used in computer-aided graphic design. The AZB consists
in dividing the space seen from the source in angular regions
and storing the facets of the model in the regions where they
belong. In this way, for each ray, only the facets stored in its
region need be analyzed. Another important trick to reduce the
computation time is to order the facets in each region according
to their distances from the source, since the closer facets have
more possibility of hiding rays.
A. Application to Direct Ray
For the direct ray, the source will be the transmitter antenna.
In this case, the space regions are spherical sectors, which we
call anxels, defined by their spherical coordinates
and ,as
illustrated in Fig. 3.
Each region is obtained by dividing the 2
radians of and
the
radians of in equal parts. Therefore, the width of the
anxels will be
(12)
where
number of regions in theta;
number of regions in phi.
For all vertices of all the facets of the model, the maximum
and minimum values of the coordinates
and are computed.
It is assumed that each facet belongs to all the anxels between
these minimum and maximum values.
This information is very efficient to compute the hiding of
a direct ray. The first step is to determine the anxel of the ray
Fig. 4. Two-dimensional view of the angular window where the reflection can
be produced.
Fig. 5. Two paths of a reflected ray.
using its spherical coordinates. Then the facets loaded in this
region are tested in the order in which they are stored (according
to the distance from the source). If one facet intersects the ray,
the algorithm is stopped and the ray contribution is not taken
into consideration. If no facet hides the ray, the electric field is
computed at the observation point.
B. Application to Reflected Ray
The algorithm for this case is applied in the same way but
taking as its source the image of each facet. The anxels are
also spherical sectors, but now are limited to lie in the angular
window region where the reflection can be produced. This
window is defined in Fig. 4.
In this case, to check the obstruction of the rays, two paths
must be considered: one from the transmitter antenna to the re-
flection point and the other, from this, to the receiver or obser-
vation point, as shown in Fig. 5.
So the intersection test must be done for both paths. For the
first one, the AZB of the direct ray is used, and for the second
one, the AZB of the reflected ray is used.
C. Application to Transmitted Ray
In this case, there are two paths, as in the reflection case: one
from the source to the transmission point in the facet and the
other from this to the observer. For the second path, the AZB
is created in the same way as in the direct case but taking as its
source the transmission point.

DE ADANA et al.: PROPAGATION MODEL BASED ON RAY TRACING 2109
Fig. 6. Keller’s cone, which defines the
coordinate for the Z-buffer for
diffraction.
Fig. 7. Angle
used to define the other coordinate in the Z-buffer for
diffraction.
D. Application to Diffracted Ray
For the diffracted ray case, instead of working with spherical
coordinates
and , it is easier to work with coordinates and
. The reason is that when a ray reaches a wedge forming an
angle
with its edge, the diffracted rays are contained in a cone
(Keller’scone [18]) with its axis on the edge, the vertexof which
is the diffraction point and has an aperture angle equal to
(see
Fig. 6). The other coordinate is given by the angle
, which is
the angle between the diffracted ray and the first facet of the
edge (see Fig. 7).
In this case, as in the reflection, a diffraction window is cre-
ated by each edge. This window is defined between the an-
gles
, and , , where the edge can produce
diffraction. The facets are stored in the corresponding anxels,
taking the angles
and of their vertices in a similar way as
for the direct or reflected rays but now considering the coordi-
nate system defined by
and .
As in the previous effects, the intersection test is performed
for two paths (Tx: diffraction point and Rx: diffraction point),
the first one using the AZB of the direct case and the second one
using the AZB created for the corresponding edge.
E. Application to Multiple Effects
For the multiple effects, the AZB is applied as a combination
of the previouscases. For instance, for reflection-diffraction,the
intersection test must be done for three paths. From the trans-
Fig. 8. 3-D view of the third floor of the Sota building.
Fig. 9. Top view of the third floor of the Sota building. The bold lines indicate
the paths considered for the analysis when the transmitter (Tx) is in the position
shown (taken from [19]).
mitter antenna to the reflection point, the AZB created for the
direct ray is used. From the reflection point to the diffraction
point, the AZB created for the image is checked. Finally, from
the diffraction point to the receiver, the AZB created by the edge
is considered.
Although multiple diffraction has not been considered in this
description, the algorithm can be also apply to these effects. For
example, for a double diffraction, the AZB would be created
for the second edge as in a simple diffraction, but in this case
the source is not a point but a line that corresponds with the
first edge where the diffraction is produced. Following the same
procedure, it could be applied for multiple diffraction.
V. V
ALIDATION
To validate the method, a set of measurements was made on
the third floor of the Sota building in Bilbao, Spain. They were
compared with code FASPRI based on the approach presented
in this paper. The geometrical model of this floor is shown in
Fig. 8. It is modeled by 175 facets, which include the floor and
ceiling, in order to consider the reflections produced in both. All

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  • ...and are the parallel and perpendicular reflection coefficients given in [14] and [15], as seen in (4) and (5) at the bottom of the page, where incident angle at the facet; facet thickness; relative permittivity of the wall medium; wave number of the wall medium...

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Abstract: In this tutorial survey the principles of radio propagation in indoor environments are reviewed. The channel is modeled as a linear time-varying filter at each location in the three-dimensional space, and the properties of the filter's impulse response are described. Theoretical distributions of the sequences of arrival times, amplitudes and phases are presented. Other relevant concepts such as spatial and temporal variations of the channel, large-scale path losses, mean excess delay and RMS delay spread are explored. Propagation characteristics of the indoor and outdoor channels are compared and their major differences are outlined. Previous measurement and modeling efforts are surveyed, and areas for future research are suggested. >

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