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Combination of Geometric and Finite Difference
Models for Radio Wave Propagation
in Outdoor to Indoor Scenarios
Guillaume de la Roche∗, Paul Flipo†, Zhihua Lai∗, Guillaume Villemaud†, Jie Zhang∗and Jean-Marie Gorce†
∗Centre for Wireless Network Design †CITI Laboratory/INRIA
University of Bedfordshire INSA Lyon - ARES project
Luton LU1 3JU - UK 69621 Villeurbanne - FRANCE
http://www.cwind.org http://www.citi.insa-lyon.fr
guillaume.delaroche@beds.ac.uk paul.flipo@insa-lyon.fr
Abstract—In this paper, a new model used to compute the
outdoor to indoor signal strength emitted by a base station is
presented. This model is based on the combination of 2 existing
models: IRLA (Intelligent Ray Launching), a 3D geometric-like
model especially optimized for outdoor predictions, and MR-
FDPF (Multi Resolution Frequency Domain ParFlow), a 2D
FDTD-like model initially implemented for indoor propagation.
The combination of these models implies the conversion of the
ray launching signals on the border of the buildings, into virtual
source flows that will be used as an input for the indoor model.
The performance of the new combined model is evaluated via
measurements, and it appears to be an efficient solution for radio
network planning, both in term of accuracy and computational
cost.
Index Terms—outdoor to indoor, Radio propagation, Channel
modeling, Ray-Launching, ParFlow.
I. INTRODUCTION
Indoor networks planning is increasingly important, that is
why tools have been developed to help operators to optimize
their networks. For example, these tools help to find the
best parameters like the positions of the emitters, the optimal
radiated power, and the best channels. Moreover, the quality
of such tools relies for an important part on the quality of
the propagation model. Hence, it is important for operators to
optimize both the indoor and the outdoor radio coverage, by
using new combined indoor/outdoor propagation models.
Furthermore, attention has been recently given to optimizing
the indoor radio coverage by using specific indoor solutions
such as Femtocells [1]. Efficient outdoor to indoor propagation
tools will be very useful for operators to study the interference
in the femtocell due to outdoor macrocells.
A. Related work
In [2], the identification of the outdoor to indoor through
walls opening was studied. In [3], it is shown that many factors
have an influence on the received power inside a building
such as the predicted penetration loss versus frequency for a
windowed wall. Moreover, reflections on the outdoor obstacles
will have a great influence on the indoor radio coverage,
that is why a cluster approach was proposed in [4]. Three-
dimensional radio propagation models for outdoor to indoor
have been proposed for urban wireless network planning [5]
and for Relay Network deployment [6].
B. Contribution
In this TD, the combination of the IRLA model (an
outdoor ray launching model) and MR-FDPF (an indoor
finite difference model) will be proposed. Since both of
these models have been shown to have good performance for
specific areas (indoor or outdoor), the new combined model
offers an optimal solution for outdoor to indoor network
planning.
The TD will be organized as follows: In the next section
an overview of the main approaches for deterministic radio
propagation will be presented, then in section III the 2 models
and their combination will be proposed. In section IV the
performance of the new outdoor to indoor model will be
presented and finally perspectives and conclusions will be
developed in section V.
II. APPROACHES FOR DETERMINISTIC RADIO
PROPAG ATIO N
A. Geometric based models
Geometric models or RO (Ray Optical) models (see Fig.1.a)
use the ray optical laws to compute the rays that are re-
flected/diffracted in the environment [7], [8]. Geometric based
models are implemented in many commercial softwares [9].
Such a model tries to search what are all the possible rays
between emitter and receivers. They can been implemented
in 3D, however it is important to notice that the complexity
of RT can be very high in scenarios where the number of
walls is high, thus where numerous reflections occur. The
two most common implementations are Ray Tracing and Ray
Launching.
Ray Launching emits the rays from the transmitter. Signal
strength degenerates as the rays propagate and additional loss
is added when rays reflect or diffract from walls.
Ray Tracing traces the rays backwards, i.e it searches all
the possible paths arriving at each receiving positions.
E
R
E
R
a) b)
Fig. 1. Geometric (or Ray Optical) based approach based on the computation
of the rays (a) vs FDTD based approach based on numerical modeling on a
discrete grid (b)
B. Finite difference based models
Finite difference models are based on the resolution of the
Maxwell equations on a discrete grid (see Fig.1.b). The most
common approach is the well known FDTD (Finite Difference
Time Domain) which has been widely applied in the industry
for the design of antennas.
Such models have also been used to compute radio cov-
erage, like the approach proposed in [10]. The advantage of
such models is that, unlike that for Ray Optical models, all
the reflections and diffractions are taken into account. One
disadvantage is that the size of the pixels of the spatial grid
has to be very small compared to the wavelength of the signal,
leading to a high complexity for large scenarios. Hence this
kind of model has been generally used in 2D for smaller
scenarios like indoors [11], [12].
C. Comparison
Geometric based models and Finite difference models are
very different and both of them have advantages and draw-
backs. Comparisons between them are given in [13]. In the
following, the main criteria are compared:
•Complexity: For FDTD it depends mainly on the size of
the scenario, whereas for RO it depends mainly on the
number of walls.
•Accuracy: FDTD is in general more accurate because the
number of reflections in not limited unlike RO.
•3D extension: RO is in general less computational de-
manding than FDTD, that is why a 3D version of the
model is easier to implement.
In the litterature, combined models also referred to as
hybrid models have been proposed [14], [15], [16], where
RO and FDTD models are combined to take advantage of
the properties of each model. Thus, in our paper, taking into
consideration the properties described in II-C, it appears as a
good choice to combine 2 models and choose between them
depending on the scenarios:
•Indoors:The scenario is not very large, and made of
numerous walls that is why the number of reflections is
very high. Moreover, in multi floor buildings, the scenario
at each floor is quite flat i.e. a 2D approximation of the
propagation is not a bad assumption. Hence in this case
the 2D FDTD model is a good option.
•Outdoors:The environment is large and propagation can
not be easily approximated with a 2D model, in particular
in scenarios with high buildings and antennas located on
the roofs. Furthermore, there is more open space areas
and the number of reflections to compute is smaller than
indoors. In such scenario 3D RT is preferred.
III. COMBINATION OF 2MODELS
In this section, the geometric like model and the FDTD like
model we used are described, and the solution to combine
them is detailed.
A. IRLA model
IRLA (Intelligent Ray Launching) is described in [17]. It is a
full 3D ray launching especially developped for urban network
planning. In this model, the buildings are approximated with
a 2.5D database (representing the shape of the buildings
and their heights). IRLA is based on a discretization of the
environment into cubes, in order to reduce the number of
reflections and diffractions to compute. Optimizations to avoid
missing rays are also implemented in this model [18].
B. MR-FDPF model
MR-FDPF (Multi-Resolution Frequency Domain
ParFlow)[19] is a FDTD-like model based on the ParFlow
method. In this approach, the electric and magnetic fields are
approximated by a unique numerical vector called flow, thus
reducing the complexity. The transposition of the model in
the frequency domain [19] allows the problem to be modeled
as a linear system, that can be solved with a multi-resolution
approach. The 2D implementation of MR-FDPF has been
shown to be very efficient for indoor radio predictions [20],
since the number of reflections and diffractions to compute is
not limited.
C. The combined approach
The new model we propose in this TD combines IRLA for
the outdoor signal prediction with MR-FDPF for the indoor
part. A great advantage of the models we use is that they are
both based on a discrete resolution of the environment for the
following reasons:
•MR-FDPF,as a FDTD-like model, solves the Maxwell’s
equations on a 2D grid.
•IRLA divides the environment into cubes for complexity
reduction.
Hence, the main idea of the combined approach is to find how
to link the 2 models, i.e. how to use the IRLA 3D outdoor radio
coverage as an input for the 2D indoor MR-FDPF simulation.
The method is illustrated in Fig.2 and can be divied into the
following steps:
•Run the IRLA prediction (Outdoor ray launching) of the
emitter.
•Compute equivalent MR-FDPF sources flows on the
borders of the building, by summing the rays arriving at
each cube on the borders of the indoor floor (see Fig.3).
•Run the indoor MR-FDPF using the new equivalent
sources as incoming flows of the bottom-up-down ap-
proach [19].
•Combine IRLA/MR-FDPF maps to plot both the outdoor
and indoor coverages.
Diffracted Rays
Reflected Rays
Direct
Paths
E
Considered
Floor Level
Fig. 2. Schematic representation of the combined approach. First the outdoor
part is simulated, then the incoming indoor flows are computed and used for
the indoor simulation
Fig. 3. Computation of the virtual source on the borders of the building.
IV. RESULTS
A. Experiments
The scenario for the evaluation of the model is the INSA
university campus in Lyon, France (see Fig.5). The 2.5D
outdoor database was generated, using Google maps for the
shape of the buildings, and a laser meter to measure the height
of each building. The indoor database was generated from the
architect maps.
The environment was discretized as represented in Fig.4 using
a grid cell size of 5cm.
Fig. 4. Computation of the virtual source on the borders of the building.
The directive antenna (E on Fig.5) was placed on a window
in one building and was pointing in the direction of the
CITI building (colored in red on Fig.5), where the indoor
measurements have been performed.
Fig. 5. outdoor to indoor scenario. In red: the building where the indoor
measurements were performed. E: represents the position of the emitter.
The equipment for the measurements is detailed in table I
(emitter) and table II (receiver). A frequency of 3.5GHz has
been chosen, which is the frequency of WiMAX (Worldwide
Interoperability for Microwave Access) in Europe.
A total of 104 measurement points were chosen (32 indoors
and 72 outdoors). In order to avoid fading effects, for each
point the mean value after a 20 seconds time average was
recorded.
TABLE I
PARAMETERS FOR THE EMISSION
Emitter Agilent Digital RF Signal Generator
Output power 0dBm
Frequency 3.5GHz
Antenna model directive
Antenna height 3 m from street level
TABLE II
PARA MET ER S FOR T HE R ECE PT ION
Receiver N9340A Handheld RF Spectrum Analyzer
Frequency 3.5GHz
Antenna model Omnidirectional antenna
Antenna height 1.5 m from floor level
B. Performance
After the indoor and outdoor measurements were loaded,
a calibration of the tool has been performed. First IRLA has
been calibrated using a simulated annealing approach. As an
illustration, the rays of the outdoor IRLA computation are
plotted in figure 6.
Fig. 6. Outdoor reflections and diffractions rays computed with IRLA model.
Using the rays on the borders of the CITI building (colored
in red on Fig.5), the incoming virtual sources are computed
using the approach presented in section III. Finally the Indoor
part of the signal was also calibrated, in particular because
the properties of the walls and the windows were not known.
For the outdoor simulation, only one material is used
representing the buildings.
For the outdoor database, 3 materials were used for the walls:
concrete, plaster and glass for the windows.
In figure 7 the simulated signal inside the CITI building
is plotted. It is verified in this figure that the effect of the
windows are very well taken into account.
In order to evaluate the accuracy of the model, the RMSE
(Root Mean Square Error) is used. It is defined as:
RM SE =v
u
u
t
1
N
N−1
X
i=0
(Mi−Si)2(1)
Where:
Nis the number of comparison points,
Miis the measured received signal at location i,
Siis the simulated received signal at location i.
Fig. 7. The final indoor radio coverage. The effects of signal penetration
trough windows are easily seen.
The performance of the model have been summarized
in table III, where the results concerning respectively the
outdoor measurements, the indoor measurements, and all the
measurements are given.
TABLE III
PER FOR MA NCE O F TH E MOD EL
X Outdoor points Indoor points All the points
Number of points 72 32 104
Pre-processing 0s 41s 41s
Simulation 58s 57s 115s
RMSE 7.9dB 2.4dB 6.2dB
V. CONCLUSIONS AND PERSPECTIVES
The solution provided in this paper has been shown to
efficiently compute the outdoor to indoor radio propagation
in one building due to the following reasons:
•It combines the advantages of a full 3D geometric model
for the outdoor part, and an indoor accurate finite differ-
ence model where 2D is sufficient due to the flatness of
the floors.
•Only the details of the considered buildings have to be
known, whereas the other buildings are only represented
by their shape and height.
•It is a deterministic model, i.e. the propagation effects
such as the losses through windows are well taken into
account, offering a RMSE between simulation and mea-
surements of about 2.4dB indoors for a short simulation
time.
•Is can be easily implemented on a standard PC and does
not require the use of expensive powerful computers.
Perspectives of this work include:
•The validation of the model in other scenarios and other
frequencies. It will be especially interesting to study
higher buildings made of many floors, and do more
measurements at each floors.
•The extension of this work to the indoor to outdoor case,
which is not so obvious and where another solution has
to be found to link the MR-FDPF results to the Ray
Launching.
•Finally, combined with an indoor to outdoor model, it
would be interesting to study the outdoor to indoor to
oudoor (for example when a metallic cupboard is located
near a window, reflecting most of the signal outside).
ACKNOWLEDGMENT
This work is supported by 2 European FP7 funded research
projects: the project “CWNETPLAN”on Combined Indoor and
Outdoor radio propagation, and the project “IPLAN”on indoor
wireless network planning. The authors would like to thank
Malcolm Foster for his useful comments and suggestions.
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