DOMINANT PATHS FOR THE FIELD STRENGTH PREDICTION
G. Wölfle and F. M. Landstorfer
Institut für Hochfrequenztechnik, University of Stuttgart,
Pfaffenwaldring 47, D-70550 Stuttgart, Germany
e-mail: [email protected]
WWW: http://www.ihf.uni-stuttgart.de
Abstract |
An algorithm for the determination of the
dominant paths for indoor wave propagation is presented.
The algorithm computes a tree of the relations between the
rooms inside the building and the branches of the tree are
used for the determination of the dominant paths. Based on
these dominant paths, three different prediction models are
presented and compared with one another and with measurements. Two of the three models are based on neural
networks, trained with measurements and the third model
is an empirical model. With the neural prediction models a
good generalization is achieved and they are very accurate
in buildings not used for the training of the neural network.
I. I NTRODUCTION
There are basically two different approaches to the prediction
of the electric field strength inside buildings, both of which have
their individual disadvantages. Empirical models, based on the
regression of data gained in measurement campaigns, are very
fast but not very accurate [1]. Deterministic models (ray–optical
models) depend heavily on the accuracy of the data base [3] and
are very time–consuming [2].
A new approach is given by prediction models based on artificial neural networks. In these models, the neural networks
are trained with measured data and adapt their parameters to
approximate the measured field strength [4]. Especially for indoor environments some successful improvements of empirical
models were developed [5], but they are based on the direct ray
and do not consider multipath propagation.
more interactions, they can generally be neglected because of
their higher attenuation. The new approach presented in this
paper introduces dominant paths to describe all rays passing the
same rooms and walls. The dominant paths for the scenarios in
figure 1 are given in figure 2.
Fig. 2: Multipath propagation: Representation of multipaths by a single dominant path
The second effect of multipath propagation is shown in figure
3. There are different dominant paths, passing different rooms
and penetrating different walls. These paths do not contribute
equally to the total field strength and cannot be represented by
a single path.
II. A NALYSIS OF MULTIPATH PROPAGATION
Fig. 3: Multipath propagation: Different dominant paths
Fig. 1: Multipath propagation: Possible rays
The difference of the path losses between two dominant
paths for the same receiver point is often greater than 6 dB.
These paths with higher attenuation can be neglected for the
computation of the over–all field strength, because their contribution is very small as compared to the main path. In most
cases it is only necessary to determine the main dominant path
to get an accurate prediction. More than one or two dominant
paths are necessary in very particular situations, but the error by
neglecting the third or fourth path is generally very small.
A further improvement of the approach with dominant paths
as compared to deterministic models consists in the fact that
small tolerances in the locations of the walls have only a limited influence on the paths, because in contrast to the ray–optics
no exact location of the reflection and diffraction points is necessary for the determination of the path.
If multipath propagation with indoor scenarios is analyzed,
two different effects must be considered. As shown in figure 1,
different rays may reach the receiver passing the same sequence
of rooms and penetrating the same walls. The contributions of
those rays which offer the same number of interactions to the
over–all field strength are very similar and if other rays show
III. D ETERMINATION OF THE DOMINANT PATHS
A. Location of rooms
The data base of a building generally contains only information about the location and the material of the walls but no
information about rooms. For determining the dominant paths,
a detailed information about the location of the rooms is mandatory, however.
A new algorithm for the computation of the location of rooms
was implemented in 2D and 3D. While the faster 2D–algorithm
can be used in cases where only a single floor in considered, the
3D–algorithm is necessary for multi–floor buildings.
In a first step the intersections of lines symbolizing the walls
are computed. Thus the corners of rooms are found (2D). In 3D
the intersecting lines define wedges. The second step combines
walls (or wedges) to rooms.
The determination of the rooms includes an analysis of the
neighboring rooms. For each room all neighboring rooms and
walls coupling to these rooms are determined. The space around
the building is also considered as a room.
B. Tree for the room–relationship
The information about the neighboring rooms is used to compute a tree of the room–structure of the building. For the building presented in figure 4 the tree of the room–structure is shown
in figure 5.
ing rooms lead to a new branch in the tree, except if the wall is
already used in this path in a layer above.
After the determination of the tree, the dominant paths between the transmitter and the receiver can easily be computed,
because the tree represents in its branches all possible dominant paths and the sequence of rooms passed. If the receiver is
located in room i , the tree must only be examined for room
i . The corresponding dominant path can be determined by following all branches from room i back to the root of the tree.
Further information about the tree and the determination of the
paths is given in [6].
C. Combination of rooms
For determining dominant paths the same algorithm should
be applicable to situations where a path passes through a sequence of rooms or where transmitter and receiver are located in
the same room. If a path passes through a sequence of rooms, all
rooms considered are combined to form a new single room by
erasing all coupling walls in the branch representing the dominant path in the room–tree (see figure 5). This combination
of different rooms to a new room is shown in figure 6 for the
two examples given in figure 1. Now the path inside the new
room can be computed by using the algorithm described in the
following section.
D. Determination of the path inside a room
If transmitter and receiver are located in the same room, the
dominant paths inside this room are determined with the information about the convex corners as shown in figure 6.
Fig. 4: Room–numbers (left) and coupling walls (right)
Fig. 6: Convex corners (or wedges) of a room and their
influence on the determination of the paths
Fig. 5: Tree of the room–structure presented in figure 4
The root of the tree corresponds to the room in which the
transmitter is located. The first layer contains all neighboring
rooms and if there is more than one coupling wall between the
room of the transmitter and the neighboring rooms, the neighboring room is placed in the first layer as many times as there
are coupling walls between the two rooms. All further layers are
determined in a similar way. All coupling walls to the neighbor-
Each room is described by its surrounding walls. For the sake
of simplicity the following explanations refer to the 2D–case.
In the 2D–case all convex corners of the room get a different
number.
There are two different scenarios for the determination of the
path between the transmitter and the receiver: Line of sight and
obstructed line of sight. The first case is very easy because the
dominant path is the direct ray between transmitter and receiver.
In obstructed line of sight the dominant path must lead via convex corners to the receiver. For the determination of the path
a tree with the convex corners is computed. All corners visible from the examined corner are new branches in the tree. As
shown in figure 7, the corner–tree starts with the corners visible
from the transmitter. The receiver is also included in the tree.
Each time the receiver is found in the tree, the corners along the
path can be determined by following the branches back to the
transmitter.
Fig. 7: Relations between the convex corners of the room
Different paths are determined for each receiver point and the
path with the smallest total attenuation L is chosen and called
minimum–loss dominant path (MLDP). It is possible to determine different types of dominant paths by adjusting the three
weighting factors w FS , wT and wI . In contrast to the model
described in [6], only one criterion (w FS = wT = wI = 1) is
chosen for the models presented in this paper.
Two of the three prediction models presented in this paper
need only the minimum–loss dominant path (MLDP) for the
prediction of the field strength. Alternative paths with higher
attenuation values are only considered in the third model, if
the difference between their attenuation L and the attenuation
LMLDP of the MLDP is smaller than a definable threshold.
IV. P REDICTION OF THE FIELD STRENGTH
E. Selection of the minimum–loss dominant path (MLDP)
The algorithm for the determination of the dominant paths
leads to more than one solution [6]. But in most cases only one
solution with the smallest path loss is necessary for an accurate
prediction. This most important path is called minimum–loss
dominant path (MLDP). The MLDP is chosen by utilizing the
user-definable criterion L:
L = wFS LFS + wT LT
+ wI LI
(1)
L represents the empirical determination of the total attenuation
Three different prediction models are presented in this paper and described in the following sections. The first two models are based on the minimum–loss dominant path (MLDP), the
last one needs further information about alternative paths (ADP
model).
A. Empirical prediction of the field strength with MLDP
The computation of the path loss of the empirical MLDP
model is given in equation (5).
LE = LFS + LT + L0
along the path and consists of three different parts:
Free space attenuation L FS
The free space loss LFS depends on path length l and frequency f :
LFS /dB = ;27:56 dB + 20 log
l
+
20
log
MHz
m
(2)
Transmission loss LT
The accumulated transmission loss of all walls passed is represented by L T . If the path intersects n walls with their
individual transmission losses L i , the total transmission loss
LT is computed from
LT
f
=
XN Li
T
(3)
i=1
Interaction loss LI
Changes in the direction of the path as given by angle i at
point i represent an additional loss. All angles i are accumulated and normalized with a factor L to give the interaction loss LI .
X
1 N LI =
i
I
L
i=1
(4)
Best results are gained with L = 5
8 If some walls
are supporting the changes in the direction (waveguiding) at a
specific point, the contribution at this point to the path loss is
reduced, depending on the support of the walls as described
in [5] for the transmitter environment.
: : : .
(5)
The offset L0 can be used for the calibration of the model.
This model is nearly similar to that of Motley and Keenan [1],
but in contrast to the latter this model is based on dominant
paths and not on direct rays. The improvement gained with using dominant paths can be seen by comparing with results obtained with the model of Motley–Keenan, as shown in figure
12.
B. Parameters of the dominant path for the neural networks
For the computation of the field strength with neural networks, the parameters of the minimum–loss dominant path must
be determined. Because the dominant paths represent a group
of nearly similar rays between transmitter and receiver (see section II), all relevant parameters of these rays governing propagation should be considered in the description of the dominant
path. Very good results have been obtained with the following
parameters:
Free space attenuation L FS along the path
As described in equation (2).
Transmission loss LT
The transmission loss is computed with equation (3).
Interaction loss LI
The accumulated angles i of changes in direction are normalized with equation (4).
Waveguiding along the path
Each dominant path represents different rays. All of them
are guided by reflections at the walls or by diffractions at the
corners of wedges in the same direction (see section II). To
include all these rays in the prediction, they are described
by the new parameter waveguiding. The waveguiding of the
walls depends on their material (reflection loss), their orientation (reflection angle) and the distance between the walls
and the path [4]. These three parameters are combined to
give the parameter waveguiding, as described in [4].
Local reflectors and shielding effects at the transmitter site
The computation of these local effects is described in [5].
Local reflectors and shielding effects at the receiver site
For each dominant path all mentioned parameters are gained
from a vector oriented data base and are normalized for the input
of the neural network. The prediction of the field strength is
based only on these parameters.
C. Neural network prediction of the field strength with MLDP
In this model an artificial neural network is used for the computation of the field strength. The parameters of the dominant
path (see section IV.B) are combined with a multi–layered feed–
forward perceptron. The backpropagation algorithm was used
to train the network with measurements. Figure 8 shows the
structure of the neural network.
input neurons represent the normalized difference of the parameters (path length, transmission loss, interaction loss and waveguiding) between the alternative and the minimum–loss dominant path (MLDP).
In contrast to the model described in [6], the relative and
not the absolute parameters of the alternative paths are used. A
relative description is much better because the neural network
must be trained with measurements and if the alternative path
is described with absolute values, more combinations of input
values (measurements) for the neural network are necessary to
achieve a good generalization.
The advantage of this model is obvious, if the results in figure 11 are compared with the results in figure 10. In shadowed
regions often two paths have nearly the same contribution to the
field strength, but the first and the second model use only the
MLDP for the prediction. This model considers also the alternative path and the prediction is more accurate. But the computation time for the ADP model increases because all alternatives
and their relative description to the MLDP wmust be computed.
E. Training patterns for the neural networks
The neural network models were trained with measurements
obtained at the University of Stuttgart. The field strength of
more than 5000 receiver points and 15 transmitter positions in
different environments was measured to get enough data for the
training and the validation of the neural networks.
To improve the generalization capability, not all possible patterns were used. If each pattern is interpreted as a vector in
vector space, the Euclidian distance between the patterns can
be computed. As patterns with very small distances contain
nearly the same information only one of them is necessary for
the training. The details of the algorithms for the selection of
the patterns are described in [5] and [6].
V. P REDICTION RESULTS
Fig. 8: Topology of the neural network for the prediction
All training patterns of the network are gained from measurements at the University of Stuttgart. For each measured point
inside the building all parameters of the dominant paths (input
values of the neural network) are determined and stored in the
training pattern together with the measured field strength.
The improvement of the neural networks compared to the
empirical model are obvious from figure 12, especially in shadowed regions and in long corridors with waveguiding effects.
D. Neural network prediction of the field strength with ADP
In this model again a neural network is used for the prediction of the field strength, but the prediction is based not only on
the MLDP. Alternative dominant paths (ADP) are also considered in the prediction model.
The neural network is similar to the network described in
figure 8, the only difference is the four additional input neurons for the description of the alternative path. These additional
A comparison between the new dominant path models and
measurements is shown in figures 9 to 11. In addition to presenting the accuracy of the three models, these figures also show
the dominant paths for different scenarios.
Compared to standard empirical models [1], the new models are more accurate and compared to deterministic models [2]
they are very fast because the computation time for whole buildings (2000 pixels) is smaller than 10 minutes on a workstation.
A comparison between the measurements and the new
MLDP–empirical–prediction model is given in figure 9 (Mean
error = 5.8 dB, standard deviation = 9.9 dB). In contrast to the
standard empirical prediction models (Motley–Keenan model:
mean error = 24 dB, std-dev = 26 dB), the dominant path model
is more accurate in nearly every situation.
The prediction of the neural MLDP model (section IV.C)
leads to a mean error of -0.4 dB and to a standard deviation
of 3.3 dB for the scenario given in figure 10.
The performance of the alternative path model (ADP model,
see section IV.D) is presented in figure 11 (mean error = 0.2 dB,
std-dev = 3.6 dB).
40
85
Measurement
Motley Keenan
Empirical model
Neural network
Alternative paths
Difference
[dB]
20
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Field strength dB[µV/m]
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-10
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Fig. 9: Difference between measurement and prediction
with the new empirical model
10
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Distance [m]
Fig. 12: Prediction and measurement in corridor 1 of the
IHF office building
40
Difference
[dB]
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A
K
A
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corridor 1
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Fig. 10: Difference between measurement and prediction
with the neural network model
40
Difference
[dB]
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Fig. 11: Difference between measurement and prediction
with the alternative path model
A comparison between the three different models and the
Motley–Keenan model is given in figure 12. For this analysis
the scenario of figure 10 was used and the three predictions for
corridor 1 are compared with one another. Figure 12 also shows
the improvement gained by the use of the neural networks for
the dominant path models.
The dominant path models were also used for the prediction
in different buildings not used for the training of the neural network and the models turned out to be very accurate even in these
buildings [6].
VI. C ONCLUSIONS
Three different prediction models for the prediction of the
electric field strength inside buildings were presented in this paper and compared with measurements. All of them are based on
dominant paths, a new and very fast approach to the determination of multipath indoor propagation. The results are highly
accurate, even in buildings not previously used for the training.
ACKNOWLEDGMENTS
The authors want to thank Deutsche Forschungsgemeinschaft (DFG) for supporting their work.
R EFERENCES
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in indoor wireless communications,” in 2nd European
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