ANN based Models for Path Loss
Prediction
I. Popescu1, I. Nafornita2, P. Constantinou1
1
Mobile Radiocommunications Laboratory, National Technical University of Athens,
Athens, Greece
Tel: +30 210 7723849, Fax: +30 210 7723851, E-mail: ileana@mobile.ntua.gr;
fkonst@mobile.ntua.gr
2
Faculty of Electronics and Communications Engineering, “Politehnica” University of
Timisoara, Timisoara, Romania
E-mail: ioan-naf@etc.utt.ro
1. Introduction
Indoor radio propagation is a very complex and difficult radio propagation
environment because the shortest direct path between transmit and receive
locations is usually blocked by walls, ceilings or other objects. Signals propagate
along the corridors and other open areas, depending on the structure of the
building. In modeling indoor propagation the following parameters must be
considered: construction materials (reinforced concrete, brick, metal, glass, etc.),
types of interiors (rooms with or without windows, hallways with or without door,
etc.), locations within a building (ground floor, nth floor, basement, etc.) and the
location of transmitter and receiver antennas (on the same floor, on different floors,
etc.) [1].
An alternative approach to the field strength prediction in indoor environment is
given by prediction models based on artificial neural networks [2] - [6].
The problem of predicting propagation loss between two points may be seen as a
function of several inputs and a single output. The inputs contain information about
the transmitter and receiver locations, surrounding buildings, frequency, etc while
the output gives the propagation loss for those inputs. From this point of view,
research in propagation loss modeling consists in finding both the inputs and the
function that best approximate the propagation loss. Given that ANN’s are capable
of function approximation, they are useful for the propagation loss modeling. The
feedforward neural networks are very well suited for prediction purposes because
do not allow any feedback from the output (field strength or path loss) to the input
(topographical and morphographical data).
The presented studies develops a number of Multilayer Perceptron Neural Networks
(MLP-NN) and Generalized Radial Basis Function Neural Networks (RBF-NN)
based models trained on extended data set of propagation path loss measurements
taken in an indoor environment. The performance of the neural network based
models is evaluated by comparing their prediction error (µ), standard deviation (σ)
and root mean square error (RMS) between their predicted values and
measurements data. Also a comparison with the results obtained by applying an
empirical model is done.
2. The measurements
The measurements used to build the neural network based model were performed
in the 1890 MHz frequency band, at the Hellenic Telecommunication Organization
premises following different scenarios. A detailed description of the measurement
procedure can be found in [8]. Each floor of the building consists of a circular sector
of 60 m in circumference located at the center of each floor and 3 branches
departing from the circular sector, where at each branch there are one main long
corridor, two short front corridors departing from the circular sector and another two
short back corridors. The offices are flanked on both sides of the main corridor and
of the two short back corridors, as shown in Figure 1 [8].
The presented study includes the single floor scenario and the procedure used to
select the measurement data is described below.
Figure 1. The building topology and the transmitter positions
In order to train the neural network the measurements collected from two branches
have been used: one branch where the transmitter was always located and only one of
the branches adjacent to it. The fast fading was eliminated, in the case of longitudinal
measurements (along the corridors), by averaging the measured received power using
a 2λ windowing technique [9]. In the case of static measurements, the average values
of the recorded samples in every position of the receiver inside the offices were
computed. Two values for the received power in each office (with closed doors and with
open doors, respectively) were obtained for different combination of the position, height
and gain of the transmitter antenna [12].
Following the filtering process of the measured data, more than 1400 measurement
locations corresponding to the non-line-of-sight (NLOS) case were obtained.
The performance of the neural network model is evaluated by making a comparison
between predicted and measured values based on the absolute mean error, standard
deviation and root mean square error.
3. The ANN Overview
3.1 Multilayer Perceptron Neural Network (MLP-NN)
Figure 2 shows the configuration of a multilayer perceptron with one hidden layers and
one output layer. The network shown here is fully interconnected. This means that each
neuron of a layer is connected to each neuron of the next layer so that only forward
transmission through the network is possible, from the input layer to the output layer
through the hidden layers. Two kinds of signals are identified in this network:
wji
φ 1 (x)
woj
x1
x0
1
w1
x1
y
x2
φ k (x)
k
wk
y
i
...
...
...
wK
xm
φ K (x)
xn-1
Input
Layer
Hidden
Layer
Output
Layer
xM
K
Input layer
Figure 2. Configuration of the MLP
H idden layer
O utput layer
Figure 3. RBF-NN architecture

The function signals (also called input signals) that come in at the input of the
network, propagate forward (neuron by neuron) through the network and reach the
output end of the network as output signals;

The error signals that originate at the output neuron of the network and propagate
backward (layer by layer) through the network.
The output of the neural network is described by the following equation:
M
  N

y  F0   w 0 j  Fh   w ji x i   
 j 0
  
  i 0

(1)
where:

woj represents the synaptic weights from neuron j in the hidden layer to the single
output neuron,

xi represents the ith element of the input vector,

Fh and F0 are the activation function of the neurons from the hidden layer and output
layer, respectively,

wji are the connection weights between the neurons of the hidden layer and the
inputs.
The learning phase of the network proceeds by adaptively adjusting the free parameters
of the system based on the mean squared error E, described by equation (2), between
predicted and measured path loss for a set of appropriately selected training examples:
E
1 m
2
 yi  d i 

2 i 1
(2)
where yi is the output value calculated by the network and d i represents the expected
output.
When the error between network output and the desired output is minimized, the
learning process is terminated and the network can be used in a testing phase with test
vectors. At this stage, the neural network is described by the optimal weight
configuration, which means that theoretically ensures the output error minimization.
3.2 Generalized Radial Basis Function Neural Network (RBF-NN)
The Generalized Radial Basis Function Neural Network (RBF-NN) is a neural network
architecture that can solve any function approximation problem. The learning process is
equivalent to finding a surface in a multidimensional space that provides a best fit to the
training data, with the criterion for the “best fit” being measured in some statistical
sense. The generalization is equivalent to the use of this multidimensional surface to
interpolate the test data.
As it can be seen from Figure 3, the Generalized Radial Basis Function Neural Network
(RBF–NN) consists of three layers of nodes with entirely different roles:

The input layer, where the inputs are applied,

The hidden layer, where a nonlinear transformation is applied on the data from the
input space to the hidden space; in most applications the hidden space is of high
dimensionality.

The linear output layer, where the outputs are produced
The most popular choice for the function  is a multivariate Gaussian function with
an appropriate mean and autocovariance matrix.
The outputs of the hidden layer units are of the form

k  x   exp   x  v kx

  x  v   2 
T
x
k
2
(3)
vx
vy
when k are the corresponding clusters for the inputs and k are the corresponding
clusters for the outputs obtained by applying a clustering technique of the input/output
data that produces K cluster centres [9].
v ky
is defined as
vky 

y p cluster k
y  p
(4)
Nk is the number of input data in the cluster centre k, and

 
d x, v kx  x  v kx
 x  v 
T
x
k
(5)
With
vkx 

x  p cluster k
x p
(6)
The outputs of the hidden layer nodes are multiplied with appropriate interconnection
weights to produce the output of the GRNN. The weight for the hidden node k (i.e., wk)
is equal to
wk 
v ky
 d x, v x
K
k
N k exp  

2

2
k 1



2




(7)
4. Models’ Implementation
The goal of the prediction is not only to produce small errors for the set of training
examples but also to be able to perform well with examples not used in the training
process. This generalization property is very important in practical prediction situation
where the intention is to use the propagation prediction model to determine the
coverage area of potential transmitter locations for which no or limited measured data
are available.
The selection of the set of training examples is very important in order to achieve good
generalization properties [7], [10], [11]. The set of all available data is separated in two
disjoint sets that are training set and test set. The test set is not involved in the learning
phase of the networks and it is used to evaluate the performance of the neural model.
An important problem that occurs during the neural network training is the
overadaptation that is the network memorizes the training examples and it does not
learn to generalize the new situations. In order to avoid overadaptation and to achieve
good generalization performances, the training set is separated in the actual training
subset and the validation subset, typically 10-20% of the full training set [7]. In order to
make the neural network training process more efficient, the input and desired output
values are normalized so that they will have zero mean and unity standard deviation.
In order to establish the optimum configuration of the MLP neural network, networks
with different architectures and different training algorithms were investigated. The
results presented here refer to the optimum MLP-NN for each propagation prediction
case.
Since the purpose is to train the neural networks to perform well for all the routes, we
should build the training set including points from the entire set of measurements data.
For training and test purpose we have used the same number of patterns as in the
prediction models, for both cases, urban and suburban environment.
The inputs of the neural network are as follows:
1. Influence of the transmitter site
 Position of the transmitter (the transmitter antenna was located always in the
same sector, in two different positions),
 Gain of the transmitter antenna
 Height of the base station antenna
2. Receiver site
 The sector where the receiver antenna is located
 Type of interior (corridor, room) where the receiver is located
3. Distances
 Distance between transmitter and starting point of measurements
 Distance covered by the mobile unit;
4. Penetration parameters
 Number of walls penetrated by the direct ray between transmitter and receiver
 Number of windows penetrated by the direct ray between transmitter and
receiver
 Accumulated losses of walls and windows penetrated by the direct ray.
The input parameters that describe the transmitter and receiver site are quantized so
the effect of each parameter is more obvious for the neural network. For example, in
order to describe the type of interior where the receiver is located, parameters like size
of the corridors are quantized as follows: 1 for the large corridor and 0.3 for the medium
corridor.
TABLE I
MLP - NN
RBF - NN
µ [dB]
2.77
1.49
σ [dB]
2.31
1.71
RMS [dB]
3.61
2.27
µ [dB]
3.05
3.09
σ [dB]
3.15
2.88
RMS [dB]
4.38
4.23
TRAINING
TEST
The attenuation factors for different types of walls intervening between transmitter and
receiver, as well as the loss for glasses were used as reported in [12] for this particular
type of building. All parameters are normalized to the range [-1, +1].
The output layer of the Artificial Neural Network consists of one neuron that provides the
received power.
A data set of 289 patterns, that represents 20% from all available patterns, was used for
training purpose. A set of 1155 patterns was used to test the model. In Table I are
represented the absolute mean error, the standard deviation and the root mean square
error obtained for the training and the test set, respectively by the proposed Multilayer
Perceptron Neural Network (MLP-NN) and the Generalized Regression Neural Network.
In Figure 4 is shown a comparison between predicted and measured values of the
received power, in case of a particular route: the receiver being located in a different
sector (from the transmitter), along the main corridor.
An empirical model corresponding to the NLOS situation, when the transmitter and the
receiver antenna are on the same floor, is:
L  L0 10n log  d    K w Lw
where:
(8)
-84
-88
Received power [dBm]
-92
-96
-100
-104
-108
-112
-116
-120
0
2
4
6
8
10
12
14
16
18
20
Covered distance [m ]
22
24
26
28
Measurements
30
32
34
RBF NN
36
MLP
Figure 4. Neural Networks prediction and measurements (received power)
L = the path loss in dB,
L0 = the path loss at 1 meter distance from the transmitter,
n = the path loss depending on the environment outside the wall,
Kw = number of penetrated walls
Lw = the penetration loss due to the wall
-62
-66
-70
Path Loss [dB]
-74
-78
-82
-86
-90
-94
-98
-102
-106
-110
0
2
4
6
8
Covered distance [m ]
10
12
14
16
18
Measurements
20
22
24
26
RBF NN
28
MLP
30
32
34
36
Empirical Model
Figure 5. Predicted and measured values
The parameter Lw depends on the type of the wall construction between the transmitter
and the receiver and the angle of incidence of the transmitted wave.
In the case where more than one wall exists between the transmitter and the receiver, a
detailed analysis is required to calculate the total loss (ΣLw).
Applying the above-mentioned model to the particular route under investigation, as it
can be seen from Figure 5, the prediction made by the neural network model is more
accurate, the improvement obtained on the RMS value being 4.37 dB.
Making a comparison between the two types of neural networks used to build the
propagation prediction models, it is noticed a slight improvement obtained by the
Generalized Regression Network over the Multilayer Perceptron model, about 0.15 dB
in the RMS sense.
5.
Conclusions
Propagation measurement results collected in the 1890 MHz band for indoor
environment were used to design neural network based models. In order to examine the
validity of the neural models, the predicted path loss by them is compared to the
measured values and to the path loss obtained by applying an empirical model.
The performances of the NN model in indoor environment presented in this work are
shown in Table 1. The designed model was trained on data measurements collected in
the 1890 MHz band. In contrast to well-known empirical models high accuracy can be
obtained, because the NN is trained with measurements inside buildings and thus
include realistic propagation effects and also consider parameters, which are difficult to
include in analytic equations. It is difficult to make a comparison between the NN based
models proposed in this work and the models proposed by the other authors due to
differences in building structure.
Acknowledgements
We would like to thank to all the team that has conducted the measurements and
delivered us the measured data in order to investigate the neural networks applicability
to the propagation path loss prediction for the environment under discussion.
References
[1] P. Constantinou, Properties of wireless channels, Wireless LAN systems, Addison Wesley, 1986.
[2] G. Wolfle, and F. M. Landstorfer, “A recursive model for the field strength prediction with neural
networks”, IEE 10th Conference on Antennas and Propagation (ICAP) 1997, Edingburgh.
[3] G. Wolfle, F. M. Landstorfer, R. Gahleitner, and E. Bonek, “Extensions to the field strength prediction
technique based on dominant paths between transmitter and recveiver in indoor wireless
communications”, EPMCC, September 1997
[4] G. Wolfle, and F. M. Landstorfer, “Prediction of the field strength inside buildings with empirical,
neural and ray-optical models”, COST 259, 1999.
[5] G. Wolfle, F. M. Landstorfer, “Field strength prediction in indoor environments with neural networks”
IEEE 47th Vehicular Technology Conference (VTC), May 1997, Phoenix, Arizona
[6] A. Neskovic, N. Neskovic, D. Paunovic, “Indoor electric field level prediction model based on the
artificial neural networks”, IEEE Communications Letters, vol. 4, no. 6, June 2000, pp. 190-192
[7] S. Haykin, Neural Networks: A Comprehensive Foundation, IEEE Press, McMillan College Publishing
Co., 1994.
[8] N. Papadakis, A. G. Kanatas, E. Angelou, N. Moraitis, and P. Constantinou, “Indoor Mobile Radio
Channel Measurements and Characterization for DECT Picocells”, Third IEEE Symposium on
Computers and Communications, Athens, Greece, 30 June-2 July, ISCC ’98.
[9] W. Honcharenko, H. L. Bertoni, J. L. Dailing, J. Qian, and H. D. Yee, “Mechanisms Governing UHF
Propagation on Single Floors in Modern Office Buildings”, IEEE Trans. on Vehicular Technology, vol.
43, No. 4, November 1992
[10] C. Christodoulou, and M. Georgiopoulos, Applications of Neural Networks in Electromagnetics,
Artech House, 2001
[11] H. Demuth, and M. Beale, Neural Network Toolbox For Use with MATLAB. User’s Guide, Version 3.0
[12] A. Kanatas, N. Moraitis, E. Angelou, and P. Constantinou, “Measurements and Channel
Characterization at 1.89 GHz in Modern Office Buildings”, European Transactions on
Telecommunications, Vol. 14, pp. 177-192, 2003.