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Simulation of Radiowaves Propagation Using Neural Networks1

Michal Steuer and Miroslav Snorek

Czech Technical University in Prague, Faculty of Electrical Engineering,

Department of Computer Science and Engineering, Karlovo Namesti 13, Praha 2, The Czech Republic,

Steuer@sun.felk.cvut.cz

Abstract: This article first summarises some basic problems in the field of calculation ofradiowaves propagation for land mobile services. New approach to the solution of this problem

using artificial neural networks is proposed here. Two examined networks are shortly introduced

at first. The adaptation of these networks to the solved problem is shown. Practical results of the

usage of these networks are described and analysed.

Keywords: Neural Networks, Electromagnetic Field Propagation, Land Mobile Services,Backpropagation, GMDH.

Introduction

Simulation of the propagation of electromagnetic field is a very complex task which is demanded to be

solved for many applications. The interest in finding the best possible solution of this problem grows withthe boom of cellular networks which are used to build mobile telephony networks or radio networks for

emergency services.

a) predicted by GMDH neuronal network b) clean map for comparison c) predicted by Backpropagation n. n.

Figure 1:Strength of electromagnetic field predicted by both the neural networks, and a clean map for comparison. Towns,

forests and rivers are drawn by the darkest colours. The strength of the field is distinguished by shades of grey drawn in a

layer above the map. So the background map shines through only if the field strength is lower than a weakest threshold. The

transmitter was situated on a 40 meters high tower and the power was radiated by an omnidirectional antenna.

A cellular network consists of several base stations (BS) located on fixed positions, and many mobilestations (MS) moving among them. To can a MS operate, it needs a good radio connection to at least one

BS. While building a radio network, the designers need to know which area will be serviced (or covered)

from a given BS. The serviced area is determined by a minimal strength of electromagnetic field on which a

MS can operate, and by radio parameters of the BS like radiated power, antenna type and position. In all this

article we only investigate the path from BS to MS, that is so called downlink. So BS is supposed to be only

a transmitter and MS is supposed to be only a receiver. Most of the services use duplex communication but

for simplicity we can say that both the paths are reciprocal. A typical serviced area is depicted in figures 1a

and 1c. The background of the figure is a map and the serviced area is drawn in shades of grey. So the places

1

This research has been supported by EuroTel Praha s.r.o., an operator in NMT and GSM radiotelephony networks.

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where the background map is visible are supposed to be uncovered, without any possibility to make the

radio connection to the BS. The prediction of radiowaves propagation, by which the serviced area in the

figure is determined, was performed by a neural network described later.

At first sight, the simulation of propagation seems to be very easy task. We simply need to calculate the

loss of the path between BS and MS for all possible positions of MS in a given area. One of the problems is

that at least one of the two radio stations is situated in a very low height, typically 2 or 3 meters above the

ground, so the propagation of the electromagnetic field is substantially influenced by the surface of theground like hills, buildings and vegetation. Therefore calculation of only free space propagation, which

works good for e.g. TV broadcast where the antennas are placed very high, does not have enough accuracy

here. A three-dimensional digital terrain model (DTM) is needed to improve the accuracy.

Short review of classical algorithms

There are several commercial computer programs on the market which solve this problem. They use digital

terrain models to take the surface of the ground into account. Two main approaches to the simulation of

radiowaves propagation can be distinguished:

Most of the commercial programs use Okumura-Hata prediction model [1], [2]. This model is based on

empirical formulas obtained by statistical evaluation of measurements done in 50's in Japan. The model

distinguishes different kinds of the areas where MS is situated: open area, forest, suburban and urban. The

basic model is sometimes improved by e.g. calculation of diffraction loss on the biggest obstacles or by line

of sight checking. But typically, the model evaluates only the direct path between BS and MS. Propagation

models of this kind are also called statistical as they are more based on statistics than on physics.

The electromagnetic signal can, however, get to the mobile station by various ways. It can be reflected by

the walls or hills, and on the corners of buildings diffractions appear. Because of this some other approach

in the calculation was introduced a few years ago. Models of this class use so called ray-tracing. Its basic

principle is similar to the ray-tracing used in computer graphics. They try to find the most important paths

from BS to MS, calculating signal attenuation and its phase in the point of the MS. By adding all the

contributions, with regards to the phase, the signal strength in the place of the MS is calculated. Thesemodels are also called multi-ray or deterministic for their clear mathematical background.

Why neuronal propagation predictor?

This article proposes a new approach how to solve this problem. We use the advantage of the robustness

and the learning capability of artificial neural networks to improve the accuracy of the classical methods of

prediction. While creating the classical models the inventors had to find out complicated models of

dependency of different kinds of obstacles on the resulting path loss. This effort is visible mainly in the case

of the deterministic models. Because of its basic features, the neural network is able to create its own

internal model of behaviour of radiowaves by just observing measured values. This happens during so called

training phase. This internal model can be later used for predicting these values in the places where the

measurements were not performed. This is called recall phase. In other words we can say that the network isable to generalise the observed measured values.

The neural network approach has good presumptions to work better than the empirical formulas of the

classical models, as the network can take into account much more details of the propagation path. In other

words, the internal formula of the network can be much more complex than the one derived from the

measured curves. The network is self-adapting so the dependence of the result on each particular parameter

is found by the network itself. The network can even refuse some parameters if it does not see any

dependency. The final accuracy of the prediction is limited mainly by the accuracy of the DTM and the

measured data. There will always be a physical limit of the accuracy of the prediction. E.g. any movement of

a car or a men on a street causes a change in the propagation. This is a stochastic element in the real

behaviour of the radiowaves. The most important advantages and disadvantages of the neuronal solution will

be summarised later.

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Neuronal networks used in our experiments

Plenty of artificial neural networks have yet been developed. All of them are, more or less, trying to imitate

the functionality of the building cells of the brain, neurones. As it is still more or less unclear how these

cells exactly work, the artificial neural network models differs each from other a lot. We have selected two

networks to try to create a propagation predictor. Both of them are supervised networks so they need somecorrect pairs of inputs and outputs to be trained.

Backpropagation is one of the most famous networks. It is probably the most often used network in all

practical applications. Its principle can be found in any textbook about neural networks [6]. An example of

its structure is in figure 2. The structure of the network must be determined before training and it can not be

changed later.

Group method of data handling (GMDH) is a neural network which is very suitable for creation ofmathematical models. An example of the network is shown in figure 3. The structure of the network is

created during training in dependence on the given training examples [5], [7], [8]. We implemented the basic

combinatorial GMDH algorithm.

In this article, we will think of the neural networks as being black boxes having n analogous inputs and just

one output. The output is also analogous and it will represent the predicted field strength. The internal

working of the networks is very important, but its description is beyond the scope of this article.

Measured training example set

Measured data is needed to evaluate and tune the classical propagation models. For the neuronal

propagation model the data is even necessary for the network to create its own model of the behaviour of theradiowaves. The network has to be trained by some examples of correct pairs of inputs/outputs. These pairs

are in our case based on measured samples of the field strength in various conditions. As the propagation

model has to work with the DTM, each sample must contain information about the place where the sample

was measured. This condition is usually satisfied by using global positioning system (GPS). So the file

resulting from the measurement contains co-ordinates for each measured sample. It is important to measure

the samples in many different positions against the transmitter, in towns, in countryside, in forest, hidden

behind a hill, with direct visibility to the transmitter and in different distances to it. If some kinds of the

samples were not represented in the measured file (e.g. no measurements in forest), the network may (but

may not) respond incorrectly if it is asked to predict the field strength in such an environment during the

recall phase. The network has a great ability to generalise the given samples. So a small mistake in the

measured file does not cause completely wrong function of the system, but leads only to a decrease of the

Figure 3: A typical GMDH neural network and a single

neuron of this network. The weights a,b,c,d,e,f are

modifiable by training.

Figure 2: A typical backpropagation neural network and

a single neuron of this network. The weights wi are

modifiable by training.

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accuracy of the predictions. The samples for our experiments were kindly provided by EuroTel Praha. They

were obtained by a measuring receiver and a GPS installed in a special measuring car.

Preparing inputs for the networks, path signature vector

As we imagine the neural network as a black box having n inputs and one output, the inputs must contain

all information about the parameters of the BS, and information about the path between the BS and the MS

obtained from the DTM. If we fed the neural network just by the rough samples in the form they weremeasured, that is by co-ordinates of both BS and MS, the only thing the network could create a model of,

would be a variation of free space propagation. It is needed to somehow give the disposal of the DTM to the

network. Getting all diverse information from the DTM, we form the n inputs, which we will call path

signature vector. To decrease the size of the path signature vector, parameters which are easy to be taken

into account outside the neural network like e.g. radiation diagram of the antenna or radiated power, are

calculated outside the network. This also allows to decrease the number of the measured samples.

As described above, there are two main approaches how to take the DTM into account: statistical and

multi-ray. Until now we made experiments only with the class of the statistical algorithms of prediction. So

we have investigated only the direct path between BS and MS. The best way to investigate this path is to

draw terrain profile between BS and MS. So the path signature is derived from the terrain profile.

Two examples of terrain profiles are depicted in figure 4 and 5. The BS is on the left side drawn by a

vertical line which represents the 40 meters high tower. The MS is on the right side. Its height above the

ground is 1.5 metres. The information obtained from the DTM consists of two parts. The first part is digital

elevation model (DEM) which contains information about ground height. The second part is called morpho

classes or clutters. It contains information about the buildings or vegetation above the ground. In the profile

the DEM is drawn by lines, and the morpho classes are distinguished by rectangles filled by different

colours.

In figure 4 the antennas of both stations are connected by a direct line. Beside this, one more line is drawn

in the figure. This is so called Fresnel zone. It determines an area where the most of energy between the

transmitter and the receiver is transferred. The profile in this figure is line of sight so there are not anyobstacles in the area where the energy is being transferred.

Figure 4: Line of sight terrain profile between BS and MS

In the figure 5, the hill on the right hand side acts as a big obstacle to the direct way of the signal. The path

is therefore non line of sight. So we suppose that a the hill will work as a diffraction edge. In this sense the

final way of the signal is drawn.

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Figure 5: Non line of sight terrain profile between BS and MS

Creating path signature

The inputs of our neural network, that is the path signature, for each calculated path loss is prepared byanalysis of the terrain profile between the actual position of the MS and the BS. At first approach we wanted

to find out if the neural network is able to reach at least the same level of accuracy as the classical

algorithms. So the path signature was constructed with regards to the profile features discussed in e.g. the

article of Okumura [1]. It is better to select more features than less. As already discussed, the network is able

to reject some features if they seems to be irrelevant to the trained problem. The path signatures created for

our experiments contained:

Length of the distance between the BS and the MS.

Clutter type in the area of the MS. This clutter type was determined by evaluating of the path from the

MS towards the BS in length of several hundred metres. In this way the network is told if the MS is in anarea of high buildings, trees or in an open area.

Effective antenna high. This value represents the high of the BS antenna but the terrain around is taken

into account. If the antenna is on a high hill, the effective height will be large, if the antenna is in a

valley, the effective height will be very low.

Height of the biggest obstacle. If there is a line of sight profile between the BS and the MS, the value will

be zero. Otherwise, the size of the obstacle is calculated as the distance between the border of the Fresnel

zone and the top of the obstacle while the Fresnel line is drawn as if the obstacle was ignored.

These were the basic components of the path singature vector, but to make the work of the neuronal net

easier, we presented them in some variations so the final number of the components was 12. To help theneural network by well known facts about the electromagnetic energy propagation, one of the components

was logarithm of the distance between BS and MS.

Results of our experiments and general comparison

We implemented both the mentioned neural networks and a system which pre-process the information

from the DTM to be given to the network as an input in the form of the path signature vector. The network

was trained using 1 000 precisely selected samples, and it was evaluated using 27 000 different samples. The

network was trained to minimise the standard deviation:

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,

where Emi is a measured sample and Epi is its corresponding predicted value. Ns is the number of all

samples.

The training of the GMDH network took about 10 minutes on a Sun Ultra 1 workstation. The training ofthe backpropagation network took a bit longer time. The results were compared with a classical propagation

model implemented in a commercial program, and with a dummy model. The classical propagation model

was based on the Okumura-Hata model with some improvements. The field strength was predicted in

constant height 1.5 meters above the ground. The results are the following:

Propagation model Standard deviation

Dummy model; field strength is everywhere equal to the average measured value 16.43 dB

Classical model based on Okumura-Hata, calculated using a commercial program 9.52 dB

Neuronal model using GMDH network (80 neurones, structure drawn in figure 6) 9.17 dB

Neuronal model using Backpropagation network (12 neurones, 2 hidden layers, fig.7) 8.87 dB

All the results were calculated on the same set of measured routes. If just a smaller part of the measured

routes was used, the deviation would differ a lot. The file of the measured samples consisted of 26 routes.

We calculated the standard deviation also on separate routes. The achieved minimal value was even below 5

dB. Some others had, however, higher deviation than the number presented in the table. The same was with

the commercial program. So it only confirms that for objective evaluation of the model, the deviation must

be calculated on all roads, in all parts of the territory.

Figure 6: Final structure of the GMDH neural network for prediction of radiowaves propagation.

It is important to explain the absolute values of the deviations. It will never be possible to achieve standard

deviation equal to zero. It is estimated that only the fact that cars and people on the streets are moving

causes changes in the field level of about 3 dB. Next, we have to take into account that the accuracy of the

DTM will always be limited. The real world is much more diverse than just terrain elevations and

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classifications of several morpho classes. We estimate that the propagation models can never achieve better

standard deviation than about 5 or 6 dB. On the other hand, our dummy model shows that even very

simple estimate of the level of the propagated field can achieve standard deviation of about 16 dB. This

value, of course, is very dependent on the type of the terrain where the measurement was performed. In a

more hilly terrain, the value would get much higher.

The GMDH network achieved better results than the classical algorithms but worse results than

backpropagation. The final structure of the network is shown in figure 6. The numbers written inside theneurones determine their original position in the layer at the time the layer was in creation. That is, the

skipped numbers belonged to neurones which later died. It can be seen in the figure that the network decided

to ignore several values from the path signature, but some others are very heavily used. E.g. neuron 9 in the

input layer represented the existence of a particular clutter type in the place of MS. The neuron 1

represented the distance between BS and MS and the neuron 4 represented its logarithm.

Figure 7: Final structure of the backpropagation neural network for prediction of radiowaves propagation

The backpropagation network achieved the best results in our evaluation. The final structure of the

network is shown in figure 7. In comparison to GMDH the structure of this network is very uniform as it

was not changed according to the training.

Advantages and disadvantages of our approach

Let us summarise where the neuronal solution is better than the classical one and vice versa.

To create the neuronal model of propagation, one must have some measured data. Without this the

network can not be formed. The number of the measured samples must be rather high (tens of thousands) so

a special automatic measuring system with a positioning equipment is needed. This is not needed by the

classical propagation models. They can be usually tuned using the measured data, but they can work withsome default settings as well. The acquisition of the measured data is usually not a great problem as the

companies who seriously work in this field must have measuring cars. The accuracy of any propagation

model is limited and some parts of the radio network simply must be measured.

The internal prediction model of the neural network can be much more complex in the mathematical

sense. The network can take into account much more parameters than the classical models as the network

adapts to the parameters automatically. In the classical model, including of any additional parameter

requests a complex research which role the parameter will play, and how to employ it to the existing model.

Creation of a very accurate DTM is a very expensive task. The neuronal prediction model can adapt even

to a DTM in which a systematic error occurs. So even a lower quality DTMs can be used.

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Although the neuronal model can reach a very high accuracy, it is also very easy to be set up. The

classical models have always some limitation in the frequency range and height of the antenna of BS and

MS. The neuronal model just need some new measured data to can adapt to the new conditions. Of course,

sometimes the preparation of the input signature needs to be changed as well. For a quick overview, one

even does not have to think about units of the measured field. The network simply predicts values in the

same units the samples were measured in. All these things make the model very flexible.

The simulation of the propagation using the neural networks is, however, a bit more time complex than

the usage of the empirical formulas. That is because we have to obtain more parameters from the terrain

profile. The simulation of the function of the neuronal network itself takes just a fraction of this time.

Although the first version of the neural network model is implemented on sequential machine, it is easy to

implement it in parallel. The neural network is also easy to implement in hardware, where the level of the

parallelism can be much higher than in the case of the standard parallel computers.

Conclusions

Our experiments show that artificial neural networks can successfully solve even so complex problem like

simulation of radiowaves propagation. Up to now this domain belonged only to classical algorithms. The

neuronal solution is very flexible and can be adapted to almost any variation of the problem. The neuronalnetwork can be adapted even to some variations of the problem where the classical solution is not yet known

or its accuracy is not guaranteed. A new adaptation, that is new training of the network, can be done just in a

few tens of minutes.

First experiments shown that the neuronal predictor of propagation can achieve even better accuracy than

the classical algorithms. Calculation of the standard deviation is, however, not the only way how to evaluate

the abilities of a propagation model.

In our future work, we would like to concentrate on better evaluation of the results achieved by different

propagation models. Next we would like to improve the implementation of the neural networks to better suit

to the application.

The authors of this article will appreciate any comments of this work. We would like to thank to employees

of RF planning department of EuroTel Praha for their support in this work. As meaning and experience of

people interested in similar subjects is very important for us, we are looking for another people and

companies who would like to cooperate in this work.

References:

[1] Yoshihisa Okumura, Eiji Ohmori, Tomihiko Kawano, Kaneharu Fukuda: Field Strength and Its Variability in VHF and UHF

Land-Mobile Radio Service,Review of the Electrical Communication Laboratory, Vol. 16, 1968, pp. 825--885,

[2] Masaharu Hata: Empirical Formula for Propagation Loss in Land Mobile Radio Services, IEEE Transactions on Vehicular

Technology, Vol. 29, 1980, No. 3, pp. 317--325.

[3] Lee William C. Y.:Mobile Cellular Telecommunications Systems, McGraw-Hill Book Company, 1989.

[4] Linnartz Jean-Paul:Narrowband Land-Mobile Radio Networks, Artech House, 1993.

[5] A.G. Ivakhnenko, G. A. Ivakhnenko: The Review of Problems Solvable by Algorithms of the Group Method of Data Handling

(GMDH), Pattern Recognition and Image Analysis, Vol. 5, No. 4, pp. 527-535, 1995.

[6] R. Rojas:Neural Networks - A Systematic Introduction, Springer 1996.

[7] Robert Hecht-Nielsen:Neurocomputing, Addison-Wesley Publishing Company 1991.

[8] Stanley J. Farlow: Self-Organizing Methods in Modeling, GMDH Type Algorithms, Marcel Dekker, Inc. 1996.