Simulation of electromagnetic field propagation generated by radio waves from antennas for mobile cellular communications.
Stankevicius, Zilvinas
1. Introduction
In process of designing the limits of sanitary area coverage of
mobile cellular communications base station antenna, the task of
prediction of electromagnetic field propagation is being solved. Initial
data for solving the this task are diagrams and tables of directivity
diagrams in vertical and horizontal planes, data of antenna mounting
position. This data is provided by the manufacturer of mobile cellular
communications antenna. The obtained information faces difficulties in
considering the main physical objects like relief, buildings, etc.
limiting electromagnetic field propagation. Moreover, predicting the
values of the electromagnetic field on building facades flats and
calculating the net values of propagation from several antennas are also
demanding tasks.
computer simulation tools are very useful for obtaining a more
accurate prediction. For this purpose, the problem of generating the
form of a radio field (intensive electromagnetic field) has to be solved
foreseeing a possibility of employing 3 D GIS data. The article provides
technique for simulating electromagnetic field propagation using an
antenna by applying a geometrical method --generate of direct visibility
rays. The task for determining the distance of ray propagation according
to the established strength of radiation is being solved. As a result of
simulation, the points of the parameter indicating the intensity of the
electromagnetic field are obtained at the intersection with 3 D objects.
2. Review of Previous Researches
As radio wave propagation in the atmosphere is difficult to
describe, most of the created expressions employ empirically determined
factors. The application of such methods was described by R. V. Pocius
(2005) and D. Radis (2001). P. Baltrenas and R. Buckus (2009) presented
the methods and results of the measurements of indoor non-ionizing
radiation. To unify expressions employed for predicting radio wave
propagation, International Telecommunication Union recommended using the
interpretation and values of parameters predicting electromagnetic field
propagation generated from antennas for mobile cellular communications
(Propagation Data and Prediction Methods ... 2009a, b; Calculation of
Free-Space ... 1994; Propagation Prediction 2009).
The carried out simulation it is crucial to determine the value of
radiation strength of the electromagnetic field generated by the antenna
in space, in a specific direction from the antenna. According to the
traditional method, such value is the sum of radiation values of the
parameters evaluated in horizontal and vertical planes, i.e. presenting
the specific values of angles. T. Vasiliadis et al. (2005), F. Gil et
al. (2001) introduced technique for calculating the strength of antenna
signal when the significance of net values was different. L. Thiele et
al. (2009) conducted an experiment validating the fact that the
prediction was more realistic when radiation value was employed and
calculated using a traditional method in a specific direction.
Waslon et al. (2002) presented a method for simulating the
electromagnetic field based on turning radiation directivity diagrams
around axis z in the vertical plane and evaluating directivity diagrams
in the horizontal plane. Hae-Won Son, Noh-Hoon Myung (1999) described a
method of hybrid 3 D ray simulation--the combination of geometrical and
imagery methods.
3. Algorithm Description
This section describes an algorithm for predicting the value of
electromagnetic field radiation generated by the antenna. The
geometrical method has been employed for ray simulation. Electromagnetic
field propagation has been simulated applying the method of free radio
wave propagation in space. The rays, the propagation distance of which
is determined applying limited signal strength, have been simulated by
the algorithm. The strength is selected according to the receiver or
other characteristics of the task being solved.
Initial data on calculation cover the coordinates of antenna centre
x, y, z, the direction of the most intensive radiation (azimuth),
antenna tilt in vertical and horizontal planes of the directivity
diagram, antenna radiation rate, effective radiated power of the
antenna. The following expressions are employed for conversion between
the effective isotropic radiated power of the antenna (EIRP) and the
effective radiated power of the antenna (ERP):
EIRP (dBw) = ERP (dBw) + 2.15, (1)
EIRP (dBm) = ERP (dBw) + 30. (2)
Wave length is calculated according to the traditional formula:
wave length = speed of light / frequency.
Equivalents to every position in the horizontal plane of the
directivity diagram are traced in the vertical plane of the same
diagram. When applying the known values of antenna orientation and the
angle of tilting for the obtained values, the direction of the running
ray is determined in space.
Ray propagation is simulated according to the calculation of the
free propagation of radio waves in space:
L = 20 log (4[pi]d/[lambda]), (3)
where L-propagation loss (dBm); d-propagation distance (m);
[lambda]-wave length (m).
The limit value of the strength of receivable radio signal
[E.sub.lim.] is selected empirically. Limit value depends on the solved
task when the evaluation of radio signal strength of a specific value
has no sense, i.e. when receiver sensitivity is lower than signal
strength in the area of measurement. After selecting value [E.sub.lim.],
limit loss of signal propagation in space is calculated as follows:
[L.sub.lim.] = EIRP - [E.sub.lim.] - [L.sub.dir.], (4)
where [L.sub.lim.]--limit loss of signal propagation in space
(dBm); EIRP--effective isotropic radiated power of the antenna (dBm);
[E.sub.lim.]--the limit value of receivable radio signal strength (dBm);
[L.sub.dir.]--loss of signal propagation in space in direction n (dBm).
The loss value of signal propagation in direction n is calculated
by summing up loss values in horizontal and vertical planes:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
where [L.sub.dir.]--the loss of signal propagation in direction n
(mW); [L.sub.horiz.]--the loss of signal in direction n in the
horizontal plane (dBm); [L.sub.vert.]--the loss of signal in direction n
in the vertical plane (dBm).
Maximum ray length is calculated in case of no obstacles:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
where [lambda]--wave length (m); [L.sub.dir.]--the loss of signal
propagation in direction n (dBm).
The determined parameters are sufficient to calculate coordinates
x, y, z at the end of the ray. As the task requires determining the
points of ray intersection with objects, 3 D spatial analysis is applied
to the other part of the algorithm. It is traced, whether the ray
intersects any of the adjacent objects (for instance, the building). In
order to reduce the number of calculations, first, all the buildings
intersected by the 2 D ray are determined. During the next stage, all
defined buildings are checked-coordinates x, y, z of the nearest 3 D
intersection point are searched (Fig. 1).
[FIGURE 1 OMITTED]
The parameters required for further calculations are established
for every determined point: the loss of radiated power up to the
intersection with the object, radiated power at the intersection point,
the diameter of the circle of the intersection with the object, distance
to the antenna, antenna coordinates x, y, z.
[L.sub.int.] = 20Log10(4[pi]) x [d.sub.min]/[lambda], (7)
where [L.sub.int.]--the loss of radiated power up to the
intersection with the object (dBm); [d.sub.min]--wave length to the
nearest obstacle (m); [lambda]-wave length (m).
[E.sub.int.] = EIPR - [L.sub.int.] - [L.sub.dir.], (8)
where [E.sub.int.]--radiated power at the intersection point (dBm);
EIRP-effective isotropic radiated power of the antenna (dBm);
[L.sub.int.]--the loss of radiated power up to the intersection with the
object (dBm); [L.sub.dir.]--the loss of signal propagation in space in
direction n (dBm).
2r = sin([pi]/180)2[d.sub.min], (9)
where r is a ray, given that rays are radiated every 1[degrees] in
vertical and horizontal planes; [d.sub.min]--ray length to the nearest
obstacle (m).
4. Experimental Calculations
Hygiene Norms HN 80:2011 stipulate that the common flow density of
microwave electromagnetic radiated energy in residential and work
environments, which not related to the sources of electromagnetic
radiation where frequency band varies from 450 MHz to 900 MHz, 1,800
MHz, 1,900 MHz, 2,100 MHz and 2500 MHz, shall be not more than 10
[micro]W/[cm.sup.2]. The plan of the radio communication base station
and locality adjoining in the radius of 300 m is analysed for
determining the sanitary protection zone and specific conditions for
land use. The net flow density of the electromagnetic field generated by
all receivers is calculated at a height of 2 m above the ground surface
and roof, the place where transmission antennas are mounted as well as
at the central level of the windows of an upper floor of the residential
building and at the central level of the windows closest to the
available residential or public purpose buildings.
The aim of the conducted experiment is to evaluate the suitability
of the created algorithm to predict the strength of the electromagnetic
field. The simulation of ray propagation requires considering a limit
value of ray propagation that is significant for evaluation in this
task. One 53.7 dBm power transmitter operating at a distance of 300 m
generates a signal of -31.38 dBm power. Thus, it is possible to
calculate the generated flow density of the electromagnetic field at a
distance
s = 4[pi]p/[[lambda].sup.2], (10)
where s--flow density of the electromagnetic field (W/m2);
p--signal power at the point of measurement (W); [lambda]--wave length
(m). We obtain that the flow density of the electromagnetic field of
0.008 [micro]W/[cm.sup.2] would be generated at a distance of 300 m. In
the worst case, when the rays of 30 transmitters enter the same object,
the flow density of the electromagnetic field shall not exceed 0.25
[micro]W/[cm.sup.2] measuring at a distance of 300 m. This empirically
bases that there is no sense to examine ray propagation in case of a
signal weaker than 31.38 dBm power.
Directivity diagrams of mobile cellular communications antenna
AV2098 (Fig. 2) provided by manufacturer's Trivec-Avant were
employed for testing the algorithm.
[FIGURE 2 OMITTED]
The parameters employed for simulating radio waves include the
minimum power of the receivable signal [P.sub.min]--31 dBm, frequency
f--900 MHz, antenna height H--148.5 m, antenna EIPR--50 dBm. Determined
intersection points of rays, building walls and power parameters of the
electromagnetic field are shown in Fig. 3.
[FIGURE 3 OMITTED]
88 (calculating different frequencies used in one antenna) radio
antennas for mobile cellular communications have been employed in the
experiment. The arrangement of antennas is provided in Fig. 4. The aim
of the experiment is to determine the areas in space where rays enter
from the biggest number of antennas and to calculate the predicted flow
density of the electromagnetic field.
The rays (Fig. 5) of radio wave propagation of 88 antennas have
been simulated employing the above described method thus determining the
intersection points (Fig. 6) of rays and building facades. Obstacles
(Fig. 7) have been considered for simulating radio ray propagation. If
several intersection points (next to each other) enter a specific facade
area from different antennas, they may be summed up, given that several
antennas radiate into the same area. For this purpose, the points are
sorted according to their dependence on building facades and taking into
account the fact that the signal enters from several antennas. The
maximum signal power generated from every antenna has been determined.
The calculations of EML strength are provided in Table 1.
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
Calculation results show that, in case of researched building
facades, the predicted strength of the electromagnetic field is between
0.2 and 0.4 [micro]W/[cm.sup.2].
5. Conclusions
The established method for predicting the strength of the
electromagnetic field allows foreseeing EML next to building facades.
Parameters affecting prediction accuracy, i.e. antenna orientation,
height and target position, now is characterize with low accuracy.
Orientation errors were not known during the experiment; the established
height error is about 2 m and the established target position errors
make up to 20 m. In order to perform monitoring EML in the nearest
antenna zone, the quality of parameters has to be additionally
controlled.
The quality of 3 D geometry expressing obstacles to radio rays is
another important factor affecting the accuracy of EML prediction. The
performed experiment has determined that 3 D geometry created based on
laser scanning from the air (minimum 1 point [m.sup.2]) is suitable for
simulation, although the structures, on which antennas are mounted, have
to be simulated more precisely. Thus, the establishment of nonexistent
obstacles to ray propagation in the locality is prevented.
The experiment has demonstrated 3 places where rays from 5-6
antennas enter building facades in the near zone of the antennas (at a
distance of about 300 m). Net predictable EML generated by all antennas
amounted to 0.4 [micro]W/[cm.sup.2]. The simulated results allow
certifying it is purposeful to perform EML monitoring by measuring EML
in the planes of neighbouring building facades.
Radio rays (receivable [P.sub.min] = 31 dBm,) simulated in the
locality of the experiment do not form the intersection with ground
surface (in the height of + 2 m). This shows that the value of EML on
the ground surface must be close to 0, because during simulation, radio
ray reflection from surfaces has not been considered.
Research has disclosed that antenna orientation and position have
the greatest affect on the EML value of neighbouring building facades.
Critical values of EML may be attained, only if a big amount (due to the
transmitters of different power and different distances between antennas
and buildings, it is impossible to predict a specific number) of
antennas is oriented into one and the same building facade. In order to
prevent such situations when installing new antennas and to adjust
orientation parameters of the available antennas, it is necessary to
perform EML monitoring.
doi: 10.3846/20296991.2012.728342
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Zilvinas STANKEVICIUS received his PhD in Measurement Engineering
from Vilnius Gediminas Technical University in 2000. He has earned his
diploma in Geodesy in 1993 and MSc in Measurement Engineering in 1995.
Since 2000 he has been actively involved in teaching and scientific
research. Since 2005, he has been employed as the head of Digital
Cartography Division at Municipal Enterprise "Vilniaus
planas". The author of more than 20 scientific articles and two
textbooks. Research interests include spatial data infrastructures,
cartographic information management and visualization, sustainable
development, spatial analysis in 3 D space.
Zilvinas Stankevicius
Department of Geodesy and Cadastre, Vilnius Gediminas Technical
University, Sauletekio al. 11, LT-10223 Vilnius, Lithuania
E-mail: zilvinas.stankevicius@vplanas.lt
Received 06 June 2012; accepted 21 September 2012
Table 1. Calculation of the predictable value of EML
Facade Signal receivable Maximum power next
from antennas, units to the facade, mW
1 5 0.005
2 5 0.006
3 6 0.002
Facade EML generated by one Net EML [micro]W/
antenna, [micro]W/ [cm.sup.2] <0}
[cm.sup.2].
1 0.06 0.3
2 0.07 0.4
3 0.03 0.2
