Dr.sc.ing., senior researcher Jelena Caiko Cooperation and

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Ražošanas procesu datorvadība
Experiance in MATHEMATICAL MODELS
OF RADIO WAVE PROPAGATION
IN WOODLAND FOR MOBILE COMMUNICATION SYSTEMS
Yelena CHAIKO
•
Thus, problem of mathematical modelling and experimental researches of radiowaves
propagation in forest is an actual problem.
The purpose of this work consists in carrying out complex researches of
radiowaves propagation for a decimeter range in large forests for base
development when designing cellular systems for mobile communication in Europe;
construction of the mathematical models determining parameters of the forest
environment; the description of the basic mechanisms of radiowaves propagation for
decimeter range in conditions of forest depending on distance between a point of
reception and base station, in view of real parameters of large forests:
dielectric permeability of trees, the sizes, density, humidity, wind loadings and so forth.
The comparative analysis theoretical and experimental researches of propagation UHF of
electromagnetic waves in large forests.
For an estimation of adequacy of the received theoretical and experimental results on propagation
UHF of electromagnetic waves to large forests it is necessary to lead their comparative analysis and
as to use the experimental results received by other authors.
1. The comparative analysis of experimental results and the models developed in work.
On diagram.1 numerical values median the normalized levels of capacity of radio signals P (d) in
locations MS as functions from distance between MS and BTS - d for working frequency of 900 MHz
provided that electromagnetic waves emitted- are vertically polarized by antenna BTS are submitted.
A level of a signal in a point of
reception MS P(d) (dBm)
Theoretical models
(1) The onebeam model
0
-20
0
2
4
6
8
(2) The twobeam model
-40
-60
(4) The model
for the mixed
path
-80
-100
Distance betw een MS and BTS d(km )
(3) The model
of diffraction
on a wedge
diagram 1. Dependences of changes of numerical values of the normalized levels of an accepted signal on average frequency
of 900 MHz received on a basis theoretically of models.
a) The one-beam model submitted by a curve (1), gives the following numerical values of function P (d):
Distance between MS and BTS d
(km)
A level of a signal in a point of reception MS
P (d) (dBm)
0.5
-51.225
1
-57.246
2
-63.266
3
-66.788
4
-69.287
5
-71.225
6
-72.809
(1) The onebeam model
A level of a signal
in a point of
reception MS P(d)
(dBm)
The one-beam model
0
-10 0
1
2
3
4
5
6
7
-20
-30
-40
-50
-60
-70
-80
Distance between MS and BTS d (km)
The two-beam model submitted by a curve (2), gives the following numerical values of function P (d):
Distance between MS
and BTS d (km)
A level of a signal in a point of reception MS P (d)
(dBm)
0.5
-42.552
1
-54.539
2
-66.634
3
-73.678
4
-78.675
5
-82.552
6
-85.719
A level of a signal
in a point of
reception MS P(d)
(dBm)
The tw o-beam m odel
0
-20 0
-40
-60
-80
-100
1
2
3
4
5
6
7
Distance betw een MS and BTS d
(km )
(2)The tw o-beam
model
At falling radiowaves on a large forest when the marge of a forest is located on distance from base send-receive
station on 1 km, values of a level of capacity in a point of reception pay off under the formula:
P(d) = P0 (d) + (-α⋅∆d),
Comm. Tower
Tree
Tree Tree
Tree Tree
Tree
2 km
Where P0 (d) - a level of capacity, defined for one-beam model dBm in a point d0=1km
A level of a signal in a point of
reception MS P (d) (dBm)
α - effective value of running factor of attenuation of the corresponding determined model forests - or α = 0.162 dB/km
(for layered structure), or α = 0.34 dB/rm - for a large forest in which trees as spheres are located by correct image in
space, ∆d - a difference of distances between position of a point of reception and position of a marge of a forest
(d0=1km), km.
For these cases of dependence of functions P0(d), P1(d) and P2(d) are submitted on diagram 12 as curves 0,1 and 2,
and numerical values of function P (d) in the table:
0
-10 0
5
10
-20
-30
(1) The onebeam model
Distance
betwee
n MS
and
BTS d
(km)
A level of a signal in a point of reception MS P (d) (dBm)
P1(d) Layered forest
P2(d) Sphere trees
1
-62,586
-62,942
2
-65,768
-66,302
3
-67,927
-68,639
4
-69,525
-70,415
5
-70,769
-71,837
6
-62,586
-62,942
(2)Layered
forest
-40
-50
(3)Sphere
trees
-60
-70
-80
Distance betw een MS and
BTS d(km )
The determined model for the mixed line, submitted the curve 3 diagram. 13, gives the following numerical values of function P (d):
Distance between MS
and BTS d
(km) MS
A level of a signal in a point of reception
MS P (d) (dBm)
0.5
-56.881
1
-63.062
2
-69.156
3
-72.702
4
-75.212
5
-77.157
6
-78.745
A level of a signal in a point
of reception MS P(d) (dBm)
The model for the mixed path
0
-20
0
1
2
3
4
5
6
7
-40
(3) Mixed path
-60
-80
-100
Distance between MS and
BTS d(km)
The model of diffraction on a wedge, submitted the curve 4 diagram 14., gives the following numerical values to function P (d):
A level of a signal in a point of reception
MS P(d) (dBm)
0.5
-72.637
1
-78.893
2
-85.029
3
-88.589
4
-91.107
5
-93.056
6
-94.647
The model of diffraction on a wedge
A level of a signal in a
point of reception MS
P(d) (dBm)
Distance between
MS and
BTS d
(km)
0
-20
0
1
2
3
4
5
6
7
-40
-60
-80
-100
Distance betw een MS and BTS
d(km)
(4)Diffraction on a
w edge
Thus, from comparison of functions P (d) for theoretical models it is visible, that:
- For two-beam model at small distances from MS up to BTS:
dmax< 4h1h2/[λ (2π-φ)] in comparison with one-beam model fluctuations of a level of a signal are observed, and with increase
in distance d falling of values of function P (d) submits Vvedensky to law (shift downwards on a level of capacity makes
about - 9dBm.);
For the determined models forests (i.e. for layered and spherical structures) arises falling a radio signal, since a marge of a forest
at its propagation inside of a forest, thus shift downwards on a level of capacity makes - for layered - 0,680 dBm.
for spherical - 0,324 dBm.);
For a case of diffraction on a wedge when a radiowave difracts on edges of trees on a marge of a forest, the level of a radio signal
in comparison with free propagation falls approximately on 20 dBm. (i.e. on wide highway located between large forests the level of
a radio signal will be lower on 20 dBm in comparison with free space);
-For the mixed lines when radiowaves are distributed a part of a line in free space, then inside a large forest, further again in free space,
etc., i.e. there is a heterogeneous (non-uniform) attenuation of a radio signal on a line and it should be reflected at calculation by use
of various models of propagation: on one part of a line one-beam, on another - determined with effective factor of attenuation, on the third
part of a line model of diffraction on a wedge, etc.
On fig. the line of measurement which becomes attached to discrets d, km = 0.5., 1.0., 2.0., 3, 4, 5,6 is schematically displayed.
100 m
0m
1000 m
2000 m
3000 m
4000 m
5000 m
At calculation it was supposed, that or the radiowave is distributed in a zone of direct visibility, or in a point of reception there
comes the sum of the reflected and direct wave, or the radiowave is distributed inside a forest, or difracts on a wedge, or the
radiowave is distributed in the mixed line.
In table are submitted values levels of capacity experimentally measured in various points of reception with change of distance
from MS up to BTS
(d = 0.5., 1.0., 2.0., 3, 4, 5,6) km.
Theory and experiment
Levels of a radio signal in a point of reception MS P (d) (dBm),
received on a basis
Experiment
0.5
-53
1
-55
2
-75
3
-71
4
-71
0
A level of a signal in a
point of reception MS
P(d) (dBm)
Distance between MS and BTS
d (km)
-20
0
1
2
3
4
5
6
7
-40
-60
-80
-100
5
-64
Distance between MS and BTS d(km)
(1)The one-beam model
(2)The tw o-beam model
(3)The mixed path
(4)Diffraction on a w edge
(5)Experiment
(6)Layered forest
(7)Shrere trees
6
-85
Apparently from diagram experimental points get in a field of curves received theoretically and in various points can or coincide
with the points received at calculations on the basis of various theoretical models of radiowaves propagation, or strongly differ.
Conclusion
•
•
•
•
•
•
•
•
1) On distance d = 0.5km MS from BTS experimental value coincides with the value received on the basis of calculation
on one-beam model (-53 dBm).
2) On distance of 1 km the level of a signal at experiment has made (-56 dBm), that is higher, than for value received on
the basis of one-beam model (-57,246 dBm), that apparently, speaks that the resulting field in a point of reception
grows out interferences of two or several radiowaves.
3) On distance 2 km from BTS sharp falling a level of a signal on the first 100м is observed, thus the radiowave was
distributed inside a large forest and the level of a radio signal made (-75 dBm), i.e. was lower than for free propagation
on 12 dBm. This value also is lower, than that follows from the determined models (layered - (-63.428 dBm) and
spherical (-63.606 dBm) structures) for the given distance that testifies to sharper attenuation of radiowaves in a forest
at through propagation. At the further deepening of the transmitter in a forest the level of a signal decreased according
to weaking of a wave in free space.
3) On distance from 3 kms up to 4 kms value of levels of a radio signal - for experiment made - 71 dBm, for one-beam
model - 69,287 dBm, for determined models-68,639 dBm (spherical structure)-67,927 dBm (layered structure), for the
mixed line-72,702 dBm i.e. experimental values got in area limited to a curve for one-beam model and the mixed line.
4) On distance from 4 km up to 5.5 km values of levels of radio signals exceed levels for one-beam model and their value
make for experiment - 64дБм, for one-beam model - 71 dBm, for determined models-69,525 dBm (layered structure)
and-70,415 dBm (spherical structure).
Let's note, that dependence of a field level on range exponential, and for small depth of penetration into a forest the
degree of attenuation is high, with increase in depth of penetration the degree goes down.
The analysis of results of experimental and theoretical researches of radiowaves propagation in mobile communication
systems has shown, that radiowaves propagation in conditions of a forest, is accompanied by effects of repeated
reflection, diffraction, dispersion of waves that results in formation of complex spatial propagation of an
electromagnetic field, thus values effective median levels get in a field of values received on the basis of theoretical
models.
The divergence of the settlement and measured values naturally, nevertheless, character of dependence of weaking
from range between a radiator and place of acceptance is defined by theoretical expression correctly.
•
2. The comparative analysis of work results and the results received by other authors on radiowaves propagation in large forests on
frequencies of 900 MHz close to average frequency (800 - 1200 MHz)
•
In communication with distinction experiments of the author and other authors as on height of base stations antena , and on density
and humidity of forest and a kind of the line, the received values of weaking of a signal differ from each other.
However results encourage that the developed models allow at designing macrocells in which there can be large forests, use the
determined models and for an estimation of integrated influence forest areas on levels of a signal in points of an arrangement of mobile
stations when they move inside a forest.
Statistical models allow to describe disseminating properties of large forests in a decimeter range. On the basis of the theory of repeated
waves dispersion it is shown, that for the description of an average field and intensity of a direct wave the model as a homogeneous
layer with effective electric parameters is applicable. These parameters are defined by density, the average sizes, values of complex
dielectric permeability of trees, and also frequency of radiation. The direct wave gives the basic contribution to intensity of an accepted
signal.
Results of work allow to predict conditions of a radio communication in forest areas depending on length of a line, heights of antena,
frequency, parameters of a large forest. Besides the received results can be applied at the decision of the inverse problems necessary for
research of forests by radiophysical methods.
•
•
•
Dreaming laboratory
Dreaming results
Nobel Prize Winners (1909)
VILHELM
OSTVALD
FOUNDER OF PHYSICAL CHEMISTRY
PROFESSOR OF RIGA TECHNICAL
UNIVERSITY
(1881 – 1887)
THANK YOU!
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