1 DETERMINATION OF RAIN ATTENUATION OF MICROWAVE SIGNALS IN AKURE, ONDO STATE USING THE INTERNATIONAL TELECOMMUNICATION UNION OF RADIO COMMUNICATION (ITU-R) MODEL BY UMEH, CHIBUIKE DOMINIC PG/M.Sc./O7/42856 DEPARTMENT OF PHYSICS AND ASTRONOMY UNIVERSITY OF NIGERIA, NSUKKA JUNE, 2010
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1
DETERMINATION OF RAIN ATTENUATION OF
MICROWAVE SIGNALS IN AKURE, ONDO STATE USING THE
INTERNATIONAL TELECOMMUNICATION UNION OF RADIO
COMMUNICATION (ITU-R) MODEL
BY
UMEH, CHIBUIKE DOMINIC
PG/M.Sc./O7/42856
DEPARTMENT OF PHYSICS AND ASTRONOMY
UNIVERSITY OF NIGERIA, NSUKKA
JUNE, 2010
2
DETERMINATION OF RAIN ATTENUATION OF
MICROWAVE SIGNALS IN AKURE, ONDO STATE USING THE
INTERNATIONAL TELECOMMUNICATION UNION OF RADIO
COMMUNICATION (ITU-R) MODEL
A THESIS PRESENTED TO THE DEPARTMENT OF PHYSICS AND
ASTRONOMY, UNIVERSITY OF NIGERIA NSUKKA IN PARTIAL
FULFILMENT OF THE REQUIREMENT FOR THE DEGREE OF MASTER OF
SCIENCE
BY
UMEH, CHIBUIKE DOMINIC
PG/M.Sc./O7/42856
JUNE, 2010
3
APPROVAL PAGE
Mr Umeh, Chibuike Dominic, a postgraduate student in the Department of
Physics and Astronomy with Registration number PG/M.Sc./07/42856 has
satisfactorily completed the requirement in course and research work for the
degree of Master of Science (M.Sc.) in Space science
is the worst attenuated polarized tilt angle on paths, rain rates and frequencies
of consideration.
Increasing the elevations angle of the antenna would reduce the attenuation
value in the earth-space and surface height alteration would have a negligible
effect. While in the horizontal/nearly horizontal path, increasing the elevation
angle would have no effect while reducing the link distance would reduce the
attenuation value
16
CHAPTER ONE
GENERAL INTRODUCTION:
Electromagnetic wave propagation as described by Maxwell’s equation is fast
becoming an area of deep concern. This is because wireless systems are
becoming more and more ubiquitous especially in Nigeria.
For most Radio Frequency (R.F.) propagation modeling; it is difficult to
visualize the electromagnetic wave by a ray [The Poyinting Vector (P)] in the
direction of propagation with respect to its Electric (E) and Magnetic field (H)
(P = EXH). Thus, in free space and air; electromagnetic waves are isotropic in
propagation with its velocity approximately equal to the speed of light; making
wave signals very vulnerable to alteration (Seybold, 2005 and Crane, 2003).
This disruption comes in form of attenuation. Attenuation is the decrease in
the intensity of a signal as a result of absorption of energy and/or scattering
out of the path of the detector. Any slight disruption is worrisome to users and
can even cause some amount of insecurity to the economy.
1.1 ELECTROMAGNETIC WAVE PROPAGATION
This is done in line of sight (LOS) propagation or beyond LOS propagation. In
LOS propagation, we consider the curvature of the earth as a fundamental
geometric unit. This helps us to determine the radio horizon or link distance (d)
for each antenna, rhd 2 where h is the height of the antenna and r ; the
radius of the earth. The curvature of the earth will be corrected using “4/3
17
earth approximation”. Thus the link distance becomes hd 2 . The
atmosphere typically bends horizontal radio frequency waves downwards due
to the variation in atmospheric density with height.
Beyond LOS propagation; there are several means of electromagnetic wave
propagation, which depends on frequency. Indirect propagation is often used.
This includes diffraction, refraction and/or multipath reflection. Diffraction and
refraction are the bending of electromagnetic waves on the sight of a blockage,
and due to in homogeneity in the medium respectively; while multipath is the
effect of reflection from multiple objects in the field of view, which can result in
many copies of the wave arriving at the receiver.
The efficiency of indirect propagation depends on the amount of margin in the
communication link and the strength of the reflected or diffracted signals. The
operating frequency has a contributing factor. Lower frequencies work best.
High frequency (HF) can penetrate buildings and heavy foliage quite easily.
Very High Frequency (VHF) and Ultra High Frequency (UHF) can penetrate
building and foliage also; but to a lesser extent. At the same time; VHF and
UHF will have a greater tendency to diffract around or reflect/scatter off of
objects in the path. Above UHF, indirect propagation is not used. So,
microwave signals are being propagated using LOS means
18
TABLE 1.00: The mode of propagation of wave using the International
Telecommunication union (ITU)’s nominal band designation.
FREQUENCY BAND
FREQUENCY RANGE
WAVELENGHT IN AIR
MODE OF PROPAGATION AND EXAMPLES
ELF < 3KHz >30KM Ground–wave and Beyond LOS
VLF 3 – 30KHz 30KM- 10KM Ground–wave and Beyond LOS
LF 30 – 300KHz 10KM-1KM Ground–wave and Beyond LOS
MF 300KHz -3MHz 1KM-100KM Ground–wave and Beyond LOS
HF 3 – 30MHz 100M-10M Ground and sky-wave but very unreliable e.g. citizen radio
VHF 30-300MHz 10M-1M For most part, through LOS and ground bounce propagation. They are sky waves and space waves e.g. Broadcast FM radio, aircraft radio, cellular/PCS telephones and Global positioning system (GPS).
UHF L S
300MHz-3GHz 1-2 GHz 2 – 4 GHz
1M-10cm Strictly LOS. They are space waves e.g. TV broadcasting and mobile phones
Strictly LOS. They are Microwaves (3- 30 GHz), satellites communication links and millimeter wave, though still under research, it is currently used in communication through a centrally located elevated repeater.
19
Microwaves are mainly used for point-to-point communication; since for use on
earth; the range of transmission is limited to LOS. Its large bandwidth is highly
advantageous due to its large capacity for transmitting information at several
polarization angles. The polarization tilt angle of most interest is linear (vertical
or horizontal) and elliptical or circular.
Vertical polarization tilt angle is when the electric field is vertical. It is produced
by the open end of a rectangular waveguide, whose narrow dimension is
vertical and whose broad face is horizontal
(http://www.satsig.net/polangle.htm). A vertical probe sticking through the
broad face of the guide typically energizes the waveguide. Inside the waveguide,
a voltage is between the centerlines of the two broad faces that forms the
vertical electric field. Horizontal polarization tilt angle is when the electric field
is horizontal unlike in the vertical polarization tilt angle. The open end of a
rectangular waveguide whose narrow dimension is horizontal and whose broad
face is vertical also forming the horizontal field produces it. While circular
polarized tilt angle lies between the vertical and horizontal field.
1.2 ATMOSPHERIC AND IONOSPHERIC EFFECTS OF RADIO WAVES
The electric field (E) depends not only on the flux density; but also on the
permittivity of the material or environment through which the wave is
propagating. Along the earth’s surface, electromagnetic waves is affected by
1. Proximity of the ground and the spherical shape of the earth.
20
2. In homogeneity of the troposphere
3. Effects of ionosphere
For the purpose of propagation, the atmosphere can be divided into three
regions (in ascending order): ionosphere, stratosphere and tropopause. For
Radio frequency (RF) propagation, the major effects from the atmosphere
include Refraction/reflection, scattering and absorption/attenuation. With the
exception of refraction; these effects are all minimal below 30 MHz. Between
30 MHz and 1GHz, refraction/reflection is the primary concern. Above 1 GHz,
Attenuation and Atmospheric multipath becomes a dominant factor. Rain
attenuation is the dominant effect of microwave signals within the tropics. The
minimum frequency for this attenuation is different from many researchers. It
starts from frequencies above 10GHz (Maitra and Chakravarty, 2002 and
Crane, 2003). Whereas, according to Seybold (2005), “rain fade starts to
become a concern above 5GHz and; by 20 – 30 GHz, it can be a significant
factor upon the link distance and the geographical location”. To clear doubts,
ITU gave 5GHz as a minimum frequency for rain attenuation (ITU-R 2001).
The unique thing is that they all fall within the microwave region.
Refractive and scattering effects of the atmosphere include troposcatter,
temperature inversion and ducting depending on the direction of
scattered/reflected rays. Atmospheric multipath causes signal enhancement/or
signal attenuation depending on the product of the interaction between the
incident and reflected waves. It occurs while there is still a direct line of sight;
21
or if several paths exist. This effect is predominant in high humidity areas
during nighttime hours.
Ionosphere propagation is essential to sky-wave propagation and provides the
basis of nearly all High frequency communications beyond the horizon. The
ionosphere consists of several layers of ionized plasma trapped in the earth’s
magnetic field. Thus; creating an electric field (due to imperfect dielectric). This
causes refraction, attenuation, depolarization and dispersion due to frequency
dependent group delay and scattering (Seybold, 2005). Attenuation of signals
at the layer is very predominant; and could be predicted by the use of complex
permittivity from field theory
This attenuation of radio signals is mainly witnessed between 45 – 55 miles in
the ionosphere; and is too high to prevent meaningful communication. It
absorbs radio frequency from 0.3 to 4 MHz. Below 300KHz, it will bend or
refract R.F. waves. Whereas; R.F. above 4 MHz will be passed unaffected. This
determines the signal that enters the atmosphere where more attenuation
takes place.
1.2.1 Atmospheric Attenuation
The atmosphere consists of various gaseous molecules, which attenuates
electromagnetic energy passing through it. In the microwave region, oxygen
and water vapor has the highest effect. Atmospheric losses depend mainly on
22
pressure, temperature and water content. This invariably is dependent with
location, altitude and the path slant angle. Determination of attenuation effect
is computed using these parameters. Local atmospheric measurements along
with the ITU-R model are used in this research.
For terrestrial links; this absorption is characterized as specific attenuation,
which can be applied to path distance to determine the total attenuation. It is
related as dA a . Where, d is the link distance (km) and a is the specific
attenuation (db) of the atmosphere. We also consider the variation in altitude
for slant path by treating the atmosphere as a series of horizontal layers with
different temperature, rainfall and pressure. The actual absorption is a
function of altitude. This simplifies computation, and makes a good estimate
of the resulting attenuation.
Various forms of water, which affect propagation at various frequencies,
include precipitation, water vapor, and suspended water droplets forming
clouds or fog. A comprehensive physical collection of data of these hydrometers
is used to determine their effects on microwave signals. The micro Rain
Radar/Disdrometer is used to collect the rain-rate data used for this study.
The Radar has already taken care of the effects of wind and drop size
distribution; and has a very high time resolution.
23
1.3 PURPOSE OF STUDY
The need for employing higher frequencies, especially in new broad band
services, has therefore encouraged research into precipitation caused
attenuation (Walter et al., 2002). A critical look at Table 1.00 shows that there
is congestion of the lower frequency spectrum. There are technological
advances and researchers aim at increasing deployment of higher microwave
bands. This seems to be attractive and expedient. On the other hand, it
subjects microwave to more adverse effects of atmospheric condition. Nigeria
Sat 1 which is launched at Low Earth Orbit is a satellite operating in S-band
(2.6-3.95GHz) and the recently launched Geosynchronous Earth Orbit (GEO)
satellite (NIGCOMSAT-1) though collapsed, was operating at L band (1.12-
1.7GHz), C band (3.95-5.85GHz), Ku band (12.4-18GHz) and Ka band (20-
40GHz). It calls for active research by purely Nigerian Scientists. Nigeria Sat-1
may experience problems of low elevation while NIGCOMSAT1 will be exposed
to increased rain-related signal degradation especially in Ka band. Nigeria has
a tropical and equatorial region, which is characterized by dominant rainfall.
Rain is the major attenuation factor of various communication signal
of GHzf 10 . So, for efficient utilization of the microwave bandwidth during
rainfall, we need to determine the relationship between this attenuation effect
and the bandwidth at various rain rate, frequency, link distance, elevation
angle of propagation, communication path and its polarized tilt angle of
reception at a particular location of interest. To achieve this, we seek a model
24
of wide acceptability and good result which encompasses our local rain
parameters to determine the extent of rain attenuation of these signals.
Researchers who based their data on temperate countries developed most of
the already existing models used by designers. Rain in these regions is mostly
of stratified structure, which is generally “light” with relatively large rain cells
diameter. However, in the tropics, rain is from convective rain cells, with
relatively small diameters, often resulting in heavy down pour for short period.
So, there is need for us to use our indigenous data for models that will suit our
region.
The goal of propagation modeling is often to determine the probability of
satisfactory performance of a communication system (Seybold, 2005). It is a
major factor in communication network planning. If the model is too
conservative, excessive cost may be incurred. If too liberal, it will result to
unsatisfactory performance. Thus, the fidelity of the modeling must fit the
intended application. The ITU R model is a good example because of its wide
acceptability and local atmospheric data consideration. The value permits the
designer to tailor the communication system design to the intended
environment.
25
1.4 LIMITATION OF STUDY
This research does not include details of meteorological studies, types of
rainfall (convectional, stratified and relief, etc) and environmental features.
Antenna size, metallic properties and design which influences signals during
rainfall are not considered. It also does not include details of attenuation
involved in ionosphere propagation for earth space path; and exact solution to
this hazard.
26
CHAPTER TWO
REVIEW OF LITERATURE
2.1 RAIN ATTENUATION OF MICROWAVE SIGNALS
The term microwave strictly refers to electromagnetic waves of frequency one
GHz and above, but generally VHF radio waves (30 – 300) MHz may be implied.
(Oyedum, 2007). Attenuation by rain can be caused by rain anywhere along the
path where the rain temperature is warm enough to maintain liquid raindrops.
In terms of temperature; the brightness temperature Ta(k) has been converted
to total Attenuation A (dB) using the relation.
am
cm
TTTTA
10log10 (2.10)
Where Tm is the mean atmospheric temperature and Tc is the equivalent of the
cosmic background radiation (2.7k). For tropical latitudes (which Nigeria falls
into) like Calcutta; the value of Tm is found to be higher than that of temperate
latitudes due to higher temperature and large water vapor (Karmakar et al.,
2002).
Rain attenuation is by far the most important of losses for frequencies above 10
GHz (Mandeep and Allnut, 2007; Animesh and Kanster, 2005; Seybold, 2005;
Crane, 2003; Charles, 2002; Walter et al., 2002 and Crane, 1982). ITU has
recommended that rain attenuation of signals begin from 5 GHz and above (ITU
– R 2001). Rain is liquid precipitation, as opposed to other kinds of
precipitation such as snow, hail and sleet (http://en.wikipedia.org/wiki/Rain).
27
It requires the presence of a thick layer of the atmosphere to have
temperatures above the melting point of water near and above the earth’s
surface (On earth, it is the condensation of atmospheric water vapor into drops
of water enough to fall often making it to the surface. The need to know the
properties of rain, which causes such attenuation and its behavior, became a
major concern to most researchers.
Adenuga et al. (2005) and Ugai et al. (1997) have shown that the general
properties of rain drops which determine such attenuation include their fall
velocities, drop deformations and fitted statistical shape functions of Drop size
distribution (DSD). Drop size distribution is the frequency distribution of drop
sizes that is characteristic of a given cloud or of a given fall of rain.
(http://amglossary.allenpress.com/glossary/dropsizedistribution). In
convective clouds, the Drop size distribution is found to change with time and
to vary systematically with height. This distribution is one of the primary
factors in determining the radar reflectivity of any fall of precipitation. From
physical principles, it may be suggested that a true global DSD cannot exist.
This is why it is very wrong to use a general estimate for determining the fade
margin of communication instruments. The microphysics of clouds and
precipitation in Rogers and Yau (1989) explains the development of raindrops
from initial stages as cloud droplets. This is as a result of strong surface
tension in very small droplets; a free energy carrier such as aerosols must exist
in order for condensation of cloud droplets to be possible. Such aerosols can
28
for instance be dust particles, salt or pollution from industry. It is found that a
large number of aerosols will create narrow DSDs for cloud droplets, while
fewer aerosols tend to give broader DSDs. So, local geography and the available
energy in the atmosphere determine the dimension of a cumulus cloud. This
makes location, latitude, altitude and season very indispensable in determining
rain attenuation of microwave signals.
Rain rate distribution is one of the most important factors for calculating
rainfall attenuation (Mandeep and Allnut, 2007). This attenuation depends
largely on rainfall intensity R (mm/h) and rain Drop size distribution (Oyedum,
2007; Walter and Gibbins, 2002). The most effective way of obtaining the
cumulative rainfall distribution is through direct measurement. In some cases;
rain rate of some locations may not be easily accessible. This is the only
condition; we introduce rainfall models with estimation to predict rainfall rate
and attenuation distribution at location of interest.
Wei and Moayeri (1999) and the IEEE (1997) have a related approach in
estimating rain attenuation. It considers rain cell, and the diameter of the
significant attenuation of rain cell is approximately equal to 2.4mm. This is
roughly in conformation with the radar reflectivity, measurements. Walter et
al., (2002) proposed quite differently; measuring a total attenuation and
subtracting the gaseous absorption create Rain attenuation statistics
29
2.1.1 Rain Attenuation on an Earth Space Path
Earth – space paths traverse attenuating regions of liquid drops (rain) and
regions of ice and snow in the atmosphere. The ice and snow contribute little to
the attenuation and may be neglected (Crane, 2003 and Oyedum, 2007). So,
rain is the major limit to system availability.
There are two aspects of rain attenuation studies over the earth space links.
i. The instantaneous relationship between the rain attenuation and point
rainfall measurements.
ii. The statistical behavior of rain attenuation vis-à-vis rain rate at a
particular location. (Maitra and Chakravarty, 2002)
In both aspects, we lay emphasis on path attenuation. Path attenuation is
essentially an integral of all individual increments of rain attenuation caused
by the drops encountered along the path. This is a physical approach to predict
rain attenuation (Mandeep and Allnut, 2007). There are several factors that
control the rain attenuation over the earth – space paths namely rain drop size
distribution, rain height and rain cell size (Maitra and Chakaravarty, 2002).
The degree of path attenuation depends on the frequency band. Specific
attenuation increases with frequency and can be more than ten times higher at
15 GHz than 2 GHz (Crane, 2003). Thus, we consider the signal band
frequency, the satellite and its longitude, the path elevation and the receiving
polarization tilt angle. Animesh and Kanster (2005) proposed that for a satellite
30
– earth microwave link, the rapidity with which the attenuation changes,
increases when the attenuation value gets higher. This was experienced as they
determined Ku and rain attenuation observation on an earth – space path in
the India Region.
In the pursuit of rain models, rain has generally been classified as stratiform,
convective, or cyclonic. Location has everything to do with how much of this
rain affect communication link.
2.2 THE ITU-R MODEL AND OTHER MODELS
Glenn and Ailes – Sengers (2002) made use of ten models to make
comparisons. ITU–R developed in 1978 by the International Telecommunication
Union; and modified until 2001, CCIR (now ITU) 1986, Brazil model developed
by M. Pontes, Japan model developed by Yoshio Karasawa, DAH model
developed by Dissanyake, Allnut and Haudara. Two-component model
developed by R. K. Crane, Leitao Watson model developed by M. J. Leito and P.
A. Watson. Misme – Waldtenfel developed by P. Misme and P. Waldtenfel in
1975, Excell model developed by Capsoni, Fedi and Paraboni and Spain model
developed by J. A. Garcia – Lopez:
Each of these models is derived with a specific intent. The CCIR and ITU – R
models have the objective of being globally applicable across a wide range of
frequencies, elevation angles, and rain climates. The DAH model seeks to
31
improve upon the overall ITU-R model performance by modifying path profiles,
as well as adjusting the calculations across a wider range of availabilities. So
would require more parameters. Both the Japan model and Brazil model are
developed as refinements to the ITU-R model which focuses on improving
prediction accuracy. The Brazil model mainly seeks to increase accuracy for
system operating in tropical/equatorial region, but lack wide acceptability.
Recently, Adenuga et al., (2005) have stressed that rain-rates with short
integration time are of interest to system engineers. The revised two-component
model estimates rain rates of short duration using the four climates dependent
parameters probability of a cell, average rain rate, probability of debris and
average debris rain rate. This also gives a better result; but not convenient for
the tropics. The selection of model for variability must then be based on
convenience.
We observe that the ITU – R forms the basis for the development of all these
models. It has received several modifications from 1978 till date. It gives room
for local geography parameters and estimates (for inaccessible areas). Other
models are still under research and lacks general global acceptability, though
may give a better result. The more recent Bryant model (Bryant et al., 2001)
improved on the ITU R model to improve its prediction accuracy in determining
slant – path rain attenuation in tropical region. It gave a better result than the
ITU – R in tropical rain only for the earth space path (Oyedum, 2007).
32
The International Telecommunication Union of Radio communication provides
a method to calculate specific rain attenuation from rain rate, which is readily
implement able since rain rates are easily obtained (even with rain gauge). This
model is currently used by many researchers and is widely acceptable
(Mandeep and Allnut, 2007 and Crane, 1985). Though has error while
determining rain attenuation on an earth Space path in the tropical region as
observed by Glenn and Ailes – Sengers (2002). Bryant et al. (2001) developed a
rain-rate distribution prediction model based on long-term hourly rain rate
statistics and excessive precipitation data. Their model used annual
precipitation occurrence and the ratio of thunderstorm to total rainfall as
input. It was able to improve on the prediction accuracy of the ITU-R model in
determining rain attenuation on an earth space path.
The ITU-R rain attenuation prediction procedures recommend the use of rain
rates measurement made at the site of interest. Most designers did not have
the luxury of spending three to five years or several months in making rain-rate
measurements at a site before starting their design (Crane, 2003). So, they
make use of estimation values of ITU-R model, which also serves as a general
comparison for most models in some location. This increases the generality of
the model.
Hassan (2007) made use of the ITU-R model to design a communication link for
satellite reception at a frequency of 10GHz in Malaysia at a rain rate value of
33
32mm/hr. He predicted that the signal would have a high attenuation value
within the range of 4.00db to 5.00db for horizontal/nearly horizontal path and
17.00db to 21.00 db for the earth space path at a frequency of 35GHz. He gave
this range of values using the analysis he got from his rain gauge
measurement. He preferred signal reception of 5GHz because of negligible
specific attenuation.
In Nigeria, Ofoeche (1992) made use of the Ajayi-Olsen model. The only model
proposed in 1985 to encompass the country’s local climatic condition. He
determined microwave signal attenuation in Ife, Ogun State. The result showed
a high deviation (more than 20%) from the estimated ITU-R model. Irrespective
of this deviation, the model is still being appraised in Nigeria due to its purely
indigenous climatic consideration.
This model was later modified recently using the ITU-R model by Bryant et al.
(2001) to form the Bryant model. Oyedum (2007) then made use of it to
determine the topographic effects of microwave propagation in Nigeria. The
horizontal or nearly horizontal path would have a negligible attenuation effect
at each topography; while the earth-space path would have improved signal
reception at higher topography. This had a correspondence with the estimated
ITU-R model and the Brazilian model.
34
Moses et al. (2009) made use of the Bryant model to further evaluate the
properties of rain which has the highest contributing effect to signal
attenuation. They considered Drop Size Distribution, rain rate and its
temperature at the moment of rainfall. Their result showed that signal
attenuation is principally a function of rain rate.
Following these reviews, the ITU-R model and the Bryant model (recently
improved ITU-R model) would be the best models for the horizontal path/nearly
horizontal path and the earth space path respectively to analyze our data.
2.3 THEORETICAL BACKGROUND
Rain availability is essentially the percentage of time that the available rain
fade margin is not exceeded. For our ITU- R model; 0.01% Rain Rate is being
used.
2.3.1 Horizontal /nearly horizontal path;
The ITU-R MODEL for fade depth (0.01% Attenuation) gives
rdRRKAtten ...01.0 (2.11)
Where RR is the 99.99% rain rate for the rain region in mm/hr
RRK . Is the specific attenuation in dB/Km. (2.12)
d is the link distance
r is the effective path length
Computing the distance factor path length gives
35
dodr
/11
(2.13)
Where for RR 100mm/h
)015.0exp(35 RRdo M (2.14)
For RR >100mm/h, we use the value 100mm/h in place of RR.
2)]2()()([ 22 CosCosKKKKK VHVH
(2.15)
KCosCosKKKK VVHHVVHH
2)]2()()([ 2
(2.16)
Where
= The elevation path angle
KH and H = Horizontal constant from interpolated Regression Coefficients
given by ITU for different frequencies
Kv and v = Vertical constant from interpolated Regression coefficient given by
ITU for different frequencies.
= Polarization tilt angle (00,450 and 90 o) for horizontal, circular and vertical
respectively. K and depends on frequency, polarization and Drop size
Distribution. (ITU-R, 2001)
2.3.2 Earth – Space (Satellite) Path:
Satellites operate at higher frequencies. This gives room for more propagation
loses. To determine the rain attenuation of such a path; we first deduce the
Figure 4.14: Graph of fade depth for different polarization tilt angle versus elevation angle at rain rate of 32mm/hr 4.4 RESULT- EARTH-SPACE PATH A General assumption for =50 and hs=0.01km. So, Z=0.7715, L=1.8288, Lsl=1.
Figure 4.17: Graph of attenuations for different polarization tilt angle versus frequency at rain rate of 32mm/hr 4.5 THE WORST ATTENUATED CONDITION
4.5.1 Increasing the surface height of the antenna, and other parameters
remaining constant, at the worst attenuated condition.
A general assumption for, =50 So, Z=0.7715, Kn=1.2511
Re=6378.1km,D=3.3876,Dm=5.3125 and L=1.8288
Table 4.34: Attenuation value for increasing the surface height of the antenna at the horizontally polarized tilt angle. K=0.263, =0.979, Asp= 7.82 (db/km) s/n hs(km) L sl (km) A(db) 1 0.015 1.66 28.33 2 0.020 1.61 27.35 3 0.025 1.55 26.37 4 0.030 1.49 25.40 5 0.035 1.43 24.42 6 0.040 1.38 23.44 7 0.045 1.32 22.47
61
Table 4.35: Attenuation value for increasing the surface height of the antenna at the circular polarized tilt angle. τ=450, K=0.248, =0.971, , Asp=7.19(db/km) s/n hs(km) L sl (km) A(db) 1 0.015 1.66 26.04 2 0.020 1.61 25.14 3 0.025 1.55 24.25 4 0.030 1.49 23.25 5 0.035 1.43 22.45 6 0.040 1.38 21.55 7 0.045 1.32 20.65 Table 4.36: Attenuation value for increasing the surface height of the antenna at the vertically polarized tilt angle. K=0.233, =0.963 , Asp=6.56(db/km) s/n hs(km) L sl (km) A(db) 1 0.015 1.66 23.77 2 0.020 1.61 22.96 3 0.025 1.55 22.14 4 0.030 1.49 21.32 5 0.035 1.43 20.50 6 0.040 1.38 19.68 7 0.045 1.32 18.86
Figure 4.18: Graph of attenuations for different polarization tilt angle versus surface height of the antenna
62
4.5.2 Increasing the elevation angle of the antenna and other
parameters remaining constant
We assumed hs=0.01km
Table 4.37: Attenuation values for increasing the elevation path angle at the horizontally polarized tilt angle
Table 4.38: Attenuation values for increasing the elevation path angle of the antenna at the circular polarized tilt angle K= 0.248, =0.9715, Asp =7.19db/km
Table 4.39: Attenuation values for increasing the elevation path angle of the antenna at the vertically polarized tilt angle K= 0.248, =0.9715, Asp =7.19db/km
Figure 4.19: Graph Attenuation (db) or Fade depth versus elevation path angle at rain rate of 32mm/hr and 35GHz
4.6 DISCUSSION OF RESULTS
Tables 4.10, 4.11, 4.12, 4.13, 4.14, 4.15, 4.16, 4.17 and 4.18 and their
subsequent figures (4.10, 4.11 and 4.12) for the horizontal/nearly horizontal
path showed that their attenuation values increases by increased frequency at
all the polarized tilt angle. This was also applicable in the earth space path