determination of rain attenuation of microwave … · acknowledgement i wish to thank the almighty...

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

____________________________ _____________________________

Prof. P.N. Okeke Prof. C.M.I Okoye

(Supervisor) (Head of Department)

______________________________________

(External examiner)

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CERTIFICATION

This work embodied in this thesis is original and has not been submitted in full

or part thereof for any other degree or professional qualification for this or any

other university.

________________________

Umeh, Chibuike Dominic

PG/M.Sc./07/42856

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DEDICATION

This work is dedicated to all lovers of communication.

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ACKNOWLEDGEMENT

I wish to thank the Almighty God for his divine assistance throughout this

programme. My profound gratitude goes to Prof. P.N Okeke, Director center for

basic space science (CBSS) UNN who not only supervised this work but also

helped to secure grant for this work through the center.

A big thank you to Mr. Ayotunji Benjamine of CBSS, who not only

painstakingly went through the manuscript, secured assistance with the radar

scientist and encouraged me during its presentation to the department. You

are indeed a pillar to reckon with. Prof. J.O. Urama who accepted to read

through this manuscript once more, thank you! Kudos to Daniel Okoh of CBSS

who spent sleepless night teaching me the software I used to analyze this work.

I must also confess the relevance of the advice and encouragement the

secretary and other staff of CBSS gave to me each time I visited the center, to

the success of this work. Thank you also to the radar scientist Dr. Adediji of

FUTA.

The dean of the faculty Prof. Mrs. F.N. Okeke and my head of Department Prof.

C.M.I Okoye ; your exemplary leadership towards the organization of the post

graduate programme is indeed worthy of emulation. well done! Other lecturers

of the department especially Profs. J.O Urama and A.A. Ubachukwu and

Emeritus Prof. A.O.E Animalu, Thank you for the academic formation. My

special gratitude goes to Profs. J.O Urama, and A.A. Ubachukwu who despite

having only me in this field never got discouraged and still gave me their best.

Thank you also for the constructive criticisms you gave to this work. Drs.

R.N.C. Eze, B.A Ezeokoye, Ms. D.N Obiorah, A.B.C. Ekwealor and Franklin

Onah. Thank you for your friendly advice especially during the trying moments.

It really worked for me.

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My deepest appreciation goes to my parents and siblings for their financial and

moral support and for always being there for me. Finally, to my friends and

classmates: Ogenna, Festus, Silas, Chinedu, Vivian, Josephat, Chinelo,

Chiamaka, Ufondu, Ifeoma, David, Ifenyinwa, Chinwe, Ekuma .C, Mbalahi,

Christopher, infact too numerous to mention. I love you all for the joy you gave

me during this programme. Thank you!

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CONTENT

1 General Introduction - - - - - - - - 1

1.1 Electromagnetic wave propagation - - - - - --1

1.2 Atmospheric Attenuation - - - - - - -4

1.3 Purpose of study - - - - - - - - -9

1.4 Limitation of Study - - - - - - - -10

2 Review of literature - - - - - - - - -10

2.1 Rain Attenuation of microwave Signals - - - - -10

2.1.1 Earth space path - - - - - - - - -12

2.2 ITU-R model and other prediction models - - - - -14

2.3 Theoretical background - - - - - - 18

2.3.1 Horizontal/nearly horizontal path - - - - - 18

2.3.2 Earth space path formulation - - - - - - -19

3 Instrumentation and Methodology - - - - - -23

3.1 The Micro rain radar (MRR) - - - - - - -23

3.1.1 Outdoor Components - - - - - -24

3.1.2 Indoor Component - - - - - - - -25

3.1.3 System Parameters - - - - - - -25

3.1.4 General features/functions of MRR - - - - -26

3.2 Methodology - - - - - - - - - -26

3.2.1 Retrieval of Microphysical Distributions and Parameters - -27

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4 Source of Data - - - - - - - - - -29

4.1 Analysis Procedure - - - - - - - -29

4.2 Result- Horizontal/nearly horizontal path - - - - -31

4.2.1 Rain rate of 20mm/hr - - - - - - - -31

4.2.2 Rain rate of 24mm/hr - - - - - - - -31

4.2.3 Rain Rate of 32mm/hr- - - - - - - - -34

4.3 The Worst attenuated condition - - - - - -35

4.3.1 Increasing the ink distance and other parameters remaining

Constant - - -- - - - - - - -35

4.3.2 Increasing the angle of elevation with other parameters remaining

constant - - - - - - - - - -37

4.4 Result-Earth space path - - - - - - - -38

4.4.1 Rain rate of 20mm/hr - - - - - - - -38

4.4.2 Rain rate of 24mm/hr - - - - - - - -40

4.4.3 Rain Rate of 32mm/hr - - - - - - - -41

4.5 The worst Attenuated condition - - - - - -42

4.5.1 Increasing the surface height of the antenna and other parameters

remaining constant - - - - - - - - -42

4.5.2 Increasing the elevation path angle and other parameters remaining

constant - - - - - - - - - -44

4.6 Discussion of Result - - - - - - - -46

4.6.1 Worst Attenuated condition-Horizontal/nearly horizontal path -47

4.6.2 Worst Attenuated condition- Earth space path - - - -47

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5 Conclusion - - - - - - - - - -49

5.1 Further research and Recommendation - - - - -51

References - - - - - - - - - - -53

Appendix A - - - - - - - - - -56

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LIST OF TABLES

1.0.0 The mode of propagation of wave using their nominal band - -3

4.1.0 Attenuation for increasing frequencies at the horizontal signal at rain rate

of 20mm/hr in the horizontal path - - - - - -31

4.11 Attenuation for increasing frequencies at the circular signal at rain rate of

20mm/hr in the horizontal path - - - - - -32

4.12 Attenuation for increasing frequencies at the vertical signal at rain rate of


4.13 Attenuation for increasing frequencies at the horizontal signal at rain rate

of 24mm/hr in the horizontal path - - - - -33





4.16 Attenuation for increasing frequencies at the horizontal signal at rain rate

of 32mm/hr in the horizontal path - - - - - -34





4.19 Attenuation for increasing the link distance at the horizontal signal 35

4.20 Attenuation for increasing the link distance at the circular signal -36

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4.21 Attenuation values for increasing the link distance at the vertical

Signal - - - - - - - - - - -36

4.22 Attenuation values for increasing the elevation angle at the horizontal

signal - - - - - - - - - - -37

4.23 Attenuation values for increasing the elevation angle at the circular

Signal - - - - - - - - - - -37

4.24 Attenuation values for increasing the elevation angle at the vertical

Signal - - - - - - - - - - -37

4.25 Attenuation for frequencies at the horizontal signal for rain rate of 20

mm/hr at the earth space path - - - - - -38

4.26 Attenuation for frequencies at the circular signal for rain rate of 20


4.27 Attenuation for frequencies at the vertical signal for rain rate of 20



mm/hr at the earth space - - - - - - -40







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4.34 Attenuation for increasing the surface height of the antenna at the

horizontal signal - - - - - - - - -43


circular signal - - - - - - - - -43


vertical signal - - - - - - - - -43

4.37 Attenuation for increasing the elevation path angle at the horizontal

signal - - - - - - - - - -44

4.38 Attenuation for increasing the elevation path angle at the circular

Signal - - - - - - - - - -45

4.39 Attenuation for increasing the elevation path angle at the vertical

Signal - - - - - - - - - -45

4.40 Appendix A - - - - - - - - - -54

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LIST OF FIGURES

3.00 An installed Micro rain radar - - - - - - -24

4.10 Graph of specific Attenuation versus frequency at rain rate of 20mm/hr

in the horizontal path - - - - - - - -32





4.13 Graph of fade depth versus link distance - - - - -36

4.14 Graph of fade depth versus elevation angle of the antenna at

32mm/hr - - - - - - - - - -38

4.15 Graph of Attenuation versus frequency at rain rate of 20mm/hr in the

earth space path - - - - - - - - -39


earth space path - - - - - - - - -41


earth space path - - - - - - - - -42

4.18 Graph of Attenuation versus surface height at 32mm/hr - -44

4.19 Graph of Attenuation versus elevation path angle at 32mm/hr -45

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ABSTRACT

Rain attenuation of microwave signals is the decrease in the intensity of the

frequency of microwave signals by rain. This effect is predominant at

frequencies of 10GHz and above. Studies were made at the C, X, Ku, K and Ka

band of rain rate values gotten from the micro rain radar at Akure, Ondo State;

(20mm/hr, 24mm/hr and 32mm/hr) at the horizontal/nearly horizontal and

earth–space paths.

It was shown that increase in frequency (GHz) of propagation and increase in

rain rate lead to a higher attenuation of microwave signals. The attenuation

would be more if propagated on the earth–space path than on the

horizontal/nearly horizontal path. The horizontal polarization tilt angle ( = o0)

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

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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

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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

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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

SHF & EHF C X Ku K Ka R Q W

3-300GHz 4-8GHz 8-12GHz 12-18GHz 18-27GHz 27-33GHz 33 – 50GHz 40 – 75GHz 75 – 110 GHz

10cm-1cm & 1cm -1mm

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.

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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.

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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;

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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

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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.

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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

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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.

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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.

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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

satellite slant path distance (using satellite slant – path geometry).

36

Where;

re is the earth’s radius (6378km)

h is the satellite height above the centre of the earth

is the elevation angle at which the satellite appears.

θ

ψ

rs

Satellite

h

re

37

is the central angle

(Ajayi and Olsen, 1985)

The distance to the satellite is a function of the satellite attitude and elevation

angle at which it is viewed (due to the earth’s curvature).

Using sine rule;

sin)2

(sin

srh

(2.17)

So, )

2(

sin

Sin

hrs (2.18)

Later, ITU-R modified this central angle using estimation values to give a form

of slant path height (Lsl)

For o5

sin)(2

sin

)(22/1

2

e

R

sRsl

rhsh

hhL (2.19)

Otherwise

kmSin

hhL sRsl

)( (2.20)

Where hs is the surface height of the antenna

The 0.01% fade depth or Attenuation (db) is then computed to give

A = dBLER (2.21)

38

R Is the specific attenuation given as equation 2.12 and LE is the effective

path length given as

LE = LR 01.0

Km (2.22)

where

LR = kmLh sl

sin)(

(2.23) which is

the horizontal projection gotten from physical consideration of the slant path

geometry

01.0 is the distance factor from standard estimation values.

Bryant et al. (2001) in order to reduce errors from this distance factor

estimation values (which is mainly from temperate countries) used the Ajayi

Olsen model and slant path length (equations 2.19 and 2.20) to form the

Bryant model for attenuation on an earth space path for the tropical regions

given as

hrmmRforDZL

LKDA sl

nm /357.1

(2.24)

Where = specific attenuation (db/km)

D = mD)/2(

Kn = exp (0.007R)

Dm = 340 R-1.2.

Z is the elevation coefficient given by

39

00 55tan1.155)exp(sin2

1 fororforZ (2.25)

is the elevation angle of slant path.

Also from ITU-R model; Lsl is given by equations 2.19 and 2.20

L=tan

Rh is the horizontal projection (2.26)

(Bryant et al., 2001)

40

CHAPTER THREE

INSTRUMENTATION AND METHODOLOGY

Attenuation by rain can be predicted accurately if the rain is precisely

described all the way along the path. Path attenuation is essentially an integral

of all individual increments of rain attenuation caused by the drops

encountered along the path. Hence micro rain radar data became

indispensable for this study.

3.1 THE MICRO RAIN RADAR (MRR)

The micro rain radar is a unique, compact 24.1 GHZ frequency Modulated –

continuous Wave (FM-CW) radar; for the measurement of vertical profiles of

rain rate, liquid water content and Drop Size Distribution (Gerhard et al.,

2002). It provides information for now-casting of precipitation ie it will detect

the start of rain from the atmosphere to the antenna dish several minutes

before the start of rain.

41

Figure 3.00 showing the diagram of installed MICRO RAIN RADAR

The system consists of an antenna dish (1), radar (2), Receiver unit (3) and Rs-

232 data transmission interface. These could be detailed into outdoor

components and indoor components.

3.1.1 Outdoor Component

a. Offset parabolic dish antenna with 0.5m efficient aperture diameter and

24.1 GHz FM-CW transmit frequency cord

b. Radar front end (electromagnetic field)

c. Transmitter control electronic housing; 26cm x 16cm x 10cm

1

2

3

42

d. Recorder unit and digital signal processor unit for FFT (Fast Fourier

Transform)-analysis for derivation of Doppler spectra (10s sampling

time)

e. Data transmission with R5232 interface for system control

f. 25m-junction cable for data transfer and power supply of outdoor

components.

3.1.2 Indoor Component

a. Power supply 220VAC/24VDC/25W

User can use either mains or 24VDC, as both are available

3.1.3 System parameter

a. Sampling time: 10s

b. Average time; adjustable; 10s to 1800s

c. Number of height steps: adjustable maximum is 30m

d. Lowest measuring height: 2 height steps

e. Automatic restart after power breakdown with fewer settings.

f. Output of measured data [spectra reflectivity, rain rate, Liquid water

content and Drop Size Distribution (DSD)] both as instantaneous and

averaged data (with selected averaging interval) NOTE; for the data

transmission of the Doppler spectra from the outdoor receiver and FFT-

electronic to the indoor data acquisition PC; a transfer time of 2-3s are used

for effective measurements.

43

3.1.4 General features/functions of MRR

a. Vertical profiles of rain rate and liquid water content up to 6km (360

miles).

b. Computes detailed Drop Size Distribution output.

c. User adjustable averaging intervals and height resolution.

d. High system reliability

e. Very little maintenance

f. Remote/long term unattended operation.

g. High quality measurements

h. No wind, sea spray or evaporation induced errors.

i. Adjustable averaging intervals 10-1800s

j. Height guage: more than 2000m (1.2 miles) with 30 range gates.

k. Battery or mains power

3.2 METHODOLOGY

The specifications of the vertical pointing complete micro rain radar (MRR 2

FM-CW mode) for data collection of various ranges is as shown

a. Transmit power – 50 mW

b. Frequency – 24.1 to 24.15GHz

c. Averaging interval- 10 to 3600s

d. Height resolution – 10 to 200m

44

e. Number of range gates- up to 30m

f. Accuracy for 1min average- 1/100 mm/hr

g. Power supply (mains driven or 24 VDC)- 24 VDC, 25W

h. Weight- 6kg (without power supply cable)

Other items to enhance performance of the MRR are optional and mainly suited

for ice and snow regions of the world.

3.2.1 Retrieval of Microphysical Distributions and Parameters

This is the analysis of how the MRR displays various ranges of required data on

the screen. To achieve this; the MRR makes use of a GRAPHIC-SOFTWARE.

There are two pieces of this soft ware supplied with the MRR. The first is the

controlling software to set the parameters; and the second is software to view

the Doppler spectra and visualize the data graphically for presentation.

Functionality can be broken down as

a. Software module for system access and control, data transfer and data

storage.

b. Software module for on-line evaluation of Doppler spectra (measured

data)

c. Software module for graphic presentation of results and data with

profiles, time series and droplet spectra, in a single graphic format,

selectable time and height ranges, smoothing functions and printer

output.

45

Though this latter software data is not used in this research, the PC

computer for this software must have the following configurations for either

the desktop models or notebook model. For desktop models: 600MHz,

Pentium M, 64MB, Windows 2000 or XP, VGA monitor, 20.0 GBHD, CD

writer, 1.44 Floppy, 1 serial, 1 parallel port; NOTE; The serial port must be

native and not provided over a PC card USB to serial adapter, as these tend

to be unreliable or cause conflicts.

For Note book models; Windows 2000 or XP, 600 MHz, Pentium M, 64MB,

14.1 TFT VGA monitor, 8.0 GBHD, ext CD-writer, 1.44 floppy, 1 serial , I

parallel port; 2 PC- cards slots. NOTE: The serial port must be native also

and not provided over a PC card or USB to serial adapter, as these tend to be

unreliable or cause conflicts. With this; the Radar can display several values

about the rainfall, Drop Size Distribution, Volume reflectivity, Liquid water

Content and Rain rate.

46

CHAPTER FOUR

SOURCE OF DATA

Data used for this study was collected by the high resolution Micro Rain Rader

located at the Federal University of Technology, Akure, Ondo State. (7o15' 0''N /

5o 12' 0'' E). The rain rate collected was from July 1st to September 25th, 2009

at 10 seconds sampling time. This falls within the peak of the rainy season in

the locality. We considered the highest rain rate value in each of the month.

July -20mm/hr

August -24mm/hr

September- 32mm/hr

The radar gave a rain height of 1600m for each of the months.

4.1 ANALYSIS PROCEDURES:

The analysis was done on two different microwave communication links:

i. Horizontal or nearly horizontal path

ii. Earth-space path

The International Telecommunication Union of Radio Communication model

(ITU – R model) and the Bryant model (Recently Improved ITU-R model) were

used to determine the attenuation of microwave signals on both paths

respectively.

These models determined the 0.01% of time attenuation of various frequencies

based on these rain rates and polarization tilt angle. The elevation angle, ( )

47

polarization tilt angle, () and link distances/surface height of the antenna were

all varied to see how it affects the attenuation value. These gave rise to certain

deductions about the relationships among frequencies, varying elevation

angles, and link distances/surface height of the antenna and polarization tilt

angle with attenuation.

In the horizontal/nearly horizontal communication path;

(a) Frequencies used were from 5 to 35GHz in steps of 5GHz

(b) Polarization tilt angle () was used for = 0o, = 45o and = 90o

(c) Elevation angle of the antenna () was from 0o to 14o in steps of 2o

(d) The link distance was from 1, 2 to 14 km in steps of 2km. (c) And (d)

were used to verify the effect of attenuation on varying elevation angles

and link distances respectively.

In the earth-space communication path;

(a) Frequencies used were from 5 to 35GHz in steps of 5GHz

(b) Polarization tilt angles () was for = 0o, 45o and 90o

(c) Elevation angle of the antenna () was from 0o to 14o in steps of

2o

(d) The surface Antenna height (hs) was from 0.01km to 0.045km in steps

of 0.005km.

(c) And (d) were also used to verify the effect of the attenuation on this path too.

We used 6378.1km as the radius of the earth and a rain height of 1.6km as

given by the radar.

48

These variations were made strictly from physical considerations.

In each of these Communication paths; model computations were done for

(a) Varying frequencies for rain rate at 20mm/hr at = 0o, 450 and 90o

(b) Varying frequencies for rain rate at 24mm/hr at = 0o, 450 and 90o

(c) Varying frequencies for rain rate at 32mm/hr at = 0o, 450 and 90o

(d) Varying the elevation angles using the worst attenuated condition

(Frequency of 35GHz and rain rate of 32mm/hr) for = 0, 45o and 90o.

(e) Varying the link distance; using the worst attenuated conditon (frequency of

35GHz

And rain rate of 32mm/hr) for = 0o 45o and 90o

Graphs of these conditions were plotted to make the necessary deductions.

Note: (d) and (e) were done only at the worst attenuated frequency to seek for a

possible solution to this effect.

4.2 RESULTS- HORIZONTAL/NEARLY HORIZONTAL PATH

An assumption was made for elevation path angle equal to zero degrees

4.2.1 Rain rate of 20mm/hr

Table 4.10: Attenuation values for increasing frequencies at the horizontally polarized tilt angle. d0=25.93, r=0.9628 S/N F(GHz) K Asp(db/km) A(db) 1 5 1.21x10-3 1.224 0.05 0.05 2 10 0.010 1.276 0.46 0.44 3 15 0.037 1.154 1.17 1.13 4 20 0.047 1.099 2.02 1.94 5 25 0.124 1.061 2.98 2.87 6 30 0.187 1.021 3.98 3.83 7 35 0.263 0.979 4.94 4.76

49

Table 4.11: Attenuation values for increasing frequencies at the circular polarized tilt angle. d0=25.93, r=0.9628 S/N F (GHz) K Asp(db/km) A(db) 1 5 1.11x10-3 1.204 0.04 0.04 2 10 0.0094 1.270 0.42 0.41 3 15 0.0355 1.140 1.08 1.04 4 20 0.0720 1.083 1.84 1.78 5 25 0.1185 1.046 2.72 2.62 6 30 0.1770 1.011 3.66 3.52 7 35 0.2480 0.971 4.55 4.38 Table 4.12: Attenuation values for increasing frequencies at the vertically polarized tilt angle, d0=25.93, r=0.9628 S/N F(GHz) K Asp(db/km) A(db) 1 5 1.01x10-3 1.180 0.03 0.03 2 10 0.0089 1.264 0.39 0.38 3 15 0.0340 1.128 1.00 0.96 4 20 0.0690 1.065 1.68 1.61 5 25 0.1130 1.030 2.47 2.38 6 30 0.1670 1.000 3.34 3.22 7 35 0.2330 0.963 4.17 4.01

Figure 4.10: Graph of specific attenuations for different polarization tilt angle versus frequency at rain rate of 20mm/hr

50

4.2.2 Rain rate of 24mm/hr Table 4.13: Attenuation values for increasing frequencies at the horizontally polarized tilt angle. d0=24.419, r=0.9602 S/N F(GHz) K Asp(db/km) A(db) 1 5 1.21x10-3 1.224 0.06 0.07 2 10 0.0100 1.276 0.58 0.55 3 15 0.0370 1.154 1.45 1.39 4 20 0.0750 1.099 2.47 2.37 5 25 0.1240 1.061 3.61 3.47 6 30 0.1870 1.021 4.80 4.61 7 35 0.2630 0.979 5.90 5.67 Table 4.14: Attenuation values for increasing frequencies at the circular polarized tilt angle. d0=24.419, r=0.9602 S/N F(GHz) K Asp(db/km) A(db)

1 5 1.11x10-3 1.204 0.05 0.05

2 10 0.0094 1.270 0.53 0.51

3 15 0.0355 1.140 1.34 1.28

4 20 0.0720 1.083 2.25 2.16

5 25 0.1185 1.046 3.29 3.16

6 30 0.1770 1.011 4.40 4.23

7 35 0.2480 0.971 5.44 5.22

Table 4.15: Attenuation values for increasing frequencies at the vertically polarized tilt angle. d0=24.42, r=0.9607 S/N F(GHz) K Asp(db/km) A(db) 1 5 1.01x10-3 1.180 0.04 0.04 2 10 0.0089 1.264 0.49 0.47 3 15 0.0340 1.128 1.23 1.18 4 20 0.0690 1.065 2.04 1.96 5 25 0.1130 1.030 2.98 2.87 6 30 0.1670 1.000 4.01 3.85 7 35 0.2330 0.963 4.97 4.78

51

Figure 4.11: Graph of specific attenuations for different polarization tilt angle versus frequency at rain rate of 24mm/hr 4.2.3 Rain rate of 32mm/h Table 4.16: Attenuation values for increasing frequencies at the vertically polarized tilt angle. d0=21.66, r=0.9559 S/N F(GHz) K Asp(db/km) A(db) 1 5 1.21x10-3 1.224 0.08 0.08 2 10 0.0100 1.276 0.83 0.80 3 15 0.0370 1.154 2.02 1.93 4 20 0.0750 1.099 3.38 3.23 5 25 0.1240 1.061 4.90 4.69 6 30 0.1870 1.021 6.44 6.15 7 35 0.2630 0.979 7.83 7.48

52

Table 4.17: Attenuation values for increasing frequencies at the circular polarized tilt angle. d0=21.66, r=0.9559 S/N F(GHz) K Asp(db/km) A(db)

1 5 1.11x10-3 1.204 0.07 0.07

2 10 0.0094 1.270 0.77 0.74

3 15 0.0355 1.142 1.86 1.77

4 20 0.0720 1.083 3.07 2.93

5 25 0.1185 1.046 4.45 4.25

6 30 0.1770 1.011 5.89 5.63

7 35 0.2480 0.971 7.19 6.87

Table 4.18: Attenuation values for increasing frequencies at the horizontally polarized tilt angle. d0=21.66, r=0.9559 S/N F(GHz) K Asp(db/km) A(db) 1 5 1.01x10-3 1.180 0.06 0.06 2 10 0.0089 1.264 0.71 0.68 3 15 0.0340 1.128 1.70 1.62 4 20 0.0690 1.065 2.78 2.64 5 25 0.1130 1.030 4.01 3.84 6 30 0.1670 1.000 5.34 5.11 7 35 0.2330 0.963 6.56 6.27

Figure 4.12: Graph of specific attenuations for different polarization tilt angle versus frequency at rain rate of 32mm/hr

53

4.3 THE WORST ATTENUATED CONDITION 4.3.1 Increasing the link distance with other parameters remaining constant Table 4.19: Attenuation values for increasing the link distance at the horizontally polarized tilt angle. d0=21.66, Asp =7.83db/km, =0.979, k=0.263 S/n d(km) R A(db) 1 2 0.9155 14.33 2 4 0.8441 26.42 3 6 0.7831 36.77 4 8 0.7303 45.72 5 10 0.6841 53.53 6 12 0.6435 60.42 7 14 0.6074 66.54 Table 4.20: Attenuation values for increasing the link distance at the circular polarized tilt angle. d0=21.66, Asp =7.19db/km, =0.9715, k=0.248 S/n d(km) R A(db) 1 2 0.9155 13.16 2 4 0.8441 24.27 3 6 0.7831 33.78 4 8 0.7303 42.00 5 10 0.6841 49.18 6 12 0.6435 55.51 7 14 0.6074 61.13 Table 4.21: Attenuation values for increasing the link distance at the vertically polarized tilt angle. d0=21.66, Asp =6.56db/km, =0.963, k=0.233 S/n d(km) R A(db) 1 2 0.9155 12.00 2 4 0.8441 22.14 3 6 0.7831 30.81 4 8 0.7303 38.32 5 10 0.6841 44.87 6 12 0.6435 50.64 7 14 0.6074 55.77

54

Figure 4.13: Graph of the fade depth or Attenuation (db) for all polarized tilt angle versus link distance 4.3.2 Increasing the angle of elevation with other parameters remaining constant Table 4.22 Attenuation values for increasing the elevation angle at the horizontally polarized tilt angle. d0=21.66, r=0.9559 S/n 0 K Asp(db/km) A(db) 1 2 0.26298 0.97899 7.824 7.479 2 4 0.26293 0.97896 7.822 7.476 3 6 0.26284 0.97892 7.818 7.473 4 8 0.26271 0.97886 7.813 7.468 5 10 0.26255 0.97879 7.806 7.461 6 12 0.26235 0.97869 7.798 7.453 7 14 0.26212 0.97858 7.787 7.444 Table 4.23 Attenuation values for increasing the elevation angle at the circular polarized tilt angle. τ=450, d0=21.66, r=0.9559 S/n 0 K Asp(db/km) A(db) 1 2 0.248 0.9715 7.19 6.87 2 4 0.248 0.9715 7.19 6.87 3 6 0.248 0.9715 7.19 6.87 4 8 0.248 0.9715 7.19 6.87 5 10 0.248 0.9715 7.19 6.87 6 12 0.248 0.9715 7.19 6.87 7 14 0.248 0.9715 7.19 6.87

55

Table 4.24: Attenuation values for increasing the elevation angle at the vertically polarized tilt angle. d0=21.66, r=0.9559 S/n 0 K Asp(db/km) A(db) 1 2 0.23302 0.96301 6.5594 6.2699 2 4 0.23307 0.96304 6.5617 6.2721 3 6 0.23316 0.96309 6.5655 6.2757 4 8 0.23329 0.96318 6.5708 6.2808 5 10 0.23345 0.96327 6.5776 6.2873 6 12 0.23365 0.96339 6.5858 6.2951 7 14 0.23388 0.96353 6.5954 6.3043

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.

7211

4.4.1 Rain rate of 20mm/hr Table 4.25: Attenuation values for increasing frequency at the horizontally polarized signal. Dm=9.3378,D=5.9438, Kn=1.1503 S/N F(GHz) K Asp(db/km) A(db) 1 5 1.21x10-3 1.224 0.05 0.19 2 10 0.010 1.276 0.46 1.80 3 15 0.037 1.154 1.17 4.63 4 20 0.075 1.099 2.02 7.96 5 25 0.124 1.061 2.98 11.74 6 30 0.187 1.021 3.98 15.71 7 35 0.263 0.979 4.94 19.48

56

Table 4.26: Attenuation values for increasing frequency at the circular polarized signal. Dm=9.3378, D=5.9438, Kn=1.153 S/N F(GHz) K Asp(db/km) A(db)

1 5 1.11x10-3 1.204 0.04 0.16

2 10 0.0094 1.270 0.42 1.67

3 15 0.0355 1.142 1.08 4.28

4 20 0.0720 1.083 1.84 7.28

5 25 0.1185 1.046 2.72 10.74

6 30 0.1770 1.011 3.66 14.44

7 35 0.2480 0.971 4.55 17.97

Table 4.27: Attenuation values for increasing frequency at the vertically polarized signal. Dm=9.3378, D=5.9438, Kn=1.153 S/N F(GHz) K Asp(db/km) A(db) 1 5 1.01x10-3 1.180 0.03 0.14 2 10 0.0089 1.264 0.39 1.54 3 15 0.0340 1.128 1.00 3.94 4 20 0.0690 1.065 1.68 6.62 5 25 0.1130 1.030 2.47 9.76 6 30 0.1671 1.000 3.34 13.19 7 35 0.2330 0.963 4.17 16.47

57

Figure 4.15: Graph of attenuations for different polarization tilt angle versus frequency at rain rate of 20mm/hr 4.4.2 Rain rate of 24mm/hr Table 4.28: Attenuation values for increasing frequency at the horizontally polarized signal. Dm=7.5028, D=4.7748, Kn=1.1829 S/N F(GHz) K Asp(db/km) A(db) 1 5 1.21x10-3 1.224 0.06 0.23 2 10 0.0100 1.276 0.58 2.23 3 15 0.0370 1.154 1.45 5.60 4 20 0.0750 1.099 2.47 9.55 5 25 0.1240 1.061 3.61 14.00 6 30 0.1870 1.021 4.80 18.59 7 35 0.2630 0.979 5.90 22.87 Table 4.29: Attenuation values for increasing frequency at the vertically polarized signal. Dm=7.5028, D=4.7748, Kn=1.1829 S/N F(GHz) K Asp(db/km) A(db)

1 5 1.11x10-3 1.204 0.05 0.20

2 10 0.0094 1.270 0.53 2.07

3 15 0.0355 1.142 1.34 5.19

4 20 0.0720 1.083 2.25 8.71

5 25 0.1185 1.046 3.29 12.77

6 30 0.1770 1.011 4.40 17.06

7 35 0.2480 0.971 5.44 21.07

58

Table 4.30: Attenuation values for various increasing frequency at the vertically polarized signal. Dm=7.5028, D=4.7748, Kn=1.1829 S/N F(GHz) K Asp(db/km) A(db) 1 5 1.01x10-3 1.180 0.04 0.17 2 10 0.0089 1.264 0.49 1.91 3 15 0.0340 1.128 1.23 4.75 4 20 0.0690 1.065 2.04 7.90 5 25 0.1130 1.030 2.98 11.57 6 30 0.1670 1.000 4.01 15.55 7 35 0.2330 0.963 4.97 19.23

Figure 4.16: Graph of attenuations for different polarization tilt angle versus frequency at rain rate of 24mm/hr 4.4.3 Rain rate of 32mm/hr Table 4.31: Attenuation values for increasing frequency at the horizontally polarized signal. Dm=5.3125, D=3.3816, Kn=1.2511 S/N F(GHz) K Α Asp(db/km) A(db) 1 5 1.21x10-3 1.224 0.08 0.34 2 10 0.0100 1.276 0.83 3.12 3 15 0.0370 1.154 2.02 7.56 4 20 0.0750 1.099 3.38 12.67 5 25 0.1240 1.061 4.90 18.36 6 30 0.1870 1.021 6.44 24.10 7 35 0.2630 0.979 7.83 29.30

59

Table 4.32: Attenuation values for increasing frequency at the circular polarized signal. Dm=5.3125, D=3.3816, Kn=1.2511 S/N F(GHz) K Asp(db/km) A(db)

1 5 1.11x10-3 1.204 0.07 0.27

2 10 0.0094 1.270 0.77 2.89

3 15 0.0355 1.142 1.86 6.95

4 20 0.0720 1.083 3.07 11.49

5 25 0.1185 1.046 4.45 16.68

6 30 0.1770 1.011 5.89 22.06

7 35 0.2480 0.971 7.19 26.94

Table 4.33: Attenuation values for increasing frequencies at the vertically polarized signal. Dm=5.3125, D=3.3816, Kn=1.2511 S/N F(GHz) K Asp(db/km) A(db) 1 5 1.01x10-3 1.180 0.06 0.23 2 10 0.0089 1.264 0.71 2.66 3 15 0.0340 1.128 1.70 6.36 4 20 0.0690 1.065 2.78 10.37 5 25 0.1130 1.030 4.01 15.05 6 30 0.1670 1.000 5.34 20.04 7 35 0.2330 0.963 6.56 24.59

60

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

0 K Asp(db/km) Z Lsl(km) L(km) A(db) 10 0.2625 0.9788 7.81 0.8412 0.86 0.91 16.98 15 0.2620 0.9785 7.78 0.9159 0.58 0.60 11.98 20 0.2612 0.9782 7.75 0.9955 0.44 0.44 9.29 25 0.2603 0.9777 7.71 1.0790 0.35 0.34 7.61 30 0.2590 0.9772 7.67 1.1658 0.30 0.28 6.45 35 0.2581 0.9766 7.62 1.2548 0.26 0.23 5.67 40 0.2568 0.9760 7.56 1.3448 0.23 0.19 5.06

s/n 0 Z Lsl(km) L(km) A(db) 1 10 0.8412 0.86 0.91 15.63 2 15 0.9160 0.58 0.60 11.07 3 20 0.9955 0.44 0.44 8.61 4 25 1.0790 0.35 0.34 7.10 5 30 1.1658 0.30 0.28 6.07 6 35 1.2548 0.26 0.23 5.34 7 40 1.3448 0.23 0.19 4.81

63

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

0 K Asp(db/km) Z Lsl(km) L(km) A(db) 10 0.2335 0.9632 6.58 0.8412 0.86 0.91 14.30 15 0.2340 0.9636 6.60 0.9160 0.58 0.60 10.16 20 0.2348 0.9640 6.63 0.9955 0.44 0.44 7.95 25 0.2357 0.9646 6.67 1.0790 0.35 0.34 6.59 30 0.2368 0.9652 6.72 1.1658 0.30 0.28 5.67 35 0.2379 0.9659 6.77 1.2548 0.26 0.23 5.03 40 0.2392 0.9666 6.82 1.3448 0.23 0.19 4.56

64

(Tables 4.25, 4.26, 4.27, 4.28, 4.29, 4.30, 4.31, 4.32 and 4.33 and figures

4.15,4.16 and 4.17). Figures 4.10 and 4.15 with their corresponding tables

were also in total agreement with the prediction of the work of Hassan (2007) in

Malaysia. The polarization tilt angle τ, for horizontal (τ = 0) has the highest

specific attenuation value; then the circular (τ = 45o) and vertical (τ=90) in that

order. As the rain rate increases; the specific attenuation value (db/km) also

increases for all the polarization tilt angles both in the horizontal/ nearly

horizontal propagation and the Earth-space propagations of microwave signals.

For the earth space path, the value of the attenuation value [A(db)] for all the

rain, frequencies and polarization tilt angle (τ) differ to their respective rain

rates, frequencies and polarization tilt angle in horizontal/ nearly horizontal

path attenuation propagation, due to the slight increase of elevation path angle

by five degrees. We chose to have this general assumption of five degrees in the

elevation path angle and not zero degrees as in the horizontal path so as to

avoid having an infinite horizontal projection (equation 2.26). So, similar

condition (equations) would hold for them. The radius of the earth is constant

all through our consideration in this path.

4.6.1 Worst Attenuated condition- Horizontal/nearly horizontal path

Tables’ 4.19,4.20 and 4.21 all showed that the attenuation value increases with

increased link distance. Figure 4.13 shows that the graph is linear from 0 to 4

km; later, it shows an exponential increase. So, clearly, when the link distance

65

increases; the attenuation value increases. The exponential curve could be as a

result of the earth’s curvature, which is widely felt as the link distance

increases. This affects the attenuation value (slight reduction). So, link

distance is an important factor while communicating on this path.

On the other hand; when the elevation angle of the antenna was increased; and

the link distance kept constant. Table 4.22, 4.23 and 4.24 show negligible

changes in attenuation values at various elevation angles. A critical look at its

figure (figure 3.42) shows that generally; no matter the angle of elevation

increase of the antenna; it will have a negligible effect on the fade depth. This is

because; at horizontal direction of frequency propagation; rain affects it greatly;

no matter the direction of the antenna. This figure further proofed that the

curves being experienced in attenuation studies were due to the earth’s

curvature.

4.6.2 Worst Attenuated condition- Earth-space path

Tables 4.34, 4.35, and 4.36 and figure 4.18 show a very slight reduction of

attenuation value when the surface height of the antenna was increased.

Figure 4.18 further confirmed our research. Attenuation of microwave signals

is predominant in the atmosphere especially during rainy condition. The slight

reduction is because; we are working with a rain height of 1.6km given by the

radar. Rain affects frequency signals greatly within this height; but as we

exceed this height; there would be no attenuation due to the absence of

66

rainfall. The slight reduction was as a result of the vertical nature of the signal,

which might be increased by decreased path length.

Finally, tables 4.37, 4.38 and 4.39 show how attenuation value decreases when

the elevation angle of the satellite was increased. Figure 4.19 depicts a sharp

reduction of attenuation value when the elevation angle of the satellite was

increased from 10 to 15 degrees. Later, it undergoes an exponential decrease

from 15 to 35 degrees then tends to become stable at above 35 degrees. This

indicates the effect of satellite location in space with the earth’s station (proper

orientation is advisable) while making communication in rainfall condition. The

stability of the signal shows that the attenuation effect could not be completely

removed with increased elevation angle of the satellite; other means should

also be employed.

67

CHAPTER FIVE

CONCLUSION

In Akure, Ondo State we have gotten a detailed quantitative value (from rain

rate and rain height measurement) on how microwave signals are being

affected by rainfall. Significant effects of attenuation of microwave signals

above 10 GHz would characterize the earth-space and horizontal/nearly

horizontal communication paths. This occurs at rain rate values between 20

mm/hr to 32mm/hr. The attenuation values would increase as the rain rate

increases. So, for better signal reception above 10 GHz rain rate duration

should be taken into consideration during the design of microwave and

millimeter wave link. The vertical polarized tilt angle would be the best-

polarized angle to receive signals, especially if the frequency is less than 10

GHz. This is because; it would have a less attenuation effect when compared

with the circular and horizontal polarized tilt angles. Increasing the frequency

of propagation leads to increase in attenuation of such signals.

In horizontal/nearly horizontal path: there is a slight reduction of Attenuation

(db) or fade depth when compared to the specific attenuation (db/Km) due to

the distance factor r and the earth’s curvature. Decreasing the link distance

could mainly reduce attenuation of microwave signals on this path due to

rainfall. Increase in link distance would have a major effect on the fade depth;

as shown when the link distance increases from 2km to 14km. On the other

hand; when the elevation angle of the antenna was increased; there was a

68

negligible effect on the specific attenuation and the expected fade depth. This

quickly tells us that the specific attenuation (db/Km) and the expected fade

depth are independent of the elevation angle. In fact, when the polarization tilt

angle is circular ( )45o ; it would have no effect on the specific attenuation

(db/Km) and the expected fade depth (db); no matter the degree the angle is

being altered. So, link distance changes has to be considered greatly; when

correction is being sought

The earth – space communication path seems to have a different result. Rain

rate has more effect on signal distortion on this path. There is a consideration

of slant path height and horizontal projection of the antenna, which is highly

influenced by the rain height. This portrays the influence of rain height on

attenuation on such path. Unlike in horizontal/nearly horizontal path; the

elevation angle of the antenna alteration plays a major effect in attenuation

than surface height variation. Increasing elevation angle reduces the

attenuation and vice versa; while surface height alteration would have a

negligible effect. This tells us the importance of proper orientation of earth with

space stations to enhance signal reception. At reduced orientation angle; the

signal would improve. This also quickly gives the idea that no matter how high

you raise your antenna towards the satellite; the signal would still be

attenuated. A close observation of figure 4.19 shows that the elevation angle

increase being uniform; the decreasing attenuation value tends to become

uniform insinuating that the entire attenuation may not be completely phased

69

out no matter the increased angle (signal crack). Other means should be used

to completely phase it out.

These alterations of parameters on both paths were not made principally to

seek a total solution for this attenuation of signal effect; rather to see how the

attenuation effect would behave when such parameters were altered and to give

a detailed understanding about attenuation studies. This gives room for so

many deduction and conclusions about Attenuation.

5.1 Further Research and Recommendation

There is dearth of data in the tropical regions. In Nigeria, the researchers could

not get a detailed rain rate characteristic data from south – east or

South - south geopolitical zones which lies within the rain forest geographical

map. This zone would be more affected by signal distortion due to excessive

rainfall. Institutions and agencies in such locations should install micro rain

radar and other geographical instrument for similar research.

The researchers only considered 0.01% percentage of time Attenuation. Further

research should be extended to other percentages of time (0.1%, 0.001% and

1%) and to other prediction models especially the Ajayi-Olsen model, which is

also suitable for tropical rain drops; comparisons, should also be made. The

effect of Drop Size Distribution (DSD), Antenna design and ionosphere effects

towards attenuation of signals should also be considered. Geographical,

70

topographic reliefs, rain studies and cloud formations should be researched on

to seek a more accurate effect of attenuation on microwave signals at Akure.

To correct the effect of this hazard; detailed satellite communication studies

should be made with the inclusion of all the parameters of the locality as it

affects attenuation. Finally, Akure has a very sunny climatic region. The effect

of sunlight towards rainfall and attenuation should be considered especially on

the effectiveness of the models we used. Equation 2.10 should be modified to

include rain rate and rain height data; we believe, it would be a better model

for Akure, Ondo state.

71

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