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UNIVERSITY OF GHANA, LEGON 
 
COLLEGE OF BASIC AND APPLIED SCIENCES 
 
 
 
THE EFFECTS OF HARMATTAN DUST AND 
RAINFALL ON MICROWAVE SIGNALS IN PARTS 
OF GHANA 
 
 
 
By 
CHRISTINE AFIA ACHEAMPONG 
(10327645) 
 
 
 
 
THIS THESIS IS SUBMITTED TO THE UNIVERSITY 
OF GHANA, LEGON, IN PARTIAL FULFILMENT OF 
THE REQUIREMENT FOR THE AWARD OF 
DOCTOR OF PHILOSOPHY IN PHYSICS DEGREE 
JULY 2019 
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DECLARATION 
I, Christine Afia Acheampong, hereby declare that except for the 
references to other peoples’ works, which have been duly 
acknowledged, this thesis is the result of my own research work towards 
earning a Ph.D. as a student of the University of Ghana, Legon, under 
the supervision of the Supervisory Committee as detailed below: 
 
 
……………………………………………………..   Date: 
………………………………………… 
CHRISTINE AFIA ACHEAMPONG 
(Candidate) 
 
……………………………………………………..   Date: 
………………………………………… 
DR. V. C. K. KAKANE  
(Principal Supervisor) 
 
……………………………………………………..   Date: 
………………………………………… 
PROF. J. K. A. AMUZU 
(Supervisor) 
 
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ABSTRACT 
Microwave signal attenuation due to harmattan and rainfall are two of 
the major constraints in selecting microwave bands in Ghana. With 
customer complaints of signal loss during these seasons, 
telecommunication companies compensate for sudden losses in signal 
strength by amplifying the signal wave. This study investigates the 
effect of harmattan and rainfall on communication link for frequencies 
ranging from 10 to 100 GHz for two locations in Ghana, namely Axim 
and Tamale.  
Visibility and rain rate measurements were made over a two-year period 
in these locations (Axim and Tamale). The signal attenuation as a result 
of harmattan dust was calculated using the Zain Elabdin model for 
visibilities from measured data. The microwave attenuation was 
obtained for frequencies ranging from 10 GHz to 100 GHz. The rain 
attenuation was determined using the ITU-R Specific Attenuation Model 
for Rain (ITU-R P.838-3) for the design of microwave communication 
systems.  
The results showed that both harmattan dust and rainfall have a 
significant impact on signal attenuation in parts of Ghana. The effect of 
attenuation due to harmattan dust was much more evident in Tamale 
whiles rain attenuation was more evident in Axim.  
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It was observed that the signal attenuation increased as the radius size 
increased for frequencies from 10 – 100 GHz.  
The signal attenuation due to harmattan dust was calculated for 
frequencies ranging from 10 – 100 GHz for both Tamale and Axim. The 
signal attenuation due to harmattan dust increased with increasing 
frequencies for both locations. Upon comparison, it was observed that 
Tamale had the higher attenuation values. Axim showed relatively low 
attenuation values from frequencies of 10 GHz to 100 GHz and ranged 
from 0.00009 dB/km to 0.03841 dB/km whiles signal attenuation values 
for Tamale increased from 0.00146 dB/km to a maximum value of 
0.6272 dB/km. This graph shows that attenuation due to dust was more 
prevalent in the Tamale than in Axim. 
Furthermore, attenuation values calculated using measured rain rate 
were highest for high rainfall rates while the lowest attenuation values 
corresponded to the lowest rainfall rates, as shown in the ITU-R rain 
attenuation model.  
 
 
 
 
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DEDICATION 
I dedicate this work to my Auslin, April, Paul, Joshua, Adriel and 
Aaron.   
  
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ACKNOWLEDGMENTS 
First, I am deeply grateful to my supervisors, Dr. V. C. K. Kakane and 
Prof. J. K. A. Amuzu for their guidance, suggestions and encouragement 
throughout my research.  
I am sincerely grateful to Dr. G. K. Nkrumah-Buandoh, Dr. Allison 
Felix Hughes, Dr. Hubert Azoda Koffi, Dr. Godfred Bright Hagan, Dr. 
Amos Kuditcher and Dr. M. N. Y. H. Egblewogbe who are all lecturers 
in the Department of Physics, University of Ghana, for the keen interest 
showed and the useful counsel they offered me.  
I am also grateful to my colleagues in this PhD journey in the 
Department of Physics - Dr. Joanna A. Modupeh Hodasi, Dr. Kofi 
Ampomah Benefo and Mr.George Kusi-Appiah. We encouraged each 
other and we were our biggest fans. I am very grateful to Mr. Harry 
Ntumi, for all the technical insight and help, especially during the 
installation of all the equipment at the various test sites. I would also 
like to say thank you to Pamphile Tossou, Frederick Tatah and all the 
technicians for the technical support offered. 
Finally, my heartfelt gratitude go to Mr. Julian Ebo Kennedy, Mr. David 
Kingsley Acheampong, Linda Acheampong, Olivia Acheampmong and 
Michael Acheampong for their prayers and warm support given to me 
all these years. God bless you all. 
 
 
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TABLE OF CONTENTS 
DECLARATION ...................................................................................... i 
ABSTRACT ............................................................................................. ii 
DEDICATION ........................................................................................ iv 
ACKNOWLEDGEMENTS ..................................................................... v 
TABLE OF CONTENTS ........................................................................ vi 
LIST OF FIGURES ................................................................................. xi 
LIST OF TABLES .................................................................................. xi 
ABBREVIATIONS ............................................................................. xviii 
 
 
CHAPTER ONE: THE PHYSICS OF RADIOWAVES AND 
THEIR PROPAGATION 
1.1 Electromagnetic Theory ..................................................................... 2 
1.2 The Theory of EM Waves .................................................................. 4 
1.2.1 The Electric Field ............................................................................ 5 
1.2.2 The Magnetic Field………. ... …………………………………….7 
1.2.3 Maxwells Equations ......................................................................... 12 
1.3 Generation of Radiowaves ................................................................... 15 
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1.4 Propagation of Radiowaves.............................................................. 16 
1.4.1 Atmospheric Propagation .............................................................. 19 
1.4.1.1 Ionospheric Propagation............................................................. 21 
1.4.1.2 Tropospheric Propagation ............................................................... 23 
1.5 Transmission of Radiowaves ........................................................... 24 
1.5.1 Modulation .................................................................................... 25 
1.5.2 Amplification ................................................................................ 27 
1.5.3 Antennae ....................................................................................... 28 
1.5.4 Transmission Systems ................................................................... 30 
1.6 Scattering and Attenuation of EM Waves ........................................ 31 
1.6.1 Rain ............................................................................................... 32 
1.6.2 Fog ................................................................................................ 32 
1.6.3 Harmattan ...................................................................................... 33 
1.7 Aim and Objectives of the Study ...................................................... 33 
1.8 Justification e of the Study ............................................................... 34 
1.9 Scope of the Study ........................................................................... 35 
1.10 General Form of the Thesis ............................................................ 36 
 
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CHAPTER TWO: STUDIES OF THE EFFECTS OF DUST, FOG 
AND RAIN ON RADIOWAVES 
2.1 Climate of Ghana ............................................................................. 38 
2.2 Effects of Dust.................................................................................. 49 
2.3 Effects of Fog ................................................................................... 50 
2.4 Effects of Rain.................................................................................. 51 
 
 
CHAPTER THREE: THE RAYLEIGH AND MIE 
ATTENUATION MODELS FOR WAVES 
3.1 Scattering And Absorption In The Atmosphere............................... 55 
3.1.1 Polarization of a Wave .................................................................. 56 
3.2 Theory of Single Particle Scattering ..................................................... 56 
3.3 Approximation Methods/Models for Scattering .............................. 59 
3.3.2 Rayleigh Approximation .................................................................. 60 
3.3.2 Mie Approximation ....................................................................... 61 
3.4 Signal Attenuation due to Harmattan Dust ...................................... 63 
3.4.1 Harmattan Dust Predicted Model  ................................................. 64 
3.4.1.1 Using Rayleigh Approximation ................................................. 65 
3.4.1.2 Using Mie Approximation ......................................................... 65 
3.4.2 Dependence on Visibility .............................................................. 66 
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3.4.4 Zain Elabdin Model ...................................................................... 67 
3.5 The  ITU-R Rain Attenuation Model ................................................ 70 
 
 
CHAPTER FOUR: STUDY SITES, EQUIPMENT AND DATA 
ACQUISITION 
4.1 Study Sites ........................................................................................ 74 
4.1.1 Axim Site ...................................................................................... 74 
4.1.2 Tamale Site.................................................................................... 76 
4.2 Equipment Used ................................................................................. 78 
4.2.1 Campbell Scientific CS120 Visibility Sensor ..................................... 79 
4.2.2 MiniOFS Optical Sensor ............................................................... 81 
4.2.3 Davis Vantage Pro 2 Weather Station ........................................... 82 
4.2.4 Campbell Scientific CR1000 Datalogger ...................................... 84 
4.3 Methodology .................................................................................... 86 
4.4 Data Analysis ................................................................................... 95 
 
 
 
CHAPTER FIVE: RESULTS AND DISCUSSIONS 
5.1 Signal Attenuation Analysis ............................................................. 97 
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5.2 Axim Measurements ........................................................................ 98 
5.2.1 Harmattan Dust Results................................................................. 98 
5.2.1.1 Attenuation for the Different Frequency Bands ......................... 98 
5.2.2 Rain Rate Measurements............................................................. 106 
5.2.3 Additional Data Analysis (Axim)  .............................................. 108 
5.3 Tamale Measurements ................................................................... 111 
5.3.1 Harmattan Dust Results............................................................... 111 
5.3.2 Rain Rate Results ........................................................................ 119 
5.3.3 Additional Data Analysis (Tamale)  ........................................... 120 
5.4 Signal Attenuation due to Dust for Different Radii ....................... 122 
5.4.1 Comparison Between the Measured and Predicted Models ........ 125 
 
 
CHAPTER SIX: CONCLUSIONS AND RECOMMENDATION 
6.1 Summary of Experiment ................................................................ 129 
6.2 Key Results .................................................................................... 129 
6.2 Further Work and Recommendations ............................................ 133 
 
REFERENCES  .................................................................................. 135 
 
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 LIST OF FIGURES 
Figure 1.1: The Electromagnetic Spectrum .............................................. 3 
Figure 1.2: Electromagnetic Wave ........................................................... 5 
Figure 1.3: Diagram showing a wire with steady line current, I and the 
vector from the source to the point, r ....................................................... 8 
Figure 1.4: Diagram showing a long straight wire carrying a steady 
current, I ................................................................................................... 8 
Figure 1.5: Magnetic Field due to current-carrying infinite wire ............ 9 
Figure 1.6: Line of Sight Propagation .................................................... 17 
Figure 1.7: Ground Wave Propagation .................................................. 18 
Figure 1.8: Sky Wave Propagation ........................................................ 19 
Figure 1.9: Atmospheric Layers ............................................................. 20 
Figure 1.10: Layers of the Ioonosphere over the period of a day .......... 22 
Figure 1.11: RadiowavesTransmission Media ....................................... 25 
Figure 2.1: Map of Ghana with its bordering countries ......................... 39 
Figure 2.2: Climatic Zones in Ghana ..................................................... 41 
Figure 2.3: Air masses and their source regions .................................... 43 
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Figure 2.4: Movements of the Inter-Tropical Convergence Zone and 
Rainfall ................................................................................................... 44 
Figure 2.5: Mean Monthly Rainfall and Temperatures .......................... 48 
Figure 3.1: Scattering Configuration ...................................................... 57 
Figure 4.1: Map of Southern Ghana ....................................................... 75 
Figure 4.2: Axim research site at the GMA office ................................. 76 
Figure 4.3: : Map of Northern Part of Ghana ......................................... 77 
Figure 4.4: Tamale research site at the GMA office .............................. 78 
Figure 4.5: Campbell Scientific CS120 Visibility Sensor ...................... 80 
Figure 4.6: Mini OFS Optical Sensor ..................................................... 82 
Figure 4.7: Vantage Pro 2 Integrated Sensor Suite (ISS) ....................... 83  
Figure 4.8: Vantage Pro 2 Console ........................................................ 84 
Figure 4.9: CR1000 Measurement and Control Datalogger ................... 86 
Figure 4.10: Setting the Transmitter ID for communication between the 
ISS and the console ................................................................................ 87 
Figure 4.11: Positioning the protective cage around the weather station at 
the Physics Department, University of Ghana ....................................... 88 
Figure 4.12: Complete ISS setup communicating with console ............ 89 
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Figure 4.13: Setting up the Davis Vantage Pro 2 Weather Station at the 
Axim site ................................................................................................ 90 
Figure 4.14: Installed Vantage Pro 2 Weather Station at the Tamale site
 ................................................................................................................ 91 
Figure 4.15: Concrete foundation for mount installation ....................... 92 
Figure 4.16: Fully mounted visibility sensor ......................................... 93 
Figure 4.17: Set up of the CS120 Visibility Sensor and Vantage Pro 2 
Weather Station at the Tamale site ......................................................... 94 
Figure 5.1: Signal Attenuation versus Frequency at S-Band for Different 
Visibilities in Axim .............................................................................. 100 
Figure 5.2: Signal Attenuation versus Frequency at C-Band for Different 
Visibilities in Axim .............................................................................. 100 
Figure 5.3: Signal Attenuation versus Frequency at X-Band for Different 
Visibilities in Axim .............................................................................. 101 
Figure 5.4: Signal Attenuation versus Frequency at Ku-Band for Different 
Visibilities in Axim .............................................................................. 101 
Figure 5.5: Signal Attenuation versus Frequency at K-Band for Different 
Visibilities in Axim .............................................................................. 102 
Figure 5.6: Signal Attenuation versus Frequency at Ka-Band for Different 
Visibilities in Axim .............................................................................. 102 
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Figure 5.7: Signal Attenuation versus Frequency at W-Band for Different 
Visibilities in Axim .............................................................................. 103 
Figure 5.8: Signal Attenuation due to harmattan against Frequency at 
Vis=3975.648936m for different radius sizes ...................................... 104 
Figure 5.9: Signal Attenuation due to harmattan against Frequency at 
Vis=3995.711m for different radius sizes ............................................ 104 
Figure 5.10: Signal Attenuation due to harmattan against Frequency at 
Vis=4012.3935m for different radius sizes .......................................... 105 
Figure 5.11: Signal Attenuation due to harmattan against Frequency at 
Vis=4016.027m for different radius sizes ............................................ 105 
Figure 5.12: Graph of Rain Attenuation versus Frequency from August - 
December 2015 .......................................................................................... 
 .............................................................................................................. 107 
Figure 5.13: Graph of Rain Attenuation versus Frequency from January - 
April 2016 .................................................................................................. 
 .............................................................................................................. 107 
Figure 5.14: Graph of Visibility versus Rain Rate in Axim ................ 109 
Figure 5.15: Graph of Visibility versus Relative Humidity (All-Day, All 
weather) in Axim  ................................................................................. 110 
Figure 5.16a: XYZ Graph of Visibility against Relative Humidity and 
Temperature  ........................................................................................ 111 
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Figure 5.16b: XYZ Graph of Temperature against Visibility and Relative 
Humidity  .............................................................................................. 111 
Figure 5.17: Signal Attenuation versus Frequency at S-Band for Different 
Visibilities in Tamale ........................................................................... 112 
Figure 5.18: Signal Attenuation versus Frequency at C-Band for Different 
Visibilities in Tamale ........................................................................... 113 
Figure 5.19: Signal Attenuation versus Frequency at X-Band for Different 
Visibilities in Tamale ........................................................................... 113 
Figure 5.20: Signal Attenuation versus Frequency at Ku-Band for 
Different Visibilities in Tamale ............................................................ 114 
Figure 5.21: Signal Attenuation versus Frequency at K-Band for Different 
Visibilities in Tamale ........................................................................... 114 
Figure 5.22: Signal Attenuation versus Frequency at Ka-Band for 
Different Visibilities in Tamale ............................................................ 115 
Figure 5.23: Signal Attenuation versus Frequency at W-Band for 
Different Visibilities in Tamale ............................................................ 115 
Figure 5.24: Signal Attenuation due to harmattan against Frequency at 
Vis=225.482m for different radii ......................................................... 117 
Figure 5.25: Signal Attenuation due to harmattan against Frequency at 
Vis=232.64m for different radii ........................................................... 117 
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Figure 5.26: Signal Attenuation due to harmattan against Frequency at 
Vis=256.95m for different radii ........................................................... 118 
Figure 5.27: Signal Attenuation due to harmattan against Frequency at 
Vis=261.70m for different radii ........................................................... 118 
Figure 5.28: Graph of Rain Attenuation versus Frequency from April - 
June 2016 .............................................................................................. 120 
Figure 5.29: Graph of Visibility versus Relative Humidity (All-Day, All 
weather) in Tamale  .............................................................................. 121 
Figure 5.30a: XYZ Graph of Visibility against Relative Humidity and 
Temperature  ........................................................................................ 122 
Figure 5.30b: XYZ Graph of Temperature against Visibility and Relative 
Humidity  .............................................................................................. 122 
Figure 5.31: Signal Attenuation due to harmattan against Visibility at 
40GHz for different radii in Tamale .................................................... 123 
Figure 5.32: Signal Attenuation due to harmattan against Visibility at 
40GHz for different radii in Axim ....................................................... 124 
Figure 5.33: Result of Measurements and Calculations of Signal 
Attenuation due to harmattan at 40GHz ............................................... 126 
Figure 5.34: Comparison of Calculated Signal Attenuation due to 
harmattan dust at Different frequencies in Axim and Tamale ............. 127 
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LIST OF TABLES 
Table 1.1: Electromagnetic Spectrum and their Frequency Bands .......... 4 
Table 1.2: Basic Equations for Maxwell’s Equations ............................ 13 
Table 1.3: Frequency Band Designations .............................................. 15 
Table 5.1: Dielectric constants for the different microwave frequency 
bands ....................................................................................................... 99 
Table 5.2: Result of Measurements and Calculations of Signal 
Attenuation Due To Harmattan at 40 GHz in Axim ............................ 125 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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LIST OF ABBREVIATIONS 
VHF   Very high frequency 
UHF   Ultra high frequency 
AM   Amplitude Modulation 
FM   Frequency Modulation 
PM   Phase Modulation 
RF   Radio frequency 
RSL   Receive Signal Level 
ITCZ   Inter Tropical Convergence Zone 
ITU-R   International Communications Union  
   Radiocommunication 
CD    Cumulative distribution 
LOS    Line-of-sight 
VSAT    Very Small Aperture Terminal 
PMMA  Polymethyl methacrylate 
ISS    Integrated Sensor Suite 
 
 
 
 
 
 
 
 
 
 
 
 
 
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CHAPTER 1 
THE PHYSICS OF RADIOWAVES AND THEIR 
PROPAGATION 
Radio waves are one of the parts that comprises an electromagnetic radiation. 
They have the longest wavelength and the shortest frequencies. Other types of the 
electromagnetic radiation are visible light, microwaves, 
infrared (IR), ultraviolet (UV), gamma-rays and X-rays. Radio waves are 
commonly used for communication; radio, television, cellphones etc.  
Changing electric and magnetic fields constitute an electromagnetic radiation. At 
every point along the wave there is an electric field coupled with a magnetic field. 
The electric field is at right angle to the magnetic field. 
A wave has properties such as speed, wavelength, and frequency. These are 
related by a simple expression (Speed =  Frequency  × Wavelength). For 
electromagnetic waves, the speed is denoted by c (the speed of light). The speed 
of light in vacuum is 3 × 108 m/s and c =  f × λ. Electromagnetic waves unlike 
mechanical waves, do not need a medium in which to propagate but they can 
propagate through vacuum. 
The wavelength (λ) is the distance measured from a point on one wave to the 
equivalent part of the next, for example from the top of one peak to the next. The 
frequency is the number of whole waves that pass a fixed point in a period of 
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time. The speed has units in meters/second, whiles frequency has its units in 
cycles per second (or Hertz, abbreviated Hz), and wavelength is measured in 
meters. 
Radio propagation talks about how radio waves travel, or are propagated from one 
point to another. Radio waves, like other types of EM radiation, are affected by 
the occurrences of reflection, refraction, diffraction, absorption, polarization, 
and scattering etc. There will be more in-depth information in the chapter.  
Electromagnetic signals are transmitted in two ways: through a guided medium or 
through an unguided medium. Guided media such as coaxial and fiber optic 
cables have fewer challenges than the wireless or the unguided channel such as 
the atmosphere. As a signal travels through the wireless conduit, it goes through 
the influence of various kinds of propagation such as reflection, diffraction and 
scattering, due to the presence of buildings, mountains and other such 
obstructions (Mark, 2005). 
 
1.1 ELECTROMAGNETIC THEORY 
Wireless communications utilize electromagnetic waves in transferring signals 
across long distances. Electromagnetic waves are made up of an electric field 
coupled with a magnetic field. Electromagnetic waves do not need a medium to 
propagate. Hence, they can travel through vacuum. Electromagnetic waves extend 
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over a wide range of frequencies. The frequency of an electromagnetic wave 
determines its characteristics. The EM wave spectrum is shown in Figure 1.1. 
 
Figure 1.1: The Electromagnetic Spectrum  
The electromagnetic spectrum is divided into different frequency bands as shown 
in Table 1.1. 
 
 
 
 
 
 
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Frequency Band Frequency (Hz) Wavelength Use 
Long wave, TV < 3 x 109 Hz 105 to  102 m TV broadcast 
Short Wave Radio 108 to  3 x 109 Hz 102 to  10-1 m AM and FM radio, 
Communication 
Microwave 3 x 109 to  3 x 1012 Hz 10-1 to  10-3 m Cell phones, Wireless 
data, Microwaves, 
Satellites 
Infrared 3 x 1012 to  4.3 x 1014 Hz 10-3 to  7 x 10-7 m Remote Controls, 
Night Vision Lighting 
Visible 4.3 x 1014 to  7.5 x 1014 7 x 10-7 to  4 x 10-7 m Vision, Photography 
Hz 
Ultraviolet 7.5 x 1014 to  3 x 1017 Hz 4 x 10-7 to 10-9 m Sun-tan lamps, Dental 
curing, Vitamin D 
source 
X-Rays 3 x 1017 to  3 x 1019 Hz 10-9 to  10-11 m Baggage Screening, 
Imaging bone defects 
Gamma Rays 3 x 1019 to  1020 Hz 10-11 to  10-15 m Cancer Treatment 
Cosmic Rays 1020 to  1022 Hz 10-15 to  10-20 m  
Table 1.1: Electromagnetic Spectrum and their Frequency Bands 
 
1.2 THE THEORY OF EM WAVES 
Electromagnetic waves have two orthogonal time-varying fields: electric and 
magnetic components that oscillate simultaneously. The planes of the electric and 
magnetic fields are perpendicular to each other and also perpendicular to the 
direction of the wave propagation (Seybold, 2005, Griffiths, 1999). 
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Figure 1.2: Electromagnetic Wave 
1.2.1 The Electric Field 
The electric field is defined as the vector force per unit charge. It is generated by 
an electric charge and is usually denoted by the symbol E. The electric field is a 
vector quantity that varies from point to point. The unit of the electric field is 
Newtons per coulomb (1𝑁⁄𝐶 = 1 𝑉⁄𝑚).  
The electric field (electrostatic field), E produced as a result of several point source 
point charges at distances 𝓇1,   𝓇2,   𝓇3,   ………… 𝓇𝑛  from a test charge, Q, is given 
by  
𝐹  1?⃗? = = ∑𝑛
𝑞𝑖
𝑖=1 ?̂?     (1.1) 𝑄 4𝜋𝜀𝑜 𝑟 2𝑖
where Q is the test charge (assuming that Q is small), qi is the stationary point 
charges, ri  is the distances between the point charges, qi and the test charge, Q, F 
is the total electric force exerted by the point charges, qi on the test charge, Q and 
εo is the permittivity in vacuum/free space 
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In more realistic conditions, the point (source) charges are usually continuous over 
a region and not discrete. Consequently, the E for continuous charges over a region 
becomes 
 
?⃗? 
𝐹 1 1
= = ∫ ?̂? 𝑑𝑞      (1.2) 
𝑄 4𝜋𝜀𝑜 𝑟2
The three main distributions used are the line charge (λ), surface charge (σ) and 
volume charge (ρ). The flux of electric field lines through any surface is a measure 
of the number of field lines passing through the surface. Considering a point 
charge q at the origin, the electric flux, ФE through a closed surface, for example a 
sphere of radius r, centered on the origin, is equal to 
  1 𝑞 𝑞Ф𝐸 = ∮ ?⃗?. 𝑑𝐴 = ∫( ?̂? ) . (2 𝑟
2 sin 𝜃 𝑑𝜃 𝑑𝜙 ?̂? ) =     (1.3) 
4𝜋𝜀𝑜 𝑟 𝜀𝑜
Hence, for any arbitrary closed surface with any charge distribution, the electric 
flux ФE is given by 
∮ ?⃗? . 𝑑𝐴 
𝑄
= 𝑒𝑛𝑐      (1.4) 
𝜀𝑜
where Qenc is the total charge enclosed by the surface.  
This is the integral form of the Gauss’ Law (known as Gauss's law in integral 
form).  Applying the divergence theorem, the differential form of the Gauss’ Law 
can be written as: Ф = ∮ ?⃗? . 𝑑𝐴 =∫ (∇⃗ ∙ ?⃗? 𝐸 ) 𝑑𝜏 𝑆 𝑉
Therefore, equation 1.4 becomes 
 
 
∫ (∇⃗ ∙ ?⃗? 
1
) 𝑑𝜏 = ∫ 𝜌𝑑𝜏      (1.5) 
𝑉 𝜀𝑜 𝑉
Since this equation holds for any volume, the integrands will be equal and hence 
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∇⃗ ∙ ?⃗? 
𝜌
=        (1.6) 
𝜀𝑜
Equation 1.6 is known as Gauss's law in differential form. 
Additionally, taking the line integral from some point a to another point b gives 
𝑏
∫ 𝐸 ∙ 𝑑𝑙 
𝑎
But 𝐴 = 𝑑𝑟?̂? + 𝑟𝑑𝜃𝜃 + 𝑟 sin 𝜃 𝑑𝜙?̂? .  
 1 𝑞 𝑏 1 𝑏 𝑞 1Therefore,  ?⃗? ∙ 𝑑𝑙 = 2 𝑑𝑟 = ∫ 𝐸 ∙ 𝑑𝑙 = ∫ (4𝜋𝜀 𝑟 𝑎 4𝜋𝜀 𝑎 𝑟2 𝑑𝑟 = 𝑟4𝜋𝜀 𝑏 − 𝑟𝑎) 𝑜 𝑜 𝑜
ra is the distance from the starting point to point, a 
 rb is the distance from the starting point to point b.  
For a closed path, the integral will be zero since 𝑟𝑏 = 𝑟𝑎. Therefore, ∮ ?⃗? ∙ 𝑑𝑙 = 𝑜. 
Applying Stoke’s theorem (curl of E) to equation 1.6 gives 
∇⃗  × ?⃗? = 0      (1.7) 
 
1.2.2 The Magnetic Field 
Electric currents produce magnetic fields. Consequently, a current-carrying wire 
can attract or repel a magnet. On the other hand, magnet exerts a force on a 
current-carrying wire. A moving charge produces both an electric and a magnetic 
field.  
 
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Consider a wire (with dl as an element of length facing the direction of flow of 
current) with fixed line current I and the vector from the source to the point r 
(Figure 1.3). 
 
Figure 1.3: Diagram showing a wire with steady line current, I and the vector from the source to 
the point r (Griffiths, 1999) 
Then the magnetic field, B at the point P can be expressed as 
 𝜇𝑜 𝑑𝑙 ×(𝑟−𝑟
′) 
?⃗? = 𝐼 ∫ ′ 3        (1.8) 4𝜋 |𝑟−𝑟 |
This expression is called the Biot-Savart Law. The constant µo is called the 
permeability of free space and 𝜇0 = 4𝜋 × 10
−7𝑁/𝐴2. 
 
 
Figure 1.4: Diagram showing a long straight wire carrying a steady current, I (Griffiths, 1999) 
 
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𝑠
Additionally, 𝑙′ = 𝑠 tan𝜃and therefore 𝑑𝑙′ = 2 𝑑𝜃 . Also 𝑠 = 𝑟 cos 𝜃 which 𝑐𝑜𝑠 𝜃
1 𝑐𝑜𝑠2𝜃 𝜇 𝐼 𝜃2 𝑐𝑜𝑠
2𝜃 𝑠
resulis in 2 = 2 . Consequently, ?⃗? =
𝑜 ∫ ( 2 ) ( 2 ) cos 𝜃𝑑𝜃 =𝑟 𝑠 4𝜋 𝜃1 𝑠 𝑐𝑜𝑠 𝜃
𝜇𝑜𝐼 𝜃2 𝜇 𝐼∫ cos 𝜃𝑑𝜃 = 𝑜 (sin 𝜃 − sin 𝜃 ). 
4𝜋 𝜃 4𝜋 2 11
 
Figure 1.5: Magnetic Field due to current-carrying infinite wire (Griffiths, 1999) 
For a straight infinite wire, 𝜃 𝜋1 = − ⁄2 and 𝜃2 =
𝜋⁄2 . Hence the magnetic field 
at a distance s from a straight infinite wire carrying a steady current I (Fig. 1.5) is 
as follows: 
 𝜇𝑜𝐼?⃗? =        (1.9) 
2𝜋𝑠
By symmetry, the magnetic field, B produced is determined only by the distance 
from the wire s and is positioned at 90 degrees to the wire. The lines of B are 
concentric circles around or loop enclosing the wire. 
The integral of B (from equation 1.9) around a circular path of radius s, centered 
at the wire is 
 
∮ ?⃗? 
𝜇
∙ 𝑑𝑙 = ∮ 𝑜
𝐼 𝜇 𝐼
𝑑𝑙 = 𝑜 ∮𝑑𝑙 = 𝜇𝑜𝐼    (1.10) 2𝜋𝑠 2𝜋𝑠
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Equation 1.10 can also be obtained for a loop with cylindrical coordinates (s, ϕ, z) 
and the current flowing along the z axis. For a bundle of wires, the collective line 
integral is 
 
∮ ?⃗? ∙ 𝑑𝑙 = 𝜇𝑜𝐼𝑒𝑛𝑐       (1.11) 
 
where Ienc stands for the total current enclosed by the integration path. This is the 
integral form of Ampere’s Law. If the flow of charge is denoted by a volume current 
density, J then the enclosed current is 
𝐼  𝑒𝑛𝑐 = ∫ 𝐽 ∙ 𝑑𝑎       (1.12) 
The integral is taken over the surface bounded by the loop. Applying Stokes’ 
theorem gives  
 
∫(∇⃗ × ?⃗? ) ∙ 𝑑𝑎 = 𝜇𝑜 ∫ 𝐽 ∙ 𝑑𝑎      (1.13) 
Hence,  
∇⃗ × ?⃗? = 𝜇  𝑜𝐽      (1.14) 
 
This expression shows Ampere’s Law in the differential form. In order to find the 
differential equations for the magnetic field, Equation 1.14 is rewritten as follows: 
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?⃗? 
𝜇
= − 𝑜 ∫ ∇⃗ ′  
1 
(𝑟 ) × ∇⃗ ′ 𝑑
3 𝑟′     (1.15) 
4𝜋 |𝑟−𝑟 |
1 𝑟 
Given the identities ∇⃗ ( ) = −  and  ∇⃗ × (𝜑𝑎)3 = (∇𝜑) × 𝑎 + 𝜑(∇ × 𝑎) 𝑟 𝑟
where φ and a are arbitrary scalar and vector functions respectively. Therefore, 
equation 1.15 becomes 
𝐽 (𝑟′) 1 1
∇⃗ × = ∇⃗ × 𝐽 (𝑟′)′ ′ +   (′ ∇⃗ × 𝐽 𝑟
′)∇⃗ × 𝐽 (𝑟′) = 0   (1.16) 
|𝑟−𝑟 | |𝑟−𝑟 | |𝑟−𝑟 |
But ∇ × 𝐽 (𝑟′) = 0. Hence equation 1.16 becomes 
 
𝜇𝑜 𝐽 (𝑟
′)
?⃗? = − ∇⃗ × ∫ 𝑑3 𝑟′′      (1.17) 4𝜋 |𝑟−𝑟 |
and the divergence of B is 
∇⃗ ∙ ?⃗? = 0     (1.18) 
 
Consider an enclosed circuit with a time-varying magnetic field. Faraday’s law 
states that an electromotive force, ε, is induced in an enclosed circuit and is given 
by the negative rate of change of the magnetic flux, ФB through the circuit. 
(Equation 1.19). The  time-varying magnetic field gives an electric field. 
𝑑Ф
𝜀 = ∮ ?⃗? ∙ 𝑑𝑙 = − 𝐵     (1.19) 
𝑑𝑡
But Ф𝐵 = ∫ ?⃗? ∙ 𝑑𝑎 . Therefore,  
𝑑?⃗? 
∮ ?⃗? ∙ 𝑑𝑙 = −∫ 𝑑?⃗⃗?      (1.20) 
𝑑𝑡
Equation 1.20 can be changed to a differential form by applying Stoke’s theorem.  
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𝑑?⃗? 
∇⃗ × ?⃗? = −      (1.21) 
𝑑𝑡
 
This is known as the Faraday’s Law. Some books refer to it as the Maxwell- 
Faraday equation.   
Beyond magnetostatics, the divergence of current density, J is not zero for steady 
currents. Hence the Ampere’s law is incorrect for unteady currents. Recounting 
from the continuity equation and Gauss’ law, Maxwell made some corrections by 
way of theoretical arguments. 
 
∇⃗ 
𝜕𝜌 𝜕 𝜕?⃗?
∙ 𝐽 = − = − (𝜀0∇⃗ ∙ ?⃗? ) = −∇⃗ ∙ (𝜀0 )   (1.22) 𝜕𝑡 𝜕𝑡 𝜕𝑡
 
∇⃗ × ?⃗? = 𝜇 𝐽 
𝜕?⃗?
0 + 𝜇0𝜀0      (1.23) 𝜕𝑡
For constant E, ∇⃗ ∙ ?⃗⃗⃗? = 𝜇 𝐽 0 . Hence the correction does not change Ampere’s law.  
 
 
1.2.3 Maxwell’s Equations 
James Clerk Maxwell, who was a Scottish scientist in the 1860's and 1870's, 
developed the scientific theory known as the Maxwell’s Equations which describe 
the electromagnetic wave propagation. The theory states that a time-varying 
magnetic field gives an electric field and a time-varying electric field gives a 
magnetic field. A time-varying magnetic field can be created by an accelerated 
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charge. There are four equations which are the foundation of the Maxwell’s 
Equations (Table 1.2). 
Law Equation Physical Interpretation 
Differential Form Integral Form 
Gauss's 𝜌 𝑞∇⃗ . ?⃗? =       Electric flux through a  ∮ ?⃗?. 𝑑𝐴 =  
𝜀 𝜀
law for E closed surface is 
  proportional to the 
charged enclosed 
Faraday's 𝜕?⃗? 𝑑𝜙 𝐵 Changing magnetic flux ∇⃗ . ?⃗? = −  ∮ ?⃗? . 𝑑𝑆 =  −  
𝜕𝑡 𝑑𝑡
law is associated with an 
electric field 
Gauss's ∇⃗ . ?⃗? = 0   The total magnetic flux ∮?⃗?. 𝑑𝐴 = 0 
law for B through a closed surface 
is zero 
Ampere- 𝜕?⃗? 𝑑𝜙 𝐸 Electric current and ∇⃗ × ?⃗? = 𝜇 + 𝜇𝜀                      ∮?⃗?. 𝑑𝑆 =  𝜇𝐼 + 𝜇𝜀  
𝜕𝑡 𝑑𝑡
Maxwell changing electric flux is 
law associated with a 
magnetic field 
Table 1.2: Basic Equations for Maxwell’s Equations 
 
ρ is the free charge densities 
J is the conduction current densities.  
The wave equation can be obtained from the Maxwell’s Equations. By applying 
free space constraints so that I and Q are both zero, the electric and magnetic 
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fields are decoupled by taking second-order derivatives of equations 1.6, 1.19, 
1.18 and 1.23. 
2  𝜕2∇ 𝐸 =  𝜇 𝜀 𝐸0 0 ⁄𝜕𝑡2      (1.24)  
∇2𝐵 =  𝜇 𝜀  𝜕
2𝐵
0 0 ⁄𝜕𝑡2     (1.25) 
 
Equation 1.24 and equation 1.25 have the formula of the general wave equation 
for a wave Ψ (x, t) traveling in the x direction with speed v:  
𝜕2𝛹 1 𝜕2𝛹
2 = 2 2        (1.26) 𝜕𝑡 𝑣 𝜕𝑡
Equating the speed in equation 1.26 with the coefficients on equation 1.24 and 
equation 1.25, the speed of electric and magnetic waves is derived, which is the 
1
speed of light symbolized with 𝑐 = = 2.997 × 108𝑚/𝑠2. 
√𝜇0𝜀0
 
Radio waves have the lowest frequency of the electromagnetic spectrum. In most 
cases, they are considered to have wavelengths ranging from 1 mm to100 km or 
frequencies within 3 kHz to 300 GHz. This range of frequencies includes the 
microwave region. Radio waves are used for satellite communication, radios, 
cellphones, television etc. In the case of radios, the waves also have a wide range 
of subcategories which include AM (Amplitude Modulation, which creates a 
wave of constant frequency but variable amplitude) and FM (Frequency 
Modulation, which creates a wave of constant amplitude but variable frequency). 
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Both AM and FM radio waves are used to carry radio signals in frequency ranges 
from 540 to 1600 kHz and from 88 to 108 MHz respectively. 
Figure 1.3 shows the various nomenclature for the frequency bands in radio 
waves. It illustrates the relationship between frequency (f) and wavelength (λ). 
Every wave can be described using either its frequency or its wavelength. 
Frequency is inversely related to wavelength and related to the speed of light by 
the equation 𝑐 = 𝑓 × 𝜆, where c represents the speed of light.  
 
Table 1.3: Frequency Band Designations  
 
1.3 GENERATION OF RADIO WAVES 
Electromagnetic waves, in general are formed by moving electrons. The electron 
has an electric field shown by electric field lines. As the electron travels, for 
instance by means of vibrations, the moving electron also creates a magnetic field. 
These combined electrical and magnetic waves form the electromagnetic wave. 
Hence all matter produces electromagnetic waves. 
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Radio waves are propagated from a transmitting antenna and are intercepted by a 
receiving antenna. The radio wave is then converted to an electrical signal and 
transmitted to devices such as a radio, cellular phones, television set etc. The 
signal is converted to mostly sound waves which transmits the information by 
broadcasting through the various devices.  
 
Radio, cellular phones, TVs etc. use radio transmission in one form or another. 
These radio waves can travel very fast through space because of its large 
frequencies and can travel through the walls because of its low wavelengths. 
Nevertheless, radio wave signals are weak through larger masses of earth as found 
in a tunnel or a cave. 
 
 
1.4 PROPAGATION OF RADIO WAVES 
Radio propagation refers to the behavior of radio waves when they are transferred, 
or are propagated from one point to another. Radio communication travels by 
means of electromagnetic waves traveling through the Earth’s atmosphere. Radio 
waves, like all other forms of electromagnetic radiation, generally travel in straight 
lines.  
In order for radio waves to propagate, antennas are used. The antenna acts as the 
beginning and end of a communication circuit. An antenna is an electrical device 
that transforms RF signals into electric currents and are conducted across a 
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transmitter and then the electric current is converted back into RF signals that are 
passed on to the receiver (Shilling, 1986). 
Electromagnetic waves do not always travel directly from the transmitter to the 
receiver. The path of these waves rely on the frequency of the wave, the distance to 
be covered. There are three different forms in which radio signals can travel: 
 Line of Sight Propagation: This is the simplest form of propagation. The 
signal travels in a straight line, like a beam of light. Both the transmitting and 
receiving antennas must be within the line of sight. This way of transmitting 
and receiving radio signals can be used for all frequencies above 30 MHz.  
 
 
 
 
 
Figure 1.6: Line of Sight Propagation 
 
The distance between the transmitter and receiver is dependent on the frequency 
or wavelength of the radio signal. The range can be increased by raising the 
height of the antenna. VHF and UHF frequencies mostly make use of line of sight 
communication. 
 
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 Ground wave Propagation: This type of propagation can speed round the 
Earth's curvature. This type of propagation works for most frequencies up to 2 
MHz but the distance between the transmitter and the receiver will differ with 
geography. An example is the difference between the desert and the ocean. This 
way of propagation tends to be used by AM radio to propagate since it travels 
through short-to-moderate distances. 
 
 
Figure 1.7: Ground Wave Propagation 
 Sky wave Propagation: This kind of propagation has the radio signal 
reflected from the ionized layer of the atmosphere (ionosphere) to the earth’s 
surface. The signal can jump back and forth between the ionosphere and 
earth’s surface. This kind of propagation is used by high frequency bands (3 to 
30 MHz) for short distance communication. For these frequencies, the ground 
slowly absorbs the signal as the frequency rises, reducing the ground wave 
range. Examples include international broadcasts. 
 
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Figure 1.8: Sky Wave Propagation 
1.4.1 Atmospheric Propagation 
The Earth’s atmosphere can be categorized into four layers. Each layer has different 
thermal, chemical, and physical properties (Figure 1.7). It extends beyond 560 km 
(348 miles) above the Earth’s surface. 
 
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Figure 1.9: Atmospheric Layers  
 
The troposphere is the lowest layer of the atmosphere and has an average height of 
10 to 11 km. It has about 75-80% of total mass of the atmosphere. The top part of 
the troposphere is known as the tropopause. The temperature in this layer generally 
decreases with height. The earth’s weather occurs in the troposphere. The 
stratosphere is the layer that lies above the troposphere. It has a height ranging from 
11 to 45-50 km. It is composed mostly of dry stable air and makes approximately 
20 to 25% of total mass. The ozone layer can be found in the stratosphere. The 
molecule of ozone (O3) strongly absorbs certain ultraviolet wavelengths, and the 
concentration of this uv radiation from the Sun causes a rise of the temperature in 
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the air. As a result, the temperature in the stratosphere increases with height, to 
about -3 ᵒC (28 ᵒF) at its upper boundary. The stratopause marks the top of the 
stratosphere. 
The next layer is the mesosphere which lies at a height of about 45 to 92 km.  The 
mesosphere makes up below 1% of the total mass. There is a sharp drop in 
temperatures to about -93 °C (-137 °F) at the top of this layer. The next layer is the 
ionosphere above the mesosphere. This layer has X-rays and ultraviolet rays that 
ionize the gases resulting in ions and free electrons. The ionosphere starts from 
about 60km above Earth’s surface and ranges upward to the top of the atmosphere. 
The ionosphere plays an important role in radio communication. 
 
1.4.1.1 Ionospheric Propagation  
The Earth’s ionosphere has the property that allows it to refract or bend radio waves 
passing through it. Ionospheric propagation happens within the range of 
frequencies from 3 to 30 MHz. The ionosphere has varying sub-regions in relation 
to their free electron density profile that specifies the degree of ionization. These 
sub-regions are known as the D, E, and F layers. The D layer is located at the 
lowermost region. This layer absorbs high-frequency radio waves. It generally 
exists during the day. As night falls, the D-layer fades then gradually disappears 
during the night.  
 
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Figure 1.10: Layers of the Ionosphere over the period of a day 
This allows radio waves to enter into an upper part of the ionosphere, such that the 
radio waves are replicated in the ionospheric region back to the earth’s surface, then 
reflected again into the ionosphere (Figure 1.8). As a result, AM radio signals from 
distant stations can be received effortlessly at night. The E layer can be located 
above the D layer. The E layer also weakens as night falls and finally vanishes. The 
E layer absorbs x rays, and it has its highest at about 65 miles (105 km).  
The F layer is positioned directly above the E layer, about 93 miles (150 km), and 
it has the highest concentration of charged particles. Though the structure of the F 
layer alters during the day, it is a fairly constant layer, where high levels of ultra-
violet radiation are absorbed. It is made up of two parts: the lower F1 layer, and the 
higher and more electron-dense F2 layer.  
Different types of electromagnetic radiation affect the different layers in the 
ionosphere. Ultraviolet rays (at wavelengths of 100 to 1000 Angstroms) ionizes the 
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F region, soft X-rays (at 10 to 100 Angstroms) ionize the E region, and hard X- rays 
(at 1 to 10 Angstroms) ionize the D region. The ionosphere is not homogeneous, 
and is changing continually. 
 
1.4.1.2 Tropospheric Propagation 
The troposphere is the lowest part of the atmosphere and is closest to the earth 
surface. The troposphere covers the space between the earth’s surface to 
approximately 9km in height at the poles and 17km to 20km at the equator and mid-
latitudes. It comprises 80% of the atmosphere's mass and 99% of it is water vapor. 
The earth’s weather system takes place in the troposphere. The upper boundary of 
the troposphere is the tropopause. The tropopause divides the troposphere from the 
stratosphere by acting as a temperature inversion. Hence the temperature reduces 
with height (by approximately 6.5 ᵒC per km) and pressure in the troposphere is 
highest at the surface and reduces with height. Saturation vapor pressure also 
declines with decreasing temperature and the water vapor content of the atmosphere 
declines sturdily with height. 
In this environment, the troposphere tends to have an important role in the 
propagation of radio waves at VHF (30-300 MHz) and UHF (300- 3000 MHz) 
frequencies. Hence, atmospheric conditions affect the propagation of radio waves 
in the troposphere (Roda, 1988, Atkins, 1991). 
  
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1.5 TRANSMISSION OF RADIO WAVES 
Radio waves are propagated through free space. The wave is transmitted through a 
straight line path. However, the path of the propagated waves is generally impeded 
by atmospheric conditions that cause the ray path to become curved due to the 
different refractive indices of the different atmospheric layers. Atmospheric gases 
and particles will absorb and scatter the radio wave energy. The amount of 
absorption and scattering will be a function of frequency and altitude above sea 
level (Freeman, 2007). The increasing use of microwaves for determining high data 
rate communication channels and determination of geophysical parameters has 
emphasized the need for better modeling and more accurate calculations of 
attenuation through clear and hydrometeor laden atmospheres. 
Microwave links are useful in wireless communication by means of radio 
frequency (RF) transmission medium. A microwave link is a communications 
system that uses a beam of radio waves in the microwave frequency range to 
propagate information between two fixed positions on the earth. Microwave links 
carry cellular telephone calls between cell sites. Wireless internet service 
providers also use microwave links to deliver high-speed internet access to their 
clients. Telephone companies transmit calls between switching centers over 
microwave links (Elfadil, 2005).  A simple one-way microwave link consists of 
four major elements: a transmitter, a receiver, transmission lines, and antennas. 
These basic components are present in every radio communications system like 
cellular telephones (Ghasemi, 2012).  
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Figure1.11: Radiowaves Transmission Media 
1.5.1 Modulation 
The IEEE definition of modulation is “a process whereby certain characteristics 
of a wave, often called the carrier signal, are varied or selected in accordance with 
a modulation function.” (Freeman, 1999). Another definition of modulation is the 
method of varying one or more parameters of a carrier signal in proportion to a 
baseband signal (also known as original transmission signal or message signal) 
carrying information to be transmitted. In most communication system practices, 
a message signal needs to be modulated to a higher frequency for radio 
transmission. Generally, no signal is made up of a single frequency sinusoid, but 
it extends over an array of frequencies called the signal bandwidth. For example, 
when an antenna is too large, modulation is applied to transmit information to a 
higher frequency. The baseband signal is demodulated when it reaches the point 
of transmission, allowing the recipient to receive the original signal. 
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Baseband signals are not transmitted directly. For many transmitters conveying 
baseband information signals simultaneously, the signals would overlap each 
other and there would be no simple way to distinguish between them. A possible 
way of solving this is by using communication at high frequencies and assigning a 
band of frequencies to each communication signal for its transmission. Hence the 
original low frequency baseband signal has to be translated into a high frequency 
signal before transmission. The high frequency signal (also known as the carrier 
signal) is then modulated. The carrier signal may be sinusoidal (continuous) or in 
pulses. A sinusoidal signal can be shown as 
𝑐(𝑡) = 𝐴𝑐 sin(𝜔𝑐𝑡 + 𝜙)     (1.27) 
where c(t) is the signal strength (voltage or current),  
Ac is the amplitude,  
ωc = 2πνc is the angular frequency 
φ is the initial phase of the carrier signal and  
t is the time.  
During the modulation process, any of the three parameters (Ac, ωc and φ) of the 
carrier signal can be regulated by the message signal. The three forms of 
modulation are: 
 Amplitude Modulation (AM) 
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The Amplitude Modulation (AM) technique regulates the strength of the 
transmitted radio wave by varying the signal as it travels along the antenna. This 
is done to include the baseband signal information. 
 
 Frequency Modulation (FM) 
In the Frequency Modulation (FM) technique, the radio station modifies the 
specific frequency of the carrier signal. 
 
 Phase Modulation (PM) 
In the Phase Modulation (PM) technique the phase of the carrier signal is 
regulated in accordance with the information baseband signal. (Freeman, 1999). 
The various techniques differ in how the carrier signal is modulated, or altered. 
FM signals are more advantageous than AM signals. Both AM and FM signals are 
susceptible to small changes in amplitude. With AM broadcasts, this results in 
static whiles FM broadcasts are unaffected since the audio signal is carried 
through changes in frequency.  
 
1.5.2 Amplification 
Amplification is the process in which the amplitude of a signal waveform is 
increased without changing other parameters of the waveform such as the 
frequency. The process is completed using an electrical circuit known as the 
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amplifier. As a result of amplification, the signal strength is also increased. This 
makes up for loss in signal strength in communication systems. The signal is 
amplified between the source of the signal and the final endpoint depending on 
where the signal becomes weakened. 
 
1.5.3 Antennae 
An antenna is an electrical conductor (usually a metallic device) used to radiate 
and receive radio waves. It is a specialized transducer that changes RF signals to 
electric currents  
There are two types of antennae: 
 Transmitting antenna – generates RF energy from electric currents. 
 Receiving antenna - collects energy from RF signals and converts it to AC 
signals.  
In a two-way communication, the same antenna can be used for transmission and 
reception. All wireless systems require an antenna for radiating and receiving RF 
signals (Seybold, 2005). The transmitter generates the signal and the receiver 
detects the signal.  
Transmitters and receivers are designed to operate over a limited range of 
frequencies. In order to transmit a signal, an antenna is used. The size of an 
antenna is constructed depending on the wavelength to allow the antenna to detect 
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the time difference of the signal. For an EM wave with high frequency, the 
wavelength will be quite short and hence such an antenna is unfeasible to 
construct and operate. Hence, for signals with high frequencies and short 
wavelengths, the information enclosed in the original low frequency baseband 
signal is transformed into high frequencies before transmission. 
In wireless systems, antennae are used to emit and collect electromagnetic energy. 
The antenna acts as the transducer between the system and free space. For many 
types of antennas the gain can be estimated from the physical measurements or 
from information of the antenna beam widths. 
Reciprocity is an essential principle of antennas that states that antenna 
performance remains the same whether radiation or reception is considered 
(Seybold, 2005). This implies that the properties of the transmitting antenna or 
receiving antenna can be measured. The estimates of antenna gain, beamwidth, 
and polarization are the same for both transmit and receive based on this principle 
of reciprocity (Seybold, 2005). 
A transmitter transfers electric charges steadily upwards and downwards along its 
antenna and causing the signal that is to be propagated into motion. These waves 
that are transmitted convey signals that are received by antennae on radios and 
television sets. The time-dependent changing electric field and changing magnetic 
field creates the magnetic field and the electric field respectively. The two travel 
together as a pair in the form of an electromagnetic wave into space. However, 
when this EM wave meets the antenna of a radio, its electric field initiates electric 
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charges up and down on the antenna. As a result, the radio detects the travelling 
radio wave. The signal is then transmitted to the radio and received as sound. 
 
1.5.4 Transmission Systems 
Currently, most telecommunication systems are digital. Analog transmission is 
continuous whiles digital transmission is discrete. Digital transmission has signals 
that are propagated in pulses and represented by binary numbers, "1" or "0".  
 
Most signals can be transmitted in either the analog or digital form. For the analog 
signal, the information is transported by the value or magnitude of some 
properties of the signal such as amplitude, frequency or a phase of a voltage, the 
amplitude or duration of a pulse, the angular position of a shaft, or the pressure of 
a fluid. 
 
Signals heard on AM and FM radio and signals heard and viewed on television 
are examples of analog transmissions. In the case of the television, the video uses 
amplitude modulation (AM), the sound subcarrier uses frequency modulation 
(FM), and the color subcarrier employs phase modulation (PM) and all are in 
analog formats (Freeman, 1999). Digital signals can be reconstructed at their end 
point in the exact form they left their starting point despite any distortion along 
the way. 
 
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1.6 SCATTERING AND ATTENUATION OF EM WAVES 
Scattering happens when the medium through which the wave is travelling 
contains substances with a much smaller size than the wavelength of the EM 
wave. These diverse phenomena result in propagation losses in the wave signal. 
Due to the characteristic randomness connected with such channels they are best 
defined with the help of statistical models (Rappaport, 2002).  
Wireless communication globally is affected by microwave attenuation which has 
an effect on the design of the microwave link (Lee, 1995) and the calculating of the 
received signal level (RSL) of the RF signal from one station to another. For a given 
path, the kind of transmission line chosen is determined by the topography, the 
amount of data being transmitted, and its price. As a result, the best quality of 
service is not achieved in the telecommunication services in areas where microwave 
attenuation is a problem. 
Attenuation is the measure of a loss in signal strength. Attenuation of microwaves 
are enhanced by atmospheric conditions such as harmattan dust and rainfall 
among others (wind, fog, snow etc.).  They affect the consistency of satellite 
paths, particularly satellite paths with frequencies above 10GHz (Elfadil et al, 
2005). Several effects of such studies have shown severe signal attenuation at 
frequencies in the region above 10 GHz. Attenuation is less evident at frequencies 
around 3 GHz (Shoewu, 2011). In Ghana, signal attenuation is highly evident in 
the northern part of the country due to the severe harmattan conditions in the 
region and in the south-western part due to the high occurrence of rainfall.  
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1.6.1 RAIN 
Rain predominately consists of water and is also a dipole molecule. For large 
amounts of rainfall within the radio wave path, the strength of signal will be 
significantly reduced. On the other hand, rain being a dipole can be used as a 
reflector thus enhancing the signal. 
 
1.6.2 FOG  
Fog is caused by tiny water droplets suspended in the air. It is generally formed 
close to the ground due to differentiated atmospheric temperatures. Fog has 
properties similar to that of clouds.  Fog, however causes severe weakening of the 
signal strength in the UHF/VHF frequency range. 
The heaviest fogs tend to happen in industrial spaces where there are lots of 
pollution particles on which water droplets can grow. More specifically, according 
to the Glossary of Meteorology from the American Meteorological Society, “fog is 
a collection of water droplets suspended in the atmosphere in the vicinity of the 
earth's surface that affects visibility”. Fog decreases visibility below 1 km. (Howard 
et al, 1998). This limit is suitable for aviation purposes. Generally, for motorists a 
maximum of 200 m is more accurate. Transport is seriously disrupted when the 
visibility drops below 50 m. These three categories are known as aviation fog, thick 
fog and dense fog. 
 
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1.6.3 HARMATTAN 
Basically, the harmattan is a dry and dusty wind which forms as a result of the 
pressure gradient on the west coast of the continent of Africa, i.e., the Atlantic 
Coast. It is typically characterized by strong winds blowing from North to South 
from late November to mid-March, often clocking speeds of 1.76 m/s. 
The Harmattan can also be defined as a dry and dusty northeasterly trade wind 
which blows from the Sahara Desert over the West African subcontinent into the 
Gulf of Guinea between the end of November and the middle of March. 
 
1.7 AIM AND OBJECTIVES OF STUDY 
The purpose of the study is to obtain relevant parameters (visibility and rain rate) 
necessary for the verification of microwave attenuation models as they apply to 
Ghana. In order to conduct this study, the specific objectives to be performed are 
as follows: 
• To determine the attenuation due to the effect of dust particles from visibility 
measurements. 
• To determine the attenuation using the ITU-R rain attenuation model from 
measured rain rate. 
• To determine any correlation between the visibility and rain rate. 
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• Additionally, on account of the fact that relative humidity data was measured, 
work is done to determine any correlation between the visibility and relative 
humidity. 
 
1.8 JUSTIFICATION OF THE STUDY 
Propagation of microwaves are adversely affected by atmospheric gases, rain, 
clouds, fog, harmattan and other atmospheric conditions. Ghana is located in the 
tropics which is a different environment from the temperate environments such as 
Europe and North America. The effects of the atmosphere on microwave signals 
is most severe in the tropics because of high rainfall intensities, high temperature, 
high relative humidity, and severe harmattan conditions which result in a more 
severe signal attenuation than what happens in the temperate region.  
Studies have been performed in the temperate regions such as Europe and North 
America and it has been observed that the model being used for research in the 
West Africa sub-region was from literature, formulated using parameters from 
temperate regions. The models built from these studies are used when setting up 
communication links in Africa, which is in a tropical region. Also most satellite 
communication equipments supplied to Africa are designed based on propagation 
measurements made in these temperate regions, which may not meet the standards 
that can cope with the harsh weather conditions experienced in the tropics. This is 
quite inaccurate since climate conditions in the tropics are different from those in 
the temperate regions. For this reason, this research looks at formulating a more 
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accurate mathematical model for microwave attenuation due to harmattan and rain 
for the tropics in the West Africa sub-region using measurements from parts of 
Ghana.  
 
1.9 SCOPE OF STUDY 
Axim in the south-western part of Ghana and Tamale in the northern part of Ghana 
are chosen as the study areas for measuring the impact of harmattan and rainfall on 
the wireless communication systems and microwave links. Axim was chosen for 
its high rainfall levels and Tamale was chosen because the region is well-known 
for its severe harmattan conditions.  
Visibility and rain rate measurements were obtained using the Campbell Scientific 
visibility sensor and the Davis Vantage Pro weather station respectively. To 
calculate the attenuation due to harmattan dust and rain, the two models used for 
are the Zain Elabdin Model and the ITU-R Specific Attenuation Model for Rain 
respectively. The attenuation due to dust was obtained by setting the visibility 
measurements in the Zain Elabdin equation. Also, the attenuation due to rain was 
calculated using rain rate measurements in the ITU-R rain attenuation model. This 
was done for both study sites. Analysis of this data is discussed in the results.  The 
effect of particle radius, rain rate, relative humidity and visibility on attenuation 
were discussed in the results. 
 
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1.10 GENERAL FORM OF THE THESIS 
Chapter 1 looks at radio waves and their propagation. Also, in this chapter, the 
objectives of this study, justification and scope of the study were all outlined. The 
limitations of the study are also stated in this chapter.  
Chapter 2 provides a comprehensive cover of the climate of Ghana. The Inter 
Convergence Zone (ITCZ) was also discussed in depth in this chapter. Literature 
reviews on the effects of harmattan dust, rain and fog on microwave signal 
attenuation are detailed in this chapter as well.  
In Chapter 3, the different modelling techniques were identified and discussed. 
The Rayleigh and Mie approximation were discussed and demonstrated with 
respect to the various attenuation prediction models. The Zain Elabdin prediction 
model and the ITU-R rain attenuation model were also discussed thoroughly in 
this chapter. 
Chapter 4 discusses the experimental methodology adopted for data collection and 
all the equipments and instruments used were discussed in detail. The study sites 
for this work were also discussed. 
Chapter 5 dealt with the analysis of all recorded data (visibility and rainfall) and how 
signal attenuation for the various study sites were determined. The effects of these 
parameters on signal attenuation was also analyzed.  
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Finally, in chapter 6, discussions are detailed to interpret the effects of these 
weather parameters on signal attenuation. A summary of the conclusions and 
recommendations for future work are also detailed in this chapter. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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CHAPTER 2 
STUDIES OF THE EFFECTS OF DUST, FOG AND RAIN ON 
RADIOWAVES 
In this chapter, the different climatic conditions of Ghana are discussed followed 
by the effects of these on radiowave attenuation. The chapter concludes with a 
review of some of the work done in area.  
 
2.1 CLIMATE OF GHANA 
Ghana is situated on the coast of West Africa (along the Gulf of Guinea), north of 
the equator. Ghana is located between latitudes of 4‐12˚N and longitudes of 4 ˚W 
– 2 ˚E. The country has a total land area of 238,535 km². Ghana shares boundary 
with Burkina Faso to the North, Cote d’Ivoire to the West and Togo to the East 
(Figure 2.1). 
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Figure 2.1: Map of Ghana with its bordering countries 
The climate of Ghana is tropical. There are two main seasons; the rainy season 
and dry season (harmattan). The rainy season occurs between March and 
September in northern Ghana.  
The southern part of Ghana has two rainy seasons occurring, from March to July 
and from September to November. Annual rainfall ranges from about 1,100 mm in 
the north to about 2,100 mm in the southeast.  
The dry season in Ghana happens when a dry desert wind (harmattan), blows from 
the northeast during the period of December to March. The harmattan lowers the 
humidity which leads to hot days and cool nights in the north. In southern Ghana, 
the effects of the harmattan are experienced in January. In most areas, the maximum 
temperature values occur in March and the minimum temperatures in August.  
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The rainfall season in the northern part of Ghana occurs from April to mid-October 
while the southern part of Ghana experiences its rainy season from March to mid-
November. Furthermore, the southern part of Ghana has a bi-modal rainfall season: 
April through June and September through November. It is generally warm and 
relatively dry along the southeast coast; hot and humid in the southwest and hot and 
dry in north. 
The climate of Ghana is influenced by the hot, dry and dusty-laden air mass that 
moves from the north east across the Sahara and by the tropical maritime air mass 
that moves from the south-west across the southern Atlantic ocean. The climate 
ranges from the bimodal rainfall equatorial type in the south to the tropical 
unimodal monsoon type in the north. The mean monthly temperature over most of 
the country always falls above 25o C. This is a result of the low latitude position 
of Ghana and the absence of high altitude areas. Ghana’s average mean annual 
temperature is about 27o C. The highest temperatures, especially in the north 
approach 40o C. For the lowest temperatures, it drops to about 15o C. (Dickson 
and Benneh, 1988; Benneh et al. 1990). 
The amount of annual rainfall for Ghana generally decrease from the south to the 
north. The extreme southwestern part of the country is the wettest area where the 
annual rainfall is over 2,000 mm. In the north, the rainfall is less than 1,100 mm 
per year. The south-eastern part is the driest area where the rainfall is about 750 
mm. Much of the rain falls in intense storms for short periods of time, particularly 
at the beginning of the season resulting in heavy runoff and erosion. The annual 
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mean relative humidity is about 80 percent in the south and 44 percent in the 
north (Dickson and Benneh, 1988; Benneh et al. 1990) 
Figure 2.2: Climatic Zones in Ghana (Dickson & Benneh, 1995) 
 
 
As shown in Figure 2.2, there are four main climatic zones marked I, II, III and IV 
(Dickson & Benneh, 1995). The rainfall seasons of Ghana are controlled by the 
movement of the inter tropical convergence zone (ITCZ).  
In order to understand the ITCZ, it is important to note that the properties of an air 
mass are determined by two factors, namely; 
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 the condition of its source region (areas of high pressure) 
 The air mass modifications as it travels from the source region to its 
destination (areas of low pressure) 
The pressure difference between the source regions and the destinations produce 
winds and the Coriolis forces cause slight modifications (Kakane, 1998). 
The climate of Ghana is influenced by two main categories of air masses; based 
on whether they are found on land or water. They are: 
 Low level air masses/ Tropical maritime air mass/ South-Westerlies – This 
air mass is moisture-laden. It produces the monsoon, a humid southwest wind 
blowing through the Atlantic Ocean.  
 High level air masses/ Tropical continental air mass / North-Easterlies.  
This air mass is hot and dry and gives rise to the dusty, harmattan winds which 
blow from the Sahara over most of West Africa from November to February. 
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Figure 2.3: Air masses and their source regions (Dickson & Benneh, 1995) 
 
The ITCZ is the narrow trough of low pressure discontinuity between the two 
pressure regions on the land and the sea as shown in Figure 2.3. The ITCZ can 
also be described as an area where two masses (northeast and southwest trade 
winds) converge and form the ascending branch of the Hadley cell. It happens 
globally between the equator and about 20ᵒ N/S. This results in heavy rains over 
the areas it passes over. The seasonal movement of the ITCZ follows the 
movement of the sun and moves from the north to the south. It is also responsible 
for the movement of the air masses. (Folland et al., 1990). Hence, the rainfall 
seasons of Ghana are controlled by the movement of the tropical rain belt (another 
name for the ITCZ) as shown in Figure 2.4.  
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Figure 2.4: Movements of the Inter-Tropical Convergence Zone and Rainfall (Dickson & Benneh, 
1995) 
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For regions south of the ITCZ, the dominant wind direction is south‐ westerly, 
blowing moist air from the Atlantic onto the continent. On the contrary, for 
regions north of the ITCZ, the dominant winds come from the north east, carrying 
hot and dusty air from the Sahara desert (‘Harmattan’).  As the ITCZ travels 
between its north and south positions throughout the year, the regions between 
these northern and southernmost positions of the ITCZ go through a shift between 
the two contrasting prevailing wind directions.  This shift is referred to as the 
West African Monsoon.  In northern Ghana, between May and November, the 
ITCZ is in its northern position and the prevailing wind is south‐westerly and this 
causes a single wet season. Between December and March when the north‐
easterly harmattan wind blows, there is a dry season. The northern and central 
regions receive 150‐250mm per month in the peak months of the wet season 
which lasts from July to September (Nkrumah et al., 2014, McSweeney et al., 
2010). 
The southern parts of Ghana have two wet seasons: the extended season from 
March to July, and a shorter wet season from September to November (Owusu et 
al., 2013). These seasons correspond to the northern and southern passages of the 
ITCZ across Ghana. The seasonal rainfall in this region differs due to variations in 
the intensity and movements of the ITCZ, and variations in the intensity and 
timing of the West African Monsoon (Nkrumah et al., 2014). 
Zone I in Figure 2.2, also known as the South-western equatorial is the rainiest 
region. In this region, there are two periods of highest rainfall separated by a short 
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dry period (known as the ‘little dry season’) usually in August. The periods of 
rainfall occur from April to May and from September to November with the little 
dry season happening from November to March. A typical example is Axim. 
The second (II) zone is the Dry equatorial region. This region also has two 
periods of rainfall maxima. This is the driest region in Ghana. Relative humidities 
are higher in the rainy seasons. An example of a station is Accra. 
The third (III) zone is the wet semi-equatorial region. Similar to the first zone, this 
zone has two rainy seasons. Temperatures and humidity are the same as in the 
south-western equatorial region. The annual rainfall for this region differs for this 
region and ranges between 1250 mm and 2000 mm. A typical example is Kumasi. 
The fourth (IV) zone is the tropical continental or savannah region. This region 
has only one rainy season which happens from May to October. This is followed 
by a long period of dry season. The mean annual rainfall values range between 
1000 mm and 1150 mm. The mean monthly temperatures 27 ᵒC in August to 36 ᵒC 
in March. Relative humidity values fall to as low as 20 % in the dry season and 
run high between 70 % and 90 % during the rainy season. 
Zones I, II and III have dry periods that originate from the movement of the ITCZ 
as detailed above. The Dry Equatorial region extends as far as to Lome (Togo) 
and is referred to as the anomalous drier zone or the Togo Gap. Various 
explanations have been given for the existence of this gap (Dickson & Benneh, 
1995, Hayward & Oguntoyinbo, 1987). The first is that the wind direction tends 
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to be parallel to the coastline and hence the tendency for convergence and uplift is 
lessened. Another is that the cooler ocean surface over which the prevailing winds 
blow before moving onto the shore cause a lowering of the surface air 
temperature and reduce the tendency for uplift and rain. A third reason given is 
that the rain giving storms from the east deposit their rain on the Akwapim-Togo 
ranges. On reaching the South-eastern coastal plains they become dry winds.  
Figure 2.5 shows the mean monthly rainfall distribution for the typical stations in 
each region. The figure shows both the little dry period in August for the Accra, 
Axim and Kumasi and the single rainy season for Zuarungu in the north. 
 
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Figure 2.5: Mean Monthly Rainfall and Temperatures (Dickson & Benneh, 1995) 
 
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2.2 EFFECTS OF DUST 
In 2009, Elabdin et al. (2009) published a paper in which a mathematical model 
was developed to depict the microwave signal attenuation due to dust. The 
mathematical model was developed to take care of all possible ratios of dust 
particle diameter to wavelength and calculate attenuation in the microwave band 
with high reliability using Mie solution of Maxwell’s equations for the scattering 
of electromagnetic wave by dielectric spherical particles. This model aided in 
obtaining convenient calculations of the microwave signal path attenuation and 
showed the relationship between attenuation and visibility, frequency, particle 
size and complex permittivity. The frequency, dust particle radius and dielectric 
constant were directly proportional to the attenuation while the visibility was 
inversely proportional to the attenuation. The predicted values from the 
mathematical model were compared with the observed experimental values and 
they were in relatively optimistic agreement. 
Eyo et al. (2003) made measurements on line-of-sight attenuation at 6.44 GHz with 
the intent of emphasizing microwave signal attenuation in harmattan weather 
conditions on a link from Akamkpa to Calabar in Nigeria. Mean signal levels were 
recorded and signal attenuation were calculated based on visibility, air temperature 
and frequency. The observed attenuations values due to harmattan weather 
conditions were compared with calculated fog attenuations using Altshuler model. 
The two results were found to be in fairly good agreement. Conclusively, 
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microwave line-of-sight link in this region was found to be prone to signal 
degradation as well as fading in harmattan season. 
Another study was done by Mohammed (2010) in which the effect of severe dust 
storms with visibility less than 1 km on some aspect of microwave propagation 
especially attenuation and depolarization at 12 GHz were presented. 
Meteorological data were collected by the Iraqi meteorological organization for 
30 years in Baghdad (1958-1988) and 10 years (1978-1988) for other four 
stations, Nasiriyah, Basrah, Rutbah and Mousl were used in this predication. The 
results showed that the microwave links located at the south close to the desert 
affected as much as seven times more than other regions. It was found that the 
attenuation exceeded 1 dB for several hours while the cross polarization was in 
the order of -16 dB in the worst cases. The measured data was compared with 
available experimental measurements on line of sight and it was found that the 
measured values were much higher than the predicted values. This discrepancy 
was explained as a result of multi-path phenomena during the measurements, 
which are common in those areas and due to inaccuracies of the visibility 
measurement during the storms. 
 
2.3 EFFECTS OF FOG 
Eyo et al. (2003) made measurements on line-of-sight attenuation at 6.44 GHz with 
the intent of highlighting microwave signal attenuation in harmattan weather 
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conditions on a link from Akamkpa to Calabar in Nigeria. Mean signal levels were 
recorded and signal attenuation were calculated based on visibility, air temperature 
and frequency. The observed attenuations values due to harmattan weather 
conditions were compared with calculated fog attenuations using Altshuler model. 
The two results were found to be in fairly good agreement. Conclusively, 
microwave line-of-sight link in this region was found to be prone to signal 
degradation as well as fading in harmattan season. 
 
2.4 EFFECTS OF RAIN 
Ojo et al. (2008) made predictions for rain rate and rain attenuation in order to 
investigate  
a microwave satellite communication links at the Ku and Ka bands. In this paper, 
tools for the prediction of rain rate and rain attenuation were presented in the form 
of contour maps for Nigeria using an enormous 30-year rainfall data bank which 
was taken from measurements made from the coast to the arid region of Nigeria. 
Rain-rate maps for the country of Nigeria were developed using the models 
purposely designed for tropical zones while International Communications Union 
Radiocommunication Sector (ITU-R) models were used for the rain attenuation 
maps. Rain rate and rain attenuation contour maps were developed for 0.1 and 
0.01% of the time using the refined Moupfouma model for rain rate maps and 
ITU-R 618 for the rain attenuation maps over Nigeria. The 0.1% of time of rain 
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attenuation was needed for very small aperture terminal (VSAT) network service-
availability. 
In 2012, Islam et al. (2012) presented an improved approach of predicting rain 
attenuation cumulative distribution (CD) over terrestrial microwave links 
operating in tropical regions. The proposed method gave an improved 
extrapolation approach for determining the values of rain attenuation at different 
exceedance probability from the measured attenuation at 0.01% of the time. The 
experimental data consisted of measured rainfall rates and rain attenuation over 
six geographically spread DIGI MINI-LINKs operating at 15 GHz in Malaysia. A 
new set of numerical coefficients was then derived for improved rain attenuation 
CD predictions in the Malaysian tropical climate. As a test, a validation was 
implemented using rain rate and rain attenuation measurements from five 
Brazilian and seven Nigerian tropical locations. When tested against 
measurements, the proposed method seemed to suggest a significant improvement 
over the existing extrapolation method adopted by ITU-R Recommendations 
P.530-14, for the prediction of rain attenuation CD over tropical regions. 
Elfadil et al. (2005) studied the rain attenuation prediction models for the design 
of microwave terrestrial line-of-sight (LOS) system. From the results, it was 
clearly shown that the Global Crane Prediction model predicted a much higher 
attenuation compared to those predicted by using ITU-R Prediction Model. This 
was proven from the attenuation difference of 200 dB/km at 120 GHz for the 
RSDs proposed by Din. In essence, all the computation from the ITU-R prediction 
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model showed a much lower estimation compared to those from the Crane 
predictions. 
In Pakistan’s tropical environment, Uzma et al. (2011) published a paper in which 
the line-of-sight microwave communication links were set up and operated for 
several years to study the microwave attenuation characteristics due to rainfall at 
frequencies of 15 and 38.6GHz. In this paper the cumulative distributions of 
microwave attenuation and the relationship between specific attenuation and 
rainfall rate were presented. In addition, a rain outage prediction model was 
proposed which not only predicted microwave radio link performance but was 
also useful in calculating the link degradations due to interference issues. From 
the results the rainfall rate, the microwave propagation characteristics, and outage 
predictions in Pakistan varied from the International Radio Consultative 
Committee predictions and ITU recommendation P530.7/8, respectively. 
In 2011, Shoewu et al. (2011) made measurements on the line-of-sight (LOS) 
attenuation at 7.2GHz in Lagos for twelve months using one of the Nigerian 
Telecommunications radio signal. The measurement was carried out with the 
intent of highlighting microwave signal attenuation in harmattan and rain weather 
conditions. The results were presented in terms of mean signal level, received 
signal level and fog attenuation, rain attenuation, multipath fading, free space loss 
and link availability. The observed attenuation values were actually due to 
harmattan dust but a fog attenuation model and rain attenuation was calculated 
(using Altshuler's model). Also, the statistics of fade distribution show fast fading 
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of longer duration of the order of 16 to 39 fades per hour during the harmattan 
period and 24 to 48 fades per hour during the period of rain. It was therefore 
shown experimentally that fog weather is better compare to the rain weather, due 
to the series fluctuation of the signal. On the other hand, transmission could be 
stable during rainy weather if there is space range, a larger antenna and also 
suitable development. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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CHAPTER 3 
THE RAYLEIGH AND MIE ATTENUATION MODELS FOR 
WAVES 
In this chapter, the various scattering and absorption leading to attenuation and 
the various models are discussed. In addition, the effects of polarization of the 
wave on attenuation is also discussed. 
 
3.1 SCATTERING AND ABSORPTION IN THE ATMOSPHERE 
The atmosphere is made up of gases, which absorb electromagnetic energy at 
different frequencies. As electromagnetic radiation propagates though our 
atmosphere, it interacts with air molecules, dust particles, rain, water vapour, fog, 
and a number of other particles. These interactions result primarily in scattering 
and absorption of the EM radiation, both of which are important for studying 
interactions in the atmosphere. The atmospheric effects can vary significantly 
with location, altitude, and the path slant angle. 
When a particle falls in the path of an electromagnetic wave, it can cause the 
radiation from the incident wave to deviate from its path. This is known as 
scattering. A particle in the path of an EM radiation can also be absorbed. As a 
result, scattering and absorption causes attenuation problems with radar and other 
measuring devices (Kumari, 2017). 
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3.1.1 Polarization of a Wave 
Polarization of a wave is defined as the orientation of the lines of electric flux in 
an electromagnetic field. The polarization of the receiving antenna should 
preferably be equal to the polarization of the received wave and the polarization 
of a transmitted wave is equal to that of the antenna from which it originated.  
 
3.2 THEORY OF SINGLE-PARTICLE SCATTERING 
Absorption and scattering by the atmosphere affects radiowaves (microwaves), 
particularly those at higher frequencies. The effects of scattering becomes harsher 
at higher frequencies. The knowledge of these scattering characteristics is vital to 
the design of effective communication systems. The theory for single particle 
scattering is the basic theory used in mathematical modelling for attenuation. 
The propagation characteristics of scattering and absorption can be modeled by 
assuming an incident plane wave (Elabdin et al, 2008). When an EM wave hits an 
object, a part of the wave is absorbed by the object and another part is scattered 
out. 
As seen in Islam et al. (2010) and Ishimaru (1997), the total electromagnetic field 
around the scattering object is divided into an incident and a scattered field as 
shown in Figure 3.1  
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Figure 3.1: Scattering Configuration (Ishimaru, 1997) 
The total amplitude of the fields at any point on the surface of a sphere is 
(Vishvakarma, 1993): 
?⃗? = 𝐸⃗⃗  ⃗𝑖 + ⃗⃗𝐸⃗⃗ 𝑠                                                           (3.1) 
?⃗? = ⃗⃗𝐻⃗⃗ ⃗⃗𝑖 + 𝐻⃗⃗ 𝑠                                                           (3.2) 
⃗⃗𝐸 ⃗𝑖 represents the incident electric field,  
⃗⃗𝐻⃗⃗ 𝑖 represents the incident magnet field  
⃗⃗𝐸⃗⃗ 𝑠 and ⃗⃗𝐻⃗⃗ 𝑠 represent corresponding scattered fields. 
 
Where the flow of energy is involved, the poynting vector, S, must be used. Hence 
the averaged poynting vector S signifies the power density. The poynting vector 
can be separated into single terms by the separation of the total field into the 
incident and scattered field (Eq. 3.1 and Eq. 3.2), which then gives  
𝑆 = 𝑆⃗⃗⃗  + 𝑆⃗⃗  ⃗ + 𝑆⃗⃗⃗⃗ 𝑖 𝑠 𝑑                                                        (3.3) 
where, 
𝑆 
1
𝑖 = 𝑅 (𝐸⃗⃗  ⃗ ⃗⃗𝑖 × 𝐻⃗⃗∗ 𝑖 )     (3.4) 2
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⃗⃗𝑆 ⃗
1
= 𝑅 (⃗⃗𝐸⃗⃗ ⃗⃗ ⃗⃗∗ 𝑠 2 𝑠 × 𝐻𝑠 )     (3.5) 
𝑆⃗⃗⃗⃗ 
1
= 𝑅 (𝐸⃗⃗  ⃗ × 𝐻⃗⃗ ⃗⃗∗ 𝑑 𝑖 𝑠 + 𝐸⃗⃗⃗⃗ 𝑠 × 𝐻⃗⃗⃗⃗∗ 2 𝑖 )   (3.6) 
 
𝐸⃗⃗  ⃗𝑖 represents the incident electric field,  
𝐻⃗⃗⃗⃗ 𝑖 represents the incident magnet field  
𝐸⃗⃗⃗⃗  and ⃗⃗𝐻⃗⃗ 𝑠 𝑠 represent corresponding scattered fields.(Ishimaru, 1997). 
 
The total power flow through the surface of this sphere is obtained by taking the 
integral of the radial component of S over the sphere. For a lossless dielectric 
particle that scatters, the net power flow will be zero. If it has a permittivity that is 
complex, the net power flow will show the absorption rate Pa of energy by the 
scatterer and is indicated as: 
 
𝑃𝑎 = 𝑃𝑖 + 𝑃𝑠 + 𝑃𝑑     (3.7) 
 
where Pa represents the integral of the radial component of S . 
The medium near the particle is assumed to be lossless, consequently the total 
flow of the energy of the incident field is zero for every closed surface (Pi = 0), 
and hence: 
 
𝑃𝑎 + 𝑃𝑠 = −𝑃𝑑     (3.8) 
 
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Maxwell’s equations are used to sum the absorbed and scattered energy. 
Consequently, the extinction or total cross-section efficiency factors is defined as 
the ratio of the rate of removal of energy (Pa + Ps) to the rate of the incident 
energy (Pi) on a unit cross-sectional area of the scatterer. The extinction is as 
shown below: 
 
𝑃𝑎+𝑃𝑠 4𝜋𝜎𝑡 = = 𝜎𝑎 + 𝜎𝑠 = 𝐼𝑚[𝑢 ∙ 𝑓(𝑢𝑃 𝑘 𝑒 𝑠
, 𝑢𝑖)]    (3.9) 
𝑖
 
From Equation 3.6,  
(2𝜋)
k represents wave number (𝑘 = 𝜔√𝜇𝜀 = ⁄𝜆) ,  
1
𝜀 ⁄2
( )  is the characteristic impedance of the medium,  
𝜇
?̂?𝑒 is the unit vector defining the polarization of the wave,  
f (us, ui) represents the scattering amplitude function; it is a function of the 
direction of propagation,  
ui of the incident field and of the direction us from the object to the observation 
point (Islam et al, 2009). 
 
3.3 APPROXIMATION METHODS/MODELS FOR SCATTERING 
Scattering of electromagnetic waves by particles can be demonstrated by two 
theoretical frameworks: 
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 Rayleigh Approximation 
 Mie Approximation 
Rayleigh scattering generally happens when the particles producing the scattering 
are smaller in size than the wavelengths of the electromagnetic radiation interacting 
with them. Hence, Rayleigh scattering is wavelength dependent. On the other hand, 
Mie scattering generally occurs when the particles causing the scattering are the 
same size as the wavelengths of the electromagnetic radiation interacting with 
them.  
  
3.3.1 Raleigh Approximation 
The scattering cross section, σs of a small dielectric is given by Ishimaru (1999) to 
be 
128 5 6 𝜀−1
2
𝜎𝑠 = 𝜋 𝑎 | |      (3.10) 3𝜆4 𝜀+2
In most instances, the scattering cross section is usually compared with the actual 
geometric cross section πa2. Therefore, the Rayleigh equation is obtained as 
𝜎𝑠 8(𝑘𝑎)
4 𝜀−1 2
2 = 4 | |       (3.11) 𝜋𝑎 3𝜆 𝜀+2
(Ishimaru, 1999) 
 
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For Rayleigh approximation, it is assumed that ka < 1, which implies that the 
particle size is comparatively smaller than the radiation wavelength. For a smaller 
dielectric sphere as compared with wavelength, the field inside the particle is 
selected to be the solution of the equivalent dielectric electrostatic problem. In the 
Rayleigh approximation, the field inside the scattering particle is not modeled 
correctly (Vishvakarma, 1993; Elabdin et al, 2009). To obtain an exact solution, 
the scattered field reflects all the properties of the object which is no longer true 
for an approximation solution. 
Hence, the total cross-section efficiency factors by Rayleigh approximation is 
expressed as: 
8 𝜀" 𝜀−1 2
𝜎𝑡 = 𝜎𝑠 + 𝜎𝑎 = [ 𝜋𝑎
2(𝑘𝑎)4 + 12𝜋𝑎2(𝑘𝑎) ] | |   
3 (𝜀′−1)2
2
+(𝜀") 𝜀+2
 (3.13) 
where, a is the particle radius 
k is the wavenumber (k =2 π / λ) 
and ε' , ε'' are the real and imaginary contributions respectively of the relative 
dielectric constant of the particles. 
 
3.3.2 Mie Approximation 
Mie scattering happens when the particles in the atmosphere are equal in size to 
the wavelengths being scattered. It is usually caused by particles in the 
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atmosphere due to dust, pollen, smoke and also rain which tends to affect longer 
wavelengths. It is known that Mie scattering usually takes place in the lower 
portions of the atmosphere where there are more prevalent larger particles. These 
larger particles are widespread when cloud conditions are overcast. 
Mie solution is a complete analytical solution of Maxwell's equations for the 
scattering of electromagnetic wave by dielectric spherical particles. Compared to 
Rayleigh scattering, Mie solutions to scattering differ by taking on all possible 
ratios of diameter to wavelength (Cachorro, 2001). Applications include dust 
particles in the atmosphere, oil droplets in water and cell nuclei in biological 
systems (for instance in cancer research) (Yushanov et al, 2013). 
Mie solutions unlike Rayleigh scattering can be used to calculate attenuation in 
microwave wave band with high reliability mainly at higher frequencies used by 
new systems with greater bandwidth. 
The extinction or total cross-section efficiency factors by Mie solutions can be 
expressed as (Collin, 1985; Elabdin et al, 2009). 
𝜆2
𝜎𝑡 = (𝑘𝑎)
3(𝑐 + 𝑐 (𝑘𝑎)2 + 𝑐 (𝑘𝑎)31 2 3 )    (3.14) 2𝜋
a denotes the particle radius,  
k denotes the wavenumber (k =2 π / λ),  
λ denotes the wavelength, 
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and c1, c2 and c3 are constants whose values depend on the real part (ε') and 
imaginary part (ε'') of the dielectric constant of the particles as: 
6𝜀"
𝑐1 = 2       (3.16) 
(𝜀′+2)2+𝜀"
′2 2
" 6 7𝜀 +7𝜀
" +4𝜀′−20 1 5
𝑐2 = 𝜀 {  2 + + 2 }   (3.17) 5 2[(𝜀′+2)2+𝜀" ] 15 3[(2𝜀′+3)2+4𝜀" ]
2 4
4 (𝜀′−1) (𝜀′+2)+[(𝜀′−1)(𝜀′+2)−9]+𝜀"
𝑐3 = { 2 }    (3.18) 3 [(𝜀′+2)2+𝜀"2]
 
 
3.4 SIGNAL ATTENUATION DUE TO HARMATTAN DUST 
The signal attenuation due to harmattan dust is generally predicted by solving the 
forward scattering amplitude function of a single particle (Brussaard, 1995). The 
solution may be calculated by using the Rayleigh approximation or Mie solutions. 
The approximation method used depends mainly on the wave number and particle 
radius. 
The attenuation of electromagnetic radiation (AT) over a path of extent L through 
precipitating particles may be written as (Roger, 1976, Elabdin et al, 2009): 
 
𝐿
𝐴𝑇 = ∫ 𝐴𝑃𝑑𝑥     (3.19) 0
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where Ap (dB/km) is the specific attenuation characterizing the precipitating 
particles. 
Several authors used the following expression to determine the attenuation due to 
rain (Olsen et al, 1978, Roger, 1976, Oguchi, 1983; Elabdin et al, 2009): 
𝑎
𝐴𝑝 =  4.343 ×  103
𝑚𝑎𝑥
∫ 𝜎𝑡(𝑎) .  𝑁 (𝑎)𝑑𝑎    (3.20) 𝑎𝑚𝑖𝑛
where N (a) da is the number of particles per unit volume of air with particles 
radius between a and a + da;  
σt (a) is the total attenuation cross section efficiency factors of particle of radius a. 
 
3.4.1 Harmattan Dust Predicted Model 
As shown from above, the attenuation of electromagnetic radiation (AT) over a 
path of extent L through harmattan dust can be expressed as: 
𝐿
𝐴𝑇 = ∫ 𝐴𝑑𝑑𝑥     (3.21) 0
where Ad is the specific attenuation characterizing the harmattan dust which can 
be expressed as: 
𝑎
𝐴𝑑 =  4.343 × 10
3 𝑚𝑎𝑥∫ 𝜎𝑡(𝑎) .  𝑁 (𝑎)𝑑𝑎    (3.22) 𝑎𝑚𝑖𝑛
Equation 3.22 can be used to express the attenuation of electromagnetic radiation 
(Ad) over a path of extent L through harmattan dust. 
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3.4.2 Using Rayleigh Approximation 
Goldhirsh (2001), in using the Rayleigh approximation method for the total cross 
section efficiency factor (σt), stated the specific attenuation due to harmattan dust, 
Ad as: 
 
2.317∙103∙𝜀" 1
𝐴 = ′ . 𝛾      (3.23) [(𝜀 +2)2+𝜀"2].𝜆 𝑉
where, V: the visibility in kilometer, 
λ: the wavelength in meter, 
γ: constants that depend on the type of land from which the harmattan dust 
originated as well as the climatic conditions, 
ε' , ε'' : the real and imaginary part of the dielectric constant of the dust particles. 
 
The Goldhirsh formulation is a modification of the Chu model which expresses 
the specific attenuation as a function of visibility and particle size distribution. It 
is suitable at wavelengths for which the Rayleigh condition is applicable which 
includes wavelengths corresponding to 48 GHz as a maximum frequency (Chu, 
1979). 
 
3.4.3 Using Mie solution 
In order to develop a mathematical model that can calculate the signal attenuation 
due to harmattan dust at higher frequencies, the Mie expression for total cross-
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section efficiency factors (σt) (Equation 3.14) was selected for substitution in 
Equation 3.22. Therefore, the attenuation due to harmattan dust (Ad) can be 
written as: 
 
𝑎 𝜆2
𝐴𝑑 =  4.343 × 10
3 𝑚𝑎𝑥∫ (𝑘𝑎)3(𝑐1 + 𝑐2(𝑘𝑎)
2 + 𝑐3(𝑘𝑎)
3) .  𝑁 (𝑎)𝑑𝑎  
𝑎𝑚𝑖𝑛 2𝜋
 (3.24) 
 
3.4.4 Dependence of Visibility 
To calculate the attenuation by the Equation 3.24 involves information for the 
number of particles of dust N. Measuring N accurately has been found to be 
challenging. Alternatively, statistical data on duststorm visibility is mostly 
accessible. For this work, visibility values are measured. Goldhirsh (2001) states 
the visibility in terms of the particle density as:  
 
5.5 ×104 5.5 ×104
𝑉 =    →  𝑁 =        (3.25) 
𝑁𝑎2 2𝑒 𝑉𝑎𝑒
 
where the unit of N is particles/m3 and ae is the equivalent particle radius in 
meters.  
 
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3.4.5 Zain Elabdin Model 
From the Elabdin et al (2009) paper, the Collin expression (Equation 3.14) was 
used to substitute for the total cross section efficiency factors (σt) and the particle 
density expression in Equation 3.25, Ad may also be expressed as:  
 
3 𝜆
2
3 5.5×10
−4
𝐴𝑑 =  4.343 × 10 [ (𝑘𝑎) (𝑐 + 𝑐 (𝑘𝑎)
2 + 𝑐 (𝑘𝑎)3 ).  ] 
2𝜋 1 2 3 𝑉𝑎2𝑒
 (3.26) 
 
Another approximation was made, assuming that every dust particle in an actual 
storm may be substituted by an equivalent particle (ae) whose radius is the mean 
radius for all dust particles. Using this assumption, the value of equivalent particle 
radius (ae) was considered as constant and Eq. 3.26 may be expressed as follows:  
𝜆23 2𝜋𝑎
3 2𝜋𝑎 2 2𝜋𝑎 3 5.5×10−4
𝐴𝑑 =  4.343 × 10 [ ( ) (𝑐1 + 𝑐2 ( ) + 𝑐3 ( )  ).  ] 2𝜋 𝜆 𝜆 𝜆 𝑉𝑎2𝑒
 (3.27) 
Then,  
4.343 × 103×5.5×10−4 1
𝐴𝑑 = [𝜆
2(𝑘𝑎𝑒)
3(𝑐1 + 𝑐2(𝑘𝑎𝑒)
2 + 𝑐3(𝑘𝑎𝑒)
3) . 2 ] 2𝜋 𝑉𝑎𝑒
 (3.28) 
1
𝐴𝑑 =  0.38 [𝜆
2(𝑘𝑎𝑒)
3(𝑐 2 31 + 𝑐2(𝑘𝑎𝑒) + 𝑐3(𝑘𝑎𝑒) ) . 2 ]   (3.29) 𝑉𝑎𝑒
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𝜆2
𝐴 =  0.38 [(𝑘𝑎 )3(𝑐 + 𝑐 (𝑘𝑎 )2 + 𝑐 (𝑘𝑎 )3𝑑 𝑒 1 2 𝑒 3 𝑒 ) ]   (3.30) 𝑉
𝜆2
𝐴𝑑 =  0.38 [(𝑐1𝑘
3𝑎𝑒 + 𝑐 𝑘
5𝑎3 + 𝑐 𝑘6𝑎42 𝑒 3 𝑒) ]    (3.31) 𝑉
By substituting k = 2π/λ in the Equation 3.31, Ad becomes  
𝜆2 8𝜋3 32𝜋5 3 64𝜋
6
𝐴𝑑 =  0.38 [(𝑐1 𝑎𝑒 + 𝑐2 𝑎 + 𝑐 𝑎
4
𝑒 3 𝑒) ]   (3.32) 𝑉 𝜆 𝜆3 𝜆4
This was simplified to get 
𝑎 𝑎3 𝑎4
𝐴𝑑 =  94.3 × 𝑐
𝑒
1 + 3721.2 × 𝑐
𝑒
2 3 + 23381 × 𝑐
𝑒
𝑉𝜆 𝑉𝜆 3 𝑉𝜆4
   (3.33) 
 
Then  
𝛼𝑎 𝛽𝑎3 𝜃𝑎4
𝐴 = 𝑒 + 𝑒 𝑒𝑑 𝑉𝜆 𝑉𝜆3 +     (3.34) 𝑉𝜆4
Where 𝛼 =  94.3 × 𝑐1, 𝛽 =  3721.2 ×  𝑐2 and 𝜃 =  23381 × 𝑐3. α β and θ are 
constants whose values depend on real (ε’) and imaginary (ε”) parts of the dielectric 
constant of the dust particles.  
565.8𝜀′′ 
𝛼 =  ′ 2       (3.35) (𝜀  + 2)  + 𝜀′′2 
′2 ′′2 ′
𝛽 =  3.7 × 103 ′′
6 7𝜀 +7𝜀 +4𝜀  −20 1 5
 · 𝜀 { ′ 2 ′′2 2 + + ′ 2 ′′2 }   (3.36) 5  [(𝜀 + 2) + 𝜀 ] 15  3[(2𝜀 + 3) + 4𝜀 ]
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′ 2(𝜀 − 1) (ε + 2)+[2 (ε′ − 1) (ε′ + 2) − 9]+ 𝜀′′4
𝜃 =  3.12 × 104  { ′ }  (3.37)  [(𝜀 + 2)2+ 𝜀′′2]2
To simplify Equation 3.34 further, the wavelength (λ) was expressed in term of 
frequencies (f) which is easier to use by microwave network engineers. 
Consequently, the specific attenuation of duststorm Ad was expressed as;  
𝛼𝑎 𝑓 𝛽𝑎3𝑓 𝜃𝑎4
𝐴𝑑 = 
𝑒 + 𝑒 + 𝑒     (3.38) 
(0.3)𝑉 (0..3)3𝑉 (0..3)4𝑉
Finally, Elabdin et al. introduced new parameters X, Y and Z where:  
 𝛼  𝛽  𝜃
𝑋 =  ,   𝑌 = ,   𝑍 =        (3.39) 
0.3 0.3 0.3
X, Y and Z were substituted into Equation 3.38 the specific attenuation due to 
duststorm Ad (dB/km) was expressed as:  
𝑎 𝑓
𝐴𝑑  =
 𝑒  (𝑋 +  𝑌𝑎 2 2𝑒 𝑓  +  𝑍𝑎
3
𝑒 𝑓
3)    (3.40) 
𝑉 
ae: the equivalent particle radius in meters,  
V: the visibility in kilometer,  
f: the frequency in GHz and;  
X, Y and Z: constants whose values depend on real (ε’) and imaginary (ε’’) parts 
of the dielectric constant of the dust particles as:  
1886 · 𝜀′′
𝑋 =  ′ 2 ′′2        (3.41)  (𝜀  + 2)  + 𝜀
6 7𝜀′2+7𝜀′′23 ′′ +4𝜀
′ −20 1 5
𝑌 = 137 × 10  · 𝜀 {  +  +  }    (3.42) 
5 [( 𝜀′+ 2)2+ 𝜀2]2 15 3[(2𝜀′+3)2+4𝜀2]
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( 𝜀′
2
−1) (𝜀′+ 2) + [2 ( ε′− 1)( ε′ + 2)− 9]+ 𝜀′′4
𝑍 = 379 × 104 { ′ 2 ′′2 2  }     (3.43) [( 𝜀 + 2) + 𝜀 ]
 
In completeing this model, some main assumptions made are as follows: 
• Particles with radius ˂ 1 mm have spherical shapes.  
• The medium near the particles (the air) is non-conducting; hence there is no power 
loss in this medium.  
• All particles are axially symmetrical.  
By substituting applicable dielectric permittivities for the various frequencies bands 
(up to W band), Equation 3.40 may be altered to fit the frequency band (Elabdin et 
al, 2008). 
 
3.4.6 THE ITU-R RAIN ATTENUATION MODEL  
The Specific Attenuation Model for Rain (ITU-R P.838-3) is a model in which the 
specific attenuation 𝛾𝑅 (dB/km) is obtained from the rain rate R (mm/h) using the 
power-law relationship: 
   𝛾𝑅 = 𝑘𝑅
𝛼      (3.44) 
𝛾𝑅 represents the specific attenuation 
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R – rain rate 
k and α – coefficients of horizontal and vertical polarization 
The values of k and α can be obtained using the relations below: 
2
log10 𝑓−𝑏
log10 𝑘 = ∑
4 𝑗
𝑗=1 𝑎𝑗 𝑒𝑥𝑝 ⌊−( ) ⌋ + 𝑚𝑘 log10 𝑓 + 𝑐𝑘    (3.45) 𝑐𝑗
2
5 log10 𝑓−𝑏𝛼 = ∑ 𝑗𝑗=1 𝑎𝑗 𝑒𝑥𝑝 ⌊− ( ) ⌋ + 𝑚𝛼 log10 𝑓 + 𝑐𝛼    (3.46) 𝑐𝑗
 where f: frequency (GHz), k : either 𝑘𝐻 or 𝑘𝑉, α : either 𝛼𝐻 or 𝛼𝑉. 
For linear and circular polarization, and for all path geometries, the coefficients k 
and α can be calculated from the values given using the following equations: 
𝑘 =  [𝑘 2𝐻  +  𝑘𝑉 +  (𝑘𝐻 − 𝑘𝑉) 𝑐𝑜𝑠 𝜃 𝑐𝑜𝑠 2 𝜏]/ 2    (3.47) 
𝛼 =  [𝑘𝐻𝛼𝐻 + 𝑘𝑉𝛼𝑉 +  (𝑘𝐻𝛼𝐻– 𝑘𝑉𝛼𝑉)𝑐𝑜𝑠
2𝜃𝑐𝑜𝑠 2 𝜏] / 2𝑘   (3.48) 
where θ is the path elevation angle and τ is the polarization tilt angle relative to 
the horizontal (τ = 45° for circular polarization). 
The ITU-R Rain Attenuation Model [ITU-R, 2001] technique is used for 
calculating approximately the long-term statistics of rain attenuation. The path 
attenuation is as shown below: 
𝐴0.01 = 𝛾𝑅𝑑𝑒𝑓𝑓 = 𝛾𝑅𝑟𝑑𝑑𝐵     (3.49) 
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deff is the effective path length of the link,  
d is the actual path length,  
r is the distance factor (r is a factor which decreases in magnitude as d increases). 
It is obtained as expressed in equation 3.44 below: 
1
𝑟 = 𝑑       (3.50) 1+ ⁄𝑑𝑜
d0 is a rainfall-rate-dependent factor, introduced to reflect the fact that the greater 
the intensity of rainfall in a storm, the smaller the physical dimensions of the 
storm are. It is given by (ITU-R, 2001, Hall et al., 1996; Pozar, 1988):  
𝑑 −0.015𝑜 = 35𝑒 𝑅0.01     (3.51) 
This is valid for R0.01 ≤ 100 mm/h. For R0.01 > 100 mm/h, the value 100 mm/h is 
used in place of R0.01. The prediction method defined above is considered to be 
effective in all parts of the world, at best for frequencies up to 40 GHz and path 
lengths up to 60 km. 
Moupfouma (1984) proposed an empirical model for predicting rain-induced 
attenuation on terrestrial paths from the knowledge of 1-minute rain intensities 
recorded in a broad range of geographical areas and the corresponding 
percentages of time p during which these rain rates are exceeded. The rain 
induced attenuation on a line-of-sight path can be shown as (Moupfouma, 1984): 
𝐴(𝑑𝐵) = 𝑘𝑅𝛼𝑑 𝛼𝑒𝑓𝑓 = 𝑘𝑅 𝑟𝑑     (3.52) 
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d (km) the actual path length, 
deff  the effective path length,  
and r is a reduction factor coefficient. 
 
 
 
 
 
 
 
 
 
 
 
 
 
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CHAPTER 4 
STUDY SITES, EQUIPMENT AND DATA ACQUISITION 
4.1 STUDY SITES 
Throughout the period between August, 2015 to January, 2018 measurements 
were taken for two different locations in Ghana. The choice of the study sites 
were based on rainfall and harmattan patterns for these areas.  
Both research sites were located on the premises of a Ghana Meteorological 
Agency office. The Ghana Meteorological Agency (GMA), established in 1957, 
provides national meteorological services (Kadi, et al, 2011). The mission of the 
GMA is to provide efficient weather and climate services by collecting, 
processing, archiving and disseminating meteorological information to end users 
such as farmers, research institutions, private and public agencies etc. and 
advisory services to the general public on environmental issues. For this research, 
the Axim and Tamale research sites were chosen.  
 
4.1.1 Axim Site 
Axim is the largest town on the coast west of Takoradi. Axim is located 64 
kilometers west of the port city of Sekondi-Takoradi in Western Region to the west 
of Cape Three Points, as shown in Figure 4.1. It is the capital of the Nzema East 
District, an area covering 2194 square kilometers (9.8 percent of the total area of 
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the Western Region).  It is situated almost halfway between Elubo and Takoradi. 
The center of the test site is at 4°51’N and 2°14’W, with elevation being about 71 
meters. The Axim settlement is situated in a tranquil and sheltered natural bay with 
a rocky beach. 
The climate of Axim is classified as tropical. There is significant rainfall for most 
months of the year and there is a short dry season which has little effect. The 
average annual temperature in Axim is 26.3 °C. About 1979 mm of precipitation 
falls annually. 
 
Figure 4.1: Map of Southern Ghana 
 
Figure 4. 2 shows the location for installation of the visibility meter and the 
weather station at the GMA office in Axim. The GMA office is situated on a 
slightly elevated ground which is conducive for visibility and rainfall 
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measurements. The area around the office is also devoid of trees therefore there is 
less obstruction to the rainfall gauge and the visibility meter.    
 
Figure 4.2: Axim research site at the GMA office 
4.1.2 Tamale Site 
Tamale is the capital town of the Northern Region of Ghana (Figure 4.3). Tamale 
is Ghana's fourth largest city. It is located at 9° 24' 2.84" N and 0° 50' 21.48" E and 
it is situated at an elevation of 196 meters above sea level. It is estimated to have a 
2013 projected population of 360,579 according to the 2010 census. The town is 
located 600 km (370 miles) north of Accra.  
According to the Köppen's climate classification, the climate of Tamale consists of 
a tropical wet and dry climate. There exists one rainy season from April to 
September or October, with the highest rainfall happening in July and August. 
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The dry season is generally from November to early April. The season is influenced 
by the dry north-easterly (harmattan) winds, while the rainy season is influenced 
by the moist south-westerly winds. The mean daytime temperatures range from 28 
(December and mid-April) to 43 (March, early April) degrees Celsius, while mean 
nighttime temperatures range from 18 (December) to 25 (February, March) degrees 
Celsius. The mean annual daily sunshine is about 7.5 hours. This lowers 
the humidity causing hotter days and cooler nights (UNDP, 2013). 
 
 
Figure 4.3: Map of Northern Part of Ghana  
 
 
The office of the GMA in Tamale is located at the Tamale airport. All 
installations and measurements were taken on the premises of the GMA office (as 
shown in Figure 4.4). The instruments were installed in an enclosed space beside 
other meteorological equipment owned by the GMA.  
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Figure 4.4: Tamale research site at the GMA office 
 
4.2 EQUIPMENT USED 
In order to study the attenuation of microwave links at 3GHz-10GHz in Axim and 
Tamale visibility and rain rate were measured. The equipments used for these 
measurements include a  
 Davis Vantage Pro 2 Weather Station  
 MiniOFS Visibility Sensor 
 Campbell Scientific CS120 Visibility Sensor 
 Campbell Scientific CR1000 Datalogger 
 
Visibility and rain rate measurements were recorded between the periods from 
August, 2015 to January, 2018.  
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In Axim, the MiniOFS visibility meter and one of the Davis weather stations were 
installed to measure/ record visibility and rain rate respectively. As stated earlier, 
the installations were set up at the Ghana Meteorological Agency office located in 
Axim. 
A Campbell Scientific Visibility Meter and a Davis Weather Station were set up 
and put in operation at the GMA office located at the Tamale Airport. Visibility 
was measured alongside the rainfall rate with one minute intervals in this location 
between the periods from April, 2016 through January, 2018. The weather station 
is equipped for measuring temperature, relative humidity, dew point, wind speed, 
direction and chill, air density and parametric pressure etc. 
 
4.2.1 Campbell Scientific CS120 Visibility Sensor 
The visibility sensor used for this research was the Campbell Scientific CS120 
(Figure 4.5). The CS120 is an infrared forward scatter visibility sensor used for 
automatic weather stations including road, marine and airport based stations. It 
uses the well-established forward scatter system for visibility measurement, 
employing a 42º scatter angle. The CS120 makes use of high speed sampling to 
decrease the number of missed events such as rain and hail and improves response 
to other suddenly changing conditions. 
 
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Figure 4.5: Campbell Scientific CS120 Visibility Sensor 
The CS120 incorporates the principle of forward scattering, which is the 
determining of the extinction coefficient (visual range) by measuring the amount 
of light scattered in the forward direction by atmospheric particulates (Muench, 
1974). 
The forward scatter sensor measures the amount of light scattered at an angle of 
42 degrees (in the case of the CS120) by small particles suspended in its sample 
volume, or large particles passing through its sample volume. The amount of 
scattering is correlated to the quantity of particles in the volume of air being 
sampled. The sample volume is defined by the intersection of the transmitted 
beam of light and the receiver’s field of view (Clark et al, 2012). 
For forward scatter visibility sensors, absorption cannot be measured directly. 
However, the relationship between the amount of absorption and the amount of 
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forward scatter under various weather conditions has been obtained by 
experimentation. By adding a back scatter receiver and thermometer to a forward 
scatter instrument, current weather can be identified, and additional factors for 
absorption added into the extinction coefficient calculations.  
Visibility is influenced by the particulates existing in the atmosphere, such as fog 
droplets, dust particles or raindrops. It is also determined by lighting conditions 
and characteristics of the object such as contrast (daytime) or brightness (if a 
light).  
 
4.2.2  Mini OFS Optical Sensor 
The Mini OFS optical fog sensor is a low price optical sensor. It is one of the 
cheapest visibility sensors on the market. It has a lower performance than other 
visibility meters. The Mini OFS can be used to measure visibility. The sensor is 
for particles in the atmosphere at a distance of about 25cm in the line of sight of 
the sensor. These microscopic particles include raindrops, fog, snow and 
harmattan dust. 
In order to keep the electronics dry, there exists a membrane ventilator that retains 
the pressure inside the sensor at the same level as the outside pressure. The 
membrane ventilator prevents water from leaking into the sensor. The mini OFS 
can measure visibilities from 20 m to 4 km. 
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Figure 4.6: MiniOFS Optical Sensor 
The sensor is mounted horizontally and facing north on a pole. The line of sight of 
the sensor closer than 5 - 10 m should be clear. The sensor comes with a PMMA 
plastic mounting bracket which isolates the sensor electrically reducing the risk 
for surge currents. It has a connected 6 m 5-wire cable.  
 
4.2.3 Davis Vantage Pro 2 Weather Station 
The Davis Vantage Pro 2 weather stations include a console and a versatile 
Integrated Sensor Suite (ISS).  
The ISS gathers outside weather data and sends the data to a Vantage Pro 2 
console. The wireless ISS is powered by solar panels and sends data by radio. The 
cabled ISS sends data by cable to one cabled Vantage Pro 2 console and receives 
power through the console. For this work, the wireless ISS is used.  
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The Vantage Pro 2 ISS (Figure 4.7) includes a rain collector, temperature sensor, 
humidity sensor and anemometer. The temperature and humidity sensors are 
mounted in a passive or fanaspirated radiation shield to reduce the effect of solar 
radiation on the sensor readings. The anemometer measures wind speed and 
direction and can be mounted separately from the rain collector and installed 
adjacent to the ISS or installed separately. The anemometer has been wind-tunnel 
tested to 200 mph.  
 
The transmitter shelter encloses the “brain” of the ISS: the sensor interface and 
the transmitter. It collects outside weather data from the ISS sensors and then 
transmits the data to the wireless console.  
 
 
Figure 4.7: Vantage Pro 2 Integrated Sensor Suite (ISS) 
 
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The console (Figure 4.8) is designed to give extremely accurate readings. 
Installing the console is relatively simple but care has to be taken in setting it up. 
Together with the ISS, assembling the Vantage Pro 2 correctly from the start will 
help ensure that all its features operate correctly with minimal time and effort. 
 
Figure 4.8: Vantage Pro 2 Console 
 
 
The use of the AC adapter in the wireless Vantage Pro 2 consoles are optional. 
Each console carries three C-cell batteries which power a wireless console for an 
estimated period of up to nine months. The Vantage Pro 2 weather station is 
designed to withstand extreme weather.  
 
4.2.4 Campbell Scientific CR1000 Datalogger 
The CR1000 datalogger (shown in Figure 4.9) is made up of a measurement and 
control module and a wiring panel. It operates with an external display and power 
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supply. The CR1000 datalogger has a low power consumption which allows it to 
operate for long periods of time on a battery recharged with a solar panel.  
The datalogger’s module measures sensors, initiates direct communications and 
telecommunications, reduces data, controls external devices, and stores data and 
programs in on-board, non-volatile storage. Its electronics are shielded from radio 
frequencies. It has a battery-backed clock to ensure precise timekeeping. The 
module can run measurement and communication functions concurrently. The on-
board, BASIC-like programming language supports data processing and analysis 
routines. Most CR1000 data loggers have a 4 MB memory.  
The CR1000 has several channel types and hence is compatible with almost every 
available sensor, including thermocouples, SDI-12 sensors, and 4 to 20 mA sensors 
(using a terminal input module). Adding a custom ASIC chip expands its pulse 
count, control port, and serial communications capabilities. The CR1000's input 
and output ports can be paired for transmission and receiving, allowing serial 
communications with serial sensors and devices.  
The CR1000 communicates with a computer through direct connect, ethernet 
interfaces, multidrop modems, short-haul modems, phone modems (land line, 
digital cellular, and voice-synthesized), RF telemetry, and satellite transmitters 
(Argos, Iridium, and Inmarsat). Data can be viewed on a computer using a 
compatible software: PConnect or Loggernet.  Its communication ports include a 
CS input/output, RS-232 and a parallel peripheral.  
 
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Figure 4.9: CR1000 Measurement and Control Datalogger 
4.3 Methodology 
Prior to the installation of the various instruments at the study sites, test runs for 
each of the weather station were done at the Physics Department of the University 
of Ghana. This was done to ensure all proper installation measures were applied 
to certify the proper operation of the instruments. 
The sensor interface of the ISS can be found in the transmitter shelter on the front 
of the ISS station. . All connections for the weather sensors are enclosed in the 
ISS. The sensor interface was checked to ensure that all sensors were connected 
correctly. 
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Figure 4.10: Setting the Transmitter ID for communication between the ISS and the console 
The Vantage Pro2 console can collect data from up to 8 different wireless 
stations. The default Transmitter ID for the ISS and console is 1. Generally, it will 
not be compulsory to change the Transmitter ID. The console and ISS should 
typically begin communicating automatically when powered up. In the case where 
the console and ISS are not communicating, the Transmitter ID has to be 
manually set. For this test run, the console and ISS communicated effectively. As 
a further check, different IDs were selected to check for communication using 
different IDs to set up the console.  
A protective cage (Figure 4.11) was made in the department of Physics, 
University of Ghana to guard the weather station.  
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Figure 4.11: Positioning the protective cage around the weather station at the Physics Department, 
University of Ghana 
Figure 4.12 shows the complete test installation of the ISS of the weather station. 
The ISS was effectively communicating with the console which was set to a 
transmission ID of 1.  
 
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Figure 4.12: Complete ISS setup communicating with console  
With the successful test installations, the weather stations were installed at the 
different study sites; Axim and Tamale.  
Rainfall rate measurements were recorded using the Davis Vantage Pro 2 Weather 
Station that was installed at the two study sites. This is needed for the study sites 
in order to predict accurate rain attenuation for the two different study sites.  
One of the Davis weather station Vantage Pro 2 was setup at the offices of the 
Ghana Meteorological Agency in Axim and the other was installed at the Ghana 
Meteorological Agency office located at the airport premises in Tamale.  
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Figure 4.13: Setting up the Davis Vantage Pro 2 Weather Station at the Axim site 
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Figure 4.14: Installed Vantage Pro 2 weather station at the Tamale site   
The CS120 sensor was securely mounted on a pole. The pole was extended to a 
height of 1.5 m approximately and clamped between the DSP plate and brackets 
by tightening using the nuts provided. 
Before installing the Campbell Scientific visibility sensor, the ground consistency 
was checked to ensure it was not loose and could support the concrete foundation 
and mount. The concrete foundation was created for the mount to be installed on 
it (as shown in Figure 4.15).  
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Figure 4.15: Concrete foundation for mount installation 
Its dimensions were at least 600 mm square and 600 mm deep. Four 12 mm 
diameter holes were drilled to a depth of 77 mm using the mount base as a 
template and the debris in the holes were cleaned. Washers and nuts positioned on 
the ends of the wedge anchor supplied (to protect the threads during installation). 
 
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Figure 4.16: Fully mounted visibility sensor 
The installation of the CS120 visibility sensor was fully completed with its 
installation on the concrete foundation. All necessary connections were done to 
ensure that the correct visibility measurements were recorded.  The CR1000 
datalogger was used to interface between the CS120 and the computer to record 
the visibility measurements using the Loggernet program.  
The CS120 is a robust instrument that operates uninterrupted weather monitoring 
for years. The sensor has been calibrated at the factory and for this research, no 
calibration was redone on site. The lenses were cleaned at least every six months 
because of the dust contaminants in the research sites. This was to guarantee that 
the lenses were free from contaminants and keep the sensor working efficiently. 
The sensor can self-diagnose dirty lenses and give a prompt in its output when the 
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lenses are contaminated to such a degree that its visibility measurements may be 
affected. 
 
 
 
Figure 4.16: Set up the CS120 Visibility Sensor and Vantage Pro 2 Weather Station at the Tamale 
site 
 
Figure 4.16 shows the full setup of both the visibility sensor and the weather 
station at the Tamale site. The visibility is measured using the Campbell Scientific 
visibility sensor and the Vantage Pro 2 weather station measured barometric 
pressure, temperature, humidity, rainfall, rain rate, wind speed and direction, 
UV/solar etc. Highs and lows and/or totals or averages of all parameters were 
recorded. 
 
 
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4.4 DATA ANALYSIS 
The measured rainfall and visibility data were collected, reviewed and evaluated 
after every few months. The data analysis process started with the collection of all 
relevant and useful data, organization of all relevant data gathered from the 
different study sites. 
The rain data and the visibility data at one-minute and one-minute intervals 
respectively were collected at both the Axim site and the Tamale site located at 
the Tamale airport from August, 2015 to January, 2018. The attenuation due to 
dust was obtained by setting the visibility measurements in the Zain Elabdin 
equation whiles the attenuation due to rain was calculated using rain rate 
measurements in the Specific Attenuation Model for Rain (ITU-R P.838-3) . 
 
The effect of particle radius, rain rate, relative humidity and visibility on 
attenuation were discussed in the results. A final step conducted was 
interpretation of the data which involved determining the meaning of the 
information gathered. 
 
 
 
 
 
 
 
 
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CHAPTER 5 
RESULTS AND DISCUSSIONS 
In this chapter, all the experimental results from the experiments outlined in 
chapter 4 are presented. As mentioned in Chapter 1, in performing this research, 
the objectives stated were as follows: 
• To determine the attenuation due to the effect of dust particles from visibility 
measurements. 
• To determine the attenuation using the ITU-R rain attenuation model from 
measured rain rate. 
• To determine any correlation between the visibility and rain rate. 
• Additionally, on account of the fact that relative humidity data was measured, 
work is done to determine any correlation between the visibility and relative 
humidity. 
The data collected during this research work was made up of visibility 
measurements, rainfall measurements, as well as other meteorological data. 
Rainfall data was set to be recorded every 5 minutes. Additionally, other 
meteorological data such as humidity, wave speed and direction, solar irradiance 
and others were recorded along with the rainfall measurements.  
 
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In the course of research, data collection for some periods were not obtained as a 
result of power fluctuations and equipment malfunctioning. However, there was 
enough data recorded to complete the research. Due to the large amounts of data 
recorded, it became necessary that visibility and rainfall values were averaged 
before analysis work was done. 
 
Hence, an analysis of the visibilities and rain rates in Axim and then Tamale are 
presented. The analysis presented includes the effect of mainly visibility and rain 
rate on microwave attenuation. Also the effects of particle size and relative 
humidity were discussed in the results. The implications of these effects, in line 
with the objectives of this work, are also discussed in this chapter.  
 
 
5.1 Signal Attenuation Analysis 
Long term visibility data were recorded in Axim and Tamale. Axim is situated in 
the Western Region whiles Tamale is in the northern region of Ghana. Harmattan 
is more frequent in Tamale whiles rainfall is highest in Axim. The main aim of 
visibility data collection was to use the available data to estimate the effect of 
harmattan dust on microwave attenuation in parts of Ghana.  
 
It is recalled in Chapter 3, the specific attenuation due to harmattan dust proposed 
by Zain is expressed as: 
 
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𝑎 𝑒𝑓
𝐴𝑑  =  (𝑋 +  𝑌𝑎
2𝑓2𝑒  +  𝑍𝑎
3
𝑒 𝑓
3) [𝑑𝐵/𝑘𝑚] 
𝑉 
 
5.2 Axim Measurements  
Visibility data as a result of the harmattan dust and rainfall rate data were 
measured and recorded. The data was analyzed using the respective attenuation 
models chosen for calculating the attenuation.  
 
 
5.2.1 Harmattan Dust Results 
Visibility data was recorded over a period between 2015 and 2016 in both Axim 
and Tamale. The recorded data was used to calculate the signal attenuation using 
the Zain Elabdin model at the different frequency bands. 
 
 
5.2.1.1 Attenuation for the Different Frequency Bands 
A more simplified attenuation formula was obtained by separating the general 
attenuation formula into separate formulae to calculate the attenuation due to 
harmattan dust for each frequency band. This makes the formula more useful for 
microwave network designers and engineers. The general formula for the signal 
attenuation due to harmattan dust particles depends on visibility, frequency, dust 
particles radius and dielectric constant as seen in Equation 3.38. The dielectric 
constant values of the dust particles are important in the determination of 
attenuation for the different frequency bands. 
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Various researchers have measured the refractive index of sand and dust samples 
(Chu, 1979, Ghobrial, 1980, Ruike et al, 2003) which were used for further 
approximations in the new subdivided formulas. It was assumed that a single 
value of the refractive index can be fitted for all frequency ranges in specific 
microwave band (Islam et al, 2010). 
Frequency Band Frequency Range (GHz) ε’ , ε” 
S-band 2 – 4 GHz 4.56, 0.251 (Ghobrial, 1980). 
C-band 4-8 GHz 4.56, 0.251 (Chu, 1979) 
X-band 8 – 12 GHz 5.73, .415 (Ruike, 2003) 
Ku-band 12 – 18 GHz 5.5, 1.3 (Ruike, 2003) 
K-band 18 – 26.5 GHz 5.1, 1.4 (Ruike, 2003). 
Ka-band 26.5 – 40 GHz 4, 1.325 (Ruike, 2003) 
W-band 56 – 100 GHz 3.5, ε” = 1.64 (Ruike, 2003) 
Table 5.1: Dielectric constants for the different microwave frequency bands (Islam et al, 2010) 
 
For visibility data recorded in Axim for the month of December, 2015, the 
attenuation due to harmattan dust for the different frequency bands was 
calculated.  
The dielectric constants used for all calculations are as shown in Table 5.1. The 
frequency bands range from 10-100 GHz. The specific attenuation as a result of 
dust was calculated for the averaged visibility values of one set of collected data 
recorded in Axim.  
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Figure 5.1 to Figure 5.9 illustrate the graph of the signal attenuation against 
frequencies in the different frequency ranges.  
 
S Band
-4
5.5x10
 Vis=3.975km
 Vis=3.995km
-4
5.0x10  Vis=4.012km
 Vis=4.016km
-4
4.5x10
-4
4.0x10
-4
3.5x10
-4
3.0x10
-4
2.5x10
2.0 2.5 3.0 3.5 4.0
Frequency (GHz)
 
Figure 5.1: Signal Attenuation versus Frequency at S-Band for Different Visibilities in Axim 
 
C Band
-3
1.1x10
 Vis=3.975km
-3  Vis=3.995km
1.0x10  Vis=4.012km
 Vis=4.016km
-4
9.0x10
-4
8.0x10
-4
7.0x10
-4
6.0x10
-4
5.0x10
4 5 6 7 8
Frequency (GHz)
 
Figure 5.2: Signal Attenuation versus Frequency at C-Band for Different Visibilities in Axim
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X Band
-3
2.0x10  Vis=3.975km
-3  Vis=3.995km
1.9x10
 Vis=4.012km
-3  Vis=4.016km
1.8x10
-3
1.7x10
-3
1.6x10
-3
1.5x10
-3
1.4x10
-3
1.3x10
8 9 10 11 12
Frequency (GHz)
 
Figure 5.3: Signal Attenuation versus Frequency at X-Band for Different Visibilities in Axim 
 
 
-2
1.0x10 Ku Band
-3
9.5x10  Vis=3.975km
 Vis=3.995km
-3
9.0x10  Vis=4.012km
 Vis=4.016km
-3
8.5x10
-3
8.0x10
-3
7.5x10
-3
7.0x10
-3
6.5x10
-3
6.0x10
12 13 14 15 16 17 18
Frequency (GHz)
 
Figure 5.4: Signal Attenuation versus Frequency at Ku-Band for Different Visibilities in Axim 
 
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K Band
-2
1.7x10  Vis=3.975km
 Vis=3.995km
-2
1.6x10  Vis=4.012km
 Vis=4.016km
-2
1.5x10
-2
1.4x10
-2
1.3x10
-2
1.2x10
-2
1.1x10
18 20 22 24 26 28
Frequency (GHz)
 
Figure 5.5: Signal Attenuation versus Frequency at K-Band for Different Visibilities in Axim 
 
Ka Band
-2
3.4x10
 Vis=3.975km
-2  Vis=3.995km
3.2x10  Vis=4.012km
 Vis=4.016km
-2
3.0x10
-2
2.8x10
-2
2.6x10
-2
2.4x10
-2
2.2x10
26 28 30 32 34 36 38 40 42
Frequency (GHz)
 
Figure 5.6: Signal Attenuation versus Frequency at Ka-Band for Different Visibilities in Axim 
 
 
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W Band
-1
1.2x10  Vis=3.975km
 Vis=3.995km
-1
1.1x10  Vis=4.012km
 Vis=4.016km
-1
1.0x10
-2
9.0x10
-2
8.0x10
-2
7.0x10
-2
6.0x10
50 60 70 80 90 100
Frequency (GHz)
 
Figure 5.7: Signal Attenuation vrs Frequency at K-Band for Different Visibilities in Axim 
 
From Figures 5.1 to Figure 5.7, it was observed that the signal attenuation 
increased with increasing frequency bands. The same trend run through for the 
different frequency bands as shown. The attenuation values increase with the 
different increasing frequency band ranges. 
 
In the Elsheikh et al (2010) paper, the Zain Elabdin dust/sand storm prediction 
models were examined based on different probability density functions obtained 
from different papers (Ghobrial 1980, Haddad et al, 1983, Row et al, 1985, 
Patterson et al, 1977, Grams et al, 1974, Bilford et al, 1971) in order to reflect the 
various ranges of dust particle sizes that may exist during the dust storm (Elsheikh 
et al, 2010). 
 
Figures 5.8 to 5.11 show the attenuation against frequency for varying dust 
particle sizes. Attenuation values were obtained for each average visibility 
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measured. The particle size of 0.7 um was obtained from a Hughes (2015) paper 
and the 10um was the particle size used for this work. The other particle sizes 
were varied to observe their effect on attenuation. 
0.08 V = (3.975 ± 0.001) km
0.07  r=10um
 r=0.7um
0.06  r=20um
 r=24um
0.05  r=28um
 r=29.1um
 r=29.7um
0.04
0.03
0.02
0.01
0.00
-0.01
0 50 100
Frequency (GHz)
 
Figure 5.8: Signal Attenuation due to harmattan against Frequency at Vis = 3975.648936m for 
different radius sizes 
 
0.08 V = (3.995 ± 0.001) km
0.07
 r=10um
 r=0.7um
0.06
 r=20um
 r=24um
0.05  r=28um
 r=29.1um
0.04  r=29.7um
0.03
0.02
0.01
0.00
-0.01
0 100 200
Frequency (GHz)
 
Figure 5.9: Signal Attenuation due to harmattan against Frequency for Vis = 3995.711m at 
different radius sizes 
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0.08 V = (4.012 ± 0.001) km
0.07  r=10um
 r=0.7um
0.06  r=20um
 r=24um
0.05  r=28um
 r=29.1um
0.04  r=29.7um
0.03
0.02
0.01
0.00
-0.01
0 50 100
Frequency (GHz)
 
Figure 5.10: Signal Attenuation due to harmattan against Frequency for Vis = 4012.395m at 
different radius sizes 
 
0.08 V = (4.016 ± 0.001) km
 r=10um
0.07  r=0.7um
 r=20um
0.06  r=24um
 r=28um
0.05  r=29.1um
 r=29.7um
0.04
0.03
0.02
0.01
0.00
-0.01
0 50 100
Frequency (GHz)
 
Figure 5.11: Signal Attenuation due to harmattan against Frequency for Vis = 4016.027m at 
different radius sizes 
 
 
 
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It was found that the signal attenuation remained within the same range of 0 
dB/km to 0.8 dB/km for all the four varying average visibilities across all the 
different particle. Generally, it is observed that attenuation increased with 
increasing frequency. Some discontinuities were observed in the trend. This was 
as a result of the transition between different frequency bands.  
The graph obtained is as expected from the equation, which is frequency is 
directly proportional to attenuation.  
 
 
5.2.2 Rain Rate Measurements 
Measurements of the rain rate in Axim during the research period was recorded 
and used to calculate the microwave attenuation within the area. The rain rate was 
recorded with a 5-minute interval. In analyzing the data, the average monthly 
values were calculated and the graphs are as shown below in Figure 5.12. 
 
 
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0.00040
 Aug 2015
 Sept 2015
0.00035
 Oct 2015
 Nov 2015
0.00030  Dec 2015
0.00025
0.00020
0.00015
0.00010
0.00005
0 20 40 60 80 100
Frequency (GHz)
 
Figure 5.12: Graph of Rain Attenuation versus Frequency from August - October 2015 
 
 
 Jan 2016
 Feb 2016
0.00010  Mar 2016
 Apr 2016
0.00005
0.00000
0 50 100
Frequency (GHz)
 
Figure 5.13: Graph of Rain Attenuation versus Frequency from August - October 2015 
 
 
 
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Figures 5.12 and 5.13 illustrate the graph of graph of attenuation due to rain 
against frequency from August 2015 to December, 2015 and then January, 2016 
to April, 2016 respectively.  The rain attenuation was calculated using the ITU-R 
model. The attenuation due to rain increased with increasing frequencies. As can 
be seen in Figure 5.12, the month of November 2015 had the highest attenuation 
values whiles August 2015 had the lowest attenuation values. 
 
From Figure 5.13, it was observed that April 2016 had the highest attenuation 
values whiles February 2016 had the lowest attenuation values. Figures 5.12 and 
5.13 correlated with bi-modal rainy seasons in southern Ghana: April through 
June and September through November. 
 
 
5.2.3 Additional Data Analysis (Axim) 
On account of the fact that relative humidity data was measured using the Davis 
weatherstation, work was done to determine any correlation between the visibility 
and rain rate and also between visibility and relative humidity. Analysis done on 
these data sets are shown in the graphs shown in Figures 5.14 to 5.16b. This 
analysis was done using measurements obtained in Axim for all weather 
(harmattan and rainfall) and all-day (morning and night) for days in 2016. 
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 Visibility
0.30
0.25
0.20
0.15
0.10
-5 0 5 10 15 20 25 30 35 40 45
Rain Rate
 
Figure 5.14: Graph of Visibility versus Rain Rate in Axim 
 
Figure 5.14 demonstrated a graph of visibility against rain rate in Axim. It was 
observed that there was no obvious correlation was observed between the 
visibility and rain rate.  
 
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0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
80 90 100
Relative Humidity
 
Figure 5.15: Graph of Visibility versus Relative Humidity (All-Day, All Weather) in Axim 
 
Figure 5.15 demonstrated a relation between visibility against relative humidity 
with measurements from Axim. A cluster was obtained showing no relation 
between the two parameters. Furthermore, analysis was done using xyz plots for 
visibility, relative humidity and temperature to determine and further relationship 
between visibility and other weather parameters such as temperature.  
 
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28
300
250 27
200
26
150
25
100
50 24
0
23
3
-50
2 8 0 0
80 (C) 80 2 m)RE 2L 6A R
E RE 0 0
TU LA (dB
/k
TIV 90 RA TE IV
0  9 1 Y
 H 2 PE E 
0
H 0U 4 M U I
LIT
MID TE MID VIS
IB
IT 0 0Y 10 ITY 010
22
  
Figure 5.16a: XYZ Graph of Visibility against Relative Humidity and Temperature 
Figure 5.16b: XYZ Graph of Temperature against Visibility and Relative Humidity  
 
Figure 5.16a and 5.16b shows xyz plots of visibility with relative humidity and 
temperature. Figure 5.16a illustrated a graph of visibility against relative humidity 
and temperature whiles Figure 5.16b illustrated a graph of temperature against 
relative humidity and visibility. In both plots, it was observed that the relative 
humidity and temperature both affect the visibility. No obvious correlation was 
obtained between the three variables. 
 
5.3 Tamale Measurements 
5.3.1 Harmattan Dust Results 
Visibility readings were recorded in Tamale for the month of December, 2016 and 
2017. The signal attenuation due to harmattan dust for the different frequency 
bands was calculated. 
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ILITY (dB/km
)
VISIB
E (C)
TEMPERAT
UR
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During the course of measurements, visibility values recorded were relatively low 
during 2016 in the Tamale during the harmattan season. Visibility was measured 
using the Campbell Scientific Visibility Sensor. For most of the events, the low 
values of visibilities ranged 0.225 km to 0.262 km.  
 
The specific attenuation as a result of harmattan dust was calculated for the 
averaged visibility values recorded in Tamale. Figure 5.17 – Figure 5.23 shows 
the graphs of the signal attenuation against frequency bands in the range of 10 - 
100 GHz. 
 
 
S Band
0.010
 Vis=0.225 km
 Vis=0.232 km
0.009  Vis=0.256 km
 Vis=0.261 km
0.008
0.007
0.006
0.005
0.004
2.0 2.5 3.0 3.5 4.0
Frequency (GHz)
 
Figure 5.17: Signal Attenuation versus Frequency at S-Band for Different Visibilities in Tamale 
 
 
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Attenuation (dB/km)
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C Band
0.020
 Vis=0.225 km
 Vis=0.232 km
0.018  Vis=0.256 km
 Vis=0.261 km
0.016
0.014
0.012
0.010
0.008
4 5 6 7 8
Frequency (GHz)
 
Figure 5.18: Signal Attenuation versus Frequency at C-Band for Different Visibilities in Tamale 
 
 
X Band
0.036
 Vis=0.225 km
0.034  Vis=0.232 km
 Vis=0.256 km
0.032  Vis=0.261 km
0.030
0.028
0.026
0.024
0.022
0.020
8 9 10 11 12
Frequency (GHz)
 
Figure 5.19: Signal Attenuation versus Frequency at X-Band for Different Visibilities in Tamale 
 
 
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Attenuation (dB/km) Attenuation (dB/km)
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Ku Band
0.17  Vis=0.225 km
 Vis=0.232 km
0.16  Vis=0.256 km
 Vis=0.261 km
0.15
0.14
0.13
0.12
0.11
0.10
0.09
12 13 14 15 16 17 18
Frequency (GHz)
 
Figure 5.20: Signal Attenuation versus Frequency at Ku-Band for Different Visibilities in Tamale 
  
 
K Band
0.30
 Vis=0.225 km
 Vis=0.232 km
0.28  Vis=0.256 km
 Vis=0.261 km
0.26
0.24
0.22
0.20
0.18
0.16
18 20 22 24 26 28
Frequency (GHz)
 
Figure 5.21: Signal Attenuation versus Frequency at K-Band for Different Visibilities in Tamale 
 
 
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Attenuation (dB/km) Attenuation (dB/km)
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Ka Band
0.60  Vis=0.225 km
 Vis=0.232 km
 Vis=0.256 km
0.55
 Vis=0.261 km
0.50
0.45
0.40
0.35
0.30
26 28 30 32 34 36 38 40 42
Frequency (GHz)
 
Figure 5.22: Signal Attenuation versus Frequency at Ka-Band for Different Visibilities in Tamale 
 
2.2 W Band
 Vis=0.225 km
2.0  Vis=0.232 km
 Vis=0.256 km
 Vis=0.261 km
1.8
1.6
1.4
1.2
1.0
50 60 70 80 90 100
Frequency (GHz)
 
Figure 5.23: Signal Attenuation versus Frequency at W-Band for Different Visibilities in Tamale 
 
As observed in the Axim data, Figures 5.17 to Figure 5.23 show the signal 
attenuation against the different frequency band for different visibilities in 
Tamale. Figure 5.17 showed that for the S-band which demonstrated the 
attenuation values increasing with increasing frequency. The same trend run 
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Attenuation (dB/km) Attenuation (dB/km)
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through for the different frequency bands as can be seen in figures 5.18 to 5.23, 
that is, from the C-band to the W- band. 
 
For Tamale, the different visibilities showed different attenuation values with the 
attenuation values reaching the highest values for the least visibilities and vice 
versa. In addition, the attenuation values increased with the increasing frequency 
band ranges.  
 
Figures 5.24 to 5.27 show the calculated attenuation using the Zain Elabdin model 
for the average visibility values measured (0.225 km, 0.232 km, 0.256 km, 0.261 
km) at frequencies ranging from 10 GHz to 100 GHz for varying dust particle 
sizes. This analysis follows from the analysis done in Axim.  
 
 
 
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1.4 V = (0.225 ± 0.001) km
1.2
1.0  r=10um
 r=0.7um
 r=20um
0.8
 r=24um
 r=28um
0.6  r=29.1um
 r=29.7um
0.4
0.2
0.0
0 50 100
Frequency (GHz)
 
Figure 5.24: Signal Attenuation due to harmattan against Frequency at Vis = 225.482m for 
different radii 
 
1.4
V = (0.232 ± 0.001) km
1.2
 r=10um
 r=0.7um
1.0
 r=20um
 r=24um
0.8  r=28um
 r=29.1um
 r=29.7um
0.6
0.4
0.2
0.0
0 50 100
Frequency (GHz)
 
Figure 5.25: Signal Attenuation due to harmattan against Frequency for Vis = 232.64m at different 
radii 
 
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Attenuation (dB/km)
Attenuation (dB/km)
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1.2
V = (0.256 ± 0.001) km
1.1
1.0
 r=10um
0.9
 r=0.7um
0.8  r=20um
 r=24um
0.7
 r=28um
0.6  r=29.1um
0.5  r=29.7um
0.4
0.3
0.2
0.1
0.0
-0.1
0 50 100
Frequency (GHz)
 
Figure 5.26: Signal Attenuation due to harmattan against Frequency for Vis = 256.95m at different 
radii 
 
1.2 V = (0.261 ± 0.001)km
1.1
 r=10um
1.0  r=0.7um
0.9  r=20um
 r=24um
0.8
 r=28um
0.7  r=29.1um
 r=29.7um
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
0 50 100
Frequency (GHz)
 
Figure 5.27: Signal Attenuation due to harmattan against Frequency at Vis = 261.70m for different 
radii 
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Attenuation (dB/km)
Attenuation (dB/km)
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It was found that the attenuation remained within the same range (~ 0.1 dB/km to 
~1.2 dB/km) for all the four varying average visibilities across all the different 
particle sizes. The attenuation values in Tamale were comparatively lesser than 
those in Axim.  
 It was observed that the signal attenuation increased as the radius size 
increased for frequencies from 10 – 100 GHz. Some discontinuities were 
observed in the trend. This was as a result of the transition between different 
frequency bands. The graph obtained was as expected from the equation since 
frequency is directly proportional to attenuation.  
 
5.3.2 Rain Rate Results  
Figure 5.28 shows the graph of rain attenuation against the frequency from April, 
2016 to June, 2016.  The rain attenuation was calculated using the ITU-R model. 
As can be seen in Figure 5.28, the month of June had the highest attenuation 
levels with its higher peak values at about 0.000425 dB/km while May had the 
lower attenuations with dip attenuation values of about 0.00008 dB/km.  
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0.0006  Apr 2016
 May 2016
 June 2016
0.0005
0.0004
0.0003
0.0002
0.0001
3.0 3.5 4.0
Frequency (GHz)
 
Figure 5.28: Graph of Rain Attenuation versus Frequency from April -June 2016 
 
 
5.3.3 Additional Data Analysis (Tamale) 
On account of the fact that relative humidity data was measured using the Davis 
weatherstation, work was done to determine any correlation between the visibility 
and rain rate and also between visibility and relative humidity. Analysis done on 
these data sets are shown in the graphs shown in Figures 5.29 to 5.30b. This 
analysis was done using measurements obtained in Tamale for all weather 
(harmattan and rainfall) and all-day (morning and night) for days in 2016. 
 
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Specific Attenuation (dB/km)
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0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
70 80 90 100
Relative Humidity
 
Figure 5.29: Graph of Visibility versus Relative Humidity (All-Day, All Weather) for Tamale 
 
Figure 5.29 demonstrates a relation between visibility against relative humidity 
with measurements from Tamale. A cluster was obtained showing no relation 
between the two parameters. Additionally, analysis was done using xyz plots for 
visibility, relative humidity and temperature to determine any further relationship 
between visibility and other weather parameters such as temperature.  
 
 
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Visibility (dB/km)
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300 30
29
28
200
27
26
25
100
24
23
3 0 4 0 0
700 2 8 2720
) 2 0 0
R 80
2 6 C 0
re ( R 8 /km
)
ela atu et la Biv 2e 0 4 per ti
0
v y (d H 9 eu  H 9
0 t
m Tem um ib
ili
id 2it 2 iy d
is
0 i0 ty 0
-2 V0
1 10 020
  
Figure 5.30a: XYZ Graph of Visibility against Relative Humidity and Temperature 
Figure 5.30b: XYZ Graph of Temperature against Visibility and Relative Humidity  
 
Figure 5.30a and 5.30b shows xyz plots of visibility with relative humidity and 
temperature. Figure 5.30a illustrates a graph of visibility against relative humidity 
and temperature whiles Figure 5.30b illustrates a graph of temperature against 
relative humidity and visibility. From the xyz plots shown in Figures 5.30a and 
5.30b, it can be observed that changes in temperature values as well as relative 
humidity values have an effect on visibility. No obvious correlation was obtained 
between the three variables. 
 
 
5.4 Signal Attenuation due to Dust for Different Radii 
Using the Zain model, the attenuation coefficients of different particle radius sizes 
were calculated at a frequency of 40GHz using information about the different 
mean radii from Elsheikh et al (2010) and the radii used for this research obtained 
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isibility (dB/k
m)
V
Temperatur
e (C)
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from different papers. The radii (ae) used were 29.7µm, 24 µm, 20 µm, 10 µm and 
0.7 µm. The radius used for this research was 10 µm whiles 0.7 µm was obtained 
from Hughes (2015) paper. The remaining radii were from the Elsheikh et al 
(2010) paper. Figures 5.31 and 5.32 showed the attenuation against visibility for 
the different particle sizes. This was done in both Tamale and Axim.   
 
0.35
0.30
0.25
 r=0.7µm
 r=20µm
0.20  r=24µm
 r=28µm
 r=29.1µm
0.15  r=29.7µm
 r=10µm
0.10
0.05
0.00
0.23 0.24 0.25 0.26
Visibility (km)
 
Figure 5.31: Signal Attenuation due to harmattan against Visibility at 40 GHz for different radii in 
Tamale 
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Attenuation (dB/km)
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-2
2.0x10
-2
1.8x10
-2
1.6x10
-2
1.4x10
-2
1.2x10
-2
1.0x10  r=0.7µm
-3
8.0x10  r=20µm
 r=24µm
-3
6.0x10  r=28µm
-3  r=29.1µm
4.0x10
-3
2.0x10
0.0
3.97 3.98 3.99 4.00 4.01 4.02
Visibility (km)
 
Figure 5.32: Signal Attenuation due to harmattan against Visibility at 40 GHz for different radii in 
Axim 
 
For both Axim and Tamale, it was observed that attenuation values increased with 
increasing particle size. For Tamale (Figure 5.31), it was observed that the largest 
particle size radius (ae = 29.7µm) reached the highest attenuation values 
calculated at frequency 40GHz at the different visibilities, whereas the smallest 
particle radius (ae = 0.7µm), attained the lowest attenuation values which was 
calculated at frequency 40GHz. Similarly for Axim, Figure 5.32 showed that the 
largest particle size radius (ae = 29.7µm) reached the highest attenuation values 
calculated at frequency of 40GHz at the different visibilities, while the lowest 
attenuation values which was calculated at frequency 40GHz were obtained for 
the smallest particle radius (ae = 0.7µm). 
 
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Attenuation (dB/km)
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Also, it was observed from Figure 5.31 that the signal attenuation graphs showed 
a very slight decline for the lower radius sizes (ae = 0.7µm and ae = 10µm) but 
had a more gradual decline for the remaining larger radii (ae = 20µm, 24µm and 
29.7µm). On the other hand, Figure 5.32 indicated that all the signal attenuation 
graphs maintained a a very slight decline for the respective visibilities. 
 
 
5.4.1 Comparison Between The Measured And Prediction Models 
Attenuation values were calculated for different values of visibility at 40 GHz in 
Axim and Tamale. This is shown in Table 5.2 below:  
Calculated Attenuation  
Visibility(km) Att. from Elsheikh paper (My Study) 
0.225482 0.141377426 0.117827039 
0.232641 0.140886547 0.1142012 
0.256953 0.139226214 0.103395704 
0.261701 0.138903168 0.101519749 
 
Table 5.2: Result of Measurements and Calculations of Signal Attenuation Due To Harmattan at 
40 GHz in Tamale 
 
Figure 5.33 represents a comparative analysis between attenuation values 
obtained from the aforementioned Elsheikh et al (2010) paper and the calculated 
attenuation values at 40GHz with visibility values from Tamale. Both sets of 
attenuation values were obtained using the Zain Elabdin model at a frequency of 
40GHz.   
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Figure 5.33: Result of Measurements and Calculations of Signal Attenuation Due To Harmattan 
Dust at 40GHz 
 
Comparatively from Figure 5.33, the attenuation recorded from the Elsheikh 
paper was much higher with a maximum and minimum attenuation value of 
0.1414 dB/km and 0.1389 dB/km respectively as compared with the maximum 
and minimum calculated attenuation value of 0.1178 dB/km and 0.1015dB/km 
respectively obtained from the measured visibilities in Axim. 
 
The graph showed a steeper decline for the calculated values than the more 
gradual decline seen for the Elsheikh paper. This implies there is a lower visibility 
due to less dust particles in the atmosphere in Tamale than in Sudan (where this 
work was done). 
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The values of the slope and the intercept for the attenuation obtained from the 
Elsheikh paper are (–0.06831 ± 3.66378 x 10-5) dB/km and (0.15678 ± 8.9646 x 
10-6) dB/km respectively. Similarly, the slope and intercept for the attenuation 
obtained from the calculated attenuation obtained from this work are (-0.44887 ± 
0.00788) dB/km and (0.21885 ± 0.00193) dB/km respectively. 
 
 Axim
0.7
 Tamale
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0 50 100
Frequency (GHz)
 
Figure 5.34: Comparison of Calculated Signal Attenuation Due To Harmattan Dust at Different 
Frequencies in Axim and Tamale 
 
Figure 5.34 shows a graph of attenuation due to harmattan dust against frequency. 
The attenuation values were calculated using the Zain Elabdin model. In Figure 
5.34, the signal attenuation due to harmattan was calculated for frequencies 
ranging from 10 – 100 GHz for both Tamale and Axim.  
 
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Attenuation (dB/km)
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The signal attenuation due to harmattan increased with increasing frequencies for 
both locations. It was observed that Tamale had the higher attenuation values. 
Axim showed relatively low attenuation values from frequencies of 10 GHz to 
100 GHz and ranged from 0.00009 dB/km to 0.03841 dB/km whiles signal 
attenuation values for Tamale increased from 0.00146 dB/km to its maximum 
value of 0.6272 dB/km. This graph shows that attenuation due to dust was more 
prevalent in the Tamale than in Axim. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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CHAPTER SIX 
CONCLUSIONS AND RECOMMENDATIONS 
6.1 Summary of Experiment 
In this study, visibility data were measured at two study sites in Axim and 
Tamale. Additionally, rainfall and other meteorological data were collected in 
Axim and Tamale.   
The recorded visibility data was then used to calculate the signal attenuation due 
to harmattan dust using the Zain Elabdin model. Similarly, the rainfall rate data 
was used to determine the rain attenuation using the ITU-R model. Also, there 
were comparisons made between calculated results using the Zain model 
attenuation model and the results from some chosen papers. Finally, work was 
done to determine any correlation between the visibility and rain rate and also 
between visibility and relative humidity. This was done for both Axim and 
Tamale. Measurements used for the analysis were obtained for all weather 
(harmattan and rainfall) and all-day (morning and night) for days in 2016. 
 
 
6.2 Key Results 
In summary, the overall result of this experiment was that both harmattan dust and 
rainfall have a significant impact on signal attenuation in parts of Ghana. The 
impact of the attenuation due to harmattan dust was much more evident in Tamale 
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whiles rain attenuation was more evident in Axim. Additionally, on analysing 
attenuation due to harmattan dust for the different frequency bands from 10 – 100 
GHz, it was observed that the signal attenuation increased with the increasing 
frequency bands for both Axim and Tamale. For the Axim site, the attenuation 
values were approximately the same for all the visibilities. On the contrary for 
Tamale, the different visibilities produced different attenuation values with the 
attenuation values reaching the highest values for the least visibilities and vice 
versa.  
 
The attenuation was calculated using the Zain Elabdin model for the four average 
visibility values at frequencies ranging from 10 GHz to 100 GHz using different 
values of particle radius obtained from the Elsheikh et al (2010) paper. It was 
observed that the signal attenuation remained within the same range of 0.1 dB/km 
to 0.12 dB/km for all the four varying average visibilities across all the different 
particle sizes for Tamale whiles attenuation in Axim remained was in the range of 
0.01 dB/km to 0.07 dB/km for all the four varying average visibilities across all 
the different particle sizes. 
It was observed that the signal attenuation increased as the radius size increased 
for frequencies from 10 – 100 GHz. Some discontinuities were observed in the 
trend. This was as a result of the transition between different frequency bands. 
The graph obtained was as expected from the equation since frequency is directly 
proportional to attenuation.  
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Furthermore, as shown in the ITU-R rain attenuation model, attenuation values 
were highest with high rainfall rates while the lowest attenuation values 
corresponded to the lowest rainfall rates.  
Using the Zain model, the attenuation coefficients of different particle radius sizes 
were calculated at a frequency of 40GHz using information about the different 
mean radii from Elsheikh et al (2010), the radius used for this research and radius 
obtained from Hughes (2015) paper. The radii (ae) used were 29.7µm, 24 µm, 20 
µm, 10 µm and 0.7 µm. The radius used for this research was 10 µm. This was 
done for both Axim and Tamale.  
For both Axim and Tamale, it was observed that the largest particle size radius (ae 
= 29.7µm) reached the highest attenuation values calculated at frequency 40GHz 
for the different visibilities, whereas the smallest particle radius (ae = 0.7µm), 
attained the lowest attenuation values which was calculated at frequency 40GHz. 
For Tamale, it was noted that the signal attenuation showed very slight decline for 
the lower radius sizes (ae = 0.7µm and ae = 10µm) but showed a more gradual 
decline for the remaining larger radii (ae = 20µm, 24µm and 29.7µm). On the 
other hand, the analysis indicated that all the signal attenuation in Axim 
maintained a relatively constant plot at the respective visibilities. 
The signal attenuation due to harmattan dust was calculated for frequencies 
ranging from 10 – 100 GHz for both Tamale and Axim. The signal attenuation 
due to harmattan dust increased with increasing frequencies for both locations. 
Upon comparison, it was observed that Tamale had the higher attenuation values. 
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Axim showed relatively low attenuation values from frequencies of 10 GHz to 
100 GHz and ranged from 0.00009 dB/km to 0.03841 dB/km whiles signal 
attenuation values for Tamale increased from 0.00146 dB/km to its maximum 
value of 0.6272 dB/km. This graph shows that attenuation due to dust was more 
prevalent in the Tamale than in Axim. 
Finally, a comparative analysis between the attenuation values obtained from the 
aforementioned Elsheikh et al paper and the calculated attenuation values against 
the visibility measurements recorded in this research. Both sets of attenuation 
values were obtained using the Zain Elabdin model at a frequency of 40GHz.  The 
attenuation recorded from the Elsheikh et al paper was much higher than the 
attenuation values obtained from the calculated attenuation values. 
 
Finally, analysis work done to obtain any correlation between visibility and rain 
rate and visibility and relative humidity showed no relation between the two 
parameters in both cases. Further analysis using xyz plots of visibility with 
relative humidity and temperature showed that changes in temperature values as 
well as relative humidity values have an effect on visibility. No obvious 
correlation was obtained between the three variables. 
 
In summary, the conclusions of this research work are as follows: 
• The two models used for calculating the attenuation due to harmattan dust and 
rain are the Zain Elabdin Model and the ITU-R Specific Attenuation Model 
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for Rain respectively. It has been successfully shown that using visibility and 
rain rate, these two models can predict attenuation in Ghana. 
• A study by Elfatih et al (2013) obtained attenuation due to dust storm in 
Sudan. It has been shown that the attenuation measured from dust particles in 
Tamale is much smaller than the attenuation values obtained from the Elfatih 
paper. Clearly the origin, size and concentration of the dust is important. 
• As expected, the impact of the attenuation due to harmattan dust was 
significantly evident in Tamale while that of rain attenuation was more 
evident in Axim. 
• Contrary to our expectation, no systematic correlation was obtained between 
visibility and rain rate. 
• Additionally, no observable correlation was obtained between the visibility 
and relative humidity. 
 
6.3 Further Research and Recommendation 
It has been noted that RF wave propagation above in the atmosphere is affected 
by the various weather conditions. While this study has clearly shown the impact 
that harmattan dust and rainfall has on microwave attenuation in parts of Ghana, it 
is recommended that this experiment be repeated over a much longer time frame, 
with a wider range of environmental conditions, and over a wider set of 
frequencies, varying particle sizes and measured signal strength. 
 
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In my study, it was not possible to measure particle size. It will be interesting for 
further work to be done to observe the effects of varying particle sizes on 
attenuation. Additionally, the availability of measured signal strength would have 
made this study easier. It is therefore recommended that further work be done 
using measured signal strength. Finally, further research on the role of relative 
humidity on attenuation is recommended.  
 
All of the above recommendations would ultimately lead to a better understanding 
of how various weather conditions affect microwave attenuation. 
 
 
 
 
 
 
 
 
 
 
 
 
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