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DEVELOPMENT OF PATH LOSS MODELS FOR SMOOTH AND CONVEX
SURFACES TERRAINS IN MALAYSIAN ENVIRONMENT
By
WONG PENG KIONG
Thesis Submitted to the School of Graduate Studies, Universiti Putra Malaysia, in
Fulfilment of the Requirements for the Degree of Master of Science
September 2004
ii
To Mother, Sisters, Brothers…
and
In memorial: Father
iii
Abstract of thesis presented to the Senate of Universiti Putra Malaysia in fulfilment of the
requirement for the degree of Master of Science
DEVELOPMENT OF PATH LOSS MODELS FOR SMOOTH AND CONVEX
SURFACES TERRAINS IN MALAYSIAN ENVIRONMENT
By
WONG PENG KIONG
September 2004
Chairman : Zulkifly Abbas, Ph.D.
Faculty : Science
This study describes the development of path loss prediction model for smooth and
convex surfaces terrains in Malaysian environment. The measurement system consists of
a spectrum analyzer and a log-periodic antenna. A computer program was developed to
acquire measured field strength data from the spectrum analyzer and convert the values to
path loss using Agilent Visual Engineering Environment (VEE). Both line-of-sight
propagation (for smooth terrain) and non-line-of-sight propagation (for convex surface
terrains) was investigated in the Serdang area. The measured path losses was compared
with various path loss prediction models such as free space loss (FSL), plane earth loss
(PEL), Walfisch-Ikegami LOS (WI), Epstein-Peterson (E-P), Deygout (D), Edward-
Durkin (E-D), Blomquist-Ladell (B-L) and Giovanelli (G). The results show that these
entire models gave unsatisfactory results when compared with the measured path losses,
iv
where for smooth terrain, the FSL, PEL and WI models overestimated the path loss as
high as 72%, 70% and 23%, respectively and for single and double convex surfaces
terrains, the E-P, D, E-D, B-L and G models overestimated the path loss as high as 25%
in all measurement frequencies. Because of 4PL and an improved version of the E-P and
G models have been developed to suit these three regions and the accuracy of these entire
models was tested where the mean error values were found to be approximately 5% for
all the measurement frequencies. An integrated UPMPL path loss model for both smooth
and convex surfaces terrains has been developed and implemented using Agilent VEE.
The UPMPL program provides the utility for calculating the signal characteristics of
radio propagation paths and is realized in the run time format version. This program
consists of four algorithms which are conversion formulas, smooth terrain, single convex
surface terrain and double convex surfaces terrain.
v
Abstrak tesis yang dikemukakan kepada Senat Universiti Putra Malaysia sebagai
memenuhi keperluan untuk ijazah Master Sains
PEMBANGUNAN MODEL KEHILANGAN LINTASAN UNTUK KEADAAN
PERMUKAAN BUMI YANG RATA DAN CEMBUNG DI KAWASAN
PERSEKITARAN MALAYSIA
Oleh
WONG PENG KIONG
September 2004
Pengerusi : Zulkifly Abbas, Ph.D.
Fakulti : Sains
Tesis ini memperihalkan pembangunan model ramalan kehilangan lintasan gelombangan
(UPMPL) untuk keadaan permukaan bumi yang rata dan cembung di kawasan
persekitaran Malaysia. Sistem pengukuran ini terdiri daripada penganalisis spektrum dan
antena log-periodic. Satu komputer program telah dibina untuk memperolehi data
kekuatan medan daripada penganalisis spektrum dan juga mengukarkan unit data
kekuatan medan ke dalam unit kehilangan lintasan dengan menggunakan perisian Agilent
VEE. Kedua-dua pancaran elektromagnet dalam lintasan lurus (untuk keadaan
permukaan bumi yang rata) dan pancaran elektromagnet dalam lintasan bukan lurus
(untuk keadaan permukaan bumi yang cembung) telah dikaji di kawasan persekitaran
Serdang. Nilai kehilangan lintasan yang diukur telah dibanding dengan pelbagai model
kehilangan lintasan yang lain seperti kehilangan ruang bebas (FSL), kehilangan bumi rata
vi
(PEL), lintasan lurus Walfisch-Ikegami (WI), Epstein-Peterson (E-P), Deygout (D),
Edward-Durkin (E-D), Blomquist-Ladell (B-L) dan Giovanelli (G). Keputusan yang
didapati menunjukkan bahawa kesemua model ini tidak sesuai bila dibandingkan dengan
nilai kehilangan lintasan yang diukur dimana FSL, PEL dan WI telah melebihi nilai
kehilangan lintasan yang diukur sebanyak 72%, 70% dan 23% untuk keadaan permukaan
bumi yang rata dan E-P, D, E-D, B-L dan G pula telah melebihi nilai kehilangan lintasan
yang diukur sebanyak 25% bagi kesemua frekuensi pengukuran untuk keadaan
permukaan bumi yang tunggal cembung ataupun kembar cembung. Dengan sebab itu,
4PL dan versi ubahsuai bagi E-P dan G model telah dibina dimana ralat min yang
didapati apabila berbanding dengan nilai kehilangan lintasan yang diukur adalah lebih
kurang 5% sahaja bagi kesemua frekuensi pengukuran. Gabungan kehilangan lintasan
UPMPL model bagi keadaan permukaan bumi yang rata, tunggal cembung dan kembar
cembung telah dibina dan dilaksanakan dengan menggunakan perisian Agilent VEE.
Kehilangan lintasan UPMPL model ini memudahkan pengiraan ciri isyarat bagi pancaran
lintasan radio dalam bentuk ‘run-time’. Program ini mengandungi 4 algoritma iaitu
formula penukaran unit, keadaan permukaan bumi yang rata, keadaan permukaan bumi
yang tunggal cembung dan keadaan permukaan bumi yang kembar cembung.
vii
ACKNOWLEDGEMENTS
First, I wish to thank my family for their support, love and encouragement. Without you,
I would have nothing. Without you, I would be nothing. Without you, I would go
nowhere. Thank you.
I would like to express my special thanks and sincere appreciation to his advisor, Dr.
Zulkifly Abbas, for his counsel and constant encouragement during my Master of Science
program and also his able guidance throughout this investigation.
No words can express my deep appreciation and gratitude to the members of the
supervisory committee, Prof. Mohd Yusof Sulaiman and Dr. Jumiah Hassan for their
advice, supervision and guidance.
Thanks are also extended to my friends and colleagues of the microwave Lab (Room
G69), past and present, for their help and support. Keep in touch!
I also wishes to thank the Ministry of Science and Technology (IRPA: 09-02-04-0547-
EA001) for their financial support and the Malaysian Communication and Multimedia
Commission for providing an important information for this research.
viii
I certify that an Examination Committee met on 2nd
September 2004 to conduct the final
examination of Wong Peng Kiong on his Master of Science thesis entitled “Development
of Path Loss Models for Smooth and Convex Surfaces Terrains in Malaysian
Environment” in accordance with Universiti Pertanian Malaysia (Higher Degree) Act
1980 and Universiti Pertainan Malaysia (Higher Degree) Regulations 1981. The
Committee recommends that the candidate be awarded the relevant degree. Members of
the Examination Committee are as follows:
W. MAHMOOD MAT YUNUS, Ph.D
Professor
Faculty of Science
Universiti Putra Malaysia
(Chairman)
ABDUL HALIM B. SHAARI, Ph.D
Professor
Faculty of Science
Universiti Putra Malaysia
(Member)
ZAIDAN ABDUL WAHAB, Ph.D
Professor Madya
Faculty of Science
Universiti Putra Malaysia
(Member)
DEEPAK K. GHODGAONKAR, Ph.D
Professor Madya
Microwave Technology Center
Universiti Teknologi Mara
(Independent Examiner)
----------------------------------------------------
GULAM RUSUL RAHMAT ALI, Ph.D.
Professor / Deputy Dean
School of Graduate Studies
Universiti Putra Malaysia
Date:
ix
This thesis submitted to the Senate of Universiti Putra Malaysia has been accepted as
fulfilment of the requirement for the degree of Master Science. The members of the
Supervisory Committee are as follows
ZULKIFLY ABBAS, Ph.D.
Lecturer
Faculty of Science
Universiti Putra Malaysia
(Chairman)
MOHD YUSOF SULAIMAN, Ph.D.
Professor
Faculty of Science
Universiti Putra Malaysia
(Member)
JUMIAH HASSAN, Ph.D.
Lecturer
Faculty of Science
Universiti Putra Malaysia
(Member)
------------------------------------------
AINI IDERIS, Ph.D.
Professor / Dean
School of Graduate Studies
Universiti Putra Malaysia
Date:
x
DECLARATION
I hereby declare that the thesis is based on my original work except for quotations and
citations which have been duly acknowledged. I also declare that it has not been
previously or concurrently submitted for any other degree at UPM or other institutions.
------------------------------------
WONG PENG KONG
Date:
xi
TABLE OF CONTENTS
Page
DEDICATION ii
ABSTRACT iii
ABSTRAK v
ACKNOWLEDGEMENTS vii
APPROVAL viii
DECLARATION x
LIST OF TABLES xiv
LIST OF FIGURES xv
LIST OF PLATES xviii
LIST OF SYMBOLS xix
CHAPTER
1. INTRODUCTION
1.1 An Overview of Wireless Communication Developments 1
1.2 The Cellular Concept 3
1.3 Graphical Programming 9
1.4 Objectives 11
1.5 Scope of the Thesis 12
2. RADIO WAVE PROPAGATION IN CELLULAR NETWORK
2.1 Maxwell’s Equations 14
2.2 Propagation in Free Space 15
2.3 Propagation over Earth Surface 17
2.4 Propagation over Irregular Terrain
2.4.1 Ground Roughness 20
2.4.2 Terrain Undulation Height 22
2.4.3 Diffraction
2.4.3.1 Fresnel Zone Geometry 24
2.4.3.2 Knife-Edge Diffraction Model 25
2.5 Large Scale Fading
2.5.1 Introduction 27
2.5.2 Log-normal Distribution 28
2.5.3 Log normal Shadowing Model 28
2.6 Coverage Prediction
2.6.1 Introduction 30
2.6.2 Coverage Probability 30
xii
3. PROPAGATION PREDICTION MODELS
3.1 Introduction 32
3.2 LOS Path Loss Prediction Model
3.2.1 COST 231 Walfisch-Ikegami LOS Model 32
3.3 NLOS Path Loss Prediction Models
3.3.1 Epstein-Peterson Model 33
3.3.2 Edward-Durkin Model 35
3.3.3 Deygout Model
3.3.3.1 Single Knife-Edge Obstacle Path 37
3.3.3.2 Double Knife-Edge Obstacles Path 38
3.3.4 Giovanelli Model 41
3.3.5 Blomquist-Ladell Model 43
3.3.6 Discussion 44
4. METHODOLOGY AND RESULTS
4.1 Measurement System
4.1.1 Measurement Setup 46
4.1.2 Calibration 48
4.1.3 Site Measurements 50
4.1.4 Transmitter Characteristics 53
4.1.5 Terrain Profile
4.1.5.1 Terrain Profile of Site 1
4.1.5.1.1 P1 56
4.1.5.1.2 P2 57
4.1.5.1.3 P3 59
4.1.5.2 Terrain Profile of Site 2
4.1.5.2.1 P4 60
4.1.5.3 Terrain Profile of Site 3
4.1.5.3.1 P5 61
4.1.6 Calculation the Path Loss from Field Strength
measurement 63
4.1.7 Software Development
4.1.7.1 Data Acquisition Program 64
4.1.7.2 Calculation of Path Loss 66
4.2 Measurement Results
4.2.1 Measurement Results for Smooth Terrain
4.2.1.1 Variation in Received Signal Strength with
Distance 70
4.2.1.2 Variation in Path Loss with Distance
a. Direct Comparison Between
Measured and Path Loss Model 74
b. Improved PEL and WI models 79
c. Validity of 4PL Model 85
xiii
4.2.2 Measurement Results for Single Convex Surface
Terrain
4.2.2.1 Variation in Received Signal Strength
with Distance 88
4.2.2.2 Variation in Path Loss with Distance
4.2.2.2.1 LOS Propagation Part 91
4.2.2.2.2 NLOS Propagation Part 94
4.2.2.2.3 Improved Prediction Model
for Single Convex Surface
Terrain 97
4.2.2.3 Coverage Probability for Single Convex
Surface Terrain 102
4.2.3 Measurement Results for Double Convex Surfaces
Terrain
4.2.3.1 Variation in Received Signal Strength
with Distance 104
4.2.3.2 Variation in Path Loss with Distance
4.2.3.2.1 NLOS Propagation Part 108
4.2.3.2.2 Improved Prediction Model
for Double Convex Surfaces
Terrain 111
4.2.3.3 Coverage Probability for Double Convex
Surfaces Terrain 116
4.3 Uncertainties Analysis
4.3.1 For Smooth Terrain 118
4.3.2 For Convex Surfaces Terrains 119
4.4 Software Development of Path Loss Propagation Model
4.4.1 Improved Path Loss Models 120
4.4.2 Development of UPMPL Path Loss Software 123
5. CONCLUSION AND SUGGESTION
5.1 Introduction 130
5.2 Main Contributions 131
5.3 Recommendations for Future Work 132
REFERENCES 134
APPENDICES 139
BIODATA OF THE AUTHOR 141

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Development path loss models

  • 1. i DEVELOPMENT OF PATH LOSS MODELS FOR SMOOTH AND CONVEX SURFACES TERRAINS IN MALAYSIAN ENVIRONMENT By WONG PENG KIONG Thesis Submitted to the School of Graduate Studies, Universiti Putra Malaysia, in Fulfilment of the Requirements for the Degree of Master of Science September 2004
  • 2. ii To Mother, Sisters, Brothers… and In memorial: Father
  • 3. iii Abstract of thesis presented to the Senate of Universiti Putra Malaysia in fulfilment of the requirement for the degree of Master of Science DEVELOPMENT OF PATH LOSS MODELS FOR SMOOTH AND CONVEX SURFACES TERRAINS IN MALAYSIAN ENVIRONMENT By WONG PENG KIONG September 2004 Chairman : Zulkifly Abbas, Ph.D. Faculty : Science This study describes the development of path loss prediction model for smooth and convex surfaces terrains in Malaysian environment. The measurement system consists of a spectrum analyzer and a log-periodic antenna. A computer program was developed to acquire measured field strength data from the spectrum analyzer and convert the values to path loss using Agilent Visual Engineering Environment (VEE). Both line-of-sight propagation (for smooth terrain) and non-line-of-sight propagation (for convex surface terrains) was investigated in the Serdang area. The measured path losses was compared with various path loss prediction models such as free space loss (FSL), plane earth loss (PEL), Walfisch-Ikegami LOS (WI), Epstein-Peterson (E-P), Deygout (D), Edward- Durkin (E-D), Blomquist-Ladell (B-L) and Giovanelli (G). The results show that these entire models gave unsatisfactory results when compared with the measured path losses,
  • 4. iv where for smooth terrain, the FSL, PEL and WI models overestimated the path loss as high as 72%, 70% and 23%, respectively and for single and double convex surfaces terrains, the E-P, D, E-D, B-L and G models overestimated the path loss as high as 25% in all measurement frequencies. Because of 4PL and an improved version of the E-P and G models have been developed to suit these three regions and the accuracy of these entire models was tested where the mean error values were found to be approximately 5% for all the measurement frequencies. An integrated UPMPL path loss model for both smooth and convex surfaces terrains has been developed and implemented using Agilent VEE. The UPMPL program provides the utility for calculating the signal characteristics of radio propagation paths and is realized in the run time format version. This program consists of four algorithms which are conversion formulas, smooth terrain, single convex surface terrain and double convex surfaces terrain.
  • 5. v Abstrak tesis yang dikemukakan kepada Senat Universiti Putra Malaysia sebagai memenuhi keperluan untuk ijazah Master Sains PEMBANGUNAN MODEL KEHILANGAN LINTASAN UNTUK KEADAAN PERMUKAAN BUMI YANG RATA DAN CEMBUNG DI KAWASAN PERSEKITARAN MALAYSIA Oleh WONG PENG KIONG September 2004 Pengerusi : Zulkifly Abbas, Ph.D. Fakulti : Sains Tesis ini memperihalkan pembangunan model ramalan kehilangan lintasan gelombangan (UPMPL) untuk keadaan permukaan bumi yang rata dan cembung di kawasan persekitaran Malaysia. Sistem pengukuran ini terdiri daripada penganalisis spektrum dan antena log-periodic. Satu komputer program telah dibina untuk memperolehi data kekuatan medan daripada penganalisis spektrum dan juga mengukarkan unit data kekuatan medan ke dalam unit kehilangan lintasan dengan menggunakan perisian Agilent VEE. Kedua-dua pancaran elektromagnet dalam lintasan lurus (untuk keadaan permukaan bumi yang rata) dan pancaran elektromagnet dalam lintasan bukan lurus (untuk keadaan permukaan bumi yang cembung) telah dikaji di kawasan persekitaran Serdang. Nilai kehilangan lintasan yang diukur telah dibanding dengan pelbagai model kehilangan lintasan yang lain seperti kehilangan ruang bebas (FSL), kehilangan bumi rata
  • 6. vi (PEL), lintasan lurus Walfisch-Ikegami (WI), Epstein-Peterson (E-P), Deygout (D), Edward-Durkin (E-D), Blomquist-Ladell (B-L) dan Giovanelli (G). Keputusan yang didapati menunjukkan bahawa kesemua model ini tidak sesuai bila dibandingkan dengan nilai kehilangan lintasan yang diukur dimana FSL, PEL dan WI telah melebihi nilai kehilangan lintasan yang diukur sebanyak 72%, 70% dan 23% untuk keadaan permukaan bumi yang rata dan E-P, D, E-D, B-L dan G pula telah melebihi nilai kehilangan lintasan yang diukur sebanyak 25% bagi kesemua frekuensi pengukuran untuk keadaan permukaan bumi yang tunggal cembung ataupun kembar cembung. Dengan sebab itu, 4PL dan versi ubahsuai bagi E-P dan G model telah dibina dimana ralat min yang didapati apabila berbanding dengan nilai kehilangan lintasan yang diukur adalah lebih kurang 5% sahaja bagi kesemua frekuensi pengukuran. Gabungan kehilangan lintasan UPMPL model bagi keadaan permukaan bumi yang rata, tunggal cembung dan kembar cembung telah dibina dan dilaksanakan dengan menggunakan perisian Agilent VEE. Kehilangan lintasan UPMPL model ini memudahkan pengiraan ciri isyarat bagi pancaran lintasan radio dalam bentuk ‘run-time’. Program ini mengandungi 4 algoritma iaitu formula penukaran unit, keadaan permukaan bumi yang rata, keadaan permukaan bumi yang tunggal cembung dan keadaan permukaan bumi yang kembar cembung.
  • 7. vii ACKNOWLEDGEMENTS First, I wish to thank my family for their support, love and encouragement. Without you, I would have nothing. Without you, I would be nothing. Without you, I would go nowhere. Thank you. I would like to express my special thanks and sincere appreciation to his advisor, Dr. Zulkifly Abbas, for his counsel and constant encouragement during my Master of Science program and also his able guidance throughout this investigation. No words can express my deep appreciation and gratitude to the members of the supervisory committee, Prof. Mohd Yusof Sulaiman and Dr. Jumiah Hassan for their advice, supervision and guidance. Thanks are also extended to my friends and colleagues of the microwave Lab (Room G69), past and present, for their help and support. Keep in touch! I also wishes to thank the Ministry of Science and Technology (IRPA: 09-02-04-0547- EA001) for their financial support and the Malaysian Communication and Multimedia Commission for providing an important information for this research.
  • 8. viii I certify that an Examination Committee met on 2nd September 2004 to conduct the final examination of Wong Peng Kiong on his Master of Science thesis entitled “Development of Path Loss Models for Smooth and Convex Surfaces Terrains in Malaysian Environment” in accordance with Universiti Pertanian Malaysia (Higher Degree) Act 1980 and Universiti Pertainan Malaysia (Higher Degree) Regulations 1981. The Committee recommends that the candidate be awarded the relevant degree. Members of the Examination Committee are as follows: W. MAHMOOD MAT YUNUS, Ph.D Professor Faculty of Science Universiti Putra Malaysia (Chairman) ABDUL HALIM B. SHAARI, Ph.D Professor Faculty of Science Universiti Putra Malaysia (Member) ZAIDAN ABDUL WAHAB, Ph.D Professor Madya Faculty of Science Universiti Putra Malaysia (Member) DEEPAK K. GHODGAONKAR, Ph.D Professor Madya Microwave Technology Center Universiti Teknologi Mara (Independent Examiner) ---------------------------------------------------- GULAM RUSUL RAHMAT ALI, Ph.D. Professor / Deputy Dean School of Graduate Studies Universiti Putra Malaysia Date:
  • 9. ix This thesis submitted to the Senate of Universiti Putra Malaysia has been accepted as fulfilment of the requirement for the degree of Master Science. The members of the Supervisory Committee are as follows ZULKIFLY ABBAS, Ph.D. Lecturer Faculty of Science Universiti Putra Malaysia (Chairman) MOHD YUSOF SULAIMAN, Ph.D. Professor Faculty of Science Universiti Putra Malaysia (Member) JUMIAH HASSAN, Ph.D. Lecturer Faculty of Science Universiti Putra Malaysia (Member) ------------------------------------------ AINI IDERIS, Ph.D. Professor / Dean School of Graduate Studies Universiti Putra Malaysia Date:
  • 10. x DECLARATION I hereby declare that the thesis is based on my original work except for quotations and citations which have been duly acknowledged. I also declare that it has not been previously or concurrently submitted for any other degree at UPM or other institutions. ------------------------------------ WONG PENG KONG Date:
  • 11. xi TABLE OF CONTENTS Page DEDICATION ii ABSTRACT iii ABSTRAK v ACKNOWLEDGEMENTS vii APPROVAL viii DECLARATION x LIST OF TABLES xiv LIST OF FIGURES xv LIST OF PLATES xviii LIST OF SYMBOLS xix CHAPTER 1. INTRODUCTION 1.1 An Overview of Wireless Communication Developments 1 1.2 The Cellular Concept 3 1.3 Graphical Programming 9 1.4 Objectives 11 1.5 Scope of the Thesis 12 2. RADIO WAVE PROPAGATION IN CELLULAR NETWORK 2.1 Maxwell’s Equations 14 2.2 Propagation in Free Space 15 2.3 Propagation over Earth Surface 17 2.4 Propagation over Irregular Terrain 2.4.1 Ground Roughness 20 2.4.2 Terrain Undulation Height 22 2.4.3 Diffraction 2.4.3.1 Fresnel Zone Geometry 24 2.4.3.2 Knife-Edge Diffraction Model 25 2.5 Large Scale Fading 2.5.1 Introduction 27 2.5.2 Log-normal Distribution 28 2.5.3 Log normal Shadowing Model 28 2.6 Coverage Prediction 2.6.1 Introduction 30 2.6.2 Coverage Probability 30
  • 12. xii 3. PROPAGATION PREDICTION MODELS 3.1 Introduction 32 3.2 LOS Path Loss Prediction Model 3.2.1 COST 231 Walfisch-Ikegami LOS Model 32 3.3 NLOS Path Loss Prediction Models 3.3.1 Epstein-Peterson Model 33 3.3.2 Edward-Durkin Model 35 3.3.3 Deygout Model 3.3.3.1 Single Knife-Edge Obstacle Path 37 3.3.3.2 Double Knife-Edge Obstacles Path 38 3.3.4 Giovanelli Model 41 3.3.5 Blomquist-Ladell Model 43 3.3.6 Discussion 44 4. METHODOLOGY AND RESULTS 4.1 Measurement System 4.1.1 Measurement Setup 46 4.1.2 Calibration 48 4.1.3 Site Measurements 50 4.1.4 Transmitter Characteristics 53 4.1.5 Terrain Profile 4.1.5.1 Terrain Profile of Site 1 4.1.5.1.1 P1 56 4.1.5.1.2 P2 57 4.1.5.1.3 P3 59 4.1.5.2 Terrain Profile of Site 2 4.1.5.2.1 P4 60 4.1.5.3 Terrain Profile of Site 3 4.1.5.3.1 P5 61 4.1.6 Calculation the Path Loss from Field Strength measurement 63 4.1.7 Software Development 4.1.7.1 Data Acquisition Program 64 4.1.7.2 Calculation of Path Loss 66 4.2 Measurement Results 4.2.1 Measurement Results for Smooth Terrain 4.2.1.1 Variation in Received Signal Strength with Distance 70 4.2.1.2 Variation in Path Loss with Distance a. Direct Comparison Between Measured and Path Loss Model 74 b. Improved PEL and WI models 79 c. Validity of 4PL Model 85
  • 13. xiii 4.2.2 Measurement Results for Single Convex Surface Terrain 4.2.2.1 Variation in Received Signal Strength with Distance 88 4.2.2.2 Variation in Path Loss with Distance 4.2.2.2.1 LOS Propagation Part 91 4.2.2.2.2 NLOS Propagation Part 94 4.2.2.2.3 Improved Prediction Model for Single Convex Surface Terrain 97 4.2.2.3 Coverage Probability for Single Convex Surface Terrain 102 4.2.3 Measurement Results for Double Convex Surfaces Terrain 4.2.3.1 Variation in Received Signal Strength with Distance 104 4.2.3.2 Variation in Path Loss with Distance 4.2.3.2.1 NLOS Propagation Part 108 4.2.3.2.2 Improved Prediction Model for Double Convex Surfaces Terrain 111 4.2.3.3 Coverage Probability for Double Convex Surfaces Terrain 116 4.3 Uncertainties Analysis 4.3.1 For Smooth Terrain 118 4.3.2 For Convex Surfaces Terrains 119 4.4 Software Development of Path Loss Propagation Model 4.4.1 Improved Path Loss Models 120 4.4.2 Development of UPMPL Path Loss Software 123 5. CONCLUSION AND SUGGESTION 5.1 Introduction 130 5.2 Main Contributions 131 5.3 Recommendations for Future Work 132 REFERENCES 134 APPENDICES 139 BIODATA OF THE AUTHOR 141