measurement, modeling and capacity analysis for novel...

Measurement, Modeling and Capacity Analysis for Novel Fixed Multi-User Single-Antenna MIMO-OFDM System

in Rural Environments

Nisal Lahiru Ratnayake

A Thesis

Submitted for the Degree of

Doctor of Philosophy

School of Electrical Engineering and Computer Science

Science and Engineering Faculty

Queensland University of Technology

February 2013

To my Wife and Parents

iii

Acknowledgments

During my stay as a PhD candidate at Queensland University of Technology, I have

received an enormous amount of support by various people and organisations. First

and foremost, I would like to express my sincere gratitude to my principal supervisor,

Dr. Karla Ziri-Castro and my associate supervisor from CSIRO, Dr. Hajime Suzuki, for

giving me this opportunity, excellent guidance, great support and technical contribu-

tions in order for me to carry out my research. Without their indispensable assistance,

the completion of this thesis would not have been possible. Also, I wish to express

my sincere gratitude to my QUT associate supervisor, Dr. Dhammika Jayalath, for his

unprecedented support and valuable advice given to me during my PhD journey. The

time spent working with my supervisors greatly shaped my professional identity and

effectively made me the researcher I am today. For this I will be eternally grateful to

them.

I gratefully acknowledge the CSIRO Ngara wireless broadband project team for

making this research a reality. My heartfelt thanks goes to the QUT High Performance

Computing group for their support related to HPC operations. Also, I wish to acknowl-

edge the members of QUT’s Science and Engineering Faculty research office, including

Ms. Diane Kolomeitz and Ms. Elaine Reyes, for their support in creating a comfortable

research environment.

I gratefully acknowledge the financial support given by QUT, by providing the QUT

Postgraduate Research Award and QUT Fee-Waiver scholarship to carry out this re-

search. Also, I would like to acknowledge funding support given by the Queensland

Government through the Smart Futures Fellowship program in the form of traveling

expenses (travel to measurement site and to national and international conferences) and

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scholarship support. In addition, I am thankful to all academic and non-academic staff

for the support given in to me in an innumerable number of ways.

Last but not least I would like to thank my wife Subani and my parents for supporting

and encouraging me in every possible way to achieve my goal.

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Abstract

High-speed broadband internet access is widely recognised as a catalyst to social and

economic development. However, the provision of broadband Internet services with

the existing solutions to rural population, scattered over an extensive geographical area,

remains both an economic and technical challenge. As a feasible solution, the Com-

monwealth Scientific and Industrial Research Organization (CSIRO) proposed a highly

spectrally efficient, innovative and cost-effective fixed wireless broadband access tech-

nology, which uses analogue TV frequency spectrum and Multi-User MIMO (MU-

MIMO) technology with Orthogonal-Frequency-Division-Multiplexing (OFDM).

MIMO systems have emerged as a promising solution for the increasing demand

of higher data rates, better quality of service, and higher network capacity. However,

the performance of MIMO systems can be significantly affected by different types of

propagation environments e.g., indoor, outdoor urban, or outdoor rural and operating

frequencies. For instance, large spectral efficiencies associated with MIMO systems,

which assume a rich scattering environment in urban environments, may not be valid for

all propagation environments, such as outdoor rural environments, due to the presence

of less scatterer densities. Since this is the first time a MU-MIMO-OFDM fixed broad-

band wireless access solution is deployed in a rural environment, questions from both

theoretical and practical standpoints arise; For example, what capacity gains are avail-

able for the proposed solution under realistic rural propagation conditions?. Currently,

no comprehensive channel measurement and capacity analysis results are available for

MU-MIMO-OFDM fixed broadband wireless access systems which employ large scale

multiple antennas at the Access Point (AP) and analogue TV frequency spectrum in

rural environments. Moreover, according to the literature, no deterministic MU-MIMO

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channel models exist that define rural wireless channels by accounting for terrain effects.

This thesis fills the aforementioned knowledge gaps with channel measurements,

channel modeling and comprehensive capacity analysis for MU-MIMO-OFDM fixed

wireless broadband access systems in rural environments. For the first time, chan-

nel measurements were conducted in a rural farmland near Smithton, Tasmania using

CSIRO’s broadband wireless access solution. A novel deterministic MU-MIMO-OFDM

channel model, which can be used for accurate performance prediction of rural MU-

MIMO channels with dominant Line-of-Sight (LoS) paths, was developed under this re-

search. Results show that the proposed solution can achieve 43.7 bits/s/Hz at a Signal-to-

Noise Ratio (SNR) of 20 dB in rural environments. Based on channel measurement re-

sults, this thesis verifies that the deterministic channel model accurately predicts channel

capacity in rural environments with a Root Mean Square (RMS) error of 0.18 bits/s/Hz.

Moreover, this study presents a comprehensive capacity analysis of rural MU-MIMO-

OFDM channels using experimental, simulated and theoretical models. Based on the

validated deterministic model, further investigations on channel capacity and the effects

of capacity variation, with different user distribution angles (θ) around the AP, were

analysed. For instance, when SNR = 20dB, the capacity increases from 15.5 bits/s/Hz

to 43.7 bits/s/Hz as θ increases from 10° to 360°. Strategies to mitigate these capacity

degradation effects are also presented by employing a suitable user grouping method.

Outcomes of this thesis have already been used by CSIRO scientists to determine

optimum user distribution angles around the AP, and are of great significance for re-

searchers and MU-MUMO-OFDM system developers to understand the advantages and

potential capacity gains of MU-MIMO systems in rural environments. Also, results of

this study are useful to further improve the performance of MU-MIMO-OFDM systems

in rural environments. Ultimately, this knowledge contribution will be useful in deliver-

ing efficient, cost-effective high-speed wireless broadband systems that are tailor-made

for rural environments, thus, improving the quality of life and economic prosperity of

rural populations.

viii

List of Abbreviations

3D three dimensional

3GPP 3rd Generation Partnership Project

ACMA Australian Communications and Media Authority

AOA Angle-of-Arrival

AOD Angle-of-Departure

AP Access Point

AWGN Additive White Gaussian Noise

BER Bit Error Rate

BS Base Station

CDMA Code Division Multiple Access

CSI Channel State Information

CSIRO Commonwealth Scientific and Industrial Research Organization

CSIT Channel State Information at Transmitter

CDFs Cumulative Distribution Functions

DEM Digital Elevation Map

DOD Direction-of-Departure

DOA Direction-of-Arrival

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DTDR Distributed Transmission-Directional Reception

FDMA Frequency Division Multiple Access

FEC Forward Error Correction

FSAF Field Strength Attenuation Factor

FTTP Fibre-To-The-Premises

GO Geometric Optics

GPS Global Positioning Satellite

GSCM Geometry-based Stochastic Channel Models

GSM Global System for Mobile Communication

GTD Geometrical Theory of Diffraction

HPC High Performance Computing

ISI Inter-Symbol Interference

ITU-R International Telecommunication Union-Radiocommunication

LA Link Adaptation

LoS Line-of-Sight

LTE Long Term Evolution

MIMO Multiple-Input Multiple-Output

MPCs Multi-Path Components

MUD Multi-User Detection

MU-MIMO Multi-User Multiple-Input Multiple-Output

MUSA-MIMO Multi-User-Single-Antenna Multiple-Input-Multiple-Output

NLoS Non Line-of-Sight

x

OFDM Orthogonal-Frequency-Division-Multiplexing

PDF Probability Density Function

PDP Power Delay Profile

QAM Quadrature Amplitude Modulation

QOS Quality-Of-Service

RAH Receiving Antenna Height

RMS Root Mean Square

RT Ray Tracing

Rx Receiver

SDMA Space Division Multiple Access

SISO Single-Input Single-Output

SM Spatial Multiplexing

SNR Signal-to-Noise Ratio

SRTM Shuttle Radar Topography Mission

STD Standard-deviation

SU-MIMO Single-User Multiple-Input Multiple-Output

TDMA Time Division Multiple Access

TCA Terrain Clearance Angle

TOA Time-of-Arrival

TDOA Time Delay-of-Arrival

Tx Transmitter

UHF Ultra High Frequency

xi

UT User Terminal

UTD Uniform Theory of Diffraction

UCA Uniform Circular Array

VCR Virtual Channel Representation

VHF Very High Frequency

WRANs Wireless Regional Area Networks

xii

List of Symbols

c Speed of Light

d Transmitter and Receiver Distance

ecc Earth Curvature Correction

f Frequency

l lth OFDM Sub-carrier

m mth Receiver

n nth Transmitter

v Diffraction v-parameter

C Channel Capacity

C MUSA-MIMO-OFDM Channel Capacity

F(v)Complex Fresnel Integral

GR Gain at Receiver

GT Gain at Transmitter

K Ricean K-Factor

PR Received Power

PT Transmitted Power

RH Horizontally Polarised Reflection Coefficient

RV Vertically Polarised Reflection Coefficient

w AWGN Noise Vector

x Input Signal Vector

y Output Signal Vector

I Identity Matrix

H Channel matrix

R Correlation Matrix

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εr Relative Permittivity

ϕ Angle of Incidence

λ Wavelength

µ Mean

θ Angle of User Distribution

θS ep Angle of User Separation

ρ Signal-to-Noise Ratio

σ Conductivity

xiv

Table of Contents

Acknowledgments v

Abstract vii

Table of Contents xv

List of Figures xxi

List of Tables xxvii

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Ngara Regional Access Solution . . . . . . . . . . . . . . . . . . . . . 3

1.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.5 Significance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.6 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.7 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.8 Organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 Principles of MIMO and Propagation 13

2.1 Introduction to MIMO Systems . . . . . . . . . . . . . . . . . . . . . 13

2.2 MIMO System Equation . . . . . . . . . . . . . . . . . . . . . . . . . 15

xv

2.3 Principles of MIMO Systems . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.1 Spatial Multiplexing . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.2 Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4 MIMO Channel Capacity . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4.1 Shannon-Hartley Theorem . . . . . . . . . . . . . . . . . . . . 19

2.4.2 MIMO Capacity:Channel Unknown at the Transmitter . . . . . 19

2.4.3 MIMO Capacity:Channel Known at the Transmitter . . . . . . . 20

2.4.4 MIMO Capacity: Open Problems and Measurement Based Results 20

2.4.5 Comparison between SU-MIMO and MU-MIMO systems . . . 21

2.5 OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.6 Fundamentals of UHF Propagation . . . . . . . . . . . . . . . . . . . . 23

2.7 Multi-path Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.7.1 Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.7.2 Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.7.3 Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.8 The Effect of Vegetation . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.9 Temporal Variations in Outdoor Environments . . . . . . . . . . . . . . 29

2.9.1 Receiver and Scatterer Movements . . . . . . . . . . . . . . . . 29

2.9.2 The Effect of Varying Weather Conditions . . . . . . . . . . . . 30

2.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3 Review on Channel Modeling 37

3.1 Channel Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.1.1 Pathloss Models . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.1.2 Fading Models . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.2 MIMO Channel Models . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.3 Physical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

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3.3.1 Deterministic Physical Models . . . . . . . . . . . . . . . . . . 46

3.3.2 Uniform Theory of Diffraction (UTD) Models . . . . . . . . . 46

3.3.3 Geometry-based Stochastic Physical Models . . . . . . . . . . 48

3.3.4 Non Geometrical Stochastic Physical Models . . . . . . . . . . 49

3.4 Analytical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.4.1 i.i.d. Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.4.2 Kronecker Model . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.5 Hybrid Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.5.1 IEEE 802.11n Model . . . . . . . . . . . . . . . . . . . . . . . 52

3.5.2 3GPP Spatial Channel Model . . . . . . . . . . . . . . . . . . 53

3.6 Multi-User MIMO Models . . . . . . . . . . . . . . . . . . . . . . . . 54

3.7 Gaps in Rural MU-MIMO Channel Modeling and Measurements . . . . 56

3.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4 Channel Measurements 59

4.1 Measurement Site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.2 Access Point and User Terminal Locations . . . . . . . . . . . . . . . . 62

4.3 Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.4 Access Point Antenna Array . . . . . . . . . . . . . . . . . . . . . . . 66

4.5 User Terminal Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.6 Weather Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.7 Data Files Naming . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.8 Data Analysis Platform . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.9 Measured MUSA-MIMO-OFDM channel . . . . . . . . . . . . . . . . 74

4.9.1 Snapshot Plots of Measured Channel . . . . . . . . . . . . . . 74

4.9.2 Channel Variation Plots in Time . . . . . . . . . . . . . . . . . 76

4.10 Channel Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

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4.11 Channel Correlation Matrix . . . . . . . . . . . . . . . . . . . . . . . . 83

4.12 Received Power and Weather Parameters . . . . . . . . . . . . . . . . . 93

4.13 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

5 Deterministic Modeling 101

5.1 Terrain Profiles Generation . . . . . . . . . . . . . . . . . . . . . . . . 104

5.1.1 Data Format . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.1.2 Curvature of Earth . . . . . . . . . . . . . . . . . . . . . . . . 105

5.1.3 Terrain Analysis Algorithm . . . . . . . . . . . . . . . . . . . 106

5.2 Diffraction Loss Predictions . . . . . . . . . . . . . . . . . . . . . . . 112

5.2.1 Diffraction Analysis at User Terminals . . . . . . . . . . . . . . 115

5.3 Deterministic Channel Model . . . . . . . . . . . . . . . . . . . . . . . 119

5.3.1 Channel Coefficients Generation . . . . . . . . . . . . . . . . . 120

5.4 Results and Validation . . . . . . . . . . . . . . . . . . . . . . . . . . 123

5.4.1 Model validation based on relative channel power . . . . . . . . 125

5.4.2 Model validation based on channel correlation matrix . . . . . . 128

5.4.3 Model validation based on channel capacity . . . . . . . . . . . 131

5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

6 Capacity Analysis 137

6.1 Channel Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

6.2 MUSA-MIMO-OFDM Channel Capacity Analysis . . . . . . . . . . . 139

6.2.1 Narrowband and Wideband MUSA-MIMO-OFDM Channel Ca-

pacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

6.3 Theoretical, Simulated and Experimental Capacity . . . . . . . . . . . 144

6.3.1 Capacity Predicted by Theoretical Models . . . . . . . . . . . . 144

6.3.2 Capacity Predicted by Deterministic Model . . . . . . . . . . . 145

xviii

6.3.3 Experimental Capacity . . . . . . . . . . . . . . . . . . . . . . 148

6.3.4 Comparison between Theoretical, Deterministic and Experimen-

tal Channel Capacity . . . . . . . . . . . . . . . . . . . . . . . 149

6.4 Novel Empirical Capacity Equation . . . . . . . . . . . . . . . . . . . 152

6.4.1 Proposed Capacity Equation . . . . . . . . . . . . . . . . . . . 152

6.4.2 Validity of Proposed Equation . . . . . . . . . . . . . . . . . . 155

6.5 Time Variations of Channel Capacity . . . . . . . . . . . . . . . . . . . 163

6.6 Capacity Variation with UT Spatial Distribution . . . . . . . . . . . . . 168

6.6.1 Capacity Variation with Random UT Spatial Distribution . . . . 168

6.6.2 Capacity Variation with Controlled UT Spatial Distribution . . . 174

6.7 Capacity Improvement with User Grouping . . . . . . . . . . . . . . . 177

6.8 Effect of User Grouping on Controlled UT Distribution . . . . . . . . . 185

6.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

7 Conclusions 189

7.1 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

7.2 Research Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

7.2.1 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

7.2.2 Awards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

7.3 Future Research Topics . . . . . . . . . . . . . . . . . . . . . . . . . . 198

A 199

A.1 Detecting LoS availability using terrain analysis algorithm . . . . . . . 199

A.2 Detecting diffraction edges . . . . . . . . . . . . . . . . . . . . . . . . 199

Literature Cited 203

xix

List of Figures

1.1 Scattered houses (red dots) in a 100 km2 rural environment using Google

Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 MUSA-MIMO in rural area . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Overview of Ngara access demonstrator [1] . . . . . . . . . . . . . . . 4

2.1 MIMO Channel Illustration . . . . . . . . . . . . . . . . . . . . . . . 15

2.2 An illustration of Spatial Channel Multiplexing [2] . . . . . . . . . . . 17

2.3 A Multi-User MIMO System . . . . . . . . . . . . . . . . . . . . . . . 22

2.4 Experiment set up [3] . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.5 Comparison of received shadowed LoS signal due to line of trees [4] . 33

2.6 Received Signal for 240 MHz and 700 MHz in different Weather Condi-

tions [5] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.1 Overview of Channel Models . . . . . . . . . . . . . . . . . . . . . . . 39

3.2 An Illustration of Multiuser MIMO Downlink [6] . . . . . . . . . . . . 54

4.1 Geographical location of the measurement site marked “A” (Google Maps) 60

4.2 AP surrounding environment . . . . . . . . . . . . . . . . . . . . . . . 61

4.3 Relative position and distances between the AP and UTs . . . . . . . . 62

4.4 MUSA-MIMO-OFDM demonstrator at laboratory . . . . . . . . . . . . 64

4.5 AP units fixed at outdoor enclosure . . . . . . . . . . . . . . . . . . . . 65

4.6 Video streaming through uplink channel . . . . . . . . . . . . . . . . . 65

xxi

4.7 Optional caption for list of figures . . . . . . . . . . . . . . . . . . . . 67


4.9 AP antenna orientation (degree from true north) . . . . . . . . . . . . . 68


4.11 Sample UT radiation pattern . . . . . . . . . . . . . . . . . . . . . . . 70

4.12 Weather station placed at the AP . . . . . . . . . . . . . . . . . . . . . 72

4.13 Weather data gathered from Weatherlink software . . . . . . . . . . . . 72

4.14 A snapshot of measured 12 AP×6 UT×1705 sub-carrier MUSA-MIMO-

OFDM channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.15 Relative channel power for AP 1-6×6 UT antenna combinations for a 5

hour measurement window in Day 5 . . . . . . . . . . . . . . . . . . . 78

4.16 Relative channel power for AP 7-12×6 UT antenna combinations for a

5 hour measurement window in Day 5 . . . . . . . . . . . . . . . . . . 79

4.17 Goodness-of-fit test to identify best fitting distribution . . . . . . . . . . 80

4.18 A comparison of theoretical and empirical CDF plots for 6 selected sub-

channels from 6 UTs . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.19 Full channel correlation matrix for 12AP×6UT antenna combinations . 84

4.20 An example of correlated and uncorrelated sub-channels . . . . . . . . 85

4.21 Correlation coefficients between AP1-UT1 (1-1 in figure) and 72 sub-

channels (12AP×6UT) for 1705 sub-carriers . . . . . . . . . . . . . . 87









xxii



4.27 K-factor, relative received power with weather variations . . . . . . . . 96

4.28 K-factor, relative received power with weather variations . . . . . . . . 97

4.29 K-factor vs wind speed . . . . . . . . . . . . . . . . . . . . . . . . . . 98

4.30 K-factor vs wind speed . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.1 Overview of the proposed MUSA-MIMO-OFDM channel model . . . . 103

5.2 AP and UT positioning in the measurement site . . . . . . . . . . . . . 105

5.3 Parameters related to earth’s curvature correction . . . . . . . . . . . . 106

5.4 Terrain heights for a 4002 km area around the measurement site includ-

ing positions of all UTs and AP . . . . . . . . . . . . . . . . . . . . . . 108

5.5 Fresnel zones geometry and related parameters . . . . . . . . . . . . . 109

5.6 Terrain profile and first Fresnel zone for AP-UT1 link . . . . . . . . . . 110





5.11 Parameters related to diffraction calculations . . . . . . . . . . . . . . . 114

5.12 Diffractional gain-Fresnel diffraction parameter(v) curve . . . . . . . . 115

5.13 Diffraction loss prediction for a 1250m × 1250m area around UT1 . . . 116





5.18 A snapshot of model output 12 AP×6 UT×1705 sub-carrier MUSA-

MIMO-OFDM channel . . . . . . . . . . . . . . . . . . . . . . . . . . 124

xxiii

5.19 Mean square error between deterministic and measured 12 AP×6 UT×1705 sub-

carrier MUSA-MIMO-OFDM channel . . . . . . . . . . . . . . . . . . 126

5.20 Full channel correlation matrix obtained from deterministic simulations

for 12 AP×6 UT×1705 antenna combinations . . . . . . . . . . . . . . 130

5.21 Simulated and experimental capacity for 20 dB SNR . . . . . . . . . . 132

6.1 MIMO multi access channel for 6 UT uplink . . . . . . . . . . . . . . . 140

6.2 Eigenvalue distribution plot for 1705 OFDM subcarriers . . . . . . . . 142

6.3 Channel capacity for 1705 OFDM sub-carriers for a given time sample

for ρ=20 dB, 25 dB and 30 dB . . . . . . . . . . . . . . . . . . . . . . 143

6.4 Standard deviations of OFDM sub-carriers for random time instances . 143

6.5 Rayleigh and ideal channel capacities with increasing number of anten-

nas for 20 dB SNR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

6.6 Simulated capacity with increasing number of antennas for 20 dB SNR . 147

6.7 Experimental capacity with increasing number of antennas for 20 dB SNR148

6.8 Theoretical, simulated and experimental capacity for 20 dB SNR . . . 151

6.9 Experimental and predicted capacity for different SNR values . . . . . 153

6.10 Error CDFs for 1×1 system with 18-40 dB SNR values . . . . . . . . . 157






6.16 Capacity for selected sub-carriers during a 1 hour time window at SNR=20 dB164

6.17 Capacity CDF over 720 measurement points . . . . . . . . . . . . . . . 165

6.18 Example of user terminal distribution around user terminals (top view) . 169

6.19 User terminals concentrated to a sector with angle θ . . . . . . . . . . . 169

xxiv

6.20 Capacity CDFs for user distribution angle variation from 10° to 120° (blue,

black and red curves represent 20 dB, 25 dB and 30 dB SNR values) . . 171





6.23 Capacity variation with angle θ . . . . . . . . . . . . . . . . . . . . . . 174

6.24 Controlled user distribution on a ring with radius d1 km with an angle θS ep175

6.25 Capacity variation with angle θS ep (d1= 20 km) . . . . . . . . . . . . . 176

6.26 Capacity variation with angle θS ep . . . . . . . . . . . . . . . . . . . . 176

6.27 Example of user grouping . . . . . . . . . . . . . . . . . . . . . . . . . 178

6.28 Capacity CDFs for 4 AP x 2 UT combination . . . . . . . . . . . . . . 181



6.31 Capacity CDFs for 32 AP x 16 UT combination . . . . . . . . . . . . . 182

6.32 Capacity CDFs for 64 AP x 32 UT combination . . . . . . . . . . . . . 183

6.33 Capacity CDFs for 128 AP x 64 UT combination . . . . . . . . . . . . 183

6.34 50th percentile capacity for different user groups and antenna combinations184

6.35 10th percentile capacity for different user groups and antenna combinations184

6.36 Capacity for different sector angles and user grouping . . . . . . . . . . 186

xxv

List of Tables

2.1 Designation of frequency bands . . . . . . . . . . . . . . . . . . . . . 24

4.1 AP and UT position information . . . . . . . . . . . . . . . . . . . . . 62

4.2 OFDM symbol parameters . . . . . . . . . . . . . . . . . . . . . . . . 66

4.3 UT Antenna Specifications [7] . . . . . . . . . . . . . . . . . . . . . . 70

4.4 Measured weather parameters . . . . . . . . . . . . . . . . . . . . . . 73

4.5 STD of channel power for 72 sub-channels over a 5 hour measurement

window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.1 Predicted diffraction loss for user terminals . . . . . . . . . . . . . . . 118

5.2 Model input parameters for deterministic modeling . . . . . . . . . . . 122

5.3 Mean square error between deterministic and measured relative powers

in dB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

5.4 Simulated and experimental capacity values for 20 dB SNR . . . . . . . 133

6.1 Theoretical, simulated and experimental capacity values for 20 dB SNR 150

6.2 Capacity difference between the actual and predicted values . . . . . . . 154

6.3 Different AP-UT combinations for 3AP×3UT capacity calculations . . 155

6.4 Hourly capacity dynamic range (obtained from experimental capacities)

and wind information . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

6.5 User allocation information about 4 AP × 2 UT case . . . . . . . . . . 179


xxvii


6.8 Percentile capacities for different user groupings . . . . . . . . . . . . 185

xxviii

Chapter 1

Introduction

1.1 Background

Ever since Guglielmo Marconi sent the first telegraph across the English Channel in

1897, new wireless communication methods and services have been implemented through-

out the world. Amongst these services, high-speed broadband Internet access is widely

recognised as a catalyst to social and economic development in the modern world. High-

speed wireless broadband access is considered to be the gateway to reach rural and

remote communities and to provide them with anticipated future services such as tele-

health, remote-education, e-Commerce and e-Government services [8]. Most of these

services will require high definition real-time two-way video and demand the broadband

infrastructure to support access speeds as high as 50 Mbps [9]. Although this is a

challenging requirement for rural and remote areas, enabling these future services will

have a profound impact to bridge the barriers of isolation between rural and populated

areas. This will ensure that no segment of society is digitally-divided and left behind.

Providing inexpensive high data rate Internet access to homes in rural and remote

areas presents many challenges. One of the main challenges is that users in rural areas

are scattered over large geographic areas, for instance tens of residences per 100 km2, as

shown in Figure 1.1. As a result, deploying a wired network for such areas is considered

to be prohibitive due to high deployment costs. For instance, the estimated cost to

provide broadband services using Fibre-To-The-Premises (FTTP) infrastructure to rural

1

2 CHAPTER 1. INTRODUCTION

areas in Australia is 101 billion Australian dollars [8]. According to Commonwealth

Scientific and Industrial Research Organization (CSIRO) analysis, the introduction of

next generation, satellite and WiMAX technologies will create economic and technical

(coverage and data rate) challenges [8]. Satellite technology has been known to be

effective in establishing wireless data links in remote areas; however it is also known

to have limited data capacity when shared between the end users. Furthermore, satellite

technologies are not cost-effective when compared with the wireless alternatives [8].

Figure 1.1: Scattered houses (red dots) in a 100 km2 rural environment using GoogleMaps

Several attempts have been made to address the challenges presented by rural and

regional wireless deployments. These early deployment efforts are related to wireless

local loop [10, 11], wireless local area networks [12, 13] and wireless metropolitan area

networks [14, 15]. However, the bandwidth efficiency gained by these technologies is

typically limited to less than 5 bits/s/Hz/cell. In order to achieve data rates comparable to

urban areas using these technologies, either a wide spectrum allocation or a large number

of base stations are required. Therefore, it is necessary to develop cost effective, highly

spectrally efficient technologies that can provide large coverage for rural environments.

In order to provide a feasible solution for rural and remote areas, a novel solution is

proposed and developed under a 2008 Australian government patent application (patent

1.2. NGARA REGIONAL ACCESS SOLUTION 3

application No. 20089045554) by CSIRO [16], ’Ngara wireless broadband access’.

Initial deployment of this solution provides rural and remote communities with a spectral

efficiency of up to 40 bits/s/Hz, enabling the same quality of digital access for rural and

urban populations. The Ngara wireless broadband access solution is a long range, cost-

effective, fixed wireless broadband technology, proposed for rural Australia.

Figure 1.2: MUSA-MIMO in rural area

1.2 Ngara Regional Access Solution

For the first time, the Ngara regional access solution was developed and implemented in

a rural Australian environment in Smithton, Tasmania in December 2010 [17]. The pro-

posed regional access solution uses an innovative point-to-multi-point wireless broad-

band technology. The key functions of this solution are:

• Multi-User Multiple-Input Multiple-Output (MU-MIMO)

MU-MIMO technology has been used in the Ngara regional access solution to

obtain high spectral efficiencies. The system employs large scale multiple an-

tennas at the Access Point (AP). Furthermore, a single receiver at a rural house


IP Network

UT Unit

Server

Server

Server

ServerServer

AP Unit

UT Unit

UT Unit

UT Unit

UT Unit

User PC

User PC

User PC

User PC

User PC

Figure 1.3: Overview of Ngara access demonstrator [1]

will be served by the large scale multiple antenna array at the AP. As shown in

Figure 1.2, many User Terminals (UTs) will be served by a single AP. Since, this

is a special case of MU-MIMO, this system is referred to as Multi-User-Single-

Antenna Multiple-Input-Multiple-Output (MUSA-MIMO). Figure 1.3, shows an

overview of the Ngara access demonstrator implemented in the rural environment.

• Space Division Multiple Access (SDMA)

The system performs SDMA, which allows the use of the same frequency at the

same time by multiple UTs. Unlike conventional multiple access schemes, such

as Frequency Division Multiple Access (FDMA), Time Division Multiple Access

(TDMA), and Code Division Multiple Access (CDMA), where the total capacity

of a base station is fixed, the capacity of the MUSA-MIMO base station increases

with the number of SDMA users. This is fundamentally a different approach to

the conventional multiple access schemes.

• Analogue TV frequency spectrum

In rural environments, a wide coverage is preferable to minimise the number

of APs for a selected area. Therefore, very high (VHF) and ultra high (UHF)

1.3. MOTIVATION 5

frequencies are preferable for fixed terrestrial wireless access systems. The Ngara

regional access solution operates in a 7 MHz bandwidth in the UHF band using a

carrier frequency of 641.5 MHz.

• Orthogonal-Frequency-Division-Multiplexing (OFDM)

Additional improvements in wide-band MIMO systems are gained by employing

OFDM. In OFDM systems [18], data is transmitted in parallel by modulating a

number of closely-spaced orthogonal subcarriers, thereby converting a frequency-

selective channel into multiple flat fading sub-channels.

• Dominant propagation paths

For the proposed solution, UTs are equipped with directional Yagi roof-top anten-

nas. Also, APs are installed on high transmission towers. Therefore, predominant

Line-of-Sight (LoS) paths are available for most of the AP-UT links. Diffracted

signals can occur if the UT antenna is below the local clutter. Therefore, LoS and

diffraction are the predominant propagation mechanisms for the proposed access

solution. Also, compared to urban environments, rural environments exhibit less

multi-path due to less scatterer densities present in rural environments [19].

In addition, some aspects of the MUSA-MIMO include a synchronization method

using Global Positioning Satellite (GPS) signals for timing and frequency references in

the UTs, accurate channel estimation and feedback algorithm and a low computational

complexity implementation of crucial signal processing components [20].

1.3 Motivation

As far as MU-MIMO systems are concerned, a few channel models [21–24] and channel

measurement results [25–27] are found in the literature. These MU-MIMO based chan-

nel measurements are available thanks to the emergence of Long Term Evolution (LTE)

systems. However, the main focus is given to the MU-MIMO downlink, and short

distance links in indoor and urban environments. So far, to the best of the author’s

knowledge, no comprehensive channel measurement and capacity analysis results are


available for MU-MIMO-OFDM fixed broadband wireless access systems which employ

large scale multiple antennas at the AP and analogue TV frequency spectrum in rural

environments. One of the main reasons behind this unavailability is the difficulty of

obtaining license to use a dedicated TV spectrum for channel measurement purposes, as

UHF and VHF bands are typically in high demand for services such as TV broadcasting.

For the first time in the world, the Ngara regional access solution was developed

and implemented in a rural Australian environment as a six user MUSA-MIMO-OFDM

SDMA system, which employs large scale multiple antennas at the AP and analogue

TV frequency spectrum. The achievable MIMO performance depend on different envi-

ronments e.g., indoor, outdoor urban, or outdoor rural and operating frequencies [28].

Therefore, analysing rural wireless channels for MUSA-MIMO-OFDM technology is

vital to understand, predict and enhance performance of MUSA-MIMO-OFDM systems

in rural environments. The main research questions that motivated this thesis are:

• Up to which extent are AP-UT sub-channels correlated while achieving the capac-

ity gain promised by the rural MUSA-MIMO-OFDM channels, and do all sub-

carriers posses similar channel correlation matrix?

• How to adopt or develop a physically meaningful model which includes underly-

ing dominant radio propagation effects for rural MUSA-MIMO-OFDM channels

in order to predict MUSA-MIMO-OFDM channel capacity?

• Based on the measurement results, what are the actual capacity gains achieved by

the MUSA-MIMO-OFDM system deployed in rural environments?

• How much capacity increment will MUSA-MIMO-OFDM channels exhibit with

the number of users in rural environments?

• Is the proposed system capable of providing stable channel capacities?

• Is there any capacity variation with different user distributions around the AP?

• What strategies to adopt to overcome possible detrimental effects on capacity when

users are closely located?

1.4. OBJECTIVES 7

1.4 Objectives

For the first time, comprehensive channel measurements were performed for the Ngara

wireless broadband access solution in a rural environment, which employs large scale

multiple antennas at the AP, and analogue TV frequency spectrum. Large spectral

efficiencies associated with large scale multiple antennas assume that a rich scattering

environment provides independent transmission paths from each transmit antenna to

each receiver antenna. However, this argument may not be valid for all propagation

environments. For instance, rural environments may exhibit less scattering richness

as less scatterers are present in rural environments [19]. The main questions from

theoretical and practical standpoint are whether the assumption of large spectral effi-

ciencies predicted with ‘rich scattering’ [29, 30], is valid for other realistic propagation

conditions, such as in outdoor rural environments. The actual capacity gains achieved by

this MUSA-MIMO-OFDM system in rural environments have not been investigated nor

verified using experimental data, and the issue still remains an open problem. Therefore,

one objective of this thesis is to investigate MUSA-MIMO-OFDM channel capacity

for the Ngara system, based on channel measurement data.

Although rural environments exhibit less scattering richness, during the experiments

users were distributed around the AP with large spatial separation. As a result, inde-

pendent transmission paths from each transmit antenna to each receiver antenna can be

available for the proposed measurement setup. It is important to investigate the amount

of correlation these sub-channels (for each sub-carrier) have between them. Therefore,

another important objective of this thesis is to investigate correlation between sub-

channels based on experimental data and verify whether or not the sub-channels

are correlated.

Based on the above analysis the thesis expects to investigate capacity increment

achieved in rural environments as the number of users increases. Therefore, another

objective is to develop an empirical capacity formula which predicts the capacity

improvements with the number of increasing users for different Signal-to-Noise

Ratio (SNR) values, in a rural environment with dominant LoS paths. Also, channel

capacity variations and the effects of weather conditions on channel capacity are


expected to be investigated in this thesis.

This research expects to develop a physically meaningful model which can be

used for accurate capacity calculations for MUSA-MIMO-OFDM systems in rural

outdoor environments. This model is expected to include dominant radio propagation

mechanisms (LoS and diffraction effects) in rural environments. Based on the model out-

put, further capacity analysis will be conducted to understand capacity variations

for different user distributions around the AP.

1.5 Significance

This research project was conducted with the collaboration of CSIRO and results have

already been used by CSIRO scientists to determine optimum user distribution angles

around the AP. As this is the first time the Ngara regional access solution has been

deployed, outcomes of this thesis have already benefited CSIRO scientists and MUSA-

MUMO-OFDM system developers to understand the advantages and capacity gains of

this system in rural environments. Also, results of this study will be useful to further

improve the performance of this system, for instance, to develop efficient user grouping

methods to maximise spectral efficiency. Finally, outcomes of this research will be useful

in delivering efficient, cost-effective broadband access to rural population scattered over

large geographical areas.

1.6 Contribution

The major contributions of this thesis are listed below.

• Analysis of MUSA-MIMO-OFDM channel capacity gain by using experimental,

simulated and theoretical models.

Currently, the capacity gains achieved by MUSA-MIMO-OFDM systems in rural

environments with dominant LoS paths have not been experimentally verified

and remain as an open problem. Therefore, for the first time, this thesis inves-

tigates how much capacity gain is possible for MUSA-MIMO-OFDM channels

1.6. CONTRIBUTION 9

under realistic propagation conditions in rural environments with dominant LoS

paths. Moreover, rural MUSA-MIMO-OFDM channel capacity is compared with

popular theoretical models, in order to measure how the channel capacity, under

realistic propagation conditions, vary with popular theoretical models. Addition-

ally, capacity results predicted by deterministic simulations are compared with

experimental capacity to prove the validity of the deterministic model.

• An empirical MUSA-MIMO-OFDM channel capacity formula.

This thesis introduces a simplified novel empirical capacity formula which can

predict capacity improvement with the number of increasing UTs (which are spa-

tially separated) for different SNR values, in a rural environment with dominant

LoS paths. This formula is useful in understanding the actual capacity gains in a

rural environment with dominant LoS paths, for SNR values between 16 dB and

40 dB. This equation is derived to predict channel capacity when the users are

spatially separated, that is when correlation coefficients between sub-channels are

less than 0.1.

• A novel deterministic channel model which can accurately predict channel capac-

ities in rural environments.

The author is not aware of any previous work proposing a deterministic channel

model for MUSA-MIMO-OFDM system in rural environments. Application of

a high resolution (3 arc-second) Digital Elevation Map (DEM) to the proposed

deterministic MUSA-MIMO-OFDM channel model improves prediction accuracy

over that using lower resolution DEM. The proposed model accounts for the terrain

between the AP and a given UT, and determines the LoS, ground reflected and

diffracted paths via a terrain analysis algorithm. The model accommodates three

dimensional representations of AP and UT antennas as well as three dimensional

antenna patterns. In addition, it generates frequency responses for all OFDM

sub-carriers. The validity of this deterministic model is verified by the channel

measurement results.


• Prediction of capacity variations for MUSA-MIMO-OFDM systems with different

user distributions around the AP.

Based on the aforementioned validated deterministic model, further rural MUSA-

MIMO-OFDM capacity analysis is performed with different user distributions

around the AP. In this study, capacity variation of MUSA-MIMO-OFDM systems

due to different user distribution angles (around the AP) were analysed. Based on

this analysis, the thesis reports capacity variations when the distribution of user

terminals are restricted to a given angle around the AP. Additionally, a possible

method for capacity improvement, by implementing an existing user grouping

method, is presented in this thesis.

1.7 Limitations

• Fixed SNR criteria

In this thesis, before the experiments, UT transmitting power was adjusted to have

approximately the same signal-to-noise ratio (SNR) at the AP from each of the

UTs. This adjustment was done as it is a capacity optimal configuration for

the fixed rural broadband application. This criteria is known as the fixed SNR

criteria [31]. As a result, this thesis focuses only on the case where the SNR at

the receiver from each UT is the same. It does not consider the case which the

receiver having different SNR from different UTs. Also, only the relative received

power was available through channel measurements.

• The number of access point and user terminal antennas

This thesis focuses on a MUSA-MIMO channel with 6 UTs and 12 AP antenna

elements at the access point. Extension of this work to a larger number of AP-UT

antennas through channel measurements in rural environments is proposed as a

future work.

1.8. ORGANISATION 11

• Uplink channel modeling

This thesis focuses only on the characterisation of uplink channel from UTs to AP,

since the uplink channel was measured during experiments. However, propagation

theory dictates that the conclusions regarding the uplink channels are applicable

to the downlink channels within the same frequency range [32].

1.8 Organisation

The content of this thesis is organised as follows.

• Chapter 2 examines the principles of MIMO technology, fundamental wave prop-

agation mechanisms and OFDM concepts. Also, this chapter highlights open

problems related to channel capacity in MIMO systems. Finally, it focuses on

the causes of temporal variations in outdoor environments.

• Chapter 3 discusses the state-of-the-art Single-Input Single-Output (SISO), MIMO,

and MU-MIMO channel models. It classifies existing MIMO and MU-MIMO

channel models as physical, analytical and hybrid. In addition, gaps in rural

MIMO/MU-MIMO channel modeling and measurements are highlighted in this

chapter. It justifies the development of a novel MUSA-MIMO-OFDM channel

model. Also, this chapter highlights the requirement of performance analysis

for the proposed MUSA-MIMO-OFDM system, based on channel measurement

results.

• Chapter 4 presents rural MUSA-MIMO-OFDM channel measurement and the

data analysis procedure. This chapter introduces the measurement environment,

AP and UT locations, and antenna related parameters for the deployed MUSA-

MIMO-OFDM system. Channel measurement results in the form of instantaneous

channel snapshots (1705 × 12 × 6 ) and channel variations are plotted against time

and are presented. This chapter also analyses the channel correlation matrix based

on the measured channel. Finally, the effects of weather conditions on the received

signal are analysed in this chapter.


• Chapter 5 discusses the development steps of the proposed novel deterministic

MUSA-MIMO-OFDM channel model. Moreover, this chapter presents informa-

tion relevant to terrain profile generation, terrain analysis, diffraction loss pre-

diction, model input parameters and MUSA-MIMO-OFDM channel co-efficients

generation procedure. Finally, model validation procedure is explained in this

chapter.

• Chapter 6, provides a detailed analysis of channel capacity for MUSA-MIMO-

OFDM channels in rural environments. Also, rural MUSA-MIMO-OFDM chan-

nel capacity is compared with popular theoretical models and capacity results pre-

dicted by deterministic simulations. Development of the novel empirical capacity

equation which can predict the capacity improvements, in rural environments with

dominant LoS paths, with the number of increasing UTs (spatially separated) is

presented under this chapter. Also, the capacity variation effects due to different

user distribution around the AP and capacity improvements due to appropriate user

grouping methods are discussed.

• Finally, Chapter 7 summarises the outcomes of this thesis and presents future

research discussions.

Chapter 2

Principles of MIMO and Propagation

This chapter examines the principles of Multiple-Input Multiple-Output (MIMO) tech-

nology and wave propagation principles. Furthermore, reasons for temporal variations in

outdoor environments and the benefits of Orthogonal-Frequency-Division-Multiplexing

(OFDM) are discussed. This chapter is organised as follows. Initially, an introduction to

the MIMO systems is provided. It discusses capacity benefits and capacity open prob-

lems in MIMO systems. Next, a comparison of Single-User Multiple-Input Multiple-

Output (SU-MIMO) and Multi-User Multiple-Input Multiple-Output (MU-MIMO) sys-

tems is provided. Additionally, the benefits of Orthogonal-Frequency-Division-Multiplexing

(OFDM) and fundamental propagation mechanisms are discussed. Finally, reasons for

temporal variations in outdoor environments are presented.

2.1 Introduction to MIMO Systems

There has never been a greater demand and need for human civilisation to cultivate

methods of information access than in the present information-driven era. As a result,

more and more information has become accessible through radio, television, and the

Internet. Therefore, the demand for higher data rates, better quality of service, and

higher network capacity is ever increasing [32].

Wireless communication technology has become more popular than wired com-

munication technology due to its enormous benefits, such as easier deployment, low

13

14 CHAPTER 2. PRINCIPLES OF MIMO AND PROPAGATION

costs and greater flexibility. Furthermore, it enables mobility to access information

anywhere, anytime [33]. Wireless communication technologies use the atmosphere

as the communication medium and utilise the vast radio spectrum for transmission of

different communication channels such as television, radio and wireless broadband.

However, due to increasing demand for wireless services the frequency spectrum has

become a scarce resource [28]. Therefore, researchers try to identify better methods for

efficient use of the radio frequency spectrum. Using complex modulation schemes is one

approach to improve the efficiency for a given bandwidth. Unfortunately, this approach

increases the complexity and the cost of radio systems.

In recent years, MIMO systems have gained significant attention both in academia

and industry as a promising solution to improve spectral efficiency [34]. MIMO systems

use multiple Transmitter (Tx) antenna elements in the Tx end and multiple Receiver (Rx)

antenna elements at the Rx end. Researchers [35, 36] have shown that systems with

multiple antennas at the Tx and Rx can significantly enhance the system throughput,

reliability and coverage, without extra bandwidth and power. In addition to ‘time’ which

is known as the natural dimension to digital data communication, the use of multiple

antennas introduces a new dimension called ‘space’ to digital communication systems [2,

34]. Therefore, MIMO technology is known as ‘space-time’ wireless technology.

The emergence of MIMO systems began in the early 1990s [34]. In 1994, Paulraj and

Kailath [37] introduced the Distributed Transmission-Directional Reception (DTDR)

technique to increase the capacity of wireless channels using multiple antennas at both

the Tx and Rx ends. Telatar [30] further illustrated the ability of capacity improvement

in wireless systems by using multiple antennas. Furthermore, Foschini et al. developed

‘BLAST’ architecture [29] which can achieve spectral efficiencies up to 10-20 bits/s/Hz.

Since then, MIMO technology has become a popular research area in both academia and

industry. However, only a few real world deployments, channel measurement experi-

ments, channel models and MIMO performance analysis in rural areas are present in the

literature [19, 38–40].

2.2. MIMO SYSTEM EQUATION 15

2.2 MIMO System Equation

Figure 2.1 illustrates a MIMO channel with multiple antenna elements at the Tx and the

Rx ends. The classical MIMO system equation can be defined as [29]:

y = Hx + w (2.1)

where, x , y , w and H represent the input signal vector, the output signal vector, the

noise vector, and the channel matrix, respectively.

Channel ‘H’

Tx

Coding Modulation

Weighting / Mapping

Weighting / Mapping

Demodulation Decoding

Rx

Figure 2.1: MIMO Channel Illustration

Since, MIMO systems are equipped with multiple antennas at both the Tx and Rx

ends, the MIMO channel is defined with respect to all Tx and Rx antenna pairs. Con-

sidering n as the Tx antennas and m as the Rx antennas, a linear time-variant MIMO

channel matrix Hm×n can be defined as [41]:


H(t, τ)m×n =

h11(t, τ) h12(t, τ) ... h1n(t, τ)

h21(t, τ) h22(t, τ) ... h2n(t, τ)

... ... ... ...

... ... ... ...

hm1(t, τ) hm2(t, τ) ... hmn(t, τ)

(2.2)

where hi j(t, τ) represents the time variant impulse response between the jth Tx an-

tenna and ith Rx antenna.

2.3 Principles of MIMO Systems

Oestges and Clerckx [34] stated that MIMO systems use the spatial domain to improve

the data rate and reduce the Bit Error Rate (BER). Spatial multiplexing improves the data

rate (capacity) of a MIMO system while diversity improves the received signal quality

(less BER) [34]. The following section will discuss spatial multiplexing and diversity

gains of MIMO systems.

2.3.1 Spatial Multiplexing

Winters [42] showed that the data rate (capacity) is improved in MIMO systems by trans-

mitting different streams of information through independent parallel channels. This

principle is known as spatial multiplexing [2]. Gesbert et al. [2] presented a basic

Spatial Multiplexing (SM) scheme with three transmitters and three receivers, which

can improve the spectral efficiency by three-fold.

The explanation of the three-fold capacity increment by Gesbert et al. [2] can be

expressed as follows. As shown in Figure 2.2, initially, the bit stream is decomposed into

three sub sequences which are transmitted simultaneously using three antennas. There-

fore, only one third of the nominal spectrum is used. Since all three antennas operate

2.3. PRINCIPLES OF MIMO SYSTEMS 17

in the same frequency spectrum, the signals are naturally mixed together in the wireless

channel. By detecting the mixing channel matrix from training symbols, the individual

bit streams are separated and estimated at the Rx. The separation process is similar

to solving for three unknowns from a linear system of three equations. Furthermore,

the above solution was derived assuming the flat fading conditions, that is, each pair

of Tx and Rx antennas yields to a single scalar channel coefficient [2]. The separation

is possible provided the equations are independent from each other. This implies that

the bit streams can be detected and merged in order to yield the original bit stream,

given each Rx antenna “seeing” a sufficiently different channel from the Tx antenna

array. Gesbert et al. stated further that, although flat fading assumption is used in this

scenario, the extension to frequency selective cases is also possible using the multiple-

carrier approach or combining the MIMO space-time detector with an equalizer in the

time domain. Therefore, under favourable conditions, such as rich-scattering scenarios,

MIMO systems can reach higher spectral efficiencies [29].

Figure 2.2: An illustration of Spatial Channel Multiplexing [2]


2.3.2 Diversity

Rappaport [32] stated that, wireless links experience random fluctuations of the signal

level in time, space and frequency. These fluctuations are known as fading, and can affect

the quality of a wireless system. Diversity techniques are employed, to reduce the impact

of fading on signal quality [32]. The diversity ensures that the Rx receives multiple

copies of the same transmitted signal. If these copies are affected by independent fading

conditions, the probability of fading all the copies at the same time decreases [34].

Therefore, the diversity helps to improve the quality of a wireless system.

Since fading is a common phenomenon in space, time and frequency domains, di-

versity techniques have also been exploited in those domains [34]. The most common

diversity technique is spatial diversity [43] in MIMO systems, whereby multiple anten-

nas are spatially separated and the Rx selects the best signal at a given time. The time

diversity can be obtained through proper coding and interleaving [34]. Furthermore,

frequency diversity is obtained using equalization techniques [44] or muti-carrier mod-

ulations. Time and frequency diversity techniques introduce a loss in time or bandwidth

when providing redundancy [34]. However, spatial or polarisation diversity does not

introduce a loss in time or bandwidth, because it is provided using multiple antennas at

the transmitter and receiver ends.

In this section, the key features of MIMO systems were examined. According to

the information stated, it is obvious that MIMO systems can offer significant improve-

ments in the data rate and Quality-Of-Service (QOS) through the principles of spatial

multiplexing and diversity. As discussed in this section a key feature of MIMO systems

is capacity improvement. Therefore, the following section will focus on the MIMO

channel capacity.

2.4 MIMO Channel Capacity

According to the pioneering work carried out by Foschini [29, 45] and Telatar [30], it

was shown that a significant capacity improvement of MIMO systems is possible under

favourable conditions. These favourable conditions include rich scattering environments

2.4. MIMO CHANNEL CAPACITY 19

and independent transmission paths from each Tx and Rx antenna. According to Gold-

smith et al. [46], the capacity gain achieved from the multiple antennas depends on the

reliable Channel State Information (CSI) at the Tx and the Rx, the channel SNR and

the correlation between the channel gains on each antenna.This section of the literature

review will investigate the MIMO channel capacity, with and without the CSI at the Tx.

2.4.1 Shannon-Hartley Theorem

The Shannon-Hartley theorem provides the theoretical maximum rate of error free data

that can be transmitted via an Additive White Gaussian Noise (AWGN) channel for a

given received signal power [32]. The Shannon’s capacity formula is given by [32]:

C = B log2

[1 +

PNoB

]= B log2

[1 +

SN

]b/s/Hz (2.3)

where C is the channel capacity, P is the received signal power (in W) and No is

the noise power density (in W/Hz). Furthermore, S/N is considered as the SNR. The

Shannon’s capacity formula is the baseline for the derivation of MIMO channel capacity

equations.

2.4.2 MIMO Capacity:Channel Unknown at the Transmitter

Foschini [29] derived the generalised (channel unknown at the transmitter) capacity

equation for time-space architectures. The following equation was derived, using the

Shannon’s capacity formula for n Tx and m Rx antennas. The Tx only knows the

channel statistics such as the distribution of the channel and distribution parameters in

this scenario. The famous capacity equation derived by Foschini is given by [29]:

C = log2

∣∣∣∣∣Im +

(ρ

n

)HH†

∣∣∣∣∣ b/s/Hz (2.4)


where |.|, (†), H, Im and ρ represent the determinant, transpose-conjugate , m × n

channel matrix, m × m identity matrix and SNR, respectively.

2.4.3 MIMO Capacity:Channel Known at the Transmitter

According to the information theoretic analysis by Gesbert et al. [2] it has been shown

that the additional performance gain can be achieved in MIMO systems with the Channel

State Information at Transmitter (CSIT). This scenario considers that the Tx knows the

random channel outcome and adjusts the transmit signal accordingly [47]. The capacity

equation, when the channel is known at the Tx is given by[30]:

C = log2

∣∣∣Im + HQH†∣∣∣ b/s/Hz (2.5)

where |.|, (†), H and Im represent the determinant, transpose-conjugate , m×n channel

matrix and m × m identity matrix, respectively. Furthermore, Q denotes the covariance

matrix of the transmitted signal vector. When no CSIT is available, Q becomes I. As a

result, Equation 2.5 maps to Equation 2.4 [2].

2.4.4 MIMO Capacity: Open Problems and Measurement Based Results

As stated above, linear capacity improvement can be obtained with the number of an-

tennas in a rich scattering environment. Past measurement results have found that large

MIMO capacities are supported in urban environments (rich scattering environments) [48,

49]. However, large spectral efficiencies associated with MIMO channels, assuming that

a rich scattering environment provides independent transmission paths from each Tx

antenna to each Rx antenna is not valid for all propagation environments. For instance,

less scatterers are present in rural environments. Therefore, rural environments may

exhibit less scattering richness [8].

The main questions from both theoretical and practical standpoints are whether large

spectral efficiencies predicted under a rich scattering assumption can be obtained in

2.4. MIMO CHANNEL CAPACITY 21

realistic propagation conditions, such as in rural environments, and what capacity in-

crements are available for different environments under realistic propagation conditions.

According to Gesbert et al. [50], the aforementioned questions remain as open problems

in the area. Comprehensive capacity analysis results based on rural channel measure-

ments [51, 52] are scarce in literature. Chizhik et al. [51] conducted channel mea-

surement experiments for a mobile MIMO system in rural environment at 2.5 GHz at

ground level Tx and Rx. However, to the best of the author’s knowledge, no channel

capacity results (based on comprehensive measurement results) are available for fixed

long range MUSA-MIMO-OFDM systems deployed in rural environments. Therefore,

based on comprehensive channel measurement results, it is important to investigate

actual capacity gains provided by the Ngara regional access solution, which is a MUSA-

MIMO-OFDM system operated at 641.5 MHz .

2.4.5 Comparison between SU-MIMO and MU-MIMO systems

An extension of basic Single-User MIMO SU-MIMO concepts can be seen in the lit-

erature for Multi-User MIMO MU-MIMO scenarios. A basic MU-MIMO system is

illustrated in Figure 2.3. In MU-MIMO systems, a Base Station (BS) coordinates with

multiple user terminals (UT) in order to achieve an increased downlink capacity. MU-

MIMO performs Space Division Multiple Access (SDMA) which enables the use of

the same frequency at the same time by multiple UTs. This can be viewed as parallel

beamforming, where different beams are formed for different users.

In one form of MU-MIMO system, the BS calculates the downlink beamforming

matrix based on estimated downlink channels. Since many users are attached to a single

BS, it selects a subset of users to be served at each point in time. This selection and

relevant rate allocation is known as scheduling [53].

Another difference between SU-MIMO and MU-MIMO is that, in SU-MIMO the

number of spatial domains that can be used is limited by the number of antennas at the Rx

terminal. Potential spatial dimensions can be wasted in a SU-MIMO system in a situation

where the Rx terminal has a smaller number of antennas compared to the BS [53]. In

MU-MIMO systems, the total number of spatial dimensions can be exploited when a


Figure 2.3: A Multi-User MIMO System

large number of users are distributed around the BS. Therefore, MU-MIMO systems

may achieve considerable gains in terms of sum capacity over SU-MIMO systems [53].

By extending the classical MIMO system equation defined in [29], the MU-MIMO

system equation for the signal received by user k can be defined as:

yk = Hkxk + wk (2.6)

where Hk, xk and yk is the propagation channel for user k, transmitted signal and re-

ceived signal by user k, respectively. Furthermore, wk represents the AWGN component

experienced by the kth user and the interference experienced by the kth user from all

other users.

2.5 Orthogonal Frequency Division Multiplexing (OFDM)

The Ngara access solution employs Orthogonal-Frequency-Division-Multiplexing (OFDM).

Therefore, this section discusses the principles of OFDM . Also, this section explains

how additional improvements in wide-band MIMO systems are gained by employing

OFDM. In OFDM systems [18], data is transmitted in parallel by modulating a num-

ber of closely-spaced orthogonal sub-carriers, thereby converting a frequency-selective

channel into multiple flat fading sub-channels. In a wideband wireless system, the

2.6. FUNDAMENTALS OF UHF PROPAGATION 23

channel shows frequency-selectivity, and the delay spread of the channel impulse re-

sponse can cause Inter-Symbol Interference (ISI), which is a challenge for designing

communication systems.

The main advantage of OFDM is that the symbol duration can be much longer,

therefore, the effect of ISI due to multipath time dispersion can be removed when the

cyclic prefix is longer than the channel delay spread [54]. Furthermore, a frequency

selective fade will cause a problematic fading depth on only a few sub-carriers. Errors

will occur on the few bits associated with those sub-carriers. Therefore, net error rate

for all the sub-carriers taken together can be made acceptably low, if coding is also

employed [54]. Due to the aforementioned advantages, OFDM has been adopted for

several wireless standards such as IEEE 802.11a, IEEE 802.11n. and IEEE 802.16e. Let

X[l] denote the complex symbols to be transmitted by an OFDM system. Therefore,

OFDM (modulated) signal can be expressed as [55]:

s(t) =

N f−1∑l=0

X[l]e j2π flt, 0 ≤ t ≤ Ts (2.7)

where fl = f0 + l∆ f and N f denotes the number of subcarriers in the system.

Parameters Ts and ∆ f represent symbol duration and sub-carrier spacing of the OFDM

system, respectively. The orthogonality condition (Ts∆ f = 1) must be satisfied to

guarantee that the OFDM signal can be demodulated properly by the receiver. CSIRO

MUSA-MIMO system is also a wideband wireless system. Therefore, it employs OFDM

to mitigate the effects of frequency selective fading and ISI.

2.6 Fundamentals of Ultra High Frequency (UHF) Propagation

Radio spectrum is a portion of electromagnetic spectrum that incorporates radio waves.

Frequencies of radio waves extend from about 30 kHz to 300 GHz [56]. This radio

frequency spectrum is classified into different ‘bands’ as shown in Table 2.1 [56]. De-

pending on the transmission frequency these waves propagate differently and they are

classified as sky-waves (ionospheric), ground waves and tropospheric waves [56]. Waves

propagated via the layers of ionosphere are known as sky waves and those that propagate


Table 2.1: Designation of frequency bands

Frequency band Frequency rangeExtremely low frequency (ELF) <3 kHzVery low frequency (VLF) 3-30 kHzLow frequency (LF) 30-300 kHzMedium frequency (MF) 300 kHz-3 MHzHigh frequency (HF) 3-30 MHzVery high frequency (VHF) 30-300 MHzUltra high frequency (UHF) 300 MHz-3 GHzSuper high frequency (SHF) 3 GHz-30 GHzExtra high frequency (EHF) 30 GHz-300 GHz

in the lower atmosphere are known as tropospheric waves. Waves that propagate very

close to Earth’s surface are known as ground-waves [56].

As shown in Table 2.1, carrier frequency used in this research (641.5 MHz) is clas-

sified under the UHF band. Therefore, fundamentals of Ultra High Frequency (UHF)

wave propagation are discussed in this section. Frequencies in UHF band are too high

to ionospheric propagation to occur. Therefore, these UHF frequencies propagate as

space waves which are classified under ground waves [56]. Analysis of spacewaves

propagation at UHF needs to account for reflection, diffraction and scattering effects,

which cause muiti-path propagation [56].

2.7 Multi-path Propagation

Multi-path propagation occurs when radio waves take multiple paths between the Tx

and Rx. When the propagation occurs through the radio channel, apart from the Line-

of-Sight (LoS) propagation, waves are reflected, refracted, diffracted, scattered and ab-

sorbed, resulting in multiple rays with differently delayed and attenuated versions at the

Rx antenna. These phenomena are discussed in the following subsections.

2.7. MULTI-PATH PROPAGATION 25

2.7.1 Reflection

Reflection is a phenomenon that occurs at an interface between two different media so

that the incident wavefront returns into the medium from which it originated. Reflection

occurs when a propagating electromagnetic wave impinges upon an object that is large

compared to the wavelength of the propagating wave [32]. In an outdoor environment,

reflection mainly occurs due to the presence of the ground (earth’s surface) and produces

ground reflected radio waves. The ground is neither a perfect conductor nor a perfect

dielectric [57]. Therefore, the theory of ground reflection and diffraction is complex.

However, by using appropriate approximations, the ground reflected of radio waves can

be modeled [57].

In reflection theory, the ratio of the incident wave to its associated reflected wave

is called the “reflection coefficient” [57]. The reflection coefficients for vertically and

horizontally polarised waves are given by [58]:

RV =εc sinϕ − Zεc sinϕ − Z

(2.8)

RH =sinϕ − Zsinϕ − Z

(2.9)

where Z = [εc − cos2ϕ]12 and εc = εr − j60σλ. Parameter ϕ is the angle of incidence,

εr is the relative permittivity, is the wavelength and σ is the conductivity of the reflecting

ground in S/m. One of the objectives of this thesis is to develop a deterministic channel

model. Therefore, ground reflections that are experienced by vertically polarized radio

waves will be accounted for in the deterministic model.

2.7.2 Diffraction

Diffraction is a well known wave propagation mechanism, which may occur over differ-

ent hills in the rural environments, over buildings in microcells, or around corners in the

indoor environment [59]. Diffraction occurs when there is a partial blocking of a portion

of the wave front by a surface with irregular edges [54]. This gives rise to bending of


waves around the obstacle, even when a LoS path does not exist between Tx and Rx.

Propagation models use two main approaches to represent diffraction, namely, wedge

diffraction and knife-edge diffraction [54].

Wedge diffraction is an important feature in city propagation environments [54].

Diffracting wedges are present at the corners of buildings, at the edge of walls where they

intersect roofs, and at the intersection of walls with the ground . Implementing Uniform

Theory of Diffraction (UTD) methods [60] which approximate irregular terrain profiles

with canonical shapes such as wedges and convex surfaces increase the complexity of

diffraction prediction models.

If the interior angle of the wedge is zero degrees, the wedge is considered as a knife-

edge. Knife-edge diffraction formulas are used for many obstructed path circumstances,

which include paths with terrain obstructions, by modifying them to apply to rounded

obstacles. The four ray model and Edwards and Durkin method [61] have been devel-

oped to predict the terrain effects using the principle of knife-edge diffraction. Therefore,

in this study, terrain obstructions were approximated as knife edges.

The extension of the single-edge diffraction theory to multiple obstacles is a mathe-

matically complex problem [56]. However, several multiple knife-edge diffraction meth-

ods such as, Bullington’s equivalent knife-edge [62], Epstein-Peterson [63], Japanese [64]

and Deygout [56] exist in the literature.

Bullington’s equivalent knife-edge method proposes to calculate diffraction loss by

replacing the real terrain obstacles with a single equivalent knife-edge at the point of

intersection of the horizon ray from each of the Tx and Rx terminals [62]. The Bullington

method produces an optimistic estimate of field strength at the receiving point [56].

Moreover, if the Bullington method is used, important obstacles can be ignored as only

a single knife-edge is considered.

The Epstein-Peterson method computes the attenuation for each obstacle and sums

them to obtain the overall loss. This method determines the attenuation due to a given

diffraction edge, by joining the peaks of preceding and following diffraction edges.

Comparing with the Millington’s rigorous solution, it was revealed that the Epstein-

Peterson method predicts large errors when two obstacles are closely spaced [56]. The

2.7. MULTI-PATH PROPAGATION 27

technique proposed by the Japanese method is similar in concept to the Epstein-Peterson

method. The Japanese method considers the effective source as the projection of the

horizon ray through that point on to the plane of one of the terminals.

The Deygout method is known as the ‘main-edge’ method because the first step of

this method is to calculate Fresnel-Kirchoff diffraction parameter (v-parameter) for each

edge alone, as if all other edges are absent [56]. The edge having the largest v-value is

termed as the main edge and its loss is calculated using the complex-Fresnel integral.

Diffraction loss due to other terrain obstructions are found with respect to a line joining

the main edge to the Tx and Rx. For a path with many obstructions, the total loss is

calculated as the sum of the individual losses for the obstacles in the order of decreasing

v-value [56]. In practice, the total loss is calculated as the sum of only three components,

the main edge and the subsidiary main edges on either side.

Among these methods, the Deygout method shows a good agreement with the rigor-

ous theory [56]. The accuracy of this model is highest when there is a dominant obstacle.

Also, correction factors are introduced for two comparable obstructions [56]. Therefore,

the Deygout method is used to calculate diffraction loss in this thesis. International

Telecommunication Union-Radiocommunication (ITU-R) P.1812-1, which is used for

propagation prediction for VHF and UHF bands, also employs the Deygout method in

diffraction loss predictions [65].

2.7.3 Scattering

Scattering occurs when the wavelength of the propagating electromagnetic wave is larger

than the dimensions of the objects that obstruct the radio channel. When a radio wave

impinges on a rough surface, the reflected energy is diffused in all directions due to

scattering.

Compared to an urban environment with large number of buildings and moving

vehicles, a rural environment can exhibit a low “scattering richness” as less scatterers

are present in rural environments [19]. Also, compared to LoS and ground reflected

paths, the effects of these scattered waves are small [57]. Investigations have shown

that, for instance, scattering which occur due to vegetation is influenced by dielectric


constant, conductivity, density, physical size and shape of the scattering objects [66].

Accounting for scattering effects due to vegetation in rural environments would need

accurate information of tree positions, physical dimensions of trees, dielectric constants

and conductivity [66]. Accounting for these information in a long range outdoor channel

model is a complex task and it would increase the complexity of the model. Therefore,

scattering effects introduced by the environment are excluded in this study.

These propagation mechanisms are responsible for creating multipath components

which are beneficial for MIMO systems. The following sections investigates effects of

vegetation and reasons for temporal variations in outdoor environments, especially in

rural areas.

2.8 The Effect of Vegetation

Several investigations [39, 56, 67] have been conducted to determine the effect of veg-

etation on wireless propagation. This section will focus on previous work conducted to

identify the effect of vegetation on the received signal power.

Majeed et al. [66] investigated variations in received power due to scattering and

absorption, when radio wave propagate through vegetated areas. According to their

experimental investigations, transmission losses are influenced by dielectric constant,

conductivity, density, physical size and shape of vegetation. This fluctuation has been

shown to be influenced by density, shape, and size of the vegetation. The authors devel-

oped a propagation model which incorporates the scattering effects caused by vegetation.

This model models tree components individually. For instance, a tree trunk as a cylinder,

branches as randomly oriented finite size cylinders and leaves as randomly oriented

thin discs and needles. However, adopting this model to predict received power (due

to vegetation loss) for a long range wireless system is a complex task, since accurate

information of tree positions, physical dimensions of trees, dielectric constants and

conductivity are needed. Therefore, a more general approach in incorporating the effects

of vegetation is highly desirable in developing an easy to use channel model.

Ostlin et al. [39] introduced a Field Strength Attenuation Factor (FSAF) due to

2.9. TEMPORAL VARIATIONS IN OUTDOOR ENVIRONMENTS 29

vegetation, according to the previous findings for tree attenuation done by Vogel et

al. [68]. The FSAF is defined as two broadly defined vegetation categories, namely

woodland and shrublands. Ostlin et al. calculated vegetation attenuation as [39]:

FS AFwoodlands =VDN.20

100

FS AFshrublands =VDN.10

100

The vegetation density (VDN) near the receiver corresponds to the average vegetation

density within a 100 m by 100 m area surrounding the receiving antenna. The FSAF has

been incorporated in the International Telecommunication Union-Radiocommunication

(ITU-R) P.1546 model as an additional improvement along with the corrections pro-

posed for Terrain Clearance Angle (TCA) and Receiving Antenna Height (RAH). After

introducing the aforementioned modifications, the model predicted closer results to the

measured data from rural Australian environments, compared to ITU-R P.1546 models.

2.9 Temporal Variations in Outdoor Environments

This section investigates the main causes which introduce temporal variations in outdoor

environments. According to the literature, moving scatters [69], wind [3–5] and rain [70,

71] (in the presence of vegetation) are identified as main contributors for time varying

effects. These effects are discussed in the following section.

2.9.1 Receiver and Scatterer Movements

Movement of the scatterers and receivers can introduce temporal variations to the re-

ceived signal. However, the proposed research will consider fixed terminals distributed

in different positions. The propagation channel is different for fixed versus mobile

terminals and permits higher data rates with fixed terminals [72]. Knowledge of wireless

channels is vital in using adaptive modulation and coding techniques, which are needed

to adjust to different channel conditions. While for mobile channels, small scale spatial


fades result in temporal fades, it (small scale spatial fades) does not introduce temporal

fades when the terminal remains at a fixed position [69]. Therefore, for fixed wireless

channels, temporal fluctuations can occur due to the movement of scatterers.

Valenzuela et al. [69] conducted an outdoor measurement campaign in urban en-

vironments, in the frequency bands of 3.5 and 5.8 GHz, to investigate the nature and

origin of temporal fluctuations. The study was conducted for both LoS and Non Line-

of-Sight (NLoS) links. The authors estimated the temporal K-factor from the measured

data, using two moment-based estimators [73]. By classifying links according to the

exposure of the user terminal antenna into a direct view of traffic, authors conclude that

temporal fades in fixed wireless systems can occur due to vehicular traffic, i.e. due to

moving scatterers. Moreover, temporal fading is significant for NLoS links, where the

remote antenna beam was exposed to traffic [69]. However, authors found that spatial

fades were large, compared to temporal fades, even for LoS cases, due to the presence

of large nearby reflecting surfaces.

According to the experiments carried out by Ahumada et al. [74, 75] it is confirmed

that moving scatterers can introduce temporal fading on the received signal. All these

experiments have been conducted in urban areas. Effect of these moving scatterers in

rural areas is less when compared to urban areas. In rural areas, moving machinery in

farms can introduce temporal fading on the received signal.

2.9.2 The Effect of Varying Weather Conditions

Several investigations [3–5, 76–78] have been carried out to examine how wireless chan-

nels behave under different weather conditions. Experiments have been conducted in

different carrier frequencies including UHF and VHF frequency bands, since frequency

itself decides the amount of attenuation introduced when exposed to diverse weather con-

ditions. Literature highlights a high correlation between vegetation and different weather

conditions when considering temporal variations in outdoor wireless channels [5]. Rain

and wind were found to be the major contributors in weather that introduces temporal

variations in outdoor wireless channels. However, only a few studies [79] can be found in

current literature, which investigates the effect of varying weather conditions in outdoor


wireless channels in the rural Australian environment. The following section of the

literature review focuses on the effect of weather conditions in outdoor wireless channels,

especially in suburban and rural areas.

Cuias et al. [3] investigated scattering and attenuation effects of isolated trees, by

artificially generated wind in different controlled speeds and directions. Long term and

short term effects have been analysed by the authors. The experiment was conducted

for 900, 1800 and 2100 MHz frequencies. Figure 2.4 illustrates the experimental set up.

Furthermore, the receiving antenna has been moved around the tree in a half circle with

a radius of 60 cm. The authors state that the long term effects are interpreted by the

median performance of the radio link when a tree is introduced into the environment.

The introduction of a tree in the radio link changes the scattering pattern compared to

the free space reference. However, the median effect of the wind seems not to follow a

specific trend, presenting small variations to the no wind situation. Hence, Cuias et al.

stated that long term effects on the radio channel occur due to the presence of the tree,

rather than to its movement caused by the wind. Short term effects due to the wind speed

and directions have been analysed using box-plots. As the general trend, whenever the

wind becomes faster, the width of the box becomes wider. It indicates that the time

variability around the mean receiving power value is incremented as the wind speed

becomes higher. Experiments carried out by Cuias et al. show that there is a correlation

between temporal variations in the received power and wind speed when the trees are

included in the vicinity of the radio link.

Figure 2.4: Experiment set up [3]

Low [80] conducted field strength measurement experiments for UHF bands in rural


districts to capture the effect of seasonal field-strength variations. The author states that

in rural areas the field strength is affected by vegetation. Therefore, measurements were

performed at 457 and 914 MHz in forest areas. The effective Tx antenna height used

for the experiment was 190m and the path length was 15 -30 km. Vertically polarised

log-periodic dipole antennas have been used at the Tx. Rx antenna heights were 2.4 m

and receiver sensitivities were -130 dBm. This measurement campaign was conducted

in 1983 and 1985. Neither transmitter power nor the direction of the Tx antennas have

been changed during the measurements. From the measurement campaign, Low [80]

concluded that:

• The field strength in forests reaches its largest values in winter and depends on the

temperature and snow cover.

• Seasonal field-strength variation is almost independent of frequency in UHF range.

• The seasonal field-strength variation is distributed with a mean value of 5 dB and

this value depends on climate; The milder the winter, the smaller the mean value.

Batariere et al. [78] experienced similar results to Low [80], from the path loss

measurements conducted through a 20 MHz wireless channel at a carrier frequency of

3.676 GHz in a suburban area in different seasons. According to the data analysis by

Batariere et al., they found that the path loss is 3 to 7 dB larger in summer than in

winter. Furthermore, they conclude that main variation in path loss with seasons is due

to foliage.

Hashim and Stavrou [4] examined the scattering effects due to vegetation in different

wind conditions. The objective of the study was to investigate the influence of vegetation

movement on the shadowed LoS signal under different wind conditions. Measurements

are taken in both controlled and outdoor environments. In the outdoor scenario, 900

and 1800 MHz carrier frequencies have been used. Authors carried out the study using

1800 MHz.

Since the Tx and the Rx were stationary in the experiment carried out by Hashim et

al.[4], the shadowing/slow-fading component was assumed to be constant and the fast

fading component was extracted by normalising the received signal values to its mean.


Figure 2.5: Comparison of received shadowed LoS signal due to line of trees [4]

Figure 2.5 illustrates the variation in received signal in windy conditions, compared

to no wind condition for the shadowed LoS signal due to the line of trees. Then, the

fading amplitude distribution constructed from measured data was compared and found

to be Rician distributed. Further analysis on the Ricean K-factor distribution in different

wind speeds has shown that, the K-factor decays exponentially with the wind speed.

Therefore, it is interesting to investigate how rural channels with light tree densities

behave under different wind speeds.

Meng et al. [5] analysed the combined effect of rain and wind over a foliage channel

for VHF (240 MHz) and UHF (700 MHz) frequency bands. According to the study, both

frequencies (240 and 700 MHz) experienced more attenuation and temporal variations

when the wind and rain become stronger. Figure 2.6 illustrates the average signal

variation for 240 and 700 MHz for varying weather conditions. According to Figure 2.6,

it can be seen that for both frequencies, attenuation increases as the strength of either

rain and/or wind increases. According to the authors, Ricean and Gaussian distribution

functions are found to be a better fit with the PDF derived for the temporal variations

due to varying weather conditions. Therefore, Ricean distribution has been used for the

analysis of the experimental results.

The Ricean K factor depends on the type of multi-path channel. Furthermore, for a

fixed channel (both Tx and Rx are stationary) Ricean K factor can be interpreted as the

ratio of the mean power to the variance of the received components [5]. Hence, the K


Figure 2.6: Received Signal for 240 MHz and 700 MHz in different WeatherConditions [5]

factor can be used to characterise the temporal variability of the propagation channel.

Further analysis by Meng et al. has shown that the Ricean K factor decreases as the

effect of rain and/or wind increases in a foliage channel.

Suzuki et al. [79] investigated the effect of wind speed on wireless broadband

channels in urban and suburban environments. According to their previous investigation,

a strong correlation between signal variation and local wind speed was observed in an

outdoor-to-indoor link (suburban area) at 2.4 GHz. Furthermore, their measurement

results have shown that in both indoor and outdoor environments, temporal variation of

received signal level often followed Ricean distribution. An increment in the signal

2.10. SUMMARY 35

variation during the day (08.00 am-08.00 pm) was also experienced. Suzuki et al.

argue that very few attempts have been made to characterise the time variation effects of

wireless broadband channels, especially the longer distance channels in the indoor-to-

outdoor environment.

As discussed in this section, weather conditions, especially wind and rain can cause

variations in the received signal in the presence of vegetation. It is important to un-

derstand these variations for accurate MIMO and MU-MIMO performance predictions.

Also, the proposed system had long distance channels and the AP tower (AP for the

uplink) was surrounded by trees. Therefore, it is interesting to analyse the variations of

received signal for different sub-channels for the proposed CSIRO Ngara access solution,

in the presence of varying weather conditions in rural environments. Furthermore, to the

best of the author’s knowledge, no studies have been conducted to analyse variations

of channel capacity due varying weather conditions such as wind speed. Therefore,

it is important to investigate whether there is a relationship between varying weather

conditions MUSA-MIMO-OFDM channel capacity in rural areas.

2.10 Summary

A detailed analysis of MIMO principles, including spatial multiplexing, diversity, array

gain, diversity gain and MIMO channel capacity with and without channel knowledge

were presented in this chapter. Also, MIMO channel capacity open problems and pre-

vious work on capacity analysis in rural environments based on channel measurements

were discussed. It was found that comprehensive capacity analysis results based on rural

channel measurements are scarce in literature. Therefore, this chapter highlights the

requirement of a comprehensive analysis of actual capacity gains provided by the Ngara

regional access solution in rural environments. In addition, propagation mechanisms

and reasons for temporal variations in outdoor environments were investigated. It was

found that, receiver and scatterer movements, vegetation and varying weather conditions

can cause variations in the received signal. Empirical work carried out by Suzuki et

al. [79] and Meng et al. [5] have already shown that temporal variations, caused by

changing weather conditions (rain and wind) in the vicinity of the wireless channel,


have a pronounced effect on the received signal. Therefore, it is important to analyse the

variations of received signal for different sub-channels for the proposed CSIRO access

solution, in the presence of varying weather conditions in rural environments.

Chapter 3

Review on Channel Modeling

This chapter discusses the state-of-art of Multiple-Input Multiple-Output (MIMO) and

Multi-User Multiple-Input Multiple-Output (MU-MIMO) channel models. It classifies

existing MIMO and MU-MIMO channel models as physical, analytical or hybrid mod-

els. Additionally, existing rural wireless deployments are analysed and the limitations

are discussed. Furthermore, it justifies the development of a novel MUSA-MIMO-

OFDM channel model and performance analysis for the Ngara regional access solution,

based on the channel measurement data and MUSA-MIMO-OFDM channel model out-

put.

This chapter is organised as follows. Firstly, existing MIMO channel models are

classified as physical, analytical and hybrid models. Then, detailed discussion on MIMO

and MUSA-MIMO channel models is provided under those classifications. Finally, gaps

in rural MIMO/MU-MIMO channel modeling and measurements are highlighted.

3.1 Channel Models

Unlike wired communications, significant variations in propagation medium (channel)

are observed in wireless communication systems. These wireless channels operate through

electromagnetic radiation from the Transmitter (Tx) to the Receiver (Rx). Multi-path

fading, path loss, time-selective fading and frequency- selective fading are the main

obstacles in wireless communications [81]. However, the MIMO technique has emerged

37

38 CHAPTER 3. REVIEW ON CHANNEL MODELING

as a cure for the first phenomenon, multi-path fading. The MIMO technique does not

repair the multi-path fading channel. For a given environment, it utilises the multi-

path richness in such a way that the reliability and spectral efficiency of the wireless

communication links are substantially improved [81].

Similar to Single-Input Single-Output (SISO) systems, MIMO systems need a set of

algorithms, coding, and transmission parameters to adapt the system to the variation

of the environment. Such sets are often referred to as Link Adaptation (LA) tech-

niques [82]. The main motivation of any LA scheme is to exploit the best possible system

performance based on some knowledge of the wireless channel. The channel knowledge

or Channel State Information (CSI), can be instantaneous channel information such as

the channel impulse response. Furthermore CSI can be obtained in an average form such

as the average Signal-to-Noise Ratio (SNR), the average channel covariance matrix or

the statistical information of the channel coefficients [81].

Therefore, accurate channel modeling is vital to understand and predict actual per-

formance, especially for MIMO systems. The following sections discuss SISO, MIMO

and MU-MIMO channel models. On the uplink of a MIMO system, the development

of MU-MIMO techniques is considered as a generalisation of MIMO (or single-user

MIMO) concepts to the multiuser case [83]. Therefore, special emphasis is given to

MIMO and MU-MIMO channel models and modeling concepts in this chapter.

3.1. CHANNEL MODELS 39

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3.1.1 Pathloss Models

Large-scale fading is caused by pathloss of the signal and can be characterised as a

function of transmitted distance and shadowing effects of large obstacles such as build-

ings and hills. Pathloss describes the loss in power as the radio signal propagates in

space. This phenomenon occurs when the Rx moves over a large distance, and it is

frequency dependent [84]. A well-known free space pathloss model, which is described

in Equation 3.1, is used to estimate pathloss for ideal LoS paths with no obstructions

between the Tx and the Rx. The free space pathloss formula can be written as 3.1:

PR

PT= GTGR

[λ

4πd

]2

(3.1)

where PR and PT are Rx and Tx power, respectively. Parameters GT , GR, and

d represents gain at the Tx antenna, gain at the Rx antenna, wavelength and distance

between Tx and Rx.

However, in real transmission environments, the received signal power does not obey

this free space pathloss model due to random variation of terrain and Rx and scat-

terer movements. Therefore, based on empirical measurements, empirical models for

pathloss in typical wireless environments (such as urban, suburban and rural) have been

developed to predict the average received signal power with the transmitted distance.

Moreover, pathloss models are included in the existing MIMO channel models [85, 86]

for power predictions. Several existing rural pathloss models [39, 87, 88] are investigated

in this subsection.

The Okumura-Hata model is a widely used empirical pathloss model which enables

prediction and system dimensioning in a cellular environment [38]. Hata derived mathe-

matical expressions by fitting the empirical curves provided by Okumura. The following

equation illustrates the Okumura-Hata model [88] for flat urban areas.

L(dB) = [69.55+26.16 log( f )−13.82 log(ht)−a(hm)]+[44.9−6.55 log(ht)] log(dl) (3.2)


where f is the carrier frequency in MHz, ht and hm are Base Station (BS) effective

antenna height and mobile station height in meters, respectively. The radio path length

is represented by dl in kilometres.

The Okumura-Hata model has been tailored to predict pathloss in rural areas. Tai-

lored rural Okumura-Hata model can be written as:

Lr = L − 4.78[log( f )]2 + 18.33 log( f ) − 40.94 (3.3)

The Okumura-Hata model is valid for 150< f (MHz)<1500, 30<ht(m)<200, 1<hm(m)<10

and 1<d(km)<20. The Cost 231-Hata model [89] (valid up to 2GHz) was introduced for

the power prediction of higher frequency systems, such as GSM at 1800 MHz or PCS at

1900 MHz. Corrections for urban, suburban and open areas have been included in the

Cost 231-Hata model [89].

Erceg et al. [90] developed a statistical pathloss model for suburban areas. This

model is defined for different terrain categories, namely, terrain type A, B and C. Terrain

type A represents hilly areas with moderate-to-heavy tree densities. Type B represents

hilly areas with light tree density or flat areas with moderate-to-heavy tree densities.

Type C is modeled for flat areas with light tree densities. The originality of the model

proposed by Erceg et al. is that the two major parameters of characterisation, i.e pathloss

exponent and shadow fading standard deviation are treated as random variables for each

macrocell. Data collected in 1.9 GHz has been used to describe these variations statisti-

cally [90]. The IEEE 802.16 SUI model [38] has been derived from the model proposed

by Erceg et al.. Since pathloss exponent and shadow fading standard deviation are treated

as random variables for each macrocell, this model is categorized as a statistical channel

model. As a result, this model does not account for actual terrain variations. In this

research, a comprehensive channel model which can account for terrain modeling was

required for accurate performance prediction of the Ngara wireless broadband access

system. Therefore, a deterministic modeling approach was selected over the statistical

approaches.


The International Telecommunication Union-Radiocommunication (ITU-R) recom-

mendation P.1546 [91] describes a method for point-to-area radio propagation predic-

tions for terrestrial services in the frequency range 30 MHz to 3000 MHz. The method

implements interpolation/extrapolation from empirically derived field-strength curves

as functions of distance, antenna height, frequency and percentage time. Later ITU-R

versions, P.1546-1 and P.1546-2, include corrections to the results obtained from inter-

polation/extrapolation to account for terrain clearance and terminal clutter obstructions.

Ostlin et al. [39] analysed the validity of three ITU-R P.1546 versions for pathloss

prediction in rural Australia. Measurements results confirmed that, on average, P.1546-

2 underestimates the field strength by more that 10 dB for typical rural Australian

areas. However, Ostlin et al. found that P.1546-2 improves the standard deviation of

the prediction error compared to the P.1546 and P.1546-1 versions.

In addition to pathloss, the transmitted signal is subjected to shadowing, which

occurs due to changes in reflecting surfaces and scattering objects along the transmission

path. The shadowing causes random attenuation to the transmitted signal [54]. The log-

normal shadowing model [92] is popular for characterising the attenuation due to shad-

owing. Small scale fading, which occurs due to multi-path components are discussed in

the following section.

3.1.2 Fading Models

Small-scale fading occurs due to the constructive and destructive addition of different

multi-path components introduced by the channel between the Tx and Rx. Hence, it

is also referred to as multi-path fading. Small-scale fading can occur over a distance

of several signal wave-lengths and is frequency dependent [54]. Depending on the

coherence bandwidth, multi-path fading channels can be categorised into frequency-

nonselective (flat) fading channels and frequency-selective fading channels. Coherence

bandwidth is the reciprocal of the delay spread, which is defined as the span of the

delays of duplicates of the transmitted signal arriving at the Rx via different paths [55].

For a flat fading channel, transmitted signal bandwidth is smaller than the coherence

bandwidth. Therefore, the spectral components of the transmitted signal are affected in


a similar manner. The channel becomes frequency-selective, if the transmitted signal

bandwidth is large when compared with the coherence bandwidth. For a frequency-

selective fading channel, the spectral components of the transmitted signal are affected

by different amplitude gains and phase shifts [55]. However, employing some multi-

carrier modulation schemes such as OFDM [93, 94], the bandwidth of each of the

multiple carriers can be confined to bandwidths that can be characterised as flat fading.

Multi-path components are received as random signals at the Rx. Therefore, multi-

path fading is modeled using one of several popular probability distribution functions

[95–98] to represent the variations of the envelope voltage. The most common distribu-

tions are

• Rayleigh

• Ricean

• Nakagami

Rayleigh distribution is assumed when a sufficiently large number of equal power

multi-path components with different phases are present at the Rx. Furthermore, it is

commonly used to describe the multi-path fading with no direct Line-of-Sight (LoS)

path. Rayleigh fading is a useful model in urban environments where many scatterers

are present. Experimental work in Manhattan [99], which is a heavily built-up city

environment, has found that received signal follows Rayleigh fading.

Probability Density Function (PDF) for a Rayleigh distributed random variable x is

given by [95]:

pr(x) =xσ2 exp

(−x2

2σ2

)(3.4)

where σ2 represents the variance of the random variable x.

The Ricean distribution is assumed when a non-fading signal component is present,

such as LoS path propagation [32]. Therefore, rural and suburban channels with less

scatterers and flat terrains can exhibit Ricean fading characteristics. PDF for a Ricean

distributed random variable x is given by [32]:


pr(x) =xσ2 exp

(−x2 − V2

2σ2

)I0

( xVσ2

)(3.5)

where, I0 is a zeroth-order modified Bessel function. Ricean factor is denoted by K.

The parameter K is defined as the ratio between the deterministic (direct path) signal

power (V2

2 ) and the variance of the multi-path (σ2) [32]. Therefore, the Ricean factor can

be written as:

K(dB) = 10 logV2

2σ2 (3.6)

The Ricean K-factor can be estimated using the measured power of a signal over

time. Several methods are employed to estimate the Ricean K-factor. One method is

to compute the distributions of the measured signal power and compare it to a set of

hypothesis distributions using a suitable goodness-of-fit test [100]. Another method

is to compute a maximum-likelihood estimate from an expectation/maximisation al-

gorithm [101]. However, the aforementioned methods are time consuming and cum-

bersome. On the other hand, Ricean K-factor generation, based on moment-method

estimation[102], is a simple and rapid approach wherein the K-factor is an exact function

of moments estimated from time-series data. Therefore, this method was employed for

Ricean K-factor generation in this thesis.

Nakagami distributed fading is expressed in terms of two parameters, namely, the

mean power Ω and fading figure mfad [97]. Unlike Rayleigh and Ricean distributions,

which are derived from real physical quantities such as Gaussian noise, the Nakagami

distribution is a mathematical construct with no physical foundation. The Nakagami

distribution can be stated as [54]:

pr(x) =2

Γ(mfad)x2mfad−1 exp

(−mfad

Ω2 x2)

; x >= 0,mfad >= 0.5 (3.7)

where, Γ(mfad) represents Gamma function.

Nakagami distribution is found to be more flexible in creating a wide range of PDF

shapes and is more mathematically tractable than the Ricean distribution due to the

3.2. MIMO CHANNEL MODELS 45

absence of modified Bessel function [54]. From the above equation it can be observed

that increasing the value of mfad corresponds to a lesser amount of fading and the case of

mfad=l corresponds to Rayleigh fading.

In this section, multi-path fading models were illustrated using popular distribution

functions, namely, Rayleigh, Ricean and Nakagami. Among these models, Ricean dis-

tribution close relates to the measured wireless channel as dominant LoS paths were

available from user terminals to the access point. Therefore, the thesis has chosen Ricean

distribution for the analysis described in Section 4.12. The following section will discuss

MIMO channel models that take advantage of multipath propagation, which has been

recognised as a pitfall in wireless communications.

3.2 MIMO Channel Models

The performance of MIMO systems heavily depends on the characteristics of prop-

agation channels [52]. Different propagation environments (such as urban, rural, in-

door and outdoor) exhibit different propagation channel characteristics. As a result, the

performance of MIMO systems can vary from one environment to another [79, 103].

Accurate characterisation and modeling of MIMO channels, in different scenarios and

environments, is vital when integrating MIMO systems into real world applications. This

fact highlights the importance of developing realistic channel models that can mimic

wireless channels and radio propagation concepts [41].

Many MIMO channel models [103–107] have been proposed in recent years. Almers

et al.[41] survey on MIMO channel models classified the existing MIMO channel models

as physical and analytical models. The electromagnetic wave propagation between

the location of the transmit array and the location of the receive array is the baseline

for characterising physical channel models [41]. On the other hand analytical channel

models characterise the impulse response of the channel mathematically, without con-

sidering the electromagnetic wave propagation [41]. Analytical models study channel

coefficients as random variables. Hybrid models are a mixture of physical and analytical

models. They are based on some form of deterministic ray based mechanism, whereas

several parameters are modeled statistically. Physical, analytical and hybrid models are


discussed in the following section.

3.3 Physical Models

3.3.1 Deterministic Physical Models

A given physical propagation model is deterministic, if it is possible to reproduce the

actual wave propagation scenario (process) for a given environment [41]. For a given

environment, the relevant propagation process can be simulated from computer pro-

grammes through the use of building databases, which accurately represent the building

or terrain features [32]. Deterministic models are more realistic and accurate, due to the

representation of the environment specific geometry [41]. The computer program has to

run multiple times when characterising different geometric environments.

Ray Tracing (RT) models are classified as deterministic models [32]. RT models use

the theory of Geometric Optics (GO) to simulate the reflections of plane surfaces and

diffraction on rectilinear edges [41]. The Tx and Rx positions are specified as the initial

step in the ray tracing procedure. Then, all possible paths from the Tx to the Rx are

determined according to geometric consideration and the rules of the GO. Geometric

optics are based on ray approximation, where a sufficiently small wavelength is assumed

compared to the dimensions of the obstacles in the environment [41]. Due to the above

approximation, RT models better reflect the urban radio propagation environment. Nor-

mally, a maximum number of consecutive reflections and diffractions are defined for a

particular run [41].

Ray tracing characterises all rays at the Rx in terms of their amplitude, phase, delay,

angle of departure, and angle of arrival [41]. Due to the accuracy of these determinis-

tic (RT) models, the deterministic modeling approach is followed in this thesis.

3.3.2 Uniform Theory of Diffraction (UTD) Models

Uniform Theory of Diffraction (UTD) models [60, 108] are implemented to predict wave

propagation over irregular terrains using theory of diffraction. In order to use UTD

3.3. PHYSICAL MODELS 47

formulations, irregular terrain profiles are approximated with canonical shapes such

as wedges and convex surfaces, by linearising and curve-fitting the raw terrain digital

data [60].

Luebbers et al. [109] implemented the Geometrical Theory of Diffraction (GTD)

- wedge diffraction for propagation prediction in hilly terrains. The authors calculated

multiple wedge diffraction from Kouyoumjian-Pathak UTD coefficients [110]. Advan-

tages of UTD multiple-wedge diffraction were found to be its capability to include

reflections, ability to model the terrain more accurately and its ability to include the

effects of finite conductivity and surface roughness. Luebbers’s model correlated well

with the measurements results and was found to be better than the Longley-Rice model,

in terms of propagation prediction [109].

An automated linearision method [111] was proposed to simplify raw digital hilly

terrain profiles into 2D straight wedges and trapezoids from digital maps, based on the

variations of the terrain elevations along a given vertical Tx-Rx profile. This method is

useful, as UTD formulations need terrain profiles to be approximated with shapes such

as wedges and convex surfaces.

Loredo et al. [108] developed an indoor three dimensional (3D) propagation model

based on the GO and UTD combination and validated the model through extensive mea-

surement campaigns. According to the authors, first order and second order statistics of

the channel and wideband parameters have been accurately obtained using the GO/UTD

model. Furthermore, implementation of the 3-D GO/UTD model accounts the full

electromagnetic field (phase, polarisation, Direction-of-Departure (DOD), Direction-

of-Arrival (DOA) and delay time) related to rays traveling from mth transmitter at the

point where they receive nth receiver antenna. However, the behaviour of the channel

(spatial and temporal variations) is complicated when the number of multi-path signals

are large and for larger outdoor cells, and statistical description of the channel is more

convenient [108]. These UTD models need detailed geometrical and electromagnetic

description of the environment. Compared to indoor scenarios, UTD techniques become

higher in complexity for larger outdoor areas and long distance links.

In rural areas, especially for the Ngara regional access solution, diffraction effects


can be prominent due to possible terrain obstructions. Therefore, selecting a suitable

Digital Elevation Map (DEM) to predict diffracted multi-path components due to terrain

obstructions is important for accurate diffraction predictions in rural areas. Due to the

complexity introduced by UTD techniques in modeling outdoor, long range wireless

channels, a less complicated yet accurate method to predict diffraction loss in rural envi-

ronments was chosen in this thesis. The Deygout method explained in Section 2.7.2, has

been used to predict diffraction loss in rural wireless channels. International Telecommu-

nication Union-Radiocommunication (ITU-R) P.1812-1, which is used for propagation

prediction for VHF and UHF bands, also employs the Deygout method in diffraction

loss predictions [65].

3.3.3 Geometry-based Stochastic Physical Models

Deterministic physical models specifically define the scatter locations, while Geometry-

based Stochastic Channel Models (GSCM) consider scatterer locations randomly, ac-

cording to a given probability distribution [41]. These models can be further divided to

single-bounce scattering [112] and multiple-bounce scattering [113] models.

The single-bounce scattering model assumes that, except for the line-of-sight (LoS)

path, all other parts consist of two other sub paths which connect the scatter to the

Tx and the Rx. Different geometry-based stochastic models differ according to the

proposed scatter distribution [41]. The simplest GSCM assumes that the scatterers are

uniformly distributed. Furthermore, the existence of far scatterers introduces temporal

and angular dispersion, which can significantly influence the performance of MIMO

systems [41]. These effects can be accounted for in GSCM by placing far scatterers at

random locations.

GSCM can be suitable for MIMO performance prediction in urban environments

as many random scatters (e.g. moving vehicles) are involved. In this research, the

existence of local scatterers are limited due to the rural environment with large open

areas. Therefore, a deterministic modeling approach was chosen over a GSCM approach.

3.3. PHYSICAL MODELS 49

3.3.4 Non Geometrical Stochastic Physical Models

Non geometrical stochastic models describe paths from the Tx to the Rx by statistical pa-

rameters such as Rayleigh amplitudes, Time-of-Arrival (TOA), Angle-of-Arrival (AOA)

and Angle-of-Departure (AOD) [106, 114]. Furthermore, these models do not consider

the physical geometry of the environment.

Saleh and Valenzuela [106] proposed a statistical model for indoor multi-path prop-

agation which assumes that the receive signal rays arrive in clusters. These rays are

assumed to have independent uniform phases, and Rayleigh amplitudes with variances

that decay exponentially with cluster and ray delays [106]. Using the above assumptions,

Saleh and Valenzuela modeled the clusters of multi-path components in delay domain

through the exponential decay process [41]. Wallace and Jensen [114] extended the

Saleh and Valenzuela model to the spatial domain to treat multi-path components inde-

pendently. Furthermore, it assumes that the DOD and DOA statistics are independent

and identical.

Zwick et al. [107] characterised the channel by multi-path components (each char-

acterised by its transfer matrix), delay, direction of arrival, and departure. The proposed

model modeled the appearance and disappearance of multi-path components over time

as a marked Poisson process (i.e. as a birth and death process).

Using non-geometrical stochastic models to model outdoor rural wireless channels

is not feasible since these models do not consider physical geometry of the environment.

As stated in Section 3.3.1, accounting for physical geometry in outdoor wireless channel

modeling is important to predict LoS and diffracted propagation paths. Non-geometrical

stochastic models determine paths from the Tx to Rx stochastically, according to a

statistical distribution. Therefore, in this thesis, a deterministic modeling approach was

chosen over non geometrical stochastic modeling.

As discussed in this subsection, physical models characterise an environment on the


basis of electromagnetic wave propagation by describing the double directional multi-

path propagation between the Tx and Rx array. They model wave propagation param-

eters, such as complex amplitude, DOA, DOD and the delay of the multi-path compo-

nents. Analytical models are discussed in the following subsection.

3.4 Analytical Models

Analytical channel models characterise the impulse response of the channel mathemat-

ically, without accounting for wave propagation. Analytical models make assumptions

regarding the propagation environments (such as rich scattering) and model channel

coefficients as random variables according to a given statistical distribution. Two popular

correlation-based analytical models are discussed in the following section.

3.4.1 i.i.d. Model

The most basic analytical MIMO channel can be considered as the i.i.d. model, which

assumes that all elements of the MIMO channel matrix (H) are uncorrelated and have

equal variance ρ2 [41]. An example of correlation matrix RH for the i.i.d. model, for

2 Tx-2 Rx case is described as:

RH2x2 =

ρ2 0 0 0

0 ρ2 0 0

0 0 ρ2 0

0 0 0 ρ2

(3.8)

The i.i.d. model is considered in rich scattering environments and mostly for the-

oretic considerations such as information theoretic analysis [30]. In practice, however,

MIMO channels can have a considerable deviation from i.i.d assumption [115].

3.4. ANALYTICAL MODELS 51

3.4.2 Kronecker Model

The Kronecker model [105, 115] assumes that the Tx and the Rx correlation are sepa-

rable. According to the Kronecker model, the correlation matrix of the channel can be

written as the Kronecker product of Tx correlation matrix RT xand the Rx correlation ma-

trix RRx. The Kronecker model has been a popular channel model due to the underlying

separability of the Tx and the Rx. Furthermore, it allows theoretical analysis of MIMO

systems [41]. As shown by Oestges [115], the Kronecker model can be implemented

when the propagation environment is Kronecker-structured. The mathematical validity

conditions and propagation validity conditions stated below have to be satisfied in order

to consider the propagation environment as Kronecker-structured [115].

• Condition 01: The Tx correlation (with respect to Rx) coefficients are independent

from the considered Rx antenna (with respect to Tx).

The above mathematical requirement can be interpreted in terms of propagation

related conditions. That is, antennas in Tx array are placed close to each other,

and have the same radiation pattern and orientation [115]. Similar conditions will

apply to the Rx array also.

• Condition 02: The magnitude of cross-correlations has to be equal to the product

of Tx and Rx correlations.

Propagation related conditions for the above mathematical requirement can be

expressed as having all AODs coupled with all AOAs with the same profile, hence,

the joint AOA-AOD spectrum is the product of marginal spectra [115]. Further-

more, Oestges [115] stated that AOD and AOA spectra have to be statistically

independent. This condition may occur in real world propagation scenarios when

the immediate surroundings of each antenna arrays are responsible for the corre-

lation between its antennas, irrespective of the impact made on the correlation by

the other end of the link.

Mathematical representation of the Kronecker model is given as [115]:

vec(H) = R12 vec(Hw) (3.9)


where Hw is the i.i.d MIMO channel and R = R 12 R H

2 is the covariance matrix defined

as R = Evec(H)vec(H)H. Operator ‘vec’ stacks the matrix H into a vector columnwise

and superscript H stands for the conjugate transposition.

Popular correlation based i.i.d and Kronecker model have been discussed under the

analytical MIMO channel models in this section. These analytical models characterise

the impulse response of the channel mathematically without accounting the actual wave

propagation. Although, these models can be used for information theoretic analysis,

they are not capable of accounting for actual wave propagation for a given environment.

Therefore, the use of deterministic modeling approach is preferred over the analytical

models in this thesis. The following section will discuss hybrid models, which are based

on both deterministic and analytical modeling concepts.

3.5 Hybrid Models

Hybrid models are based on deterministic and analytical/stochastic modeling approaches.

Most hybrid models are based on the directional channel modeling concept. In these

models, channel coefficients are generated as a sum of rays, similar to the RT based

method discussed in Section 3.3.1. However, the DOD, Time Delay-of-Arrival (TDOA)

and path strengths are realisations of random processes [116] similar to the statistical

models discussed in Section 3.3.4. IEEE 802.11n and 3GPP spatial channel model are

two popular hybrid models. A review of these models is presented in the following

section.

3.5.1 IEEE 802.11n Model

This channel model was developed for indoor environments in the 2GHz and 5GHz

bands with a focus on MIMO wireless LANs [41]. This model considers environments

such as small and large offices, residential homes and open spaces with both LoS and

NLoS. The IEEE 802.11n model uses a non-geometric stochastic approach, which is

described in Section 3.3.4. It describes directional impulse response as a sum of clusters.

Each cluster consists of up to 18 delay taps separated by at least 10 ns. Based on the

3.5. HYBRID MODELS 53

measurement data, the number of clusters was found to be 2 to 6 with a variation of

overall RMS delay spread between 0 to 150 ns [41].

3.5.2 3GPP Spatial Channel Model

The 3rd Generation Partnership Project (3GPP) spatial channel model was developed by

3GPP/3GPP2 groups for outdoor environments. The model is defined for three types of

environments, namely, suburban macro, urban macro and urban micro [41]. This model

is considered as generalised one, which represents the MIMO channel as a superposition

of Multi-Path Components (MPCs) with stochastic powers, AODs, AOAs and times

of arrival. In order to generate the MIMO channel matrix, the 3GPP channel model

requires the input parameters, namely, general parameters, link dependent parameters

and antenna parameters. Moreover, Winner I and Winner II [117] can be considered as

extensions of the 3GPP spatial channel model.

Although channel models such as the 3GPP spatial model [86] and, Winner I and

Winner II [117] accommodate MIMO channels, these models do not include terrain

modeling. As discussed in Section 3.3, terrain modeling is important in modeling out-

door wireless channels. On the other hand, these models consider superposition of

Multi-Path Components (MPCs) with random powers, AODs, AOAs and times of arrival.

Therefore, a deterministic outdoor model, which includes accurate terrain modeling and

actual wave propagation (rather that randomly generated path powers, AODs and AOAs)

between the Tx and Rx is required. Due to the aforementioned reasons, a deterministic

outdoor model is preferred over the hybrid modeling approach.

As discussed in this subsection, hybrid models are based on directional channel infor-

mation such as AOD, AOA and TDOA. These models are considered to be a combination

of physical models and stochastic models. The next subsection discusses MU-MIMO

models, which are derived by extending basic single user MIMO concepts.


3.6 Multi-User MIMO Models

As shown by Spencer et al. [6] , there are two communication problems to consider

in MU-MIMO systems. Those are the ‘uplink’ through which all users transmit data

to the same base station, and the ‘downlink’ through which the base station transmits

data to multiple users simultaneously. A comprehensive illustration of the multiuser

downlink MIMO system is provided in reference [6]. Furthermore, as stated by Spencer

et al., single user MIMO systems benefit from co-ordination between all transmitters and

receivers. However, in MU-MIMO systems it is assumed that there is no co-ordination

between the users (receivers). Therefore, MU-MIMO systems are more complex com-

pared to the Single User (SU) MIMO systems.

Figure 3.2: An Illustration of Multiuser MIMO Downlink [6]

The challenge at the uplink is that users transmit data to the base station over the

same channel and the base station has to separate the users using methods such as array

processing and Multi-User Detection (MUD) [6]. In the literature, little attention is given

to MU-MIMO uplink compared to MU-MIMO downlink. In the downlink channel, the

base station transmits the data simultaneously to many users. As shown in Figure 3.2,

the base station may attempt to transmit data over the same channel to two users, causing

inter-user interference for User 1 generated by the signal sent to User 2 and vice versa.

Spencer et al. [6] recommends avoiding the multiple access interference by intelligently

3.6. MULTI-USER MIMO MODELS 55

designing the transmitted signal at the transmitter. Therefore, if the CSI is available at

the transmitter, it has knowledge about the level of interference created by relevant users,

and can take measures to eliminate those effects via intelligent beamforming or the use

of dirty paper codes [6].

Research shows that, only a few MU-MIMO channel models [21–24] have been

proposed in the area of MIMO channel modeling. It has been identified that the inter-

user interference in MU-MIMO downlink is a great concern. Fugen et al. [21] proposed

a new modeling approach which introduced an interference component in the MU-

MIMO system equation and proposed a multiuser double-directional channel model.

The authors claimed that this model provides an accurate description of interference

conditions for multiuser channel modeling and modeled the downlink case received

signal from the following equation [21].

yk = Hkxk + nk +

K∑µ=1,µ,k

Hi f ,µxµ (3.10)

A flat fading channel has been assumed in this scenario. This means that the multi-

path components arrive at the receiver within the symbol period. According to Equa-

tion 3.10, the received signal is considered as three parts. The first part shows the trans-

mitted signal (xk), which is sent to the user (k) through the propagation channel (Hk).

The second part nk represents the white Gaussian noise. The interference received by

the user xµ though the propagation channel is represented by the channel matrix Hi f ,µ.

Jensen et al. [23] stated that for MU-MIMO networks with mobile nodes or scat-

terers, it is difficult to create channel models that effectively represent the accurate

relationship between channels to different users as a function of their relative position

due to the rapid variation in CSI. The authors use the channel covariance matrix to

address this problem. They follow an analytical method to model MU-MIMO channels

by exploring the position-dependent properties of the covariance using an analytical

framework. However, as stated by the authors, extending this understanding to a usable

MU-MIMO model requires additional work.

Wenjie et al. [22] proposed a novel approach to model the multiuser MIMO channels.


This model characterises the key features in physical environments such as the geometry

and roughness of the scattering surface [22]. The scatterers are modeled as random

rough surfaces and the height of the scatterers are considered to be a Gaussian process.

Finally, they compared the proposed model with the existing correlation based MIMO

channel models, such as the Kronecker model and virtual channel representation model.

The benefits of the model are the ability of calculating the theoretical channel gains and

spatial correlation, based on the scattering surface profile. However, it is restricted to

certain environments, such as large plane scatterers and requires the scattering surface

parameters.

One of the most recent analytical MU-MIMO modeling approaches was proposed by

Czink et al. [24]. This model is capable of modeling interference in the spatial domain

and it characterises the amount of eigenspace alignment on a continuous scale between

fully aligned and maximally non-aligned. Channel measurements obtained through an

indoor office environment and an outdoor-to-indoor cubicle style office environment

have been used to parametrise this model. Channel measurements were performed

for short distance links with 3.8 GHz and 2.45 GHz for indoor and outdoor-to-indoor

environments, respectively.

3.7 Gaps in Rural MU-MIMO Channel Modeling and Measure-

ments

This section discusses the gaps and limitations identified in the literature review. As

discussed in the literature review, MIMO systems and models have been proposed as a

solution to increase bandwidth efficiency in wireless networks. However, current MIMO

channel models have given more emphasis to indoor and urban environments [69, 74, 79,

107, 108, 118], whereas rural environments [51, 119] are given little attention. As far

as MU-MIMO systems are concerned, few channel models [21–24] and channel mea-

surement results [25–27] are found in the literature. These MU-MIMO based channel

measurements are available thanks to the emergence of the LTE systems. However, the

main focus is given to the MU-MIMO downlink, and short distance links in indoor and

urban environments.

3.8. SUMMARY 57

The IEEE 802.22 [120] standard is the first worldwide effort to define a standard-

ised interface for the opportunistic use of TV bands, especially targeted for rural and

remote areas. These Wireless Regional Area Networks (WRANs) which use TV band

carriers, support a larger coverage range compared to other IEEE 802 standards due to

the favorable propagation characteristics of TV frequency bands [120]. The prominent

target application of WRANs is wireless broadband access in rural and remote areas,

with performance equivalent to fixed broadband access technologies serving urban and

suburban areas.

Although IEEE 802.22 is a promising standard in providing wireless broadband

services to rural areas, most of the related work is based on spectrum sensing, spec-

trum management and IEEE 802.22 physical layer level simulations and system level

simulations [120–124]. Currently, no comprehensive channel measurement and sys-

tem performance analysis results are available for MU-MIMO-OFDM fixed broadband

wireless access systems that use TV carrier frequencies in rural environments. One of

the main reasons behind this unavailability could be due to the difficulty of obtaining

license to use a dedicated TV spectrum for channel measurement purposes as VHF and

UHF bands are typically in high demand for services such as TV broadcasting.

For the first time in the world, the Ngara regional access solution was developed

and implemented in a rural Australian environment as a six user MUSA-MIMO-OFDM

SDMA system, which employs large scale multiple antennas at the AP and analogue

TV frequency spectrum. Therefore, a detailed analysis of channel measurement data is

performed in this research. Also, this research project focuses on developing a physically

meaningful, yet easy to use model to understand and mimic underlying radio propagation

mechanisms in the rural Australian environment for the Ngara regional access solution.

Based on the channel measurement data and model output, a detailed capacity analysis

for the Ngara regional access solution is conducted in this research.

3.8 Summary

In this chapter, existing MIMO/MU-MIMO channel models are classified as physical,

analytical and hybrid models. The electromagnetic wave propagation between the Tx


array and the Rx array is the baseline for characterising physical/deterministic chan-

nel models. On the other hand, analytical/stochastic channel models characterise the

impulse response of the channel mathematically, without considering the electromag-

netic wave propagation. Analytical channel models consider channel coefficients as

random variables. Hybrid models are based on deterministic and stochastic modeling

approaches. In most hybrid models, channel coefficients are generated as a sum of rays,

similar to the deterministic approach. However, DOD, TDOA and path strengths are

realisations of random processes [116]. A detailed discussion on MIMO and MU-MIMO

channel models has been provided under those classifications.

According to the literature, currently, more emphasis has been given on modeling

MU-MIMO downlink in indoor and urban environments for short distance links. Little

emphasis has been given [51, 119] to channel modeling in rural environments. Moreover,

discussion on MU-MIMO uplink, MU-MIMO/MIMO channel measurements for rural

channels and performance analysis of MU-MIMO systems deployed in rural environ-

ments are scarce in the literature. In this chapter an extensive review of existing MIMO

and MU-MIMO models was conducted. This review has verified that, currently, no

deterministic MU-MIMO-OFDM channel model exists which is capable of modeling

outdoor rural MU-MIMO-OFDM channels while accounting for terrain effects. This

finding highlights the requirement of developing a physically meaningful yet easy to use

model to mimic the underlying radio propagation mechanisms in rural environments for

the performance prediction of outdoor rural MU-MIMO-OFDM channels. Therefore, a

deterministic MUSA-MIMO-OFDM channel model is developed in this thesis, which

accounts for the terrain effects in outdoor rural environments, for the performance pre-

diction of the Ngara regional access solution. In addition, in literature, no comprehensive

channel measurement and system performance analysis results are available for MU-

MIMO-OFDM fixed broadband wireless access systems, which use TV carrier frequen-

cies in rural environments. Moreover, it provides an analysis of channel measurement

data for the MUSA-MIMO-OFDM system. Based on the channel measurement data

and model output, a detailed capacity analysis for the proposed MUSA-MIMO-OFDM

system is conducted. This research will fill the aforementioned knowledge gaps in the

following chapters.

Chapter 4

Channel Measurements

This chapter focuses on rural Multi-User-Single-Antenna Multiple-Input-Multiple-Output

Orthogonal-Frequency-Division-Multiplexing (MUSA-MIMO-OFDM) channel measure-

ment and analysis. One of the aims of this chapter is to introduce the measurement envi-

ronment, Access Point (AP), User Terminal (UT) locations and antenna related parame-

ters of the deployed MUSA-MIMO-OFDM system. This chapter describes experiments

conducted to collect MUSA-MIMO-OFDM uplink channel data in a rural environment

for the 641.5 MHz carrier frequency. Also, the chapter provides information about the

data analysis platform. Then, instantaneous channel and channel variations over time

are presented. Next, channel fading statistics and the spatial structure of the measured

channel are analysed based on the measured data. Finally, the correlation between

received power and weather parameters is analysed.

4.1 Measurement Site

Experiments were conducted in a farmland near Smithton from 2010-12-10 to 2010-12-

15. As shown in Figure 4.1, it is a town situated at the far north-west coast of Tasmania,

Australia. It contains a population of 3,361 [125] people. Smithton experiences four

seasons [126] and the experiments were conducted during the summer season. Summer

in Smithton is between December and February, and the maximum daily temperatures

average between 17.10C and 19.30C [127]. Moreover, Smithton records an annual mean

rainfall of 881.5 mm and records higher average wind speeds (around 10-20 km/h)

59

60 CHAPTER 4. CHANNEL MEASUREMENTS

compared to most of the cities in Australia [127].

Smithton has an agriculture based economy, consisting primarily of beef and dairy

farming [125]. As a result, farmlands with a large open areas are common in Smithton.

Most of these farmlands are grass lands, which are used to feed cows. Figure 4.2 shows

such a grass land situated close to the AP. Moreover, only a few local scatterers such

as trees were present in the measurement site as shown in Figure 4.2(a) and 4.2(b).

Therefore, compared to an urban environment, with a large number of buildings and

moving vehicles, this rural environment exhibits a low “scattering richness” [29, 42] due

to the aforementioned properties. Since the measurement site was a farmland with large

open areas, a dominant propagation path was available from the AP to UTs. Availability

of dominant propagation paths from the AP to UTs will be verified by terrain analysis

presented in Chapter 5.

Figure 4.1: Geographical location of the measurement site marked “A” (Google Maps)

4.1. MEASUREMENT SITE 61

(a) AP surrounding environment

(b) Nearby trees at AP

Figure 4.2: AP surrounding environment


4.2 Access Point and User Terminal Locations

AP and UTs were positioned in farmlands. Six UTs were placed around the AP with

different distances, ranging from 10 m to 8.4 km. Figure 4.3 illustrates relative positions

and distances between the AP and six UTs. Also, longitude-latitude, elevation, and

antenna height information related to the AP and six UT sites are stated in Table 4.1.

UT3- 4.3 km

UT2- 10 m

UT1- 5.5 km

UT5- 3.4 km

UT6- 3.7 km

UT4- 8.4 km

Access Point

Figure 4.3: Relative position and distances between the AP and UTs

Table 4.1: AP and UT position information

Site Latitude Longitude Elevation Antenna height DistanceAP -4057′33′′ 14511′35′′ 264 m 71 m 0 km

UT1 -4054′34′′ 14511′57′′ 169 m 9 m 5.5 kmUT2 -4057′33′′ 14511′35′′ 264 m 1.5 m 10 mUT3 -4055′29′′ 14510′09′′ 205 m 9 m 4.3 kmUT4 -4054′08′′ 14515′31′′ 125 m 6 m 8.5 kmUT5 -4059′18′′ 14510′55′′ 242 m 9 m 3.3 kmUT6 -4058′23′′ 14509′12′′ 235 m 9 m 3.6 km

4.3. MEASUREMENT SETUP 63

4.3 Measurement Setup

Channel measurements were conducted using the MUSA-MIMO-OFDM demonstrator

developed by the CSIRO ICT Center. Figure 4.4 shows the MUSA-MIMO-OFDM

demonstrator being tested in a laboratory environment. The AP units and the outdoor

enclosure (white cabinet), where the AP units were installed at the measurement site, are

shown in Figure 4.5.

The AP was equipped with the following units:

• A twelve channel radio power amplifier and antenna switch unit

• A twelve channel radio up-converter and down-converter unit

• A twelve channel high performance digital signal processing unit

• A GPS receiver that provides accurate timing and frequency references

Each UT is equipped with the following units

• A digital signal processing module that generates and decodes radio packets in

real-time

• A radio up-converter and down-converter module

• A radio power amplifier module

• A GPS receiver to provide accurate timing and frequency references

During the uplink measurements, each UT streamed digital video to the AP for

technology demonstration purposes. Then, the AP was connected to an Ethernet switch

that separated the six streaming channels to six personal computers. Figure 4.6 shows

the video content received from UT1 and UT2. During the experiments, approximately

1.8 billion samples of channel coefficients were collected over 6 measurement days. It

should be noted that, due to some technical difficulties, measurements were not per-

formed continuously, leaving periods of blank time. The sampling interval of the mea-

sured data was 4 s. As stated in Section 2.9.2, outdoor wireless channels can experience


variations due to varying weather conditions. Therefore, weather data was collected in

parallel to uplink channel measurements.

Figure 4.4: MUSA-MIMO-OFDM demonstrator at laboratory

During the experiments, the center frequency of operation and the bandwidth of the

measured channel were 641.5 MHz and 7 MHz, respectively. This band is typically

utilised for television broadcasting, and a scientific spectrum license was acquired by

CSIRO from the Australian Communications and Media Authority (ACMA) prior to the

measurement for operating in this band. The maximum Root Mean Square (RMS) UT

transmitting power from the power amplifier was 7.5 W. Before the experiments, UT

transmitting power was adjusted to have approximately the same SNR at the AP from

each of the UTs. This adjustment was done as it is a capacity optimal configuration for

the fixed rural broadband application.

The channel measurements were performed in frequency domain, with 1,705 occu-

pied OFDM sub-carriers with sub-carrier spacing of 3906.25 Hz. The FFT size was

2048. Since 1705 occupied OFDM sub-carriers were utilised during the experiments, at

a given instant of time, 12×6×1705 MUSA-MIMO-OFDM channels were established.

Further information related to OFDM symbol parameters and modulation information

4.3. MEASUREMENT SETUP 65

Figure 4.5: AP units fixed at outdoor enclosure

Figure 4.6: Video streaming through uplink channel


are shown in Table 4.2.

Table 4.2: OFDM symbol parameters

Number of occupied sub-carriers 1705

Number of data sub-carriers 1680

Sub-carrier spacing 3.90625 kHz

OFDM symbol duration (without guard interval) 256 µs

Cyclic prefix 64 µs

OFDM symbol modulation 64QAM

FEC Convolutional

FEC rate 3/4

4.4 Access Point Antenna Array

MUSA-MIMO-OFDM uplink was established between six UT Tx antennas and the AP

Rx antenna array. The AP antenna array was installed on a commercial broadcasting

tower in Smithton at a height of 71 m from the ground. Figure 4.7 illustrates the

broadcasting tower and AP array mounted at the top of the tower.

The AP was a 12 element antenna array, with a vertically polarised folded dipole

antenna as an element. Twelve antennas were placed in three tiers to form a Uniform

Circular Array (UCA) in horizontal space with a radius of 40 cm (approximately one

wavelength). In vertical space, each UCA was placed with a level separation of 40 cm, as

shown in Figure 4.8(a). This arrangement was chosen to avoid antenna mutual coupling

effects [20]. Detailed information of antenna orientation within the array, with respect

to true north, is presented in Figure 4.9. As shown in the figure, indeces A2/F4, A25/F8,

A29/F9, A12/F3, A22/F7, A34/F12, A11/F2, A14/F5, A30/F11, A3/F1, A17/F6 and

A31/F10 represent AP1 to AP12 antennas, respectively.

4.4. ACCESS POINT ANTENNA ARRAY 67

(a) AP installed transmission tower

(b) AP array on the tower

Figure 4.7: AP transmission tower

(a) Antenna Array Structure (b) AP folded dipole antenna

Figure 4.8: AP antenna mode and photo showing actual AP antenna element


Figure 4.9: AP antenna orientation (degree from true north)

4.5. USER TERMINAL ANTENNA 69

4.5 User Terminal Antenna

As stated in the previous section, six UTs were positioned around the AP in farmlands.

Out of the six UT sites, five were (except UT2) placed near existing residential houses,

representing a practical deployment of fixed wireless broadband services in rural areas.

The UT2 was placed close to the AP in order to verify the robustness of the system from

near-far effects. At each UT site, a highly directional commercial Yagi antenna (ZCG

Scalar Y809) was used as the UT transmitting antenna. The main lobe of the UT antenna

was pointed towards the AP site at each of the UT sites. Figure 4.10 illustrates the UT1

Yagi antenna and the UT1 Yagi antenna directed towards the AP.

(a) UT Yagi antenna

(b) UT1 antenna placed near a rural residence

Figure 4.10: Photo showing Yagi antenna used at UT1 site

The distances from the UTs to the AP ranged from 10 m to 8.4 km. At each UT

site, Yagi antennas were mounted above the local clutter. The UT1, UT3, UT5 and

UT6 antennas were mounted on masts at a 9 m height. The height of the UT4 mast

was 6 m due to logistical limitation. The UT2 was on a tripod approximately 1.5 m

height from the ground as it was installed in the demonstration site for the visitors

to observe. Each UT antenna had 9 elements, 11.5 dBd nominal gain, and vertically

polarised. The radiation pattern and the technical specification of the UT antenna are

shown in Figure 4.11 and Table 4.3, respectively.


Figure 4.11: Sample UT radiation pattern

Table 4.3: UT Antenna Specifications [7]

Model Y809

Construction Aluminium

Maximum Bandwidth 60 MHz

Frequency range 616-676 MHz

Number of elements 9

Nominal gain 11.5 dBd

Polarisation Vertical

Return loss Better than -15 dB

VSWR Better than 1.5:1

Impedance 50 ohms

E-plane at 3 dB 34

H-plane at 3 dB 42

Front-to-back ratio 15 dB

4.6. WEATHER DATA COLLECTION 71

4.6 Weather Data Collection

A Davis Vantage Pro2 [128] wireless weather station was selected to measure weather

conditions at the measurement site. It includes a Vantage Pro2 console, integrated sensor

suite and mounting hardware. The connection from the outdoor integrated sensor suite

to data logger and console was established through a wireless link which supports a

200-250 m distance. This weather station is suitable to collect weather data in outdoor

environments because its outdoor integrated sensor suite can be battery powered. The

integrated sensor suite includes a rain collector, temperature and humidity sensors, an

anemometer, and a 12 m anemometer cable.

The Davis data logger can be connected to the weather station through a USB inter-

face to store weather data when the weather station is not connected to the computer.

The weather station and the data logger support logging intervals of 1, 5, 10, 15, 30, 60,

and 120 minutes. Subsequently, the stored data in the data logger can be exported to a

computer through the Davis WeatherLink software.

The weather station was mounted on a tripod and placed near the AP to measure

weather conditions as shown in Figure 4.12. Wind speed, rain intensity, humidity, baro-

metric pressure, solar radiation and air density were recorded at 60 s logging intervals.

Weather data was collected in parallel with the channel measurements over six days.

Weather data was recorded from 4:17 p.m. on Day 1 to 9:29 a.m. on Day 6. Before

obtaining data, system times of the MUSA-MIMO-OFDM demonstrator and weather

station were synchronised in order to evaluate any correlation between the received

power and weather conditions in time.

Subsequently, weather data stored in the data logger was extracted using the Davis

Weatherlink software and converted to a text file. This weather data file was imported

to Matlab software for further processing and analysis purposes. Figure 4.13 shows

a weather data sample obtained from the Weatherlink software. Table 4.4 illustrates

the maximum and the minimum values of weather parameters measured during the

experiments. An analysis on channel measurement and weather data collected from

this experiments will be presented from Section 4.9 onwards of this chapter.


Figure 4.12: Weather station placed at the AP

Figure 4.13: Weather data gathered from Weatherlink software

4.7. DATA FILES NAMING 73

Table 4.4: Measured weather parameters

Weather Parameter Minimum Maximum

Wind Speed 0 m/s 12.5 m/s

Rain Intensity 0 mm/hr 2.3 mm/hr

Temperature 8.2 C 19.2 C

Humidity 61% 91%

Barometric Pressure 100.7 kPa 102.3 kPa

Air Density 1.15 kg/m3 1.21 kg/m3

Solar Radiation 0 W/m2 1482 W/m2

4.7 Data Files Naming

During the experiments, each snapshot of the channel was saved as a separate data file.

Therefore, each data file is a snapshot of the channel for a given time instance. Each of

these data files were organised as three dimensional matrices, with 12×6×1705 complex

channel coefficient entries. In order to find the measurement time of the snapshot, the

data file was named with the date and time (e.g. channel 20101215082907.mat for the

date 15th of December, 2010, and time 08:29:07).

4.8 Data Analysis Platform

A large amount of computational power and storage resources were required for the

data analysis process. Therefore, QUT’s High Performance Computing (HPC) facility

was used to allocate large memory and storage resources while processing the channel

measurement data. Matlab1 software was used to develop programs and functions in

order to analyse data. Processing a large number of channel coefficients using Matlab

(more than 1.8 billion in many data files) required memory resources beyond a single

personal computer. Therefore, simulations related to this research were conducted on

QUT’s HPC platform (SGI Altix XE Computational Cluster) which has the following

configuration.

1Matlab Version 7.9 R2009b developed and distributed by the Math Works Inc.


• SUSE Linux Operating System

• 1316 × 64 bit Intel Xeon Cores (2.66GHz)

• 27.5 TeraFlop Theoretical (Double Precision), 47.9 TeraFlop (Single Precision)

• 88 compute nodes of six/eight core with dual processor configuration

• 9,376 GB of main memory

4.9 Measured MUSA-MIMO-OFDM channel

4.9.1 Snapshot Plots of Measured Channel

In this section, measured uplink MUSA-MIMO-OFDM channels were analysed. In this

thesis, a sub-channel is defined as the channel between any AP antenna and UT antenna,

for a given sub-carrier. Figure 4.14 illustrates a snapshot of 12×6×1705 sub-channels

created by 12 AP antennas, 6 UT antennas and 1705 sub-carriers. This sample snapshot

was taken on the fifth measurement day (Day 5) at 10:00:05 a.m. In this snapshot,

each column and row represents an AP and UT antenna, respectively. Hence, each sub-

plot represents an AP-UT combination. The Y-axis of each sub-plot represents relative

channel power in dB and the X-axis covers 7 MHz bandwidth, which includes 1705 sub-

carriers.

4.9. MEASURED MUSA-MIMO-OFDM CHANNEL 75

−2

02

−40

−20020

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1−A

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Relative channel power (dB)

−2

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4.9.2 Channel Variation Plots in Time

This section analyses how much variations do rural MUSA-MIMO-OFDM sub-channels

experience in time. To observe these variations, a movie file was created by appending

snapshots taken in different time instances. Snapshot movie file has confirmed that, for

a given sub-channel, similar time variation effects were observed for all OFDM sub-

carriers. Therefore, the following analysis focuses on time variation effects for a single

OFDM sub-carrier.

Measured sub-channels for a single OFDM sub-carrier in Day 5 for a 5 hour time

window, are shown in Figure 4.15 and 4.16. Figure 4.15 represents sub-channels created

by AP antennas 1-6 and 6 UTs. Also, Figure 4.16 represents sub-channels created by AP

antennas 7-12 and 6 UTs. Each sub-plot of the figures presents power plots for a given

AP and 6 UT antenna combinations.

Table 4.5: STD of channel power for 72 sub-channels over a 5 hour measurementwindow

STD of sub-channels UT1 UT2 UT3 UT4 UT5 UT6dB dB dB dB dB dB

AP1 0.98 1.03 1.16 1.01 1.12 1.64AP2 1.07 1.11 1.18 1.15 1.13 1.10AP3 0.76 0.90 0.86 0.70 0.80 0.64AP4 1.03 1.04 1.16 1.04 1.12 1.07AP5 0.86 0.86 0.97 0.91 0.66 0.63AP6 0.74 0.70 0.76 0.81 0.78 0.71AP7 1.09 0.76 1.27 0.87 0.80 0.67AP8 1.32 0.81 1.41 1.17 0.62 0.58AP9 0.89 1.38 1.06 1.81 0.81 0.50

AP10 1.22 1.40 1.28 1.21 1.21 1.19AP11 0.73 0.73 0.89 0.77 0.97 0.81AP12 0.88 0.85 1.05 0.91 1.82 1.08

Table 4.5 presents Standard-deviation (STD) values for 72 sub-channels for the se-

lected 5 hour measurement window. The minimum STD value of 0.5 dB was recorded

by AP9-UT6 sub-channel and the maximum of 1.81 dB was recorded by sub-channel

AP12-UT2. No deep fading in any of the 72 sub-channels were observed during this

measurement window. This is due to the fact that the measurements were obtained from


a fixed wireless system, rather than from a mobile wireless system. Moreover, as verified

by terrain analysis in Chapter 5, dominant paths from all UTs to all AP antennas were

available during the measurements. Due to the aforementioned reasons, less variations

were observed for the 72 sub-channels over time, as shown in Figure 4.15 and 4.16.

Using channel measurement data, further studies were conducted in the rest of the

sections of this chapter. These studies include:

• Analysis of channel statistics and distribution functions for different UTs around

the AP

• Analysis of channel correlation between different sub-channels

• Analysis of channel correlation with respect to different sub-carriers

• Identifying relationships between the channel power and weather parameters

Channel measurement data was used to validate the deterministic model, and to

analyse channel capacity in rural environments in Chapter 5 and 6, respectively.


10.0

0 a.

m.

11 a

.m.

12.0

0 p.

m.

1.00

p.m

.2.

00 p

.m.

3.00

p.m

.−

40

−20020

A

P1−

UT

1A

P1−

UT

2A

P1−

UT

3A

P1−

UT

4A

P1−

UT

5A

P1−

UT

6

10.0

0 a.

m.

11 a

.m.

12.0

0 p.

m.

1.00

p.m

.2.

00 p

.m.

3.00

p.m

.−

40

−20020

A

P2−

UT

1A

P2−

UT

2A

P2−

UT

3A

P2−

UT

4A

P2−

UT

5A

P2−

UT

6

10.0

0 a.

m.

11 a

.m.

12.0

0 p.

m.

1.00

p.m

.2.

00 p

.m.

3.00

p.m

.−

40

−20020


A

P3−

UT

1A

P3−

UT

2A

P3−

UT

3A

P3−

UT

4A

P3−

UT

5A

P3−

UT

6

10.0

0 a.

m.

11 a

.m.

12.0

0 p.

m.

1.00

p.m

.2.

00 p

.m.

3.00

p.m

.−

40

−20020

A

P4−

UT

1A

P4−

UT

2A

P4−

UT

3A

P4−

UT

4A

P4−

UT

5A

P4−

UT

6

10.0

0 a.

m.

11 a

.m.

12.0

0 p.

m.

1.00

p.m

.2.

00 p

.m.

3.00

p.m

.−

40

−20020

A

P5−

UT

1A

P5−

UT

2A

P5−

UT

3A

P5−

UT

4A

P5−

UT

5A

P5−

UT

6

10.0

0 a.

m.

11 a

.m.

12.0

0 p.

m.

1.00

p.m

.2.

00 p

.m.

3.00

p.m

.−

40

−20020

Tim

e

A

P6−

UT

1A

P6−

UT

2A

P6−

UT

3A

P6−

UT

4A

P6−

UT

5A

P6−

UT

6

Figu

re4.

15:R

elat

ive

chan

nelp

ower

forA

P1-

6×6

UT

ante

nna

com

bina

tions

fora

5ho

urm

easu

rem

entw

indo

win

Day

5


10.0

0 a.

m.

11 a

.m.

12.0

0 p.

m.

1.00

p.m

.2.

00 p

.m.

3.00

p.m

.−

40

−20020

A

P7−

UT

1A

P7−

UT

2A

P7−

UT

3A

P7−

UT

4A

P7−

UT

5A

P7−

UT

6

10.0

0 a.

m.

11 a

.m.

12.0

0 p.

m.

1.00

p.m

.2.

00 p

.m.

3.00

p.m

.−

40

−20020

A

P8−

UT

1A

P8−

UT

2A

P8−

UT

3A

P8−

UT

4A

P8−

UT

5A

P8−

UT

6

10.0

0 a.

m.

11 a

.m.

12.0

0 p.

m.

1.00

p.m

.2.

00 p

.m.

3.00

p.m

.−

40

−20020


A

P9−

UT

1A

P9−

UT

2A

P9−

UT

3A

P9−

UT

5A

P9−

UT

6

10.0

0 a.

m.

11 a

.m.

12.0

0 p.

m.

1.00

p.m

.2.

00 p

.m.

3.00

p.m

.−

40

−20020

A

P10

−U

T1

AP

10−

UT

2A

P10

−U

T3

AP

10−

UT

4A

P10

−U

T5

AP

10−

UT

6

10.0

0 a.

m.

11 a

.m.

12.0

0 p.

m.

1.00

p.m

.2.

00 p

.m.

3.00

p.m

.−

40

−20020

A

P11

−U

T1

AP

11−

UT

2A

P11

−U

T3

AP

11−

UT

4A

P11

−U

T5

AP

11−

UT

6

10.0

0 a.

m.

11 a

.m.

12.0

0 p.

m.

1.00

p.m

.2.

00 p

.m.

3.00

p.m

.−

40

−20020

Tim

e

A

P12

−U

T1

AP

12−

UT

2A

P12

−U

T3

AP

12−

UT

4A

P12

−U

T6

Figu

re4.

16:R

elat

ive

chan

nelp

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12×

6U

Tan

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ra5

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sure

men

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inD

ay5


4.10 Channel Statistics

Wireless channels experience fading due to the constructive and destructive addition of

different multi-path components introduced by the channel between Tx and Rx [129].

As stated in Chapter 2, Rayleigh and Ricean distributions are the most popular fading

distributions for modeling wireless channels. Rayleigh distribution is assumed when a

sufficiently large number of equal power multi-path components with different phases

are present at the Rx. On the other hand, a Ricean distribution is assumed when a non-

fading signal component is present, such as in LoS path propagation [32].

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

Value

Cum

ulat

ive

Pro

babi

lity

Cumulative Distribution Function

empiricalriceanrayleigh

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.1

−0.05

0

0.05

0.1

Value

Err

or

CDF Error

riceanrayleigh

Figure 4.17: Goodness-of-fit test to identify best fitting distribution

In this thesis, the most suitable fading distribution was selected by comparing the

empirical channel distribution with a set of hypothesised distributions (Rayleigh and

Ricean) using the goodness-of-fit [100] as the selection criteria. For this task, a Matlab

function was developed to find the best fitting Rayleigh and Ricean distributions for

the measured data with minimum fitting error as illustrated in Figure 4.17. Among the

selected Rayleigh and Ricean curves, the best fitting curve was selected by considering

minimum fitting error (among distribution curves) as the selection criteria as shown in

4.10. CHANNEL STATISTICS 81

Figure 4.17. Through this step, it was identified that the Ricean fading distribution (com-

pared to Rayleigh fading distribution) better suited the empirical channel distribution.

This verification agrees with the literature since the Ricean distribution is assumed when

a non-fading signal component is present, such as LoS path propagation [32].

Figure 4.18 shows the empirical channel distributions and the best fitting theoretical

Ricean distribution plots with different Ricean K-factors for 6 sub-channels selected

from 6 UTs (with AP1 antenna combination). Also, this figure shows the difference

(error) between the empirical and theoretical distributions. Although, due to space

limitations 6 selected sub-channels were presented in Figure 4.18, all 72 sub-channels

(12AP×6UT) exhibited Ricean fading distribution with similar Ricean K-factor values.

In this analysis, Ricean CDF for each AP-UT sub-channel was presented with the best

fitting Ricean K-factor. For instance, for AP1-UT1, K=27 gives the best fitting Ricean

CDF. With this best fitting Ricean K-factor, the maximum deviation between empirical

CDF and Ricean CDF was recorded as 0.025 (2.5%) error. Also, for all the CDFs the

maximum error between empirical CDF and Ricean CDF is 5.7%. This error has been

included as a measure of the goodness-of-fit. As the maximum error that can be observed

is 5.7%, it can be stated that the error depicted in Figure 4.18 is small.

In a Ricean fading distribution, the K-factor is defined as the ratio between the

deterministic (direct path) signal power and the variance of the multipath [32]. The

K-factor indicates the severity of the fading in the wireless channel [129]. For instance,

when K=0, it represents a Rayleigh channel with deep fading. When K=∞, it represents

a channel without fading [32]. Even though mobile channels in urban environments

with dominant LoS paths record K factors less than 10 dB, experiments on fixed wire-

less channels with suburban environments have recorded K-factor values greater than

20 dB [79]. This is due to the fact that mobile wireless channels in environments

undergo more fading compared to fixed wireless channels. In this study, the channel

measurement results obtained in rural environments exhibit higher Ricean K-factors

(greater than 20 dB). This is due to the fact that, wireless channels created by the Ngara

regional access solution do not experience temporal variations, which occur due to the

movement of the Rx or Tx nodes, but by the movements in the environment as it is a

“fixed” wireless broadband installation.


0 2.6 4.2 5.40

0.5

1

Empirical and theorical CDFs for UT1_AP1

CD

FU

T1_A

P1

EmpiricalRicean(K=27)

0 2.6 4.2 5.4−0.1

−0.05

0

0.05

0.1

Difference (Error) for UT1_AP1

Err

or

−7 −1 1.4 30

0.5

1


CD

FU

T2_A

P1

EmpiricalRicean(K=23)

−7 −1 1.4 3−0.1

−0.05

0

0.05

0.1


Err

or

−5.5 −3.6 −2.20

0.5

1


CD

FU

T3_A

P1

EmpiricalRicean(K=25.4)

0.1 −5.5 −3.6 −2.2−0.1

−0.05

0

0.05

0.1


Err

or

0 1.7 30

0.5

1


CD

FU

T4_A

P1


−3 0 1.7 3 4−0.1

−0.05

0

0.05

0.1


Err

or

−17 −9.5 −6.8 −5.20

0.5

1


CD

FU

T5_A

P1


−17 −9.5 −6.8 −5.2−0.1

−0.05

0

0.05

0.1


Err

or

−26 −21.5 −20 −18 −170

0.5

1


CD

FU

T6_A

P1


−26 −21.5 −20 −18 −17−0.1

−0.05

0

0.05

0.1


Err

or

Figure 4.18: A comparison of theoretical and empirical CDF plots for 6 selected sub-channels from 6 UTs

4.11. CHANNEL CORRELATION MATRIX 83

4.11 Channel Correlation Matrix

This section analyses the spatial structure of the AP-UT combinations, based on the

channel measurement data. This analysis demonstrates the degree of correlation between

different sub-channels. For instance, the analysis will uncover whether the measured

sub-channels were fully correlated, fully de-correlated or partially correlated.

If a snapshot of the measured channel for a selected sub-carrier is given by H12×6,

then H12×6 can be defined as:

H12,6 =

α1,1 α1,2 · · · α1,6

α2,1 α2,2 · · · α2,6

......

. . ....

α12,1 α12,2 · · · α12,6

where αm,n is the complex channel coefficient between mth Rx and nth Tx antenna.

Full channel correlation matrix sufficiently characterises the spatial structure of a

measurement system. Therefore, full channel correlation matrix is analysed in this study.

Full channel correlation matrix R is given by [130]:

R72×72 = Eh72×1hH

72×1

(4.2)

where h72×1 = vec(H12×6) and vec(:) operator stacks the columns of a matrix into

a vector. E stands for the mathematical expectation operator and ()H represents the

conjugate transpose operation. In order to calculate R72×72, channel coefficients from a

five hour measurement window (more than 3000 samples as shown in Figure 4.15 and

4.16) were selected.


A1−

U1

A5−

U1

A9−

U1

A1−

U2

A5−

U2

A9−

U2

A1−

U3

A5−

U3

A9−

U3

A1−

U4

A5−

U4

A9−

U4

A1−

U5

A5−

U5

A9−

U5

A1−

U6

A5−

U6

A9−

U6A

12−

U6

A1−

U1

A5−

U1

A9−

U1

A1−

U2

A5−

U2

A9−

U2

A1−

U3

A5−

U3

A9−

U3

A1−

U4

A5−

U4

A9−

U4

A1−

U5

A5−

U5

A9−

U5

A1−

U6

A5−

U6

A9−

U6

A12

−U

600.

51

00.

1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Cor

rela

tion

Coe

ffic

ient

Figu

re4.

19:F

ullc

hann

elco

rrel

atio

nm

atri

xfo

r12A

P×6U

Tan

tenn

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ns


Figure 4.19 represents the correlation coefficient between all AP-UT sub-channel

combinations. It shows full channel correlation matrix for a selected sub-carrier. The

color scale in Figure 4.19 denotes correlation coefficient variation between 0 and 1. As

shown in the figure, lower correlation coefficients (less than 0.1) and higher correlation

coefficients (greater than 0.9) are represented in blue and maroon colors, respectively.

In this figure, Each AP-UT combination is denoted as A-U due to space limitations.

Each column represents the correlation between one sub-channel against all other sub-

channels. For instance, column A1-U1 represents the correlation coefficient between

AP1-UT1 sub-channel and all 72 sub-channels, stacked into a vector.

In row A1-U1, the first 12 elements represent correlation coefficients between the

AP1-UT1 sub-channel and APX-UT1 sub-channels, where 1 ≤ X ≤ 12. Correlation

coefficients between the AP1-UT1 sub-channel and APX-UT1 sub-channels corresponds

to an AP-UT link configuration shown in Figure 4.20(a). As the link distance becomes

larger, the correlation coefficient between such sub-channels increases. As shown in

Figure 4.19, such channels are highly correlated with correlation coefficients close to 1.

In column 1, elements 13-72 represent correlation coefficients between AP1-UT1

sub-channel and APX-UTY sub-channels, where 1 ≤ X ≤ 12 and 2 ≤ Y ≤ 6. Correlation

coefficients between AP1-UT1 sub-channel and APX-UTY sub-channels corresponds to

an AP-UT link configuration shown in Figure 4.20(b). Therefore, such AP-UT sub-

channels are uncorrelated as shown in Figure 4.19 with a correlation coefficient close to

0. This is due to the fact that in the proposed MUSA-MIMO system, UTs are spatially

separated, and hence sub-channels between different users are uncorrelated.

AP2

AP1

UT1

(a) Correlated AP1-UT1 and AP2-UT1 sub-channels

UT2

UT1

AP2

AP1

(b) Uncorrelated AP1-UT1 and AP2-UT2 sub-channels

Figure 4.20: An example of correlated and uncorrelated sub-channels


As shown in the above analysis, for the uplink, each AP antenna (Rx) ‘sees’ un-

correlated channels from each UT (Tx). On the other hand, each UT ‘sees’ correlated

channels from AP antennas. Aforementioned results are based on the analysis of a single

OFDM sub-carrier. The next analysis will focus on whether all OFDM sub-carriers show

the same behavior with respect to channel correlation.

Figures 4.21-4.26 represent correlation coefficients between different sub-channels,

for measured 1705 OFDM sub-carriers. Figure 4.21 represents correlation coefficients

between sub-channels AP1-UT1 (1-1 as shown in the figure) and 72 sub-channels. Each

sub-plot in Figure 4.21 shows correlation coefficients for 1705 OFDM sub-carriers. Sim-

ilarly, Figures 4.22-4.26 represent correlation coefficients between sub-channels AP1-

UT2 (1-2), AP1-UT3 (1-3), AP1-UT4 (1-4), AP1-UT5 (1-5), AP1-UT6 (1-6) and 72

sub-channels, respectively.

According to the correlation plots shown below, it can be seen that all OFDM sub-

carriers experience similar correlation between any 2 sub-channels. Therefore, all OFDM

sub-carriers agree with the correlation plot shown in Figure 4.19. From these results, it

can be concluded that for any given OFDM sub-carrier, each AP antenna ‘sees’ uncor-

related channels from each UT. Also, each UT ‘sees’ correlated channels from the AP

antennas.


0 17050

0.51

1−1&1−1

0 17050

0.51

1−1&2−1

0 17050

0.51

1−1&3−1

0 17050

0.51

1−1&4−1

0 17050

0.51

1−1&5−1

0 17050

0.51

1−1&6−1

0 17050

0.51

1−1&7−1

0 17050

0.51

1−1&8−1

0 17050

0.51

1−1&9−1

0 17050

0.51

1−1&10−1

0 17050

0.51

1−1&11−1

0 17050

0.51

1−1&12−1

0 17050

0.51

1−1&1−2

0 17050

0.51

1−1&2−2

0 17050

0.51

1−1&3−2

0 17050

0.51

1−1&4−2

0 17050

0.51

1−1&5−2

0 17050

0.51

1−1&6−2

0 17050

0.51

1−1&7−2

0 17050

0.51

1−1&8−2

0 17050

0.51

1−1&9−2

0 17050

0.51

1−1&10−2

0 17050

0.51

1−1&11−2

0 17050

0.51

1−1&12−2

0 17050

0.51

1−1&1−3

0 17050

0.51

1−1&2−3

0 17050

0.51

1−1&3−3

0 17050

0.51

1−1&4−3

0 17050

0.51

1−1&5−3

0 17050

0.51

1−1&6−3

0 17050

0.51

1−1&7−3

Cor

rela

tion

Coe

ffic

ient

0 17050

0.51

1−1&8−3

0 17050

0.51

1−1&9−3

0 17050

0.51

1−1&10−3

0 17050

0.51

1−1&11−3

0 17050

0.51

1−1&12−3

0 17050

0.51

1−1&1−4

0 17050

0.51

1−1&2−4

0 17050

0.51

1−1&3−4

0 17050

0.51

1−1&4−4

0 17050

0.51

1−1&5−4

0 17050

0.51

1−1&6−4

0 17050

0.51

1−1&7−4

0 17050

0.51

1−1&8−4

0 17050

0.51

1−1&9−4

0 17050

0.51

1−1&10−4

0 17050

0.51

1−1&11−4

0 17050

0.51

1−1&12−4

0 17050

0.51

1−1&1−5

0 17050

0.51

1−1&2−5

0 17050

0.51

1−1&3−5

0 17050

0.51

1−1&4−5

0 17050

0.51

1−1&5−5

0 17050

0.51

1−1&6−5

0 17050

0.51

1−1&7−5

0 17050

0.51

1−1&8−5

0 17050

0.51

1−1&9−5

0 17050

0.51

1−1&10−5

0 17050

0.51

1−1&11−5

0 17050

0.51

1−1&12−5

0 17050

0.51

1−1&1−6

0 17050

0.51

1−1&2−6

0 17050

0.51

1−1&3−6

0 17050

0.51

1−1&4−6

0 17050

0.51

1−1&5−6

0 17050

0.51

1−1&6−6

0 17050

0.51

1−1&7−6

0 17050

0.51

1−1&8−6

0 17050

0.51

1−1&9−6

Subcarrier Number0 1705

00.5

11−1&10−6

0 17050

0.51

1−1&11−6

0 17050

0.51

1−1&12−6

Figure 4.21: Correlation coefficients between AP1-UT1 (1-1 in figure) and 72 sub-channels (12AP×6UT) for 1705 sub-carriers


0 17050

0.51

1−2&1−1

0 17050

0.51

1−2&2−1

0 17050

0.51

1−2&3−1

0 17050

0.51

1−2&4−1

0 17050

0.51

1−2&5−1

0 17050

0.51

1−2&6−1

0 17050

0.51

1−2&7−1

0 17050

0.51

1−2&8−1

0 17050

0.51

1−2&9−1

0 17050

0.51

1−2&10−1

0 17050

0.51

1−2&11−1

0 17050

0.51

1−2&12−1

0 17050

0.51

1−2&1−2

0 17050

0.51

1−2&2−2

0 17050

0.51

1−2&3−2

0 17050

0.51

1−2&4−2

0 17050

0.51

1−2&5−2

0 17050

0.51

1−2&6−2

0 17050

0.51

1−2&7−2

0 17050

0.51

1−2&8−2

0 17050

0.51

1−2&9−2

0 17050

0.51

1−2&10−2

0 17050

0.51

1−2&11−2

0 17050

0.51

1−2&12−2

0 17050

0.51

1−2&1−3

0 17050

0.51

1−2&2−3

0 17050

0.51

1−2&3−3

0 17050

0.51

1−2&4−3

0 17050

0.51

1−2&5−3

0 17050

0.51

1−2&6−3

0 17050

0.51

1−2&7−3

Cor

rela

tion

Coe

ffic

ient

0 17050

0.51

1−2&8−3

0 17050

0.51

1−2&9−3

0 17050

0.51

1−2&10−3

0 17050

0.51

1−2&11−3

0 17050

0.51

1−2&12−3

0 17050

0.51

1−2&1−4

0 17050

0.51

1−2&2−4

0 17050

0.51

1−2&3−4

0 17050

0.51

1−2&4−4

0 17050

0.51

1−2&5−4

0 17050

0.51

1−2&6−4

0 17050

0.51

1−2&7−4

0 17050

0.51

1−2&8−4

0 17050

0.51

1−2&9−4

0 17050

0.51

1−2&10−4

0 17050

0.51

1−2&11−4

0 17050

0.51

1−2&12−4

0 17050

0.51

1−2&1−5

0 17050

0.51

1−2&2−5

0 17050

0.51

1−2&3−5

0 17050

0.51

1−2&4−5

0 17050

0.51

1−2&5−5

0 17050

0.51

1−2&6−5

0 17050

0.51

1−2&7−5

0 17050

0.51

1−2&8−5

0 17050

0.51

1−2&9−5

0 17050

0.51

1−2&10−5

0 17050

0.51

1−2&11−5

0 17050

0.51

1−2&12−5

0 17050

0.51

1−2&1−6

0 17050

0.51

1−2&2−6

0 17050

0.51

1−2&3−6

0 17050

0.51

1−2&4−6

0 17050

0.51

1−2&5−6

0 17050

0.51

1−2&6−6

0 17050

0.51

1−2&7−6

0 17050

0.51

1−2&8−6

0 17050

0.51

1−2&9−6


00.5

11−2&10−6

0 17050

0.51

1−2&11−6

0 17050

0.51

1−2&12−6



0 17050

0.51

1−3&1−1

0 17050

0.51

1−3&2−1

0 17050

0.51

1−3&3−1

0 17050

0.51

1−3&4−1

0 17050

0.51

1−3&5−1

0 17050

0.51

1−3&6−1

0 17050

0.51

1−3&7−1

0 17050

0.51

1−3&8−1

0 17050

0.51

1−3&9−1

0 17050

0.51

1−3&10−1

0 17050

0.51

1−3&11−1

0 17050

0.51

1−3&12−1

0 17050

0.51

1−3&1−2

0 17050

0.51

1−3&2−2

0 17050

0.51

1−3&3−2

0 17050

0.51

1−3&4−2

0 17050

0.51

1−3&5−2

0 17050

0.51

1−3&6−2

0 17050

0.51

1−3&7−2

0 17050

0.51

1−3&8−2

0 17050

0.51

1−3&9−2

0 17050

0.51

1−3&10−2

0 17050

0.51

1−3&11−2

0 17050

0.51

1−3&12−2

0 17050

0.51

1−3&1−3

0 17050

0.51

1−3&2−3

0 17050

0.51

1−3&3−3

0 17050

0.51

1−3&4−3

0 17050

0.51

1−3&5−3

0 17050

0.51

1−3&6−3

0 17050

0.51

1−3&7−3

Cor

rela

tion

Coe

ffic

ient

0 17050

0.51

1−3&8−3

0 17050

0.51

1−3&9−3

0 17050

0.51

1−3&10−3

0 17050

0.51

1−3&11−3

0 17050

0.51

1−3&12−3

0 17050

0.51

1−3&1−4

0 17050

0.51

1−3&2−4

0 17050

0.51

1−3&3−4

0 17050

0.51

1−3&4−4

0 17050

0.51

1−3&5−4

0 17050

0.51

1−3&6−4

0 17050

0.51

1−3&7−4

0 17050

0.51

1−3&8−4

0 17050

0.51

1−3&9−4

0 17050

0.51

1−3&10−4

0 17050

0.51

1−3&11−4

0 17050

0.51

1−3&12−4

0 17050

0.51

1−3&1−5

0 17050

0.51

1−3&2−5

0 17050

0.51

1−3&3−5

0 17050

0.51

1−3&4−5

0 17050

0.51

1−3&5−5

0 17050

0.51

1−3&6−5

0 17050

0.51

1−3&7−5

0 17050

0.51

1−3&8−5

0 17050

0.51

1−3&9−5

0 17050

0.51

1−3&10−5

0 17050

0.51

1−3&11−5

0 17050

0.51

1−3&12−5

0 17050

0.51

1−3&1−6

0 17050

0.51

1−3&2−6

0 17050

0.51

1−3&3−6

0 17050

0.51

1−3&4−6

0 17050

0.51

1−3&5−6

0 17050

0.51

1−3&6−6

0 17050

0.51

1−3&7−6

0 17050

0.51

1−3&8−6

0 17050

0.51

1−3&9−6


00.5

11−3&10−6

0 17050

0.51

1−3&11−6

0 17050

0.51

1−3&12−6



0 17050

0.51

1−4&1−1

0 17050

0.51

1−4&2−1

0 17050

0.51

1−4&3−1

0 17050

0.51

1−4&4−1

0 17050

0.51

1−4&5−1

0 17050

0.51

1−4&6−1

0 17050

0.51

1−4&7−1

0 17050

0.51

1−4&8−1

0 17050

0.51

1−4&9−1

0 17050

0.51

1−4&10−1

0 17050

0.51

1−4&11−1

0 17050

0.51

1−4&12−1

0 17050

0.51

1−4&1−2

0 17050

0.51

1−4&2−2

0 17050

0.51

1−4&3−2

0 17050

0.51

1−4&4−2

0 17050

0.51

1−4&5−2

0 17050

0.51

1−4&6−2

0 17050

0.51

1−4&7−2

0 17050

0.51

1−4&8−2

0 17050

0.51

1−4&9−2

0 17050

0.51

1−4&10−2

0 17050

0.51

1−4&11−2

0 17050

0.51

1−4&12−2

0 17050

0.51

1−4&1−3

0 17050

0.51

1−4&2−3

0 17050

0.51

1−4&3−3

0 17050

0.51

1−4&4−3

0 17050

0.51

1−4&5−3

0 17050

0.51

1−4&6−3

0 17050

0.51

1−4&7−3

Cor

rela

tion

Coe

ffic

ient

0 17050

0.51

1−4&8−3

0 17050

0.51

1−4&9−3

0 17050

0.51

1−4&10−3

0 17050

0.51

1−4&11−3

0 17050

0.51

1−4&12−3

0 17050

0.51

1−4&1−4

0 17050

0.51

1−4&2−4

0 17050

0.51

1−4&3−4

0 17050

0.51

1−4&4−4

0 17050

0.51

1−4&5−4

0 17050

0.51

1−4&6−4

0 17050

0.51

1−4&7−4

0 17050

0.51

1−4&8−4

0 17050

0.51

1−4&10−4

0 17050

0.51

1−4&11−4

0 17050

0.51

1−4&12−4

0 17050

0.51

1−4&1−5

0 17050

0.51

1−4&2−5

0 17050

0.51

1−4&3−5

0 17050

0.51

1−4&4−5

0 17050

0.51

1−4&5−5

0 17050

0.51

1−4&6−5

0 17050

0.51

1−4&7−5

0 17050

0.51

1−4&8−5

0 17050

0.51

1−4&9−5

0 17050

0.51

1−4&10−5

0 17050

0.51

1−4&11−5

0 17050

0.51

1−4&12−5

0 17050

0.51

1−4&1−6

0 17050

0.51

1−4&2−6

0 17050

0.51

1−4&3−6

0 17050

0.51

1−4&4−6

0 17050

0.51

1−4&5−6

0 17050

0.51

1−4&6−6

0 17050

0.51

1−4&7−6

0 17050

0.51

1−4&8−6

0 17050

0.51

1−4&9−6


00.5

11−4&10−6

0 17050

0.51

1−4&11−6

0 17050

0.51

1−4&12−6

0 17050 0.51

1−4&9−4



0 17050

0.51

1−5&1−1

0 17050

0.51

1−5&2−1

0 17050

0.51

1−5&3−1

0 17050

0.51

1−5&4−1

0 17050

0.51

1−5&5−1

0 17050

0.51

1−5&6−1

0 17050

0.51

1−5&7−1

0 17050

0.51

1−5&8−1

0 17050

0.51

1−5&9−1

0 17050

0.51

1−5&10−1

0 17050

0.51

1−5&11−1

0 17050

0.51

1−5&12−1

0 17050

0.51

1−5&1−2

0 17050

0.51

1−5&2−2

0 17050

0.51

1−5&3−2

0 17050

0.51

1−5&4−2

0 17050

0.51

1−5&5−2

0 17050

0.51

1−5&6−2

0 17050

0.51

1−5&7−2

0 17050

0.51

1−5&8−2

0 17050

0.51

1−5&9−2

0 17050

0.51

1−5&10−2

0 17050

0.51

1−5&11−2

0 17050

0.51

1−5&12−2

0 17050

0.51

1−5&1−3

0 17050

0.51

1−5&2−3

0 17050

0.51

1−5&3−3

0 17050

0.51

1−5&4−3

0 17050

0.51

1−5&5−3

0 17050

0.51

1−5&6−3

0 17050

0.51

1−5&7−3

Cor

rela

tion

Coe

ffic

ient

0 17050

0.51

1−5&8−3

0 17050

0.51

1−5&9−3

0 17050

0.51

1−5&10−3

0 17050

0.51

1−5&11−3

0 17050

0.51

1−5&12−3

0 17050

0.51

1−5&1−4

0 17050

0.51

1−5&2−4

0 17050

0.51

1−5&3−4

0 17050

0.51

1−5&4−4

0 17050

0.51

1−5&5−4

0 17050

0.51

1−5&6−4

0 17050

0.51

1−5&7−4

0 17050

0.51

1−5&8−4

0 17050

0.51

1−5&9−4

0 17050

0.51

1−5&10−4

0 17050

0.51

1−5&11−4

0 17050

0.51

1−5&12−4

0 17050

0.51

1−5&1−5

0 17050

0.51

1−5&2−5

0 17050

0.51

1−5&3−5

0 17050

0.51

1−5&4−5

0 17050

0.51

1−5&5−5

0 17050

0.51

1−5&6−5

0 17050

0.51

1−5&7−5

0 17050

0.51

1−5&8−5

0 17050

0.51

1−5&9−5

0 17050

0.51

1−5&10−5

0 17050

0.51

1−5&11−5

0 17050

0.51

1−5&1−6

0 17050

0.51

1−5&2−6

0 17050

0.51

1−5&3−6

0 17050

0.51

1−5&4−6

0 17050

0.51

1−5&5−6

0 17050

0.51

1−5&6−6

0 17050

0.51

1−5&7−6

0 17050

0.51

1−5&8−6

0 17050

0.51

1−5&9−6


00.5

11−5&10−6

0 17050

0.51

1−5&11−6

0 17050

0.51

1−5&12−6

0 17050

0.51

1−5&12−5



0 17050

0.51

1−6&1−1

0 17050

0.51

1−6&2−1

0 17050

0.51

1−6&3−1

0 17050

0.51

1−6&4−1

0 17050

0.51

1−6&5−1

0 17050

0.51

1−6&6−1

0 17050

0.51

1−6&7−1

0 17050

0.51

1−6&8−1

0 17050

0.51

1−6&9−1

0 17050

0.51

1−6&10−1

0 17050

0.51

1−6&11−1

0 17050

0.51

1−6&12−1

0 17050

0.51

1−6&1−2

0 17050

0.51

1−6&2−2

0 17050

0.51

1−6&3−2

0 17050

0.51

1−6&4−2

0 17050

0.51

1−6&5−2

0 17050

0.51

1−6&6−2

0 17050

0.51

1−6&7−2

0 17050

0.51

1−6&8−2

0 17050

0.51

1−6&9−2

0 17050

0.51

1−6&10−2

0 17050

0.51

1−6&11−2

0 17050

0.51

1−6&12−2

0 17050

0.51

1−6&1−3

0 17050

0.51

1−6&2−3

0 17050

0.51

1−6&3−3

0 17050

0.51

1−6&4−3

0 17050

0.51

1−6&5−3

0 17050

0.51

1−6&6−3

0 17050

0.51

1−6&7−3

Cor

rela

tion

Coe

ffic

ient

0 17050

0.51

1−6&8−3

0 17050

0.51

1−6&9−3

0 17050

0.51

1−6&10−3

0 17050

0.51

1−6&11−3

0 17050

0.51

1−6&12−3

0 17050

0.51

1−6&1−4

0 17050

0.51

1−6&2−4

0 17050

0.51

1−6&3−4

0 17050

0.51

1−6&4−4

0 17050

0.51

1−6&5−4

0 17050

0.51

1−6&6−4

0 17050

0.51

1−6&7−4

0 17050

0.51

1−6&8−4

0 17050

0.51

1−6&9−4

0 17050

0.51

1−6&10−4

0 17050

0.51

1−6&11−4

0 17050

0.51

1−6&12−4

0 17050

0.51

1−6&1−5

0 17050

0.51

1−6&2−5

0 17050

0.51

1−6&3−5

0 17050

0.51

1−6&4−5

0 17050

0.51

1−6&5−5

0 17050

0.51

1−6&6−5

0 17050

0.51

1−6&7−5

0 17050

0.51

1−6&8−5

0 17050

0.51

1−6&9−5

0 17050

0.51

1−6&10−5

0 17050

0.51

1−6&11−5

0 17050

0.51

1−6&12−5

0 17050

0.51

1−6&1−6

0 17050

0.51

1−6&2−6

0 17050

0.51

1−6&3−6

0 17050

0.51

1−6&4−6

0 17050

0.51

1−6&5−6

0 17050

0.51

1−6&6−6

0 17050

0.51

1−6&7−6

0 17050

0.51

1−6&8−6

0 17050

0.51

1−6&9−6


00.5

11−6&10−6

0 17050

0.51

1−6&11−6

0 17050

0.51

1−6&12−6


4.12. RECEIVED POWER AND WEATHER PARAMETERS 93

4.12 Received Power and Weather Parameters

As shown in Chapter 2, fixed wireless channels may experience fading due to scattering

by moving objects such as windblown trees or foliage in the environment. Also, as far as

weather parameters are concerned, rain and wind were found to be the major contributors

that introduce temporal variations in outdoor wireless channels. Previous studies [131]

have also shown that temperature and humidity have little or no correlation with the

variations of the received signal level. Moreover, this study has observed that, only wind

speed shows considerable variations in time to match with the variations of received

power of UTs 1-6. Since no rain was observed during the channel measurements, this

study focuses mainly on the effect of wind speed on MUSA-MIMO-OFDM channels.

According to the literature, Ricean K-factor analysis can be performed to understand

the effect of wind speed on MUSA-MIMO-OFDM channels. The key parameter of

Ricean distribution is the Ricean K-factor, which is defined as the power ratio of the fixed

dominant path and fluctuating components [56]. It determines the severity of fading. As

a dominant path for all the sub-channels was present during the experiments, the Ricean

K-factor was calculated, for each OFDM sub-carrier of 12×6 sub-channels, to analyse

the relationship between the wind speed and the Ricean K-factor.

In the literature, several methods have been employed to estimate the Ricean K-

factor. One method is to compute the distributions of the measured signal power and

compare it to a set of hypothesis distributions using a suitable goodness-of-fit test [100].

Another method is to compute a maximum-likelihood estimate from an expectation/maximisation

(EM) algorithm [101]. As the above methods are cumbersome and time consuming,

moment-method estimation of the Ricean K-factor [102] method was used in this study.

It is a simple and rapid method based on calculating the first and second moments of the

time-series data. The equations employed from moment-method to calculate the Ricean

K-factor are discussed below.

The complex signal path gain of a narrowband wireless channel can be written as:

g(t) = V + v(t) (4.3)


where V is the complex constant and v(t) is a complex, zero-mean random time

variation caused by moving scatterers such as wind-blown foliage. Since each OFDM

sub-carrier is considered separately, a narrowband wireless channel is assumed for this

analysis. The power gain Gp of the complex signal path gain is given by |g(t)|2. In order

to calculate the first moment or the time average of Gp for data samples, the following

equation [102] was implemented.

Ga = |V |2 + |v(t)|2 + 2Re(V × v(t)) (4.4)

Then, the second moment or the rms fluctuation of Gp about Ga is given by:

Gv =[(Gp −Ga)2

] 12 (4.5)

Using further calculations as stated in [102] and defining σ2 ≡ |v(t)|2, dominant

power component (|V |2) and fluctuating power component σ2 can be written in terms of

first and second moments as [102]:

|V |2 =[(G2

a −G2v)] 1

2 (4.6)

σ2 = Ga −[(G2

a −G2v)] 1

2 (4.7)

Then, the Ricean K-factor can be calculated using:

K =|V |2

σ2 (4.8)

The equations above were used to calculate the Ricean K-factor for each OFDM sub-

carrier and each MUSA-MIMO sub-channel. The K-factor was derived for every one

minute, to match with the weather data samples. Thirty samples were included when

obtaining the average in Equation 4.8. In literature [5], more than 9 samples were con-

sidered to be satisfactory to average out most of the fluctuations due to random fading,


in order to get a good estimate of σ2. Figures 4.27 and 4.28 show the Ricean K-factor

and relative channel power for six links (AP1-UTX, where 1 ≤ X ≤ 6), wind speed, rain

intensity, humidity, temperature, barometric pressure and air density for a 5 hour window

for Day 2. As presented in the figures, temperature, barometric pressure and air density

show slow variations compared to the K-factor variations. No rain was recorded during

this measurement window. Wind speed and humidity show considerable variations over

time. However, literature has verified that humidity has little or no correlation [131] with

the received signal. Therefore, further analysis has been conducted to find correlation

between received power and wind speed.

Figure 4.29 presents the relation plots between the wind speed and the Ricean K-

factor. Each subplot in Figure 4.29, represents a sub-channel of 12AP × 6UT combi-

nation and contains data for all OFDM sub-carriers. The X and Y axis of the subplots

represent wind speed in m/s and the Ricean K-factor in dB, respectively. Each of these

subplots contain data samples for wind speeds ranging from 0-11 m/s. According to

these subplots, the Ricean K-factor shows a declining trend with the wind speed. In

order to model this trend, 6×12 sub-channel K-factors were plotted against wind speed

as shown in Figure 4.30.

The trend curve was generated by regression analysis using the Matlab software with

the least fitting error to the experimental data. The proposed trend curve is given by:

y = 0.3x2 − 4x + 26 (4.9)

where x and y represent wind speed in m/s and Ricean K-factor in dB, respectively.

According to Figure 4.30, a saturation effect can be found for the wind speed above

7 m/s. Similar observations (saturation above 6 m/s) has been reported in previous

research work [131]. However, when the wind speed is less than 6 m/s, the trend curve

can be represented as in Equation 4.9.


−10

0

10

UT

1 (

dB

)

10.00 a.m. 11.00 a.m. 12.00 p.m. 1.00 p.m. 2.00 p.m. 3.00 p.m.10

20

30

40

K−

fac U

T1(d

B)

−10

0

10

UT

2 (

dB

)

10.00 a.m. 11.00 a.m. 12.00 p.m. 1.00 p.m. 2.00 p.m. 3.00 p.m.10

20

30

40

K−

fac U

T2 (

dB

)

−10

0

10

UT

3 (

dB

)

10.00 a.m. 11.00 a.m. 12.00 p.m. 1.00 p.m. 2.00 p.m. 3.00 p.m.10

20

30

40

K−

fac U

T3 (

dB

)0

2

4

6

8

Win

d s

pee

d (

m/s

)

10.00 a.m. 11.00 a.m. 12.00 p.m. 1.00 p.m. 2.00 p.m. 3.00 p.m.0

10

20

30

Rai

n (

mm

)

60

80

100

Hum

idit

y (

%)

10.00 a.m. 11.00 a.m. 12.00 p.m. 1.00 p.m. 2.00 p.m. 3.00 p.m.12

14

16

18

20

Tem

p(0

C)

102

102.2

102.4

Pre

ssure

(kP

a)

10.00 a.m. 11.00 a.m. 12.00 p.m. 1.00 p.m. 2.00 p.m. 3.00 p.m.0.070.0720.0740.0760.078

Air

den

sity

(kg/m

3)

Figure 4.27: K-factor, relative received power with weather variations


−10

0

10U

T4 (

dB

)

10.00 a.m. 11.00 a.m. 12.00 p.m. 1.00 p.m. 2.00 p.m. 3.00 p.m.10

20

30

40

K−

fac U

T4(d

B)

−10

0

10

UT

5 (

dB

)

10.00 a.m. 11.00 a.m. 12.00 p.m. 1.00 p.m. 2.00 p.m. 3.00 p.m.10

20

30

40

K−

fac U

T5 (

dB

)

−10

0

10

UT

6 (

dB

)

10.00 a.m. 11.00 a.m. 12.00 p.m. 1.00 p.m. 2.00 p.m. 3.00 p.m.10

20

30

40

K−

fac U

T6 (

dB

)

0

2

4

6

8

Win

d s

pee

d (

m/s

)

10.00 a.m. 11.00 a.m. 12.00 p.m. 1.00 p.m. 2.00 p.m. 3.00 p.m.0

10

20

30

Rai

n (

mm

)

60

80

100

Hum

idit

y (

%)

10.00 a.m. 11.00 a.m. 12.00 p.m. 1.00 p.m. 2.00 p.m. 3.00 p.m.12

14

16

18

20T

emp(0

C)

102

102.2

102.4

Pre

ssure

(kP

a)

10.00 a.m. 11.00 a.m. 12.00 p.m. 1.00 p.m. 2.00 p.m. 3.00 p.m.0.070.0720.0740.0760.078

Air

den

sity

(kg/m

3)

Figure 4.28: K-factor, relative received power with weather variations


Fi

gure

4.29

:K-f

acto

rvs

win

dsp

eed


0 1 2 3 4 5 6 7 80

5

10

15

20

25

30

35

40

Wind Speed (m/s)

Ric

ean

K−

fact

or (

dB)

x − Experimental

y = 0.3x2−4x+26

Figure 4.30: K-factor vs wind speed

Reasons for this trend can be explained as follows. The Ricean K-factor is defined as

the power ratio of the fixed dominant path and fluctuating components. At higher wind

speeds, the K-factor decreases since more contribution from multipath effects (as a result

of more fluctuations) are introduced from nearby windblown trees. Although the LoS

path was not obstructed during the experiments, trees were present in the vicinity of the

AP as shown in Figure 4.11. Therefore, compared to low wind speeds, a small decrease

in the K-factor was observed at high wind speeds. However, from Figure 4.29, it can be

seen that the effect of wind speed on different sub-channels vary due to different AP-UT

orientations. This is due to the fact that the relative geometry of fixed scatters are differ-

ent for different AP-UT orientations [131]. Therefore, a universal weather incorporated

MIMO channel model, which account for the relative geometry of fixed scatterers and

variations of wind speed and rain intensity effects in outdoor environments, is proposed

as future work from this study.


4.13 Summary

This chapter presented rural MUSA-MIMO-OFDM channel measurements and data

analysis procedure. It introduced the measurement environment, AP, UT locations and

antenna related parameters for the deployed MUSA-MIMO-OFDM system. Moreover,

the data collection and data analysis procedure were presented in this chapter.

Instantaneous channel and channel variations over time were analysed in this chapter.

It was shown that rural MUSA-MIMO-OFDM channels which use 641.5 MHz carrier

frequency, under go less variations without deep fades over time. Availability of domi-

nant propagation paths, presence of less scatterers in large open rural environments, and

fixed AP and UTs were identified as the main reasons for these low variations. Moreover,

it was identified that, rural MUSA-MIMO-OFDM channels follow Ricean fading distri-

bution with high K-factor values. These results agree with the similar studies conducted

for fixed wireless broadband links. The next focus of this chapter was to analyse the full

channel correlation matrix of AP-UT combinations using the channel measurement data.

As stated in Section 4.11, initially channel correlation matrix was analysed for a selected

single sub-carrier. This analysis has uncovered that for the selected sub-carrier and for

uplink case, each AP antenna ‘sees’ uncorrelated sub-channels from each UT. Then, this

analysis was extended for all 1705 sub-carriers to verify whether all sub-carriers posses

the same channel correlation matrix or not. As stated in Section 4.11, it was verified

that, all sub-carriers exhibit similar correlations (correlation coefficients between 0 and

0.1) for any given 2 sub-channels. Therefore, as verified by Section 4.11, for any given

sub-carrier, each AP antenna sees uncorrelated sub-channels from each UT. Finally, the

correlation between the channel power and weather parameters was analysed.

Chapter 5

Deterministic Modeling

It is vital to predict system performance accurately when planning the deployment of

MUSA-MIMO-OFDM systems in rural areas as under prediction generates areas where

there are no services, and over prediction means a wasteful investment. This chapter

focuses on developing a channel model capable of predicting accurate MUSA-MIMO-

OFDM channel capacity for a given rural environment. Although channel models such

as the 3GPP spatial model [86], Winner I and Winner II [117] support Multiple-Input-

Multiple-Output (MIMO) channels, these models do not accommodate terrain modeling.

Terrain modeling is important in accurate outdoor channel modeling. On the other hand,

as stated in Chapter 3, these models are ray-based stochastic channel models which

consider superposition of Multi-Path Components (MPCs) with random powers, Angle-

of-Departure (AOD) and Angle-of-Arrival (AOA). As a result, these models do not faith-

fully predict site-specific performance. Therefore, as highlighted in Chapter 3, a novel

channel model is required to predict the MUSA-MIMO-OFDM system performance in

rural areas.

Physical and analytical MIMO channel modeling approaches are employed to model

MIMO channels. Analytical channel models characterize the impulse response of the

channel mathematically, without accounting for wave propagation. These models make

assumptions regarding the propagation environment (such as rich scattering) and model

channel coefficients, as random variables according to a given statistical distribution.

As described in Chapter 3, physical propagation models are further classified as

101

102 CHAPTER 5. DETERMINISTIC MODELING

deterministic, geometry-based stochastic and non-geometrical stochastic [41]. A given

physical propagation model is deterministic, if it is possible to reproduce the actual wave

propagation scenario for a given environment. The relevant propagation process can

be simulated from computer programs by using building databases and terrain profiles,

which accurately represent the building or terrain features [32]. Deterministic models

are more realistic and accurate, due to the representation of environment specific geom-

etry [41]. Therefore, a deterministic modeling technique is followed to model the rural

wireless channels for the proposed MUSA-MIMO-OFDM system in this thesis.

For the first time, a deterministic MUSA-MIMO-OFDM channel model suitable for

the proposed MUSA-MIMO-OFDM system in rural areas is presented. It accurately

models the terrain between the Access Point (AP) and a given User Terminal (UT) and

determines the Line-of-Sight (LoS), ground reflected and diffracted paths via a terrain

analysis algorithm. The model accommodates three dimensional representations of AP

and UT antennas as well as three dimensional antenna patterns. In addition, it generates

frequency responses for all Orthogonal-Frequency-Division-Multiplexing (OFDM) sub-

carriers. An overview of the model input parameters and model development steps are

shown in Figure 5.1.

103

MU

SA

-MIM

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del

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ital

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on

Map

(DE

M)

Ap

ply

Ea

rth

Cu

rva

ture

Corr

ect

ion

Ter

rain

An

aly

sis

Ter

rain

An

alysi

s

Alg

ori

thm

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Pa

th

Ref

lect

ed R

ay

s

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efle

ctio

n

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ays

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ion

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ss

Pred

icti

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/UT

Posi

tio

ns

AP

/UT

Hei

ghts

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idth

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atte

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odel


As the experiments were conducted in a rural farmland, very few buildings were

present in the propagation environment. Therefore, digital elevation data were used to

model the terrain. The following section discusses terrain profile generation procedure

for a given AP-UT combination.

5.1 Terrain Profiles Generation

The Ngara access solution is a long range fixed wireless system which employs APs

with multiple antenna elements at high positions. Also, as described in Chapter 4, UT

antennas are placed on the roof top of rural houses to appear above the local clutter. As

a result, the AP and UTs appear above the local clutter, resulting in a channel dominated

by a LoS path. As stated in Section 2.7.2, diffraction effects are significant in outdoor

rural wave propagation, when the LoS is obstructed by the terrain [132]. In this research,

a Digital Elevation Map (DEM) was used to generate accurate terrain profiles, in order

to incorporate propagation mechanisms deterministically.

Finding a suitable digital elevation map for terrain analysis was a significant chal-

lenge encountered in this research. Nine arc-seconds (or approximately 270 m) res-

olution DEM is available at the Australian Geo-science website [133]. In a 9 arc-

seconds digital map, adjacent data points (terrain heights) are approximately 270 m

apart. However, a DEM with better resolution improves the accuracy of the analysis. The

Shuttle Radar Topography Mission (SRTM) elevation data [134], which was originally

published by NASA, has 3 arc-second (or approximately 90 m) resolution. Since the

SRTM3 DEM data has a better resolution compared to the 9 arc-second Australian Geo-

science DEM, SRTM3 DEM data was used in the analysis.

The terrain profile analysis is important to determine the LoS path and multi-path

components for UTs around the AP. The locations of the AP (Wills Hill tower) and UTs

are required to generate terrain profiles. Relevant positions and the co-ordinates of the

AP and UTs are shown in Figure 5.2.

5.1. TERRAIN PROFILES GENERATION 105

Figure 5.2: AP and UT positioning in the measurement site

5.1.1 Data Format

Terrain heights related to the above coordinates can be extracted from the SRTM3 ver-

sion 2 1 data files. The SRTM3 version 2 1 data are available in ‘.hgt’ file format. The

filename extension ‘.hgt’ simply stands for the word ‘height‘, referring to the elevation.

These files are in raw format (no headers and no compression) with 16-bit signed inte-

gers. The elevation measured is given in meters above sea level and arranged in a latitude

and longitude array [135]. The 3-arc-second files with data corresponding to Australia

have 1201 columns and 1201 rows of data in each file, with a total file size of 2,884,802

bytes. Each data file covers a terrain of 1 degree of latitude and 1 degree of longitude.

5.1.2 Curvature of Earth

In order to ensure an accurate terrain profile generation, the curvature of the earth was

taken into consideration. Figure 5.3 illustrates earth curvature correction (ecc) at a dis-

tance dc from the Tx. The total distance between the Tx and Rx was taken as d.


dc

d

ecc

Rx

Tx

Figure 5.3: Parameters related to earth’s curvature correction

By using the geometry in Figure 5.3, an equation for the earth curvature correction

was formulated as:

ecc =a(ecrr − b)

b(5.1)

where

a = ecrr cos(

d2ecrr

)and

b =a

cos(∣∣∣∣ d

2ecrr−

dcecrr

∣∣∣∣)The parameter ecrr is the radius of earth with correction for radio refraction and was

taken as 6370 ∗ 43 km in this study. All the distances in Equation 5.1 are measured in

kilometres. This ecc value is used for accurate terrain profile generation in the following

sections.

5.1.3 Terrain Analysis Algorithm

A Matlab program was developed to extract terrain profiles for UT positions around

the AP. The program takes longitudes and latitudes (in decimal degrees) of the AP and

UTs as the input parameters. The developed program is attached in Appendix A. Terrain


heights generated by simulations of a 400 km2 area at the measurement site and positions

of all UTs and the AP are shown in Figure 5.4. After generating terrain profiles, a

terrain analysis algorithm was developed to determine the availability of LoS path and

any terrain obstructions of LoS. Only the main steps related to the algorithm is presented

in Appendix A.

For a given terrain profile, the terrain analysis algorithm determines the availability

of LoS path or diffraction edges. If the terrain does not block the first Fresnel zone

ellipsoid, then the diffraction loss can be minimal [56]. Therefore, for a given AP-UT

profile, the terrain analysis algorithm determines if the LoS path is available, and whether

or not the first Fresnel zone is obstructed by the terrain profile.


Figu

re5.

4:Te

rrai

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ight

sfo

ra40

02km

area

arou

ndth

em

easu

rem

ents

itein

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posi

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ofal

lUT

san

dA

P


The Fresnel zone radius rn f r for the n f rth Fresnel zone is given by [56]:

rn f r =

√n f rλd1d2

d1 + d2(5.2)

where, d1 is the distance from the Tx to the point where the Fresnel radius is calcu-

lated, d2 is the distance from the Fresnel zone calculation point to the Rx and λ is the

wavelength of the signal. Figure 5.5 illustrates the first, second and third Fresnel zones

for a given propagation path. The parameter n f r denotes the Fresnel zone number.

fr

fr

fr

Figure 5.5: Fresnel zones geometry and related parameters

After generating the first Fresnel zone and terrain profile data, obstructions to the LoS

path can be detected. Under this step, the algorithm detects whether or not the LoS path

is obstructed by the terrain profile. To determine the LoS path availability, the algorithm

checks whether all first Fresnel zone heights between the AP and UT are greater than the

terrain heights. If this condition is satisfied, the algorithm detects no obstructions to the

LoS path. Otherwise, obstructions to the LoS path are present.

If the first Fresnel zone is obstructed, the algorithm calculates possible diffraction

edges. In order to detect diffraction edges, the algorithm calculates intersection points

between the terrain profile and the LoS path. Then, the maximum terrain height between

two intersection points will be calculated. This maximum terrain height corresponds to

a diffraction edge. Terrain profiles generated by the terrain analysis algorithm for UT

positions around the AP are shown in Figures 5.6-5.10.

These figures present predicted LoS paths and first Fresnel zones for UTs around the

AP. A terrain plot for UT 2 is not included as the distance between the AP and UT 2 was


0 1000 2000 3000 4000 50000

50

100

150

200

250

300

350

Distance (m)

Ter

rain

hei

ght (

m)

TerrainLoS path1st Fresnel zone

Figure 5.6: Terrain profile and first Fresnel zone for AP-UT1 link

0 1000 2000 3000 40000

50

100

150

200

250

300

350

Distance (m)

Ter

rain

hei

ght (

m)




0 1000 2000 3000 4000 5000 6000 7000 80000

50

100

150

200

250

300

350

Distance (m)

Ter

rain

hei

ght (

m)



0 1000 2000 30000

50

100

150

200

250

300

350

Distance (m)

Ter

rain

hei

ght (

m)




0 1000 2000 30000

50

100

150

200

250

300

350

Distance (m)

Ter

rain

hei

ght (

m)



10 m, which is less than the minimum resolution provided by the 3-arc-second (90 m)

DEM. Figure 5.7 and 5.9 show an unobstructed first Fresnel zone. Therefore, diffraction

loss for AP-UT3 and AP-UT5 links are negligible.

Figure 5.6, 5.8 and 5.10 illustrate obstructed first Fresnel zones due to terrain. In such

situations, diffraction loss has to be taken into consideration when modeling the channel

deterministically. These observations suggest that modeling of diffraction loss is vital

for accurate performance prediction in rural environments. Therefore, the following

section presents diffraction loss prediction calculations and simulation results for 5 UT

terminals.

5.2 Diffraction Loss Predictions

Diffraction is a well known wave propagation mechanism, which may occur over differ-

ent hills in rural environments, over buildings in microcells, or around corners in indoor

environments [59]. Diffraction occurs when there is a partial blocking of a portion of the

wave front by a surface with irregular edges [54]. This gives rise to bending of waves

around the obstacle, even when a LoS path does not exist between the Tx and the Rx.

5.2. DIFFRACTION LOSS PREDICTIONS 113

In this study, terrain obstructions were determined by the aforementioned terrain

analysis algorithm to determine the diffraction loss. After detecting terrain obstructions,

the diffraction losses due to terrain obstructions were calculated. Implementing the

Uniform Theory of Diffraction (UTD) method [60], which approximates irregular terrain

profiles with canonical shapes such as wedges and convex surfaces, would increase the

complexity of the model. Therefore, in this study, terrain obstructions were approxi-

mated as knife edges. The extension of the single-edge diffraction theory to multiple

obstacles is a mathematically complex problem [56]. However, several multiple knife-

edge diffraction methods, such as, Bullington’s equivalent knife-edge [62], Epstein-

Peterson [63], Japanese [64] and Deygout [56] exist in the literature.

Amongst these models, as shown in Section 2.7.2, the Deygout method agrees best

with the rigorous theory [56]. The accuracy of this model is highest when there is a

dominant obstacle. Also, correction factors were introduced for two comparable obstruc-

tions [56]. Therefore, the Deygout method was selected to predict diffraction loss due

to terrain obstructions in this study. ITU-R P.1812-1 [65], which is used for propagation

prediction for VHF and UHF bands, also employs the Deygout method in predicting

diffraction loss.

The Deygout method is known as the ‘main-edge’ method because the first step of

this method is to calculate the Fresnel-Kirchoff diffraction parameter (v-parameter) for

each edge independently, as if all other edges are absent [56]. The edge having the

largest v-value is defined as the main edge and its loss is calculated using the complex-

Fresnel integral. Diffraction loss due to other terrain obstructions are found with respect

to a line joining the main edge to the Tx and Rx. For a path with many obstructions,

the total loss is calculated as the sum of the individual losses for the obstacles in the

order of decreasing v-value [56]. In practice, the total loss is calculated as the sum of

only three components, the main edge and the subsidiary main edges on either side.

After employing the Deygout method, the v-parameter and complex Fresnel integral

were calculated for the main edge and the subsidiary main edges on either side.


When a straight-edged obstructing screen or knife-edge is inserted between the Tx

and Rx, the resultant field at the Rx is obtained by the vector summation of all the fields

due to the secondary sources in the half-plane above the knife-edge. Evaluating complex

Fresnel integral is the classical approach to find the field behind an absorbing knife-edge

to that obtained in the free space. According to diffraction theory, the v-parameter and

the complex-Fresnel integral F(v) are given by [56]:

v = h

√2(d1 + d2)λd1d2

(5.3)

F(v) =EE0

=(1 + j)

2

∫ ∞

ve− jπt2

2 dt (5.4)

where d1 and d2 denote the distance from the Tx to the diffraction edge and the

diffraction edge to the Rx (along the LoS path), respectively. The parameter h represents

the height of the obstacle and the wavelength is represented by λ. Parameters d1, d2 and

h are shown in the Figure 5.11. These distances were determined by the terrain analysis

algorithm after detecting the diffraction edges for a given terrain profile. Once, d1, d2

and h are determined, the model evaluates F(v) which is stated in Equation 5.4.

Figure 5.11: Parameters related to diffraction calculations

After calculating the complex-Fresnel integral from diffraction theory, gain (G(v))

and the phase (φ(v)) of the diffracted signal with respect to the LoS path can be calculated

as a function of complex Fresnel integral and v-parameter as:

G(v) = 20 × log |F(v)| (5.5)


−8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8−35

−30

−25

−20

−15

−10

−5

0

5

Fresnel−diferential parameter (v)

Dif

frac

tiona

l ga

in (

dB)

Figure 5.12: Diffractional gain-Fresnel diffraction parameter(v) curve

φ =π

2v2 (5.6)

The diffractional gain versus the Fresnel diffraction parameter (v) curve, shown in

Figure 5.12, was obtained from Equations 5.4 and 5.5. This curve provides diffractional

gain for a given Fresnel-diffraction parameter.

5.2.1 Diffraction Analysis at User Terminals

In this step, diffraction loss around 5 UTs are analysed for a single OFDM sub-carrier

using the Deygout method. Figures 5.13-5.17 illustrate predicted diffraction loss for a

1250 m x1250 m area around 5 UTs. A unit distance in the grid corresponds to 90 m

distance. This grid provides significant information about diffraction loss around the

UTs. This information is of great significance as it aids in the optimum positioning of

the UTs with minimal diffraction loss in a rural environment.

According to Table 5.1, UTs 1, 4 and 6 experience diffraction losses. These results

exhibit a correlation between terrain obstructions and diffraction loss experienced by

each Rx, as shown in Figures 5.6,5.8 and 5.10, where the first Fresnel zone of UTs 1,4


0 250

500 750

1000

0

250

500

750

1000

02550

Distance (m)Distance (m)

Dif

fact

ion

Los

s (d

B)

0

10

20

30

40

50S

NE

W

Figure 5.13: Diffraction loss prediction for a 1250m × 1250m area around UT1

0

250

500

750

1000

0

250

500

750

1000

0

25

50


Dif

fact

ion

Los

s (d

B)

0

10

20

30

40

50

E

S W

N



0

250

500

750

1000

0

250

500

750

1000

0

2550


Dif

fact

ion

Los

s (d

B)

0

10

20

30

40

50

E

S W

N


0 250

500 750

1000

0

250

500

750

1000

02550


Dif

fact

ion

Los

s (d

B)

0

10

20

30

40

50

E

S W

N



0 250

500 750

1000

0

250

500

750

1000

0

25

50

Distance (m)

Distance (m)

Dif

fact

ion

Los

s (d

B)

0

10

20

30

40

50S

NE

W


and 6 are partially obstructed. Compared to UT 4, UT 1 and UT 6 experience a higher

diffraction loss as UT 1 and UT 6 cause a higher terrain obstruction (diffraction edge

closer to the LoS) than UT 4. On the other hand the first Fresnel zone of UTs 3 and 5

are not obstructed. Therefore, these UTs do not experience any diffraction loss due to

terrain.

Table 5.1: Predicted diffraction loss for user terminals

User Terminal Diffraction Loss (dB)1 3.03 04 1.05 06 2.6

Diffraction experienced by UTs 1, 4 and 6 can be minimised by relocating them.

For instance, diffraction experienced by UT 1 can be minimised by relocating it ap-

proximately 125 m north east or 360 m south. Therefore, the diffraction modeling

tool contributes to determine the optimal location for UTs in rural environments. The

predicted diffraction loss will be accounted for in the deterministic model to accurately

predict the channel frequency response.

5.3. DETERMINISTIC CHANNEL MODEL 119

5.3 Deterministic Channel Model

This section presents the developed deterministic MUSA-MIMO-OFDM channel model.

Assuming proper time and frequency synchronisation, and proper cyclic extension of

OFDM symbols that provide a frequency domain flat fading channel, the MUSA-MIMO-

OFDM channel during one symbol time can be described as:

yl,m =

NUT∑n=1

hl,m,nxl,n + wl,m (5.7)

where yl,m and xl,n are the received symbol at the mth AP receiver and the transmitted

symbol from the nth UT transmitter, respectively. The subscript l indicates the lth OFDM

sub-carrier. Additive White Gaussian Noise (AWGN) at the mth AP receiver is wl,m. The

channel coefficient hl,m,n represents the propagation channel coefficient including antenna

characteristics between the nth UT transmitter and the mth AP receiver for the lth OFDM

sub-carrier.

Equation 5.7 can be written in a vector-matrix form as:

yl = Hlxl + wl; (5.8)

where Hl is a NAP ×NUT matrix whose mth row and nth column element is hl,m,n.

The model takes the following factors into consideration:

• Availability of LoS path and terrain obstructions

The model analyses the terrain between AP and UT locations and verifies the

availability of LoS path or terrain obstructions using the terrain analysis algorithm

explained in Section 5.1.3. If the LoS path is not obstructed, the model generates

the LoS path and ground reflected rays. As described in Section 5.2.1, propagation

through diffraction is employed when the first Fresnel zone is obstructed by the

terrain. Estimating the exact ground reflected path over a realistic terrain is mathe-

matically complicated and a high processing power utilising task. Therefore, plane

earth propagation assumption is used to determine ground reflected rays [57].


• OFDM sub-carriers

This model runs 1705 iterations in Matlab for each sub-channel (12AP×6UT) to

generate channel coefficients by changing the propagation wavelength. The sub-

carrier spacing maintained between two consecutive iterations was 3906.25 Hz.

From this step, the deterministic model generates a 3-D channel coefficient matrix,

which corresponds to the 1705 OFDM sub-carriers and, the 12 AP and 6 UT

antennas. Therefore, this model can assist in the design of MUSA-MIMO-OFDM

systems1.

• Three dimensional location of the antennas

Precise geometry of the AP antenna array (based on vector representation) and the

effect of terrain heights were included in this deterministic model. Positioning of

all UT terminals and AP antenna elements on the XY plane (azimuth plane) were

done with respect to true North. The terrain heights for AP and UTs, which were

stated in Table 4.1, were used to predict the simulated channel.

• Three dimensional antenna patterns

A vertically polarised dipole antenna pattern was employed for each of the AP

antennas in the model. The UT antenna pattern was also accounted for and the

main lobe of each UT Yagi antenna was pointed towards the AP antenna array

during the channel measurement experiments and simulations.

5.3.1 Channel Coefficients Generation

Important parameters used in channel coefficient generation are stated in Table 5.2.

Complex channel coefficients for LoS and ground reflected (GR) kth path between the

nth UT transmitting antenna and the mth AP receiving antenna for the lth OFDM sub-

carrier are given by [52]:

kLoSl,m,n =

Pn

dLoSm,n

(hLoSUT,n · h

LoSAP,m) exp

(− j2π fl

dLoSm,n

c

)(5.9)

1Note that the computational complexity of generating MUSA-MIMO channels for 1,705 OFDM sub-carriers independently can be reduced by taking into account the coherence of MUSA-MIMO channels infrequency. This should be considered in a future work

5.3. DETERMINISTIC CHANNEL MODEL 121

kGRl,m,n =

Pn

dGRm,n

((Fm,n · hGRUT,n) · hGR

AP,m) exp(− j2π fl

dGRm,n

c

)(5.10)

where Pn is a UT specific constant which depends on the UT transmitting power

setting. The kth path length between nth UT antenna and mth AP antenna is dm,n, and

the vector effective height [136] of the nth UT antenna and the mth AP antenna for the

kth path is hUT,n and hAP,m, respectively. For instance, hLoSUT,n and hGR

UT,n represent vector

effective heights for LoS and ground reflected paths for nth UT antenna. The difference

between LoS and GR terms is that they denote two different propagation paths (LoS

path and ground reflected path) from the AP to UT. The parameter Fm,n is a dyad (a

vector operator) which performs dot product with the vector hGRUT,n. It represents the

reflection co-efficient of the ground in vector form. Relative permittivity [137], relative

permeability [138] and conductivity [137] for the rural Tasmanian ground were selected

as 10, 1 and 0.005 S/m, respectively. The carrier frequency at the lth OFDM sub-carrier

is fl and c is the speed of light.

If LoS obstruction is detected by the terrain analysis algorithm, propagation through

diffraction will be calculated using the v-parameter and the complex-Fresnel integral

F(v) stated in Equation 5.3 and Equation 5.4. Then, channel component for the diffracted

path is calculated using:

kDiffl,m,n =

F(v)Pn

dLoSm,n

(hDiffUT,n · h

DiffAP,m) exp

(− j(2π fl

dLoSm,n

c+ φ)

)(5.11)

where φ is the phase of the diffracted signal with respect to an imaginary LoS path,

which is calculated according to Equation 5.6. As stated in Equation 5.3, d1 and d2

denote distances from the Tx to the diffraction edge and the diffraction edge to the Rx

(along the LoS path), respectively. For Equation 5.11, these distances were determined

by the terrain analysis algorithm after detecting the diffraction edges. Once, d1, d2 and h

are determined, the model evaluates F(v) which is required by Equation 5.11.

Ray-based models (deterministic and hybrid) assume that the electromagnetic field

in space can be computed as a superposition of plane waves. This classical assumption

was introduced in the 70’s by Jakes [63]. If no LoS obstruction is detected by the


Table 5.2: Model input parameters for deterministic modeling

Channel parametersCarrier frequency 641.5 MHz

Number of sub-carriers 1705Sub-carrier spacing 3.90625 kHz

Location parametersAP [-4057′33′′, 14511′35′′, 71 m]

UT1 [-4054′34′′, 14511′57′′, 9 m]UT2 [-4057′33′′, 14511′35′′, 1.5 m]UT3 [-4055′29′′, 14510′09′′, 9 m]UT4 [-4054′08′′, 14515′31′′, 6 m]UT5 [-4059′18′′, 14510′55′′, 9 m]UT6 [-4058′23′′, 14509′12′′, 9 m]

Ground parametersRelative permittivity(ground) 10 [137]Relative permeability(ground) 1 [138]

Conductivity(ground) 0.005 S/m [137]Earth’s effective radio refraction radius 6370 ∗ 4

3 kmAntenna parameters

AP Verticaly polarised dipole antenna gain patternUT Yagi antenna gain pattern

terrain analysis algorithm, the complex channel coefficient (hl,m,n) between the nth UT

transmitting antenna and the mth AP receiving antenna for the lth OFDM sub-carrier is

given by:

hLoS + GRl,m,n = kLoS

l,m,n + kGRl,m,n (5.12)

If terrain obstructions are detected according to the terrain analysis algorithm, the

complex channel coefficient (hl,m,n) between the nth UT transmitting antenna and the

mth AP receiving antenna for the lth OFDM sub-carrier is given by:

hDiff + GR-Dl,m,n = kDiff

l,m,n + kGR-Dl,m,n (5.13)

In the above equation, kGR-Dl,m,n represents the complex coefficient of the ground reflected

5.4. RESULTS AND VALIDATION 123

path between diffraction edge and AP receiving antenna.

5.4 Results and Validation

Figure 5.18 shows a simulated 12× 6× 1705 MUSA-MIMO-OFDM channel created for

12 AP antennas, 6 UT antennas and 1705 sub-carriers using the novel deterministic

simulation model presented in this chapter. In this snapshot, each column and row

represents an AP and UT antenna, respectively. Hence, each sub-plot represents an

AP-UT combination. The Y-axis of each sub-plot represents relative channel power in

dB and the X-axis covers 1705 sub-carriers within 7 MHz bandwidth. The accuracy of

the deterministic channel model is validated with respect to the measured channel during

the experiments conducted in Smithton, Tasmania. In order to validate this model, three

performance parameters are employed. The rationale for selecting these performance

parameters are discussed below.

• Relative channel power

It is important to evaluate how accurately the deterministic model predicts channel

coefficients (hl,m,n) between the nth UT transmitting antenna and the mth AP re-

ceiving antenna for the lth OFDM sub-carrier. Therefore, relative channel power

was selected as a performance parameter to evaluate the accuracy of the model.

• Channel correlation matrix

The spatial structure or the correlation between sub-channels determine the per-

formance of a given MIMO system [52]. For instance, if two sub-channels are

highly correlated, performance degradation can be expected in MIMO systems in

rural environment [52]. Therefore, the channel correlation matrix of measured

channel and deterministic channel correlation matrix are compared to evaluate the

accuracy of the proposed deterministic channel model.


−2

02

−40

−20020

UT

1−A

P1

−2

02

−40

−20020

UT

1−A

P2

−2

02

−40

−20020

UT

1−A

P3

−2

02

−40

−20020

UT

1−A

P4

−2

02

−40

−20020

UT

1−A

P5

−2

02

−40

−20020

UT

1−A

P6

−2

02

−40

−20020

UT

1−A

P7

−2

02

−40

−20020

UT

1−A

P8

−2

02

−40

−20020

UT

1−A

P9

−2

02

−40

−20020

UT

1−A

P10

−2

02

−40

−20020

UT

1−A

P11

−2

02

−40

−20020

UT

1−A

P12

−2

02

−40

−20020

UT

2−A

P1

−2

02

−40

−20020

UT

2−A

P2

−2

02

−40

−20020

UT

2−A

P3

−2

02

−40

−20020

UT

2−A

P4

−2

02

−40

−20020

UT

2−A

P5

−2

02

−40

−20020

UT

2−A

P6

−2

02

−40

−20020

UT

2−A

P7

−2

02

−40

−20020

UT

2−A

P8

−2

02

−40

−20020

UT

2−A

P9

−2

02

−40

−20020

UT

2−A

P10

−2

02

−40

−20020

UT

2−A

P11

−2

02

−40

−20020

UT

2−A

P12

−2

02

−40

−20020

UT

3−A

P1

Relative power (dB)

−2

02

−40

−20020

UT

3−A

P2

−2

02

−40

−20020

UT

3−A

P3

−2

02

−40

−20020

UT

3−A

P4

−2

02

−40

−20020

UT

3−A

P5

−2

02

−40

−20020

UT

3−A

P6

−2

02

−40

−20020

UT

3−A

P7

−2

02

−40

−20020

UT

3−A

P8

−2

02

−40

−20020

UT

3−A

P9

−2

02

−40

−20020

UT

3−A

P10

−2

02

−40

−20020

UT

3−A

P11

−2

02

−40

−20020

UT

3−A

P12

−2

02

−40

−20020

UT

4−A

P1

−2

02

−40

−20020

UT

4−A

P2

−2

02

−40

−20020

UT

4−A

P3

−2

02

−40

−20020

UT

4−A

P4

−2

02

−40

−20020

UT

4−A

P5

−2

02

−40

−20020

UT

4−A

P6

−2

02

−40

−20020

UT

4−A

P7

−2

02

−40

−20020

UT

4−A

P8

−2

02

−40

−20020

UT

4−A

P9

−2

02

−40

−20020

UT

4−A

P10

−2

02

−40

−20020

UT

4−A

P11

−2

02

−40

−20020

UT

4−A

P12

−2

02

−40

−20020

UT

5−A

P1

−2

02

−40

−20020

UT

5−A

P2

−2

02

−40

−20020

UT

5−A

P3

−2

02

−40

−20020

UT

5−A

P4

−2

02

−40

−20020

UT

5−A

P5

−2

02

−40

−20020

UT

5−A

P6

−2

02

−40

−20020

UT

5−A

P7

−2

02

−40

−20020

UT

5−A

P8

−2

02

−40

−20020

UT

5−A

P9

−2

02

−40

−20020

UT

5−A

P10

−2

02

−40

−20020

UT

5−A

P11

−2

02

−40

−20020

UT

5−A

P12

−2

02

−40

−20020

UT

6−A

P1

−2

02

−40

−20020

UT

6−A

P2

−2

02

−40

−20020

UT

6−A

P3

−2

02

−40

−20020

UT

6−A

P4

−2

02

−40

−20020

UT

6−A

P5

−2

02

−40

−20020

UT

6−A

P6

Fre

quen

cy (

MH

z)−

20

2−

40

−20020

UT

6−A

P7

−2

02

−40

−20020

UT

6−A

P8

−2

02

−40

−20020

UT

6−A

P9

−2

02

−40

−20020

UT

6−A

P10

−2

02

−40

−20020

UT

6−A

P11

−2

02

−40

−20020

UT

6−A

P12

Figu

re5.

18:A

snap

shot

ofm

odel

outp

ut12

AP×

6U

T×

1705

sub-

carr

ierM

USA

-MIM

O-O

FDM

chan

nel


• Channel capacity

The main objective of developing this deterministic model was to accurately pre-

dict rural MUSA-MIMO-OFDM channel capacity , through modeling the rural

MUSA-MIMO-OFDM channels. Therefore, channel capacity was chosen as the

third performance metric to validate the accuracy of this deterministic channel

model.

5.4.1 Model validation based on relative channel power

This section validates the proposed deterministic channel model by implementing rela-

tive channel power as a performance metric. The model’s accuracy was quantified using

the root mean square error (RMSE) for the aforementioned performance metric. In this

analysis, RMSE of relative channel power for 12×6×1705 sub-channels were calculated.

This value was calculated as [4]:

PRMS E =

√√ΣN

i=1

(Pl,m,n − ˆPl,m,n

)2

N(5.14)

where Pl,m,n and ˆPl,m,n represent measured and deterministic channel powers for nth

UT transmitting antenna and the mth AP receiving antenna for the lth OFDM sub-carrier.

PRMS E was calculated based on 3000 sample (N=3000) values. Figure 5.19 represents

RMSE calculated for 12 × 6 × 1705 sub-channels. In the figure, each column represents

an AP antenna and each row represents a UT antenna, and X-axis represents 1705 sub-

carriers that are spanned over 7 MHz channel.

Table 5.3 represents maximum, minimum and mean for each sub-plot (12×6) shown

in Figure 5.19. According to Table 5.3 the maximum and minimum average RMSE

values are 0.70 dB and 0.14 dB, respectively. According to analysis, all 12 × 6 ×

1705 sub-channels, average RMSE values vary between 0.14-0.70 dB. Due to these

low RMSE values, the deterministic model can be considered to accurately predict the

relative received power for this system in environments with a dominant LoS path. In

Figure 5.19, sub-channels that are originating from UT2, experience higher average

RMSE values compared to the other UTs.


−2

02

01234U

T1−

AP

1

−2

02

01234U

T1−

AP

2

−2

02

01234U

T1−

AP

3

−2

02

01234U

T1−

AP

4

−2

02

01234U

T1−

AP

5

−2

02

01234U

T1−

AP

6

−2

02

01234U

T1−

AP

7

−2

02

01234U

T1−

AP

8

−2

02

01234U

T1−

AP

9

−2

02

01234UT

1−

AP

10

−2

02

01234UT

1−

AP

11

−2

02

01234UT

1−

AP

12

−2

02

01234U

T2−

AP

1

−2

02

01234U

T2−

AP

2

−2

02

01234U

T2−

AP

3

−2

02

01234U

T2−

AP

4

−2

02

01234U

T2−

AP

5

−2

02

01234U

T2−

AP

6

−2

02

01234U

T2−

AP

7

−2

02

01234U

T2−

AP

8

−2

02

01234U

T2−

AP

9

−2

02

01234UT

2−

AP

10

−2

02

01234UT

2−

AP

11

−2

02

01234UT

2−

AP

12

−2

02

01234U

T3−

AP

1

Root Mean Square Error −RMSE (dB)

−2

02

01234U

T3−

AP

2

−2

02

01234U

T3−

AP

3

−2

02

01234U

T3−

AP

4

−2

02

01234U

T3−

AP

5

−2

02

01234U

T3−

AP

6

−2

02

01234U

T3−

AP

7

−2

02

01234U

T3−

AP

8

−2

02

01234U

T3−

AP

9

−2

02

01234UT

3−

AP

10

−2

02

01234UT

3−

AP

11

−2

02

01234UT

3−

AP

12

−2

02

01234U

T4−

AP

1

−2

02

01234U

T4−

AP

2

−2

02

01234U

T4−

AP

3

−2

02

01234U

T4−

AP

4

−2

02

01234U

T4−

AP

5

−2

02

01234U

T4−

AP

6

−2

02

01234U

T4−

AP

7

−2

02

01234U

T4−

AP

8

−2

02

01234U

T4−

AP

9

−2

02

01234UT

4−

AP

10

−2

02

01234UT

4−

AP

11

−2

02

01234UT

4−

AP

12

−2

02

01234U

T5−

AP

1

−2

02

01234U

T5−

AP

2

−2

02

01234U

T5−

AP

3

−2

02

01234U

T5−

AP

4

−2

02

01234U

T5−

AP

5

−2

02

01234U

T5−

AP

6

−2

02

01234U

T5−

AP

7

−2

02

01234U

T5−

AP

8

−2

02

01234U

T5−

AP

9

−2

02

01234UT

5−

AP

10

−2

02

01234UT

5−

AP

11

−2

02

01234UT

5−

AP

12

−2

02

01234U

T6−

AP

1

−2

02

01234U

T6−

AP

2

−2

02

01234U

T6−

AP

3

−2

02

01234U

T6−

AP

4

−2

02

01234U

T6−

AP

5

−2

02

01234U

T6−

AP

6

Fre

quen

cy (

MH

z)−2

02

01234U

T6−

AP

7

−2

02

01234U

T6−

AP

8

−2

02

01234U

T6−

AP

9

−2

02

01234UT

6−

AP

10

−2

02

01234UT

6−

AP

11

−2

02

01234UT

6−

AP

12

Figu

re5.

19:M

ean

squa

reer

rorb

etw

een

dete

rmin

istic

and

mea

sure

d12

AP×

6U

T×

1705

sub-

carr

ierM

USA

-MIM

O-O

FDM

chan

nel


Tabl

e5.

3:M

ean

squa

reer

rorb

etw

een

dete

rmin

istic

and

mea

sure

dre

lativ

epo

wer

sin

dB

AP

Num

ber

UT

1U

T2

UT

3U

T4

UT

5U

T6

max

min

avg.

max

min

avg.

max

min

avg.

max

min

avg.

max

min

avg.

max

min

avg.

AP1

0.52

0.13

0.22

0.27

0.18

0.20

0.4

0.13

0.23

0.30

0.2

0.23

0.45

0.15

0.24

0.34

0.12

0.16

AP2

0.21

0.11

0.14

0.36

0.15

0.19

0.49

0.10

0.15

0.37

0.1

0.15

0.98

0.14

0.32

0.42

0.12

0.15

AP3

0.45

0.15

0.23

0.74

0.14

0.26

0.82

0.14

0.34

0.42

0.14

0.23

0.96

0.19

0.41

0.34

0.15

0.18

AP4

0.29

0.17

0.21

0.93

0.24

0.51

0.47

0.17

0.22

0.34

0.18

0.22

0.36

0.14

0.19

0.22

0.17

0.22

AP5

0.25

0.15

0.17

0.30

0.17

0.20

0.33

0.14

0.19

0.51

0.16

0.25

0.74

0.17

0.30

0.32

0.17

0.21

AP6

0.27

0.18

0.20

0.51

0.22

0.30

0.40

0.20

0.24

0.30

0.20

0.24

0.43

0.18

0.26

0.73

0.20

0.36

AP7

0.34

0.15

0.21

0.74

0.16

0.31

0.49

0.17

0.26

0.84

0.20

0.39

0.34

0.11

0.14

0.34

0.13

0.17

AP8

0.35

0.24

0.27

0.67

0.30

0.38

0.40

0.24

0.31

0.40

0.27

0.31

0.46

0.18

0.30

0.74

0.14

0.26

AP9

0.87

0.30

0.47

0.91

0.30

0.52

0.45

0.29

0.35

0.44

0.27

0.33

0.73

0.19

0.36

0.71

0.31

0.41

AP1

00.

360.

240.

291.

830.

280.

700.

390.

210.

250.

400.

230.

310.

710.

230.

360.

380.

230.

29A

P11

0.25

0.19

0.22

0.89

0.27

0.57

0.39

0.21

0.24

0.42

0.28

0.31

0.37

0.13

0.20

0.33

0.18

0.21

AP1

20.

850.

140.

320.

440.

150.

240.

470.

130.

280.

640.

200.

390.

720.

170.

310.

410.

130.

15A

vg.p

erU

T0.

240.

360.

250.

280.

280.

23O

vera

llav

g.0.

27


Reasons for these higher variations can be explained as follows. During the experi-

ments, the UT2 was placed on a tripod (approximately 1.5 m height from the ground) as

it was installed in the demonstration site for the visitors to observe. As a result, presence

of local sectaries (human body, telecommunication hut, and vehicles, which were not

included in the modeling) can affect sub-channels originating from UT2. Therefore,

higher variations and higher average RMSE values are observed in sub-channels that

are originating from UT2. In addition, a mild frequency selectivity for only few sub-

channels (especially sub-channels originating from UT2) is observed using measurement

results as shown in Figure 4.14, while the results from the deterministic model does not

demonstrate the observed frequency selectivity. This may be attributed to the fact that

not all objects which may potentially contribute to multi-path were not modeled, e.g. the

metal tower structure near AP antenna and tree nearby UT antenna.

According to Table 5.3, it can be observed that the proposed deterministic channel

model closely predict the measured channel with an overall average RMSE of 0.27 dB

for all 12 × 6 × 1705 sub-channels. As stated in Section 3.3.1, deterministic models are

more realistic and accurate compared to the analytical models, due to the representation

of the environment specific geometry [32, 41] such as accurate AP-UT positions and

terrain profiles. Although higher computational resources are required, these models

deterministically characterise rays between the AP at the UT in terms of their amplitude,

phase, angle of departure, and angle of arrival [41]. Due to the accuracy of deterministic

models, the deterministic modeling approach was followed in this thesis. Validation

results of this model also agrees with the literature, as it accurately predicts the measured

MUSA-MIMO-OFDM channels as shown by the aforementioned analysis.

5.4.2 Model validation based on channel correlation matrix

Compared to urban environments, rural environments exhibit low scattering richness,

especially when a dominant LoS path is available [19, 52]. As a result, the spatial struc-

ture or the correlation between sub-channels, predominantly determine the performance


of rural MIMO channels which has dominant LoS paths [52]. For instance, if two sub-

channels are highly correlated, performance degradation can be expected in MIMO sys-

tems in rural environment [52]. Full channel correlation matrix sufficiently characterises

the spatial structure of a MIMO system. Therefore, the full channel correlation matrix of

measured channel and deterministic channel correlation matrix are compared to evaluate

the accuracy of the proposed deterministic channel model. The deterministic correlation

matrix was calculated using the Equation 4.2 for 1000 realisations. In order to create

multiple realizations of the deterministic channel, UT positions were rotated around the

access point while ensuring similar distances from the AP to each UT, and similar angle

of separation between each UTs as identical to the experimental set-up channel structure.

Figure 5.20 represents the correlation coefficient between all AP-UT sub-channel

combinations for a selected sub-carrier. As similar to Figure 4.19, the color scale in Fig-

ure 5.20 denotes correlation coefficients between 0 and 1. In this figure, lower correlation

coefficients ( values less than 0.1 ) and higher correlation coefficients ( values greater

than 0.9) are represented in blue and maroon colors, respectively. This correlation matrix

presents the mutual correlation values between all channel matrix elements. For instance,

column A1-U1 shows the correlation coefficient between AP1-UT1 sub-channel and all

72 sub-channels, stacked into a vector.

The spatial structure of the deterministic channel correlation matrix can be analysed

as follows. Row A1-U1 is considered as an example in the deterministic channel correla-

tion matrix. In row A1-U1, the first 12 elements depicts correlation coefficients between

the AP1-UT1 sub-channel and APX-UT1 sub-channels, where 1 ≤ X ≤ 12. Correlation

coefficients between the AP1-UT1 sub-channel and APX-UT1 sub-channels correspond

to the AP-UT link configuration shown in Figure 4.20(a) in Section 4.11. As shown in

Figure 4.19, such channels are highly correlated with correlation coefficients close to 1.

In row A1-U1, elements 13-72 represent correlation coefficients between AP1-UT1

sub-channel and APX-UTY sub-channels, where 1 ≤ X ≤ 12 and 2 ≤ Y ≤ 6. Correlation

coefficients between AP1-UT1 sub-channel and APX-UTY sub-channels corresponds to

an AP-UT link configuration shown in Figure 4.20(b). Such AP-UT sub-channels are

uncorrelated as shown in Figure 4.19 with a correlation coefficient close to 0.


A1−

U1A

5−U

1A9−

U1A

1−U

2A5−

U2A

9−U

2A1−

U3A

5−U

3A9−

U3A

1−U

4A5−

U4A

9−U

4A1−

U5A

5−U

5A9−

U5A

1−U

6A5−

U6A

9−U

6

A1−

U1

A5−

U1

A9−

U1

A1−

U2

A5−

U2

A9−

U2

A1−

U3

A5−

U3

A9−

U3

A1−

U4

A5−

U4

A9−

U4

A1−

U5

A5−

U5

A9−

U5

A1−

U6

A5−

U6

A9−

U60

0.51

00.

1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figu

re5.

20:F

ullc

hann

elco

rrel

atio

nm

atri

xob

tain

edfr

omde

term

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1705

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tions


As shown in the above example (for row A1-U1), by comparing all 72× 72 elements

in Figure 4.19 and Figure 5.20, it can be verified that the full channel correlation ma-

trix obtained using the deterministic simulations is fully consistent with that obtained

from the measurement results. Therefore, the spatial structure obtained using channel

measurements agrees with that of the measurement results. As the spatial structure

predominantly determine the performance (such as channel capacity) of rural MIMO

channels which have dominant LoS paths [52], both measurement results and deter-

ministic simulations should be able to show similar performances in terms of channel

capacity which will be analysed in the following section.

5.4.3 Model validation based on channel capacity

As stated before, the main objective of developing this deterministic model is to accu-

rately predict rural MUSA-MIMO-OFDM channel capacity, through modeling the rural

MUSA-MIMO-OFDM channels. Therefore, channel capacity was chosen as the third

performance metric to validate the accuracy of the proposed model.

The model’s accuracy was quantified using the root mean square (RMS) error. This

RMS value (Crms) is calculated as [4]:

Crms =

√√ΣN

i=1

(C(i) − ˆC(i)

)2

N(5.15)

where N is the number of sample points. Parameters C(i) and ˆC(i) represent mea-

sured an deterministic channel capacities of the ith sample. One thousand sample values

(N values) were used to calculate Crms in this analysis.

The procedure of calculating the measured and simulated capacities will be discussed

in detail in Chapter 6. For the purpose of illustrating the accuracy of the model, capacity

values have been presented in this chapter. As an example, Figure 5.21 represents the

measured and simulated channel capacities for 20 dB SNR. The capacity results against

the number of Rx (nr) can be divided in to two parts, when the number of Tx (nt) and nr

antennas is increased in unison from 1 to 6 (satisfying the relationship nr=nt) and when

nr > 6, while nt = 6.


Figure 5.21 shows that capacities predicted by the deterministic simulations are

consistent with that obtained from the measurement results. Also, Table 5.4 indicates

the difference between actual and deterministically predicted capacity values. It can

be observed that the maximum capacity prediction error introduced by the deterministic

simulations is 0.30 bits/s/Hz observed at nr=6. The calculated Root Mean Square (RMS)

error between the experimental and predicted capacity curves is 0.18 bits/s/Hz. There-

fore, according to capacity results, it can be verified that the deterministic channel model

is capable of predicting the channel capacity accurately for rural environments with

dominant LoS paths.

This validated model will be used for further capacity analysis in Chapter 6, where

channel capacity variations for different user distributions around the AP are analysed.

Based on the results it can be concluded that this novel deterministic channel model is

useful in predicting the MUSA-MIMO-OFDM channel capacity for different AP-UT an-

tenna distributions in the rural environment under study. As this is a deterministic model

which is based on accurate terrain information, this model can be of use when predicting

MUSA-MIMO-OFDM channel capacity for rural environments with dominant LoS or

diffracted paths.

1 2 3 4 5 6 7 8 9 10 11 125

10

15

20

25

30

35

40

45

nr

Cap

acity

(b/

s/H

z)

Measured

Simulated

nt=n

r nt=6

Figure 5.21: Simulated and experimental capacity for 20 dB SNR


Table 5.4: Simulated and experimental capacity values for 20 dB SNR

nr Simulated Experimental Error(bits/s/Hz) (bits/s/Hz) (bits/s/Hz)

1 6.65 6.56 -0.092 11.81 12.05 0.243 17.25 17.42 0.174 22.52 22.78 0.265 28.04 28.28 0.246 33.63 33.93 0.307 36.44 36.66 0.228 38.54 38.67 0.139 40.26 40.26 0

10 41.62 41.62 011 42.8 42.74 -0.0612 43.85 43.70 -0.15


5.5 Summary

Although channel models such as 3GPP spatial model [86], Winner I and Winner II [117]

accommodate MIMO and MU-MIMO systems, these models do not account for the

terrain between the AP and UT. Accounting for terrain is important for outdoor channel

modeling to predict governing propagation mechanisms between the AP and UTs. On

the other hand, as stated in Chapter 3, these models are ray-based stochastic channel

models, which consider the superposition of MPCs with random powers, AOD and

AOA. As a result, these models do not faithfully predict site-specific performance.

Therefore, as highlighted in Chapter 3, a novel channel model is required to predict the

MUSA-MIMO-OFDM system performance in rural areas. Since, deterministic models

are more realistic and accurate, due to the representation of the environment specific

geometry [41] such as terrain profiles, deterministic modeling technique was followed to

model the rural wireless channels in this chapter. The author is not aware of any previous

work proposing a deterministic channel model for MUSA-MIMO-OFDM system in

rural environments. Therefore, for the first time, a deterministic MUSA-MIMO-OFDM

channel model suitable for MUSA-MIMO-OFDM systems in rural areas was developed

through this research. Moreover, the application of the best available resolution (3

arc-second [134]) digital elevation map (DEM) in the proposed model improves the

prediction accuracy over those using lower resolution DEMs. The model accounts for

the terrain between the AP and a given UT, and determines the LoS, ground reflected and

diffracted paths via a terrain analysis algorithm. Furthermore, the model accommodates

three dimensional representations of AP and UT antennas as well as three dimensional

antenna patterns. It generates frequency responses for all OFDM sub-carriers. The main

objective of developing this deterministic model was to predict rural MUSA-MIMO-

OFDM channel capacity accurately through modeling the rural MUSA-MIMO-OFDM

channels. The accuracy of the deterministic channel model was validated with respect

to the measured channel during the experiments conducted in Smithton, Tasmania. It

was verified that the developed model accurately predicts the channel capacity for rural

environments with dominant LoS paths, with a RMS error of 0.18 bits/s/Hz between the

experimental and predicted capacity values. Based on the results we can conclude that

5.5. SUMMARY 135

this novel deterministic channel model is useful in predicting the channel capacity for

different AP-UT antenna distributions in the rural MUSA-MIMO-OFDM environment

under study. As this is a deterministic model that is based on accurate terrain modeling,

this model can be used to predict MUSA-MIMO-OFDM channel capacity for other rural

environments with dominant LoS or diffracted paths.

Chapter 6

Capacity Analysis

This chapter presents a detailed analysis of channel capacity for Multi-User-Single-

Antenna Multiple-Input-Multiple-Output Orthogonal-Frequency-Division-Multiplexing

(MUSA-MIMO-OFDM) systems that have dominant Line-of-Sight (LoS) paths and are

deployed in rural environments. Measured rural MUSA-MIMO-OFDM channel ca-

pacity is compared with popular theoretical models and capacity results predicted by

deterministic simulations. Furthermore, the chapter presents the development of a novel

empirical channel capacity equation. This equation is capable of predicting capacity

improvements in rural environments that have dominant LoS paths, with an increasing

number of spatially separated User Terminals (UTs). Next, variations in channel capacity

are analysed. Then, capacity variation effects, due to different user distributions around

the Access Point (AP), are analysed based on the results of the validated deterministic

model presented in Chapter 5. Moreover, results from this chapter indicate that chan-

nel capacity degradation effects due to different user distributions can be mitigated by

employing a suitable user grouping method.

6.1 Channel Capacity

Channel capacity is defined as the tightest upper limit on the amount of mutual informa-

tion which can be reliably transmitted through a communication link. According to the

Shannon capacity theorem, this mutual information is the maximum data rate that can be

transmitted over a channel with an arbitrarily small error probability [46]. The channel

137

138 CHAPTER 6. CAPACITY ANALYSIS

capacity is a measure of channel availability or goodness. The larger the capacity value,

the more information that can be sent reliably by the system at a higher data rate.

As stated in Chapter 2, MIMO systems can be utilised to obtain improved capacity in

wireless systems. Recent research efforts have shifted from Single-User MIMO (SU-MIMO)

to Multi-User MIMO (MU-MIMO) systems, due to its added advantages in utilising spa-

tial diversity as discussed in Chapter 2. Although, a significant capacity improvement is

possible using MIMO systems under favorable conditions such as “rich scattering” [29,

42], this assumption is not necessarily valid for all the environments. For instance, rural

environments exhibit less multi-path compared to urban environments [19], due to the

presence of less scatterer densities. This question arises as how rural MIMO systems can

achieve improvements in channel capacity in the absence of rich scattering conditions.

Although MU-MIMO has been incorporated in the latest wireless standards, such as

Long Term Evolution (LTE) and Long Term Evolution Advanced (LTE-A) [139], very

few implementation work and channel measurements, which are based on real world

experiments, have been so far reported in the literature [25–27]. As described in Chap-

ter 3.7, these studies mainly focus on MU-MIMO short distance channels in indoor and

urban environments. Moreover, the actual capacity gains achieved by MUSA-MIMO-

OFDM systems in rural environments have not been investigated and verified, based on

the experimental data. Therefore, for the first time, this chapter presents a comprehensive

study of MUSA-MIMO-OFDM channel capacity in a rural environment with dominant

LoS paths, based on the channel measurement data obtained from a six user MUSA-

MIMO-OFDM uplink channel in a rural environment, using the experimental set-up

described in Chapter 4.

Two different criteria can be employed to evaluate MUSA-MIMO-OFDM channel

capacity [31]. The first criteria, called fixed Tx power capacity, assumes a power-limited

system where the Tx power is fixed. The second criteria, called fixed SNR capacity,

assumes an interference-limited system where Tx power can be adjusted without a limit

to provide a fixed average signal-to-noise ratio (SNR) at Rx. It should be noted here that

this thesis focus on fixed SNR capacities for MUSA-MIMO-OFDM uplink channels. In

practice, this corresponds to the use of transmit power control on the UT transmitter to

6.2. MUSA-MIMO-OFDM CHANNEL CAPACITY ANALYSIS 139

equalize the receive SNR for different UTs.

6.2 MUSA-MIMO-OFDM Channel Capacity Analysis

As the uplink channel was measured during the channel measurement experiments,

MUSA-MIMO-OFDM uplink channel capacity was analysed under this section. Six

UTs around the AP were considered as Tx antennas and twelve AP antennas were

considered as Rx antennas. In MU-MIMO systems, the uplink channel model is defined

as MIMO multiple-access channel (MAC) [46]. An illustration for MIMO MAC for 6

UT case is shown in Figure 6.1. In the presented MIMO MAC model, let uk ∈ CNT×1

be the transmitted signal vector of UT k, and let w ∈ CMR×1 the noise vector where

w ∼ N(0, I) is circularly symmetric Gaussian with identity covariance. Then, received

signal is equal to [46]:

y = H1u1 + H2u2 + ..... + Hkuk + w (6.1)

y = H

u1

..

uk

+ w (6.2)

where H = [H1..Hk].

This research focuses on a special case of a multi-user system which has a single an-

tenna at the UT (NT = 1). Before the experiments, UT transmitting power was adjusted

to have approximately similar SNR at the AP from each of the UTs. This adjustment was

done as it is a capacity optimal configuration for the fixed rural broadband application.

Also, it should be noted that this research focuses on the sum capacity of the MUSA-

MIMO system. Due to the aforementioned reasons, sum capacity of the MUSA-MIMO

system under interest is same as to the capacity of an equivalent point-to-point MIMO

system [40, 46, 52].


Figure 6.1: MIMO multi access channel for 6 UT uplink

Then, the MUSA-MIMO-OFDM uplink channel matrix (H) is characterised by its

coefficient hl,m,n, which is defined as the complex ratio of the signal output from the

mth Rx antenna over the signal input to the nth Tx antenna, at the lth OFDM sub-carrier.

The number of Tx antennas, Rx antennas and OFDM sub-carriers are assumed to be

nt, nr and n f , respectively. Normalisation is important to facilitate a fair comparison of

channel capacities of MIMO systems [140]. The normalised channel matrix is obtained

by [40, 52]:

gl,m,n =hl,m,n√

var[hl,m,n

] (6.3)

where the normalisation was performed for each UT, to equalise the difference in

pathloss. Practically such a normalisation can be performed by having different trans-

mitting power at the UT and receiving similar SNR values at the AP.

This study assumes that the proposed MUSA-MIMO uplink system has perfect knowl-

edge of the channel. When the MIMO channel is completely known by the Rx, but is

unknown to the Tx, the channel capacity of lth OFDM sub-carrier is given by [42]:

C(l) =

nt∑k=1

log2

(1 +

ρ

ntλ(k, l)

)(6.4)


where ρ is the average of the Signal-to-Noise Ratio (SNR) per Rx over MIMO

sub-channels and OFDM sub-carriers. The parameter λ(k, l) is the kth eigenvalue of

G(l)∗G(l) and superscript ∗ denotes the complex conjugate transpose. G(l) is the nor-

malised channel coefficient matrix at sub-carrier l. Measured channel H(l) was a 12 × 6

matrix with complex entries. The channel capacity defined in this study is the sum of nt

users.

Since the OFDM capacity (or wideband capacity [140]) is defined as the average

capacity of all occupied OFDM sub-carriers (n f ), the MUSA-MIMO-OFDM capacity is

given by [141]:

C =1n f

n f∑l=1

nt∑k=1

log2

(1 +

ρ

ntλ(k, l)

)(6.5)

Equation 6.5 was employed to calculate the MUSA-MIMO-OFDM channel capacity.

6.2.1 Narrowband and Wideband MUSA-MIMO-OFDM Channel Capacity

In this study, narrowband channel capacity is defined as the capacity for a single OFDM

sub-carrier as shown in Equation 6.4. On the other hand, wideband channel capac-

ity [140] (or MUSA-MIMO-OFDM channel capacity) is defined as the average capacity

of all OFDM sub-carriers as defined in Equation 6.5.

Figure 6.2 illustrates the eigenvalue distribution of a given time instant for 1705

OFDM sub-carriers. Figure 6.3 presents capacity values when ρ=20 dB, 25 dB and

30 dB, respectively. Equation 6.4 and 6.5 were used to calculate narrowband channel

capacities (for each OFDM sub-carrier) and wideband channel capacity. Wideband

capacity values when ρ=20 dB, 25 dB and 30 dB were recorded as 43.7 bits/s/Hz,

53.58 bits/s/Hz and 63.5 bits/s/Hz. In order to quantify narrowband capacity variations

with respect to wideband capacity, the Standard-deviation (STD) of capacity across 1705

sub-carriers (σC) was evaluated as:

σC =

√√√∑n f

l=1

(C(l) − C

)2

n f(6.6)


0 200 400 600 800 1000 1200 1400 1600 18000

5

10

15

20

25

30

Subcarrier number

Eig

an V

alue

(lin

ear

scal

e)

Eig 1Eig 2Eig 3Eig 4Eig 5Eig 6

Eig 1

Eig 2

Eig 3

Eig 4

Eig 5

Eig 6

Figure 6.2: Eigenvalue distribution plot for 1705 OFDM subcarriers

RecordedσC when ρ=20 dB, 25 dB and 30 dB were 0.216, 0.217 and 0.218 bits/s/Hz,

respectively. As shown in Figure 6.4, for 300 time instances, σC values varied between

0.2 bits/s/Hz and 0.25 bits/s/Hz. Further analysis ofσC has verified that the maximumσC

value recorded was 0.25 bits/s/Hz. As this is a low STD, it indicates that the narrowband

capacity shows low deviations from wideband capacity. From now on, unless specified

otherwise, wideband capacity will be considered and it will be referred as MUSA-

MIMO-OFDM capacity.

These results agree with coherence bandwidth observation from the measurements.

In literature, coherence bandwidth is defined as the range of frequencies over which the

channel can be considered ’flat’ [32]. Also, it is defined as the 3 dB bandwidth of the

channel [32]. Based on this definition, coherence bandwidth of measured channels was

observed to be greater than 7 MHz (except few sub-channels, especially sub-channels

originating from UT2). As stated in the literature, such a large coherence bandwidth is

expected in rural and suburban environments since corresponding delay spread for such

environments vary between 200-310 ns [32].


0 200 400 600 800 1000 1200 1400 1600 180040

45

50

55

60

65

Subcarrier number

Cap

acity

(b/

s/H

z)

Capacity @ 20dBMean @ 20dBCapacity @ 25dBMean @ 25dBCapacity @ 30dBMean @ 30dB

Figure 6.3: Channel capacity for 1705 OFDM sub-carriers for a given time sample forρ=20 dB, 25 dB and 30 dB

0 50 100 150 200 250 3000.2

0.25

Time instant (SNR=30dB plot)

STD

(bi

ts/s

/Hz)

0 50 100 150 200 250 3000.2

0.25


STD

(bi

ts/s

/Hz)

0 50 100 150 200 250 3000.2

0.25


STD

(bi

ts/s

/Hz)

Figure 6.4: Standard deviations of OFDM sub-carriers for random time instances


6.3 Capacity Calculations Based on Theoretical, Simulated and Ex-

perimental Approaches

Since this is the first time that the Ngara access solution is implemented in a rural area, it

is important to investigate possible capacity gains for this solution under realistic prop-

agation conditions. Therefore, the rural MUSA-MIMO-OFDM channel capacity was

compared with popular theoretical models, in order to access how the measured channel

capacity under realistic propagation conditions vary with popular theoretical models.

For this purpose, the ideal model which provides the absolute upper bound capacity

and Rayleigh channels which are feasible under popular rich scattering environments

were selected. Rayleigh channels were selected to understand the amount of variation

measured rural MUSA-MIMO-OFDM channel capacity show compared to popular rich

scattering environments.

Also, the capacity predicted by deterministic simulations was compared with the

measured capacity to validate the deterministic model described in Chapter 5. Then,

using this deterministic model, further analysis was performed to understand the effects

of different user distributions on rural MUSA-MIMO-OFDM channel capacity. The

following section describes a detailed analysis of rural MUSA-MIMO-OFDM channel

capacity using theoretical, simulated and experimental approaches.

6.3.1 Capacity Predicted by Theoretical Models

Two theoretical channel models were employed to calculate capacity for ideal and rich

scattering conditions. The first was an ideal model that assumes completely uncorrelated

parallel sub-channels. In this case, H becomes a diagonal matrix whose elements have

equal amplitudes [29]. This model sets an absolute upper bound of MIMO channel ca-

pacity. The channel capacity predicted by this model can be calculated by Equation 6.5.

The second theoretical channel model is the Rayleigh channel model which has

identically and independently distributed (i.i.d.), complex, zero mean, unit variance

entries [29]. This statistical model corresponds to a propagation channel that exhibits

rich scattering conditions [41]. The channel matrix for the Rayleigh channel model can

6.3. THEORETICAL, SIMULATED AND EXPERIMENTAL CAPACITY 145

be defined as:

HRayleigh = Normal(0,

1√

2

)+√−1 ∗ Normal

(0,

1√

2

)(6.7)

Since these are random channels, one thousand realisations of Rayleigh channel

matrices were generated using a Matlab program to calculate the mean Rayleigh channel

capacity for each OFDM sub-carrier. Since, the expectation over 1000 realisations were

obtained, Equation 6.5 was extended to calculate the expected Rayleigh channel capacity

as:

¯CRayleigh = E1n f

n f∑l=1

nt∑k=1

log2

(1 +

ρ

ntλ(k, l)

)(6.8)

where E represents the expectation of 1000 realisations.

Figure 6.5 illustrates both the ideal and Rayleigh capacities for SNR=20 dB. In order

to understand the capacity increment with the number of Tx and Rx antennas and to

compare it with the measured channel, the number of Tx and Rx antennas was increased

in unison from 1 to 6, satisfying the relationship nr=nt as shown in Figure 6.5. The

number of Rx and Tx antennas are represented by nr and nt, respectively. In this region,

the ideal and Rayleigh MUSA-MIMO-OFDM channel capacities scale linearly with nt.

When nr > 6, nt was kept constant at 6 to match with the actual Tx and Rx antenna

numbers of the measured channel. In this region, a linear increase in channel capacity

cannot be observed as nt was fixed. However, the capacity improves with nr due to

improved receiver space diversity. As the ideal model is defined as a square matrix (a

diagonal matrix) with equal number of Tx and Rx, it is not defined in nr > 6, nt = 6

region. The following section discusses the MUSA-MIMO-OFDM channel capacity

predicted by the novel deterministic model developed in Chapter 5.

6.3.2 Capacity Predicted by Deterministic Model

The deterministic model described in Chapter 5 was used to simulate three dimensional

propagation for the experiment set-up described in Chapter 4. The AP and UT positions,


1 2 3 4 5 6 7 8 9 10 11 125

10

15

20

25

30

35

40

45

nr

Cap

acity

(b/

s/H

z)

IdealRayleigh

nt=6n

t=n

r

Figure 6.5: Rayleigh and ideal channel capacities with increasing number of antennasfor 20 dB SNR


1 2 3 4 5 6 7 8 9 10 11 125

10

15

20

25

30

35

40

45

nr

Cap

acity

(bi

ts/s

/Hz)

nt=n

r nt=6

Figure 6.6: Simulated capacity with increasing number of antennas for 20 dB SNR

antenna heights and other input parameters (as shown in Chapter 5) were specified as

the initial step in the deterministic simulation procedure. Then, possible paths from the

UT to AP were determined according to the rules of Geometric Optics (GO) by the

terrain analysis algorithm as stated in Chapter 5. Based on this model, the simulated

channel matrix (HSimulated) is obtained for 1705 sub-carriers. This, HSimulated matrix was used

to calculate the MUSA-MIMO-OFDM channel capacity using Equation 6.5.

In order to compare the capacity increment predicted by the deterministic model

with the measured channel, the number of Tx and Rx antennas was increased in unison

from 1 to 6, satisfying the relationship nr=nt. As shown in Figure 6.6, the capacity

predicted by the deterministic model scales linearly with nt in the nr=nt region, similar

to Figure 6.5. When nr > 6, nt was kept constant at 6 to match with the actual Tx and

Rx antenna numbers used for the measured channel. In this region, linear increase in

channel capacity cannot be observed as nt was fixed. For nr > 6, nt = 6, the capacity

improves with nr due to improved receiver space diversity. The next section presents the

MUSA-MIMO-OFDM capacity calculated using measured data from the experimental


1 2 3 4 5 6 7 8 9 10 11 125

10

15

20

25

30

35

40

45

nr

Cap

acity

(bi

ts/s

/Hz)

nt=n

r nt=6

Figure 6.7: Experimental capacity with increasing number of antennas for 20 dB SNR

set-up described in Chapter 4.

6.3.3 Experimental Capacity

In this section experimental channel capacity corresponds to the measured channel ca-

pacity, which is of great significance as it provides an insight of the actual channel

capacity that can be supported by MUSA-MIMO-OFDM channels when deployed in a

rural environment with dominant LoS paths. The experimental channel capacity can be

compared against capacities predicted by ideal and popular rich scattering environments

to assess the performance of the system, in terms of channel capacity.

In this study, measured channel matrices obtained from the channel measurement

experiments were used to calculate experimental channel capacity. As in the previous

calculations, experimental MUSA-MIMO-OFDM channel capacity was calculated using

Equation 6.5. As temporal variations in channel capacity are not considered in this

section and to make a fair comparison, mean capacity over 300 time instances was


used to calculate the experimental channel capacity. As shown in Figure 6.7, in nr=nt

region, experimental capacity also scales linearly with nt. Despite having a fixed nt when

nr > 6, capacity improves with nr due to improved receiver space diversity.

This thesis focuses on the uplink channel of the proposed MUSA-MUMO system.

Figure 4.19 illustrates the full channel correlation matrix for the proposed AP-UT con-

figuration during the experiments. As far as the uplink is concerned, each UT channel

is fully uncorrelated (compared to other UTs) as shown in Figure 4.20(b). Therefore,

according to the experiment set-up, the author does not work with other (nonzero) levels

of correlation among UTs, other than non-zero correlation case. This is due to the fact

that the UTs are spatially separated during the experiments as explained in Section 4.11.

6.3.4 Comparison between Theoretical, Deterministic and Experimental Channel

Capacity

Channel capacities predicted by theoretical, deterministic and experimental methods are

compared in this section. Figure 6.8 illustrates capacity predicted by the experimental,

ideal, Rayleigh and simulated methods with SNR=20 dB. Similar to the previous figures

(Figures 6.5 to 6.7), this figure can be separated into two parts. When nr < 6, number

of Tx and Rx antennas was increased in unison from 1 to 6, satisfying the relationship

nr=nt. When nr > 6, nt was kept constant while increasing nr.

As shown in Figure 6.8, in the nr=nt region, capacity scales linearly with different

gradients for each capacity curve. The ideal model shows the highest capacity incre-

ment, thus perceives the highest gradient. Similar capacity scaling gradients (with small

variations) were observed for the Rayleigh, experimental and the deterministic model.

Comparing the experimental and Rayleigh capacities, the experimental capacity of this

rural environment exhibits a slightly higher value than that predicted by the Rayleigh

channel model. It is important to note that each UT had a dominant LoS path from the

AP during the experiments. Moreover, due to the characteristics of the measurement

environment stated in Section 4.1, this rural environment was expected to exhibit low

scattering richness. However, the comparison shows that the environment under interest

supports higher channel capacities than a rich scattering environment. This is due to


Table 6.1: Theoretical, simulated and experimental capacity values for 20 dB SNR

nr Ideal Rayleigh Simulated Experimental(bits/s/Hz) (bits/s/Hz) (bits/s/Hz) (bits/s/Hz)

1 6.66 6.55 6.65 6.562 13.32 11.55 11.81 12.053 19.97 16.81 17.25 17.424 26.63 22.14 22.52 22.785 33.30 27.59 28.04 28.286 39.95 33.04 33.63 33.937 35.87 36.44 36.668 37.98 38.54 38.679 39.66 40.26 40.2610 41.06 41.62 41.6211 42.26 42.8 42.7412 43.3 43.85 43.70

the fact that UTs of this MUSA-MIMO system were spatially separated and the uplink

channels associated to different UTs were distinct. In space, this corresponds to UTs

having sufficient azimuthal angle separation [52]. This reasoning was verified by the

channel correlation analysis presented in Section 4.11. In Section 4.11, it was shown

that each AP antenna ‘sees’ spatially separated channels from each UT.

It has been empirically demonstrated that urban (N-LoS) channels follow the Rayleigh

distribution [99] and LoS channels are predominantly Ricean distributed [32]. In this the-

sis, Rayleigh model is used as a benchmark for N-LoS channel coefficients whereas LoS

channels (Ricean channels) are generated by the deterministic channels model. Accord-

ing to the Figure 6.8, it has been verified that MUSA-MIMO systems with dominant LoS

paths (Ricean channels) perform better than in rich scattering environments (Rayleigh

channels), given that UTs are spatially separated. To the best of the author’s knowledge,

this is the first experimental verification that. MUSA-MIMO systems with dominant LoS

paths (Ricean channels) perform better than in rich scattering environments (Rayleigh

channels), when the UTs are spatially separated.

Table 6.1 shows that capacity predicted by the deterministic model closely follows

the experimental capacity. It can be observed that the maximum capacity prediction error

introduced by the deterministic model is 0.30 bits/s/Hz when nr=6. From Table 6.1,


1 2 3 4 5 6 7 8 9 10 11 125

10

15

20

25

30

35

40

45

nr

Cap

acity

(b/

s/H

z)

ExperimentalIdealRayleighSimulated

nt=n

r nt=6

Figure 6.8: Theoretical, simulated and experimental capacity for 20 dB SNR


calculated Root Mean Square (RMS) error between the experimental and predicted

capacity curves is 0.18 bits/s/Hz. Therefore, the deterministic channel model accurately

predicts the experimental capacity with an RMS error of 0.18 bits/s/Hz. This validated

model will be used for further capacity analysis of the MUSA-MIMO-OFDM system in

rural environments.

6.4 Novel Empirical Capacity Equation

As this is the first practical deployment of MUSA-MIMO-OFDM channels in rural

environments, it is important to understand and predict rural MUSA-MIMO-OFDM

capacity improvements based on the experimental results. Therefore, a novel simplified

empirical rural capacity equation which can predict MUSA-MIMO-OFDM capacity

in rural environments is derived in this section. The objective of this equation is to

predict the capacity improvement with the number of increasing UTs which are spatially

separated, in a rural environment that has dominant LoS propagation paths.

6.4.1 Proposed Capacity Equation

In order to develop this equation, rural MUSA-MIMO-OFDM capacity curves for SNR

values 16 dB to 40 dB (incremented by 2 dB steps) were generated by incrementing the

number of AP and UT antennas. Compared to mobile wireless channels, fixed wireless

channels in rural areas support stable channel capacities. This argument was verified by

analysing the mean MUSA-MIMO-OFDM capacity for different measurement hours.

Calculated mean capacities in different measurement hours were similar and more de-

tails of stable channel capacities are stated in Section 6.5. Therefore, MUSA-MIMO-

OFDM capacity averaged over a one hour measurement window (720 time instances)

was considered in this analysis. Then, a multi-variate linear regression analysis was

performed using the statistical tool available in Maltab software to derive this novel

empirical formula.

Based on the results of multi-variate linear regression analysis, an empirical capacity

equation is proposed as:

6.4. NOVEL EMPIRICAL CAPACITY EQUATION 153

1 2 3 4 5 6

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

n

Cap

acity

(bi

ts/s

/Hz)

16 dB

20 dB

40 dB

30 dB

Predicted by EmpiricalEquation

Experimental

Figure 6.9: Experimental and predicted capacity for different SNR values

CRURAL = n × log2

(1 + A ×

ρ

n

)+

1.1n

A = 0.45, if ρ >20 dB.

A = 0.485, if ρ ≤ 20 dB.

(6.9)

where n = nt = nr.

Predicted MUSA-MIMO-OFDM channel capacities by Equation 6.9 are shown in

Figure 6.9. Experimental channel capacities obtained using a different measurement

window (mean capacity of a different hour with 720 time instances) are also presented in

the figure and show a good match with predicted capacity values. Equation 6.9 defines

capacity for the n = nt = nr region as it provides the freedom of the selection of nt and nr.

The case for nr > 6 is limited to nt = 6 from the empirical results. Defining an equation

for capacity in nr > 6, nt = 6 region would have a limited scope on the application of

such equation. Therefore, the capacity equation was defined only for the n = nt = nr


case. Inclusion of the correction term, 1.1/n, enables Equation 6.9 to generate best fitting

empirical equation for experimental rural MUSA-MIMO-OFDM capacities. Therefore,

the correction term enables to accurately predict rural MUSA-MIMO-OFDM capacity

for a spatially separated user distribution. This has been verified by the error analysis

performed in Section 6.4.2.

Table 6.2 compares the difference between the actual and predicted capacities for

1 ≤ n ≤ 6 and 16 dB ≤ SNR ≤ 16 dB values. The magnitude of the maximum

difference was recorded as 0.23 bits/s/Hz. The average of differences (magnitude of the

capacity differences were calculated) recorded was 0.14 bits/s/Hz and all values ranged

from 0 to 0.23 bits/s/Hz. Therefore, capacities predicted by the empirical equation

closely matches with the actual channel capacities in the selected measurement window.

Since, this is an empirical equation based on experimental data gathered from a rural

environment, the applicability of this equation is limited to rural environments with

dominant LoS paths, similar AP antenna array structure, spatially separated UTs and

same received SNR from different users at the base station. However, the proposed

novel equation provides a foundation for the analysis of channel capacity performance

of MUSA-MIMO systems in rural environments.

Table 6.2: Capacity difference between the actual and predicted values

S NR nr=1 nr=2 nr=3 nr=4 nr=5 nr=6dB (bits/s/Hz) (bits/s/Hz) (bits/s/Hz) (bits/s/Hz) (bits/s/Hz) (bits/s/Hz)16 -0.17 +0.18 +0.20 +0.16 +0.17 +0.2318 -0.18 +0.19 +0.16 0 -0.01 +0.1620 -0.17 +0.16 +0.08 +0.13 -0.19 +0.1722 -0.07 +0.23 +0.21 +0.17 0 0.1524 -0.06 +0.21 +0.22 +0.01 0 +0.0226 -0.06 +0.21 +0.21 +0 -0.02 +0.0128 0 +0.21 +0.23 -0.01 -0.10 -0.1030 -0.06 +0.21 +0.21 -0.01 -0.19 -0.1332 -0.06 +0.22 +0.19 -0.14 -0.17 -0.2134 -0.06 +0.21 +0.19 -0.10 -0.18 -0.2136 -0.06 +0.22 +0.19 -0.07 -0.19 -0.2238 -0.06 +0.22 +0.18 -0.13 -0.22 -0.2240 -0.02 +0.21 +0.18 -0.18 -0.22 -0.22


6.4.2 Validity of Proposed Equation

This section investigates the validity of the proposed equation using different subsets

of AP and UT antennas. When developing the above equation, AP and UT antennas

were increased from 1×1 to 2×2 up to 6×6. Since the measured channel has 12×6 AP-

UT combinations, different AP-UT subsets can be chosen to calculate capacity when

nt < 6 and nr < 12. In order to check the validity of the proposed model in different

rural environments, 100 different AP-UT combinations were considered by selecting AP

antennas and UTs randomly from the channel measurements. Table 6.3 illustrates an

example of AP-UT selection for 3AP×3UT capacity calculations. These 100 different

AP-UT combinations create 100 different subsets of rural environments for 3AP×3UT

capacity calculations.

Table 6.3: Different AP-UT combinations for 3AP×3UT capacity calculations

Combination Chosen APs Chosen UTs1 2,4,6 1,3,42 1,3,12 2,5,63 4,7,9 1,2,3.. ... ...

50 1,2,12 1,4,6.. ... ...

100 5,10,11 4,5,6

Then, experimental MUSA-MIMO-OFDM channel capacity for each antenna com-

bination was calculated using Equation 6.5. Also, Equation 6.9 was used to predict

channel capacity for a given SNR value and n. The difference between predicted and

experimental capacity is defined as the prediction error of the proposed equation for a

given antenna combination.

Figures 6.10-6.15 illustrate error Cumulative Distribution Functions (CDFs) for in-

creasing AP-UT antennas and different SNR values. Each subplot in these figures shows

error CDF for 100 random antenna combinations. Figure 6.10 and 6.11 show that all

antenna combinations exhibit errors less than 0.5 bits/s/Hz for SNR values. Moreover,

Figure 6.12 shows that, for 3AP×3UT antennas, around 75 antenna combinations exhibit

errors less than 0.5 bits/s/Hz and the rest of the antenna combinations exhibit errors less


than 1 bits/s/Hz.

Figure 6.13 and 6.14 demonstrate that, for 4AP×4UT and 5AP×5UT antennas,

around 50 antenna combinations exhibit errors less than 0.5 bits/s/Hz and the rest of

the antenna combinations exhibit errors less than 1 bits/s/Hz. Figure 6.15 shows that,

for 6AP×6UT antennas, more than 75 antenna combinations exhibit errors less than

1 bits/s/Hz and the rest of the antenna combinations exhibit errors less than 1.5 bits/s/Hz.

Compared to the actual capacity values, the maximum prediction error of the capacity

equation was 5%. Also, more than 80% of prediction errors were less than 2%. There-

fore, the proposed empirical capacity equation satisfactorily predicts channel capacity

increment with the number of antennas. This is a significant contribution towards the

performance analysis of rural MUSA-MIMO systems, as it provides a relatively simple

equation that is capable of accurately predicting channel capacity for increasing number

of spatially separated UTs. The next section analyses time variation effects of MUSA-

MIMO capacity.


0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F1x1 18dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)C

DF

1x1 20dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

1x1 22dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

1x1 24dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F1x1 26dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)C

DF

1x1 28dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

1x1 30dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

1x1 32dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F1x1 34dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

1x1 36dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

1x1 38dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

1x1 40dB SNR

Figure 6.10: Error CDFs for 1×1 system with 18-40 dB SNR values


0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

2x2 18dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

2x2 20dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

2x2 22dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

2x2 24dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

2x2 26dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

2x2 28dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

2x2 30dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

2x2 32dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

2x2 34dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

2x2 36dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

2x2 38dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

2x2 40dB SNR



0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F3x3 18dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)C

DF

3x3 20dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

3x3 22dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

3x3 24dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F3x3 26dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)C

DF

3x3 28dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

3x3 30dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

3x3 32dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F3x3 34dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

3x3 36dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

3x3 38dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

3x3 40dB SNR



0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

4x4 18dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

4x4 20dB SNR

0 0.5 1 1.5 20

0.25

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0.75

1

Error(bits/s/Hz)

CD

F

4x4 22dB SNR

0 0.5 1 1.5 20

0.25

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0.75

1

Error(bits/s/Hz)

CD

F

4x4 24dB SNR

0 0.5 1 1.5 20

0.25

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0.75

1

Error(bits/s/Hz)

CD

F

4x4 26dB SNR

0 0.5 1 1.5 20

0.25

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0.75

1

Error(bits/s/Hz)

CD

F

4x4 28dB SNR

0 0.5 1 1.5 20

0.25

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0.75

1

Error(bits/s/Hz)

CD

F

4x4 30dB SNR

0 0.5 1 1.5 20

0.25

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0.75

1

Error(bits/s/Hz)

CD

F

4x4 32dB SNR

0 0.5 1 1.5 20

0.25

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0.75

1

Error(bits/s/Hz)

CD

F

4x4 34dB SNR

0 0.5 1 1.5 20

0.25

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0.75

1

Error(bits/s/Hz)

CD

F

4x4 36dB SNR

0 0.5 1 1.5 20

0.25

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0.75

1

Error(bits/s/Hz)

CD

F

4x4 38dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

4x4 40dB SNR



0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F5x5 18dB SNR

0 0.5 1 1.5 20

0.25

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1

Error(bits/s/Hz)C

DF

5x5 20dB SNR

0 0.5 1 1.5 20

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1

Error(bits/s/Hz)

CD

F

5x5 22dB SNR

0 0.5 1 1.5 20

0.25

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1

Error(bits/s/Hz)

CD

F

5x5 24dB SNR

0 0.5 1 1.5 20

0.25

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1

Error(bits/s/Hz)

CD

F5x5 26dB SNR

0 0.5 1 1.5 20

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1

Error(bits/s/Hz)C

DF

5x5 28dB SNR

0 0.5 1 1.5 20

0.25

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0.75

1

Error(bits/s/Hz)

CD

F

5x5 30dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

5x5 32dB SNR

0 0.5 1 1.5 20

0.25

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1

Error(bits/s/Hz)

CD

F5x5 34dB SNR

0 0.5 1 1.5 20

0.25

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0.75

1

Error(bits/s/Hz)

CD

F

5x5 36dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

5x5 38dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

5x5 40dB SNR



0 0.5 1 1.5 20

0.25

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0.75

1

Error(bits/s/Hz)

CD

F

6x6 18dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

6x6 20dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

6x6 22dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

6x6 24dB SNR

0 0.5 1 1.5 20

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0.75

1

Error(bits/s/Hz)

CD

F

6x6 26dB SNR

0 0.5 1 1.5 20

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0.75

1

Error(bits/s/Hz)

CD

F

6x6 28dB SNR

0 0.5 1 1.5 20

0.25

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1

Error(bits/s/Hz)

CD

F

6x6 30dB SNR

0 0.5 1 1.5 20

0.25

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0.75

1

Error(bits/s/Hz)

CD

F

6x6 32dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

6x6 34dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

6x6 36dB SNR

0 0.5 1 1.5 20

0.25

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1

Error(bits/s/Hz)

CD

F

6x6 38dB SNR

0 0.5 1 1.5 20

0.25

0.5

0.75

1

Error(bits/s/Hz)

CD

F

6x6 40dB SNR


6.5. TIME VARIATIONS OF CHANNEL CAPACITY 163

6.5 Time Variations of Channel Capacity

This section focuses on analysing time variations of MUSA-MIMO channel capacity in

a rural environment using channel measurement data. Also, it provides an understanding

of the stability of the system in terms of channel capacity. In order to understand

time variations experienced by a single sub-carrier and MUSA-MIMO-OFDM capac-

ity (mean capacity over all OFDM sub-carriers), capacity for 5 selected sub-carriers (out

of 1705 sub-carriers) and MUSA-MIMO-OFDM capacity were plotted for a one hour

measurement window as shown in Figure 6.16. Variations of 1705 OFDM sub-carriers

were not shown in this figure as a large number of plots are required for this task. As

evidenced by 5 selected sub-carriers, fluctuations in capacity across 1705 sub-carriers

are highly correlated.

In addition, as shown in Figure 6.16, it can be observed that fluctuations of MUSA-

MIMO-OFDM capacity (mean capacity), are highly correlated with fluctuations of sin-

gle sub-carrier capacities. However, due to the averaging across all sub-carriers, the

amplitude of fluctuations of the mean capacity is reduced, compared to that of a single

sub-carrier. Therefore, time variations of MUSA-MIMO channel capacity for both single

sub-carrier capacity and MUSA-MIMO-OFDM capacity is analysed in this study.

In order to gain a better understanding of channel capacity temporal variations,

capacity dynamic range was observed. Capacity dynamic range is defined as the dif-

ference between the maximum and the minimum value of the MIMO-OFDM channel

capacity [103]. In this study 90% of the capacity dynamic range, which is the difference

between the top 95% and the bottom 5% values, has been observed to exclude extreme

conditions. Figure 6.17 illustrates channel capacity CDFs and 90% of the capacity

dynamic range for a selected sub-carrier over a one hour measurement window (720

time samples).


0 10 20 30 40 50 6043

44

45

Sub−carrier 1

0 10 20 30 40 50 6043

44

45

Sub−carrier 400

0 10 20 30 40 50 6043

44

45

Cap

acity

bits

/s/H

z

Sub−carrier 800

0 10 20 30 40 50 6043

44

45

Sub−carrier 1200

0 10 20 30 40 50 6043

44

45

Sub−carrier 1600

0 10 20 30 40 50 6043

44

45

Time (mins)

Mean Capacity

Figure 6.16: Capacity for selected sub-carriers during a 1 hour time window atSNR=20 dB


43.3 43.4 43.5 43.6 43.7 43.8 43.9 44.00

20

40

60

80

100

Channel Capacity (bits/s/Hz)

CD

F (%

)

95 %

5 % Dynamic Range

Figure 6.17: Capacity CDF over 720 measurement points

Out of the six measurement days, Day 5 and Day 6 had continuous data for most

of the measurement hours. Therefore, Day 5 and Day 6 were chosen in this analysis.

Table 6.4 illustrates 90% of capacity dynamic range, calculated for ten hours in Day 5

and Day 6. In this study, time variations for both MUSA-MIMO-OFDM and single

OFDM channel capacities were observed for 20 dB SNR.

During Day 5, the maximum and minimum MUSA-MIMO-OFDM capacity dy-

namic ranges observed were 0.28 bits/s/Hz and 0.21 bits/s/Hz, respectively. Moreover,

for Day 5, small variations in the MUSA-MIMO-OFDM capacity dynamic range were

observed with an average hourly variation rate of 0.23 bits/s/Hz. It is a 0.5% variation

from the mean MUSA-MIMO-OFDM capacity recorded during the measurement hours

presented in Table 6.4 for Day5. Compared to Day 5, Day 6 exhibited more variations

in MUSA-MIMO-OFDM capacity dynamic range. During Day 6, the maximum and

minimum MUSA-MIMO-OFDM capacity dynamic ranges observed were 0.84 bits/s/Hz

and 0.53 bits/s/Hz, respectively. Also, Day 6 recorded an average hourly variation rate of

0.68 bits/s/Hz which is a 1.5% variation from the mean MUSA-MIMO-OFDM capacity

measured during the measurement window in Day 6.

Similar variations on channel capacity were observed for a single OFDM sub-carrier.


As shown in Table 6.4, the maximum and minimum MUSA-MIMO-OFDM capacity

dynamic ranges observed were 0.34 bits/s/Hz and 0.26 bits/s/Hz, respectively. In Day 5,

small variations in single OFDM sub-carrier capacity dynamic range were observed with

an average hourly variation rate of 0.29 bits/s/Hz. It is a 0.65% variation from the mean

single OFDM sub-carrier capacity during measurement hours in Day 5. Compared to

Day 5, Day 6 exhibited higher variations in single OFDM sub-carrier capacity dynamic

range. During Day 6, the maximum and minimum MUSA-MIMO-OFDM capacity

dynamic ranges observed were 0.92 bits/s/Hz and 0.59 bits/s/Hz, respectively. Day 6

recorded an average hourly variation rate of 0.75 bits/s/Hz which is a 1.7% variation from

mean single OFDM sub-carrier capacity measured during the measurement window in

Day 6.

Reasons for different capacity variations for Day 5 and Day 6 were further analysed

accounting for the weather conditions, as high variations in wind conditions were ob-

served during the experiments. Table 6.4 illustrates the mean wind speed during each

measurement hour. In Day 5, the highest capacity dynamic ranges for MUSA-MIMO-

OFDM and single OFDM sub-carrier (0.28 bits/s/Hz and 0.34 bits/s/Hz) were observed

while having the highest mean wind speed (µWind) of 2.52 m/s and the lowest dynamic

ranges (0.21 bits/s/Hz and 0.26 bits/s/Hz) were observed when (µWind) was 1.97 m/s.

In Day 6, the highest and lowest capacity dynamic ranges (MUSA-MIMO-OFDM

capacity 0.84 bits/s/Hz and 0.53 bits/s/Hz, and for a single OFDM sub-carrier capac-

ity 0.92 bits/s/Hz and 0.59 bits/s/Hz) were recorded for µWind values of 5.78 m/s and

3.72 m/s, respectively. As illustrated in Table 6.4, comparatively high variations in

channel capacity at higher wind speeds, and low variations in channel capacity in low

wind speeds were observed.

For these two days only 0.5% and 1.5% variation in MUSA-MIMO-OFDM capacity

dynamic range and only 0.65% and 1.7% variation in single OFDM sub-carrier capacity

dynamic range were experienced. Therefore, according to channel capacity dynamic

range analysis, MUSA-MIMO uplink channels deployed in rural Smithton area support

stable channel capacities. To the best of author’s knowledge, this study is the first to

report the amount of variation in terms of MUSA-MIMO-OFDM channel capacity in


rural environments.

Table 6.4: Hourly capacity dynamic range (obtained from experimental capacities) andwind information

Day Hour Dynamic Range for Dynamic Range for µWind WindMUSA-MIMO-OFDM Single OFDM Direction

(Hrs) (bits/s/Hz) (bits/s/Hz) (m/s)5 10-11 0.28 0.34 2.52 W,SW,NW5 11-12 0.21 0.26 1.97 W,NW,WNW5 12-13 0.24 0.30 2.31 W,WNW5 13-14 0.22 0.27 2.19 W,WNW5 14-15 0.22 0.26 2.2 W,WNW6 07-08 0.84 0.92 5.78 NW,NNW6 09-10 0.64 0.71 3.95 NW,NNW6 10-11 0.74 0.82 4.64 NW,NNW6 11-12 0.53 0.59 3.72 W,WNW6 12-13 0.65 0.72 4.02 W,WNW


6.6 Capacity Variation with UT Spatial Distribution

This section analyses capacity variation of MUSA-MIMO-OFDM systems due to dif-

ferent spatial distributions of UTs around the AP. To the best of the authors knowledge,

capacity variation of MUSA-MIMO-OFDM systems due to different spatial distributions

of UTs in rural areas with dominant LoS propagation remains as an open problem.

The validated deterministic model, which was stated in Chapter 5, was used to analyse

capacity variation effects for the proposed MUSA-MIMO-OFDM system due to different

UT spatial distributions. Simulations were performed at:

• Random UT spatial distributions

• Controlled UT spatial distributions

6.6.1 Capacity Variation with Random UT Spatial Distribution

This section analyses capacity variation with random UT spatial distribution. In reality,

UTs (rural houses) are not regularly distributed in a given area. Therefore, during the

initial analysis, UTs were assumed to be distributed randomly in angle following a

uniform distribution with reference to the centre of the AP array. Figure 6.18 illustrates

n UTs randomly distributed within the boundaries of two concentric circles (with the

radius of d1 and d2) in the order of increasing angle from the reference.

In order to analyse the effects of random UT spatial distributions, the UT distribution

angle with reference to the centre of the AP array, is restricted to an angle θ as shown

in Figure 6.19. Deterministic simulations were performed while increasing θ from

10° to 360° in 10° steps to find the relationship between channel capacity and the angle

of user distribution.

6.6. CAPACITY VARIATION WITH UT SPATIAL DISTRIBUTION 169

AP

UT1

UT8

UT9

UT10

UT(n-2)

UT(n-1)

UT(n)

UT7

UT6

UT5

UT4

UT3UT3 UT2

AP

d1d2

Ref

Figure 6.18: Example of user terminal distribution around user terminals (top view)

AP

UT1

UT6

UT5

UT4UT3

UT2

AP

d1

d2

θ

Figure 6.19: User terminals concentrated to a sector with angle θ


For each simulation, the carrier frequency was taken as 641.5 MHz. The distances

d1 and d2 were taken as 5 km and 25 km, respectively. Similar to the experimental

setup, 12 element AP antenna array at a height of 71 m from the ground, and 6 randomly

positioned UT antennas placed at 9 m from the ground, were used in the simulations. For

each θ angle, 1000 realisations of random UT antenna positions were conducted within

the sector angle θ. Therefore, for a given θ angle, 1000 channel frequency responses

which represent different UT distributions were available from simulations.

Figures 6.20-6.22 illustrate channel capacity CDFs corresponding to 1000 realisa-

tions for 10 ≤ θ ≤ 360. Blue, black and red CDF plots represent 20 dB, 25 dB

and 30 dB SNR values, respectively. According to the figures, an increment in channel

capacity can be observed with θ. In order to further analyse these variations, mean

capacity of 1000 realisations for a given θ was calculated.

Figure 6.23 shows the mean capacity values for 1000 realisations, against θ. As θ

increases from 10° to 360°, the capacity also increases. It can be observed that when θ

increases from 10° to 180°, there is a significant improvement in capacity for all SNR

curves. When θ increases from 180° to 360°, there is a slight increment in capacity

compared to the capacity improvement when θ increases from 10° to 180°. For instance,

when SNR = 20dB, the capacity increases from 15.5 bits/s/Hz to 40.3 bits/s/Hz as θ

increases from 10° to 180°. When θ increases from 180° to 360°, the capacity increases

from 37.5 bits/s/Hz to 40.3 bits/s/Hz. Also, the capacity value when θ=10° is as low as

15.5 bits/s/Hz compared to 40.3 bits/s/Hz when θ=360°.

In the above analysis, a random user distribution confined to different angles was

considered. In order to have a better understanding of how the distribution of UTs

around the AP affects the system capacity, more controlled user distribution scenarios

were analysed as stated in the next section.


20 40 60 800

0.25

0.5

0.75

1

Capacity (bits/s/Hz)

CD

F

Angle Θ =100

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =200

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =300

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =400

20 40 60 800

0.25

0.5

0.75

1


CD

FAngle Θ =500

20 40 60 800

0.25

0.5

0.75

1

Capacity (bits/s/Hz)C

DF

Angle Θ =600

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =700

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =800

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =900

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =1000

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =1100

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =1200

Figure 6.20: Capacity CDFs for user distribution angle variation from 10° to 120° (blue,black and red curves represent 20 dB, 25 dB and 30 dB SNR values)


20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =1300

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =1400

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =1500

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =1600

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =1700

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =1800

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =1900

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =2000

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =2100

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =2200

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =2300

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =2400

Figure 6.21: Capacity CDFs for user distribution angle variation from130° to 240° (blue, black and red curves represent 20 dB, 25 dB and 30 dB SNRvalues)


20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =2500

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =2600

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =2700

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =2800

20 40 60 800

0.25

0.5

0.75

1


CD

FAngle Θ =2900

20 40 60 800

0.25

0.5

0.75

1

Capacity (bits/s/Hz)C

DF

Angle Θ =3000

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =3100

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =3200

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =3300

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =3400

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =3500

20 40 60 800

0.25

0.5

0.75

1


CD

F

Angle Θ =3600

Figure 6.22: Capacity CDFs for user distribution angle variation from250° to 360° (blue, black and red curves represent 20 dB, 25 dB and 30 dB SNRvalues)


0 30 60 90 120 150 180 210 240 270 300 330 36015

20

25

30

35

40

45

50

55

60

Angle Θ in degrees

Cap

acity

(bi

ts/s

/Hz)

SNR=20dBSNR=25dBSNR=30dB

Figure 6.23: Capacity variation with angle θ

6.6.2 Capacity Variation with Controlled UT Spatial Distribution

In this analysis, the angle of separation between the users was kept constant during each

realisation. This constant angle of separation θS ep was increased from 0° to 60° with

1° steps during different realisations. When θ=0° the users were concentrated to a point

and when θ=60° all six users were separated by 60° angle to spread around 360° cover-

age area. For each 1° incremented step, 1000 channel frequency responses were obtained

by changing the reference randomly as shown in Figure 6.24. All UTs were distributed

on a ring with radius d1 km. Also, simulations were performed for different d1 distances

from 5 km to 25 km increasing d1 by 5 km steps. For each simulation, the carrier

frequency was taken as 641.5 MHz.

Figure 6.25 shows the capacity values for 20 dB, 25 dB and 30 dB SNR against

θS ep. Similar capacity variation results were obtained when d1 distance was increased

in 5 km steps from 5 km to 25 km. Figure 6.25 shows channel capacities for d1=20 km

at different θS ep angles. For analysis purposes SNR=20 dB curve was considered. It


UT1

UT6UT5

UT4

UT3

UT2

AP

d1

θSep

Ref

θSep

θSep

θSepθSep

Figure 6.24: Controlled user distribution on a ring with radius d1 km with an angle θS ep

can be observed that when θS ep=0°, the channel matrix becomes rank 1. As the angular

separation between UTs (Tx) increases, the capacity also increases as each AP antenna

(Rx) sees more uncorrelated UT channels. When θS ep=0° the capacity was recorded

as 8.25 bits/s/Hz. As θS ep is increased, the capacity also increases and reaches the

maximum at θS ep=30°. Recorded capacity value when θS ep=30° was 43.9 bits/s/Hz.

As θS ep is increased from 30° (corresponds to θ=180°) to 60° (correspond to θ=360°) no

additional capacity improvement can be observed for the given AP antenna array. This

is in accordance with results from the previous section, as θS ep=30° corresponds to a

UT distribution of θ=180° and θS ep=60° corresponds to a UT distribution of θ=360°.

The above variations can be explained by analysing the eigenvalue distribution for

different user separation angles as shown in Figure 6.26. As θS ep=0°, only one eigen-

value (out of 6 eigenvalues) is dominant. This eigenvalue distribution relates to a fully

correlated channel matrix. As θS ep increases the single dominant eigenvalue diminishes

and correlation between sub-channels reduces. Therefore, capacity increment can be

experienced when θS ep is increased from 0° to 30°. As θS ep is increased from 30° to

60°, no significant change in eigenvalue distribution can be observed. Therefore, no


0 10 20 30 40 50 600

10

20

30

40

50

60

70

Angle θSep

Cap

acity

(b/

s/H

z)

SNR=20dBSNR=25dBSNR=30dB

Figure 6.25: Capacity variation with angle θS ep (d1= 20 km)

010

2030

4050

600

1

2

3

4

5

6

0

20

40

60

Eigen value number

Angle θSep

Eig

en v

alue

(lin

ear

scal

e)

0

10

20

30

40

50

60

70

Figure 6.26: Capacity variation with angle θS ep

6.7. CAPACITY IMPROVEMENT WITH USER GROUPING 177

additional capacity improvement can be observed.

It should be noted that capacity archived by experiments for 20 dB SNR is 43.7 bits/s/Hz.

Controlled user distribution results have also shown that the maximum possible capacity

that can be obtained at 20 dB SNR is 43.9 bits/s/Hz. This capacity was obtained when

θS ep was around 30°or higher. UT distribution of the experimental setup also confirmed

that minimum angular separation between neighbouring UTs were greater than 30°.

Therefore, capacities calculated using experimental data were the highest achievable

capacities due to the separated UTs in azimuthal angle.

In order to minimise the effects of aforementioned ill-conditioned channels, closely

located users can be separated using a suitable user grouping method. After implement-

ing a suitable user grouping method, UTs with small angular separation can be assigned

into different frequency channels or time slots. Therefore, capacity improvement possi-

bilities with a suitable UT grouping method is discussed in the next section.

6.7 Capacity Improvement with User Grouping

This section analyses possible capacity improvements introduced by employing a suit-

able user grouping method for the proposed MUSA-MIMO-OFDM system. According

to the previous analysis, it was observed that higher capacities can be reached when

the angle separation of users are increased. Therefore, a suitable user grouping method

proposed in [142], which maximises the minimum angle of separation among any neigh-

bouring UTs is employed in this analysis.

Assuming nUT UTs are allocated to each group and mUG number of user groups can be

created using different frequency channels or timeslots, the indexes of UTs in the iUGth

group can be written as [142]:

Group iUG : iUG + (s − 1)mUG, s = 1, 2, 3, ...., n (6.10)

Equation 6.10 allocates users with maximum angular separation to a single group.

For instance, if 12 users are positioned around the AP and they are numbered in the


UT1

AP d1d2

UT2

UT3

UT4

UT5

UT6

UT7

UT8

UT9

UT10UT11

UT12

Ref

Figure 6.27: Example of user grouping

order of increasing angle from a reference, two user groups can be created according

to Equation 6.10 by allocating UTs 1,3,5,7,9,11 to Group 1 and UTs 2,4,6,8,10,12

to Group 2. To order the number of UTs in the order of increasing angle, location

information of UTs at the AP is required. This location information can be obtained

by the GPS receiver at each UT. Figure 6.27 illustrates two user groups (blue and red

colour UTs) with 6 UTs assigned into each group. The grouping method is applied after

arranging the UTs in the order of increasing angle from the reference. As the number of

groups increases, the minimum angle separation among any neighbouring UTs within a

group also increases.

In this study, UTs were assumed to be randomly distributed within the boundaries

of two concentric circles with radii 5km and 25 km, respectively. Moreover, users were

distributed on a flat terrain. As a result, only LoS and ground reflected components were

accounted when deriving channel coefficients and Equation 5.12 was employed for this

task. In this study, two user, four user and eight user groups were considered. In addition,

as a reference, a no user grouping scenario was investigated to identify the capacity

improvement due to user grouping. Several AP-UT antenna combinations, 4 AP × 2 UT,


8 AP × 4 UT, 16 AP × 8 UT, 32 AP × 16 UT, 64 AP × 32 UT and 128 AP × 64 UT were

employed in this analysis. Since the number of AP antennas were increased during the

simulations, a Uniform Circular Array (UCA) was employed instead of a 3 tier antenna

array.

Simulation procedure can be explained using an example for 4 AP × 2 UT antenna

combinations. In this example, the total number of users is fixed as 16, whose locations

were randomly generated. In each realisation, before applying the grouping method,

users were arranged in the order of increasing angle from the reference as shown in

Figure 6.18. Then the grouping method presented in Equation 6.10 was used to assign

random users into groups. In order to create a no user grouping scenario, 2 UTs were

randomly chosen from the 16 users. To simulate 2 user grouping scenario, 2 UTs were

randomly selected from 8 users within each of two groups created by Equation 6.10.

Similarly, for 4 user grouping scenarios, 2 UTs were randomly selected from each of

4 groups. For 8 user grouping scenarios, 2 UTs are directly determined from 8 groups.

One thousand realisations of 16 randomly generated users were performed for the 4 AP ×

2 UT antenna configuration during the simulations.

After applying the user grouping method, each user grouping scenario has a fixed

number of SDMA users for each group. As an example, for 4 AP × 2 UT antenna com-

bination, all user grouping scenarios (no grouping, 2 user, 4 user and 8 user grouping) are

having 2 SDMA users for each group as shown in column 5 in Table 6.5. Although the

number of users are fixed for each scenario, the minimum angle of separation increases

with the number of user groups. Tables 6.5-6.7 present user allocation information for

8 AP × 4 UT and 16 AP × 8 UT as examples.

Table 6.5: User allocation information about 4 AP × 2 UT case

4 AP × 2 UT Case No of No of No users SDMA users selectedtotal users groups within group from each group

No Grouping 16 1 16 22 User Grouping 16 2 8 24 User Grouping 16 4 4 28 User Grouping 16 8 2 2








While keeping the total number of users fixed (for Table 6.5, this is 16), the number

of users from which 2 SDMA users are selected varies from 16, 8, 4, 2 for no grouping,

2 user grouping, 4 user grouping, and 8 user grouping scenarios.

Figures 6.28-6.33 illustrate capacity Cumulative Distribution Functions CDFs gener-

ated for 4 AP × 2 UT, 8 AP × 4 UT, 16 AP × 8 UT, 32 AP × 16 UT, 64 AP × 32 UT and

128 AP × 64 UT antenna combinations. For each antenna combination, capacity CDFs

for no user, 2 user, 4 user and 8 user groupings were calculated for 1000 realisations

(1000 random UT antenna positions around 360° coverage).

Then 50th percentile (median) and 10th percentile values for each user grouping

and antenna combination were recorded in this analysis. The tenth percentile value

was chosen as 90% of realisations have achieved at least this capacity value or more.

Table 6.8 records 50th and 10th percentile values obtained from Figures 6.28-6.33. In

order to provide a better illustration of capacity improvement due to user grouping, the

50th percentile capacity for different user groupings and antenna combinations were

plotted as shown in Figure 6.34. Figure 6.34 shows that capacity for a given antenna

combination can be improved using the grouping method presented in Equation 6.10.

This capacity improvement becomes significant as the number of AP and UT antennas

were increased.


5 10 15 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Capacity (b/s/Hz), SNR = 20 dB

Cum

ulat

ive

Prob

abili

ty

No Grouping2 User Grouping4 User Grouping8 User Grouping

Figure 6.28: Capacity CDFs for 4 AP x 2 UT combination

15 20 25 30 350

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Cum

ulat

ive

Prob

abili

ty




35 40 45 50 55 60 65 700

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Cum

ulat

ive

Prob

abili

ty



80 90 100 110 120 1300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Cum

ulat

ive

Prob

abili

ty




180 190 200 210 220 230 240 250 2600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Cum

ulat

ive

Prob

abili

ty



350 400 450 5000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Cum

ulat

ive

Prob

abili

ty




0

100

200

300

400

500

Antenna Combination

4APx

2UT

8APx

4UT

16A

Px8U

T

32A

Px16

UT

64A

Px32

UT

128A

Px64

UT

Cap

acity

(bi

ts/s

/Hz)


Figure 6.34: 50th percentile capacity for different user groups and antenna combinations

0

100

200

300

400

500

Antenna Combination

4APx

2UT

8APx

4UT

16A

Px8U

T

32A

Px16

UT

64A

Px32

UT

128A

Px64

UT

Cap

acity

(bi

ts/s

/Hz)


Figure 6.35: 10th percentile capacity for different user groups and antenna combinations

6.8. EFFECT OF USER GROUPING ON CONTROLLED UT DISTRIBUTION 185

Table 6.8: Percentile capacities for different user groupings

Antenna 50th percentile capacity 10th percentile capacitycombination (bits/s/Hz) (bits/s/Hz)

No UG 2 UG 4 UG 8 UG No UG 2 UG 4 UG 8 UG4 AP x 2 UT 14.54 14.79 14.85 14.90 12.18 13.19 13.42 13.448 AP x 4 UT 27.97 28.92 29.17 29.29 23.93 26.73 27.1 27.29

16 AP x 8 UT 54.31 57.59 58.39 58.50 48.18 54.1 55.84 56.1332 AP x 16 UT 105.7 113.4 115.2 115.8 98.17 108.1 111.9 112.364 AP x 32 UT 209.2 224.5 229.3 230.1 198.7 216.9 224.4 225.3

128 AP x 64 UT 415.9 448.8 460 461.3 399.4 438.8 452.7 454.6

According to the analysis, for a selected antenna combination, channel capacity

increases with the number of user groups. According to the records shown in Table 6.8,

compared to no user grouping case, significant capacity increment can be observed as

the number of user groups are increased from 0 to 2 and 2 to 4. However, only a slight

capacity improvement can be observed as the number of user groups are increased from

4 to 8, especially for larger arrays. Similar results can be observed for 10th percentile

capacity values as shown in Table 6.8 and Figure 6.35.

Reasons for this capacity increment can be explained as follows; The user grouping

method which was employed in this analysis maximises the minimum angle of sep-

aration among any neighbouring UTs. As the number of user groups increases, the

minimum angle of separation between neighbouring UTs becomes higher for a given

user group. UTs in a given user group experience higher angular separation. Therefore,

as shown in Section 6.6.2, capacity increases due to improved spatial separation.

6.8 Effect of User Grouping on Controlled UT Distribution

More simulation work has been conducted in order to understand how this user grouping

method improves performance when users were restricted to a specific sector angle.

In this study, only a single AP-UT antenna combination was analysed. Therefore, a

12AP × 6UT antenna combination was selected as it is a similar AP-UT combination

to the measurement system. Channel capacities were calculated for no user grouping, 2

user, 4 user and 8 user grouping scenarios while changing the angle of user distribution


from 10° to 360°. Users were randomly positioned in a restricted sector angle θ and

around the AP between two concentric circles with 5 km and 25 km radii, respectively.

Then, 1000 realisations were performed for each restricted sector angle θ. In each

realisation, before applying the grouping method, users were arranged in the order of

increasing angle from the reference as shown in Figure 6.18. Then the grouping method

presented in Equation 6.10 was employed to assign random users into groups.

0 50 100 150 200 250 300 350 40015

20

25

30

35

40

45

50

55

Sector angle (Θ) in degrees

Cap

acity

(bi

ts/s

/Hz)

No Grouping2 User Group4 User Group8 User Group

Figure 6.36: Capacity for different sector angles and user grouping

Figure 6.36 illustrates capacities calculated for the 12AP × 6UT antenna combination

with no user grouping, 2 user, 4 user and 8 user grouping scenarios. As shown in the

figure, an increment in mean capacity (mean capacity over 1000 realisations) can be

observed when the angle of user distribution is increased. Capacity plots for different

user groups show an improvement in capacity when the UTs were distributed in a specific

sector angle due to increased number of user groups. For instance, when the UTs were

distributed in a 90° angle, capacity for the no user grouping scenario was recorded

as 38.6 bits/s/Hz. For 2 user, 4 user and 8 user cases, capacities were recorded as

6.9. SUMMARY 187

42.2 bits/s/Hz, 44.7 bits/s/Hz and 46.4 bits/s/Hz, respectively. Also, when θ = 150 ,

no user, 2 user, 4 user and 8 user grouping capacities were 44.7 bits/s/Hz, 49.6 bits/s/Hz,

52.2 bits/s/Hz and 53.6 bits/s/Hz.

As shown in Section 6.7, this user grouping method maximises the minimum UT

angular separation. Moreover, when a higher number of user groups are employed, the

minimum angular separation between UTs becomes higher. Therefore, even when the

UTs are restricted to a smaller angle, 8 user group capacity shows the highest value.

For a given user distribution angle, when the number of user groups were reduced, the

capacity also reduced. Therefore, implementing a user grouping method which accounts

for the user location is important when improving the uplink capacity of the MUSA-

MIMO-OFDM systems.

6.9 Summary

A comprehensive capacity analysis for an innovative MUSA-MIMO-OFDM fixed wire-

less broadband access system in rural environments was presented in this chapter. Also,

rural MUSA-MIMO-OFDM channel capacity was compared with popular theoretical

models and capacity results predicted by deterministic simulations. Results showed that,

experimental capacity calculated from the rural channel measurement was better than the

channel capacity obtained from the conventional Rayleigh channel assumption. More-

over, capacities predicted by deterministic simulations exhibited a good agreement with

the experimental capacity. Development of a novel empirical capacity equation which

can predict the capacity improvements in rural environments with dominant LoS paths,

with the number of increasing UTs (which are spatially separated) was presented within

this chapter. Also, capacity variation results due to different user distribution around

the AP were presented in this chapter. Results showed a degradation in MUSA-MIMO-

OFDM capacity when the angle of user distribution was restricted to small angles. These

results have already been used by CSIRO scientists to determine optimum user distribu-

tion angles around the AP. Moreover, this study showed that capacity degradation effects

when the angle of user distribution was restricted to small angles can be eliminated by

implementing an appropriate user grouping method. Finally, the chapter presented time


variations of MUSA-MIMO channel capacity in a rural environment based on capacity

dynamic range analysis. This study concluded that the proposed system supports stable

channel capacities in rural environments. Capacity results of this chapter have already

benefited CSIRO scientists and system developers to understand the advantages and

capacity gains of MUSA-MUMO-OFDM systems in rural environments.

Chapter 7

Conclusions

7.1 Concluding Remarks

For the first time, this thesis focused on channel measurement results, deterministic

modeling and capacity analysis for a novel MUSA-MIMO-OFDM system, proposed

to provide high-speed broadband services to scattered rural population. The proposed

system was developed under a 2008 Australian government patent application (patent

application No. 20089045554) by CSIRO [16]. The system was implemented by CSIRO

in a farmland near Smithton, Tasmania and channel measurements were conducted over

six days from 2010-12-10 to 2010-12-15. The author involved in the channel measure-

ment and lead the measurement of weather information on site.

Twelve access point (AP) antennas and six user terminals (UTs) were implemented

during the channel measurements. Experiments were carried out by using 641.5 MHz

as the carrier frequency. Channel measurements were performed with 1,705 occupied

OFDM sub-carriers. The experiments were conducted in an environment with large

open areas and few local scatterers. As a result, dominant propagation paths were

available from the AP to the UTs. Due to the presence of low scatterer densities, channel

measurements were performed in an environment with less scattering richness.

For the purpose of highlighting the contributions and discussing conclusions, this

section presents the motivated research questions as stated in Chapter 1. The main

research questions that motivated this thesis are:

189

190 CHAPTER 7. CONCLUSIONS

1. Up to which extent are AP-UT sub-channels correlated while achieving the capac-

ity gain promised by the rural MUSA-MIMO-OFDM channels, and do all sub-

carriers posses similar channel correlation matrix?

2. How to adopt or develop a physically meaningful model which includes underly-

ing dominant radio propagation effects for rural MUSA-MIMO-OFDM channels

in order to predict MUSA-MIMO-OFDM channel capacity?

3. Based on the measurement results, what are the actual capacity gains achieved by

the MUSA-MIMO-OFDM system deployed in rural environments?

4. How much capacity increment will MUSA-MIMO-OFDM channels exhibit with

the number of users in rural environments?

5. Is the proposed system capable of providing stable channel capacities?

6. Is there any capacity variation with different user distributions around the AP?

7. What strategies to adopt to overcome possible detrimental effects on capacity when

users are closely located?

In order to answer question 1, the spatial structure (channel correlation matrix) of

AP-UT combinations were analyzed using the channel measurement data. This analysis

uncovered that, for case of uplink and for a given AP antenna, each AP-UT combination

exhibited very low correlation values between 0 and 0.1. Therefore, this analysis has ver-

ified that, for the uplink, each AP antenna (Rx) sees channels with very low correlation

(uncorrelated) from each UT (Tx). The analysis was further extended to investigate the

channel correlation matrix for all sub-carriers to verify whether all sub-carriers posses

same channel correlation matrix or not. It was verified that, all sub-carriers exhibit a

similar correlation for any given 2 sub-channels. Therefore, it has been concluded that

for any given sub-carrier, each AP antenna sees uncorrelated sub-channels from each

UT.

The second question has been answered in Chapter 5. This chapter focused on

developing a novel channel model capable of predicting accurate MUSA-MIMO-OFDM

7.1. CONCLUDING REMARKS 191

channel capacity for a given rural environment. Before developing this model, the possi-

bility of adopting an existing model had also been considered. Therefore, in Chapter 4,

a detailed review of existing MIMO and MU-MIMO channel models was conducted. In

the literature, physical, analytical and hybrid MIMO channel modeling approaches are

employed to model MIMO channels.

Analytical channel models characterize the impulse response of the channel mathe-

matically, without accounting for wave propagation. These models make assumptions

regarding the propagation environment (such as rich scattering) and model channel coef-

ficients as random variables according to a given statistical distribution. Physical prop-

agation models are further classified as deterministic, geometry-based stochastic and

non-geometrical stochastic [41]. A given physical propagation model is deterministic,

if it is possible to reproduce the actual wave propagation scenario (process) for a given

environment.

Although channel models such as the 3GPP spatial model [86], Winner I and Win-

ner II [117] accommodate MIMO and MU-MIMO systems, these models do not account

terrain between the AP and UT. Accounting for terrain is important for outdoor channel

modeling to predict governing propagation mechanisms between the AP and UTs. As

stated in Chapter 3, these models are ray-based stochastic channel models which con-

sider superposition of MPCs with random powers, AOD and AOA. As a result, these

models do not faithfully predict site-specific performance. Therefore, as highlighted

in Chapter 3, a novel channel model was required to predict the MUSA-MIMO-OFDM

system performance in rural areas. Deterministic models are more realistic and accurate,

due to the representation of the environment specific geometry [41] such as terrain

profiles. Therefore, a deterministic modeling technique was followed to model the rural

wireless channels for the proposed MUSA-MIMO-OFDM system.

The author is not aware of any previous work proposing a deterministic channel

model for MUSA-MIMO-OFDM system in rural environments. Therefore, for the first

time, a deterministic MUSA-MIMO-OFDM channel model suitable for MUSA-MIMO-

OFDM systems in rural areas was developed through this research. Moreover, the appli-

cation of the best available resolution (3 arc-second [134]) digital elevation map (DEM)


in the proposed model improves the prediction accuracy over that using the lower res-

olution DEMs. The model accounts for terrain between the AP and a given UT, and

determines the LoS, ground reflected and diffracted paths via a terrain analysis algo-

rithm. Furthermore, the model accommodates three dimensional representations of AP

and UT antennas as well as three dimensional antenna patterns. It generates frequency

responses for all OFDM sub-carriers. Another outcome generated through developing

this model was a diffraction loss prediction tool as stated in Chapter 5.

The main objective of developing this deterministic model was to predict rural MUSA-

MIMO-OFDM channel capacity accurately through modeling the rural MUSA-MIMO-

OFDM channels. The accuracy of the deterministic channel model was validated with

respect to the measured channel during the experiments conducted in Smithton, Tasma-

nia. It was verified that the developed model accurately predicts the channel capacity for

rural environments with dominant LoS paths, with a root mean square (RMS) error of

0.18 bits/s/Hz between the experimental and predicted capacity values.

Questions 3 and 4 were addressed by Chapter 6. According to the analysis in Chap-

ter 6, the proposed system achieved a spectral efficiency of 43.7 bits/s/Hz at 20 dB SNR.

Compared to the spectral efficiency achieved by the proposed system, conventional tech-

nologies may achieve 6.6 bits/s/Hz in the near future, as demonstrated by Telstra [143].

Since this is the first time a MUSA-MIMO-OFDM system was implemented in a rural

area, it is interesting to investigate how much capacity gain is possible under realistic

propagation conditions with dominant LoS paths for the proposed system. Therefore,

the rural MUSA-MIMO-OFDM channel capacity was compared with two theoretical

models, in order to measure how the channel capacity under realistic propagation con-

ditions varied with the theoretical predictions. For this purpose, the ideal model which

provides the absolute upper bound capacity and Rayleigh channels which are feasible

under popular rich scattering environments were selected.

In Chapter 6, it was shown that the channel capacity scales linearly with the number

of transmitter antennas (when the number of transmitter and receiver antennas are equal).

Comparing the experimental and Rayleigh capacities, the experimental capacity of this

rural environment exhibits a slightly higher value (in the range of 0.5-1 bits/s/Hz) than


that predicted by the Rayleigh channel model. It is important to note that each UT had

a dominant LoS path from the AP during the experiments. Therefore, the propagation

channel of this rural environment is expected to exhibit low scattering. However, the

comparison result shows that this environment supported a higher channel capacity than

a rich scattering environment. This is due to the fact that the UTs of this MUSA-MIMO

system were spatially separated and the uplink channels associated to different UTs were

distinct as verified by the correlation analysis. In space, this corresponds to UTs having

sufficient azimuthal angle separation. To the best of the author’s knowledge, no previous

work has experimentally shown that MU-MIMO with LoS performs better than in a rich

scattering environment, which is represented by a Rayleigh channel.

As an answer for question 4, Chapter 6 introduces a simplified novel empirical

formula which can predict capacity improvement with the number of increasing UTs

for different SNR values, in a rural environment with dominant LoS paths. This formula

is useful in understanding the actual capacity gains in a rural environment with dominant

LoS paths, for SNR values between 16 dB and 40 dB. This equation was derived to pre-

dict channel capacity when users are spatially separated, with the correlation coefficient

between each sub-channels is less than 0.1.

Question 5 analyses variations of channel capacity in time to understand the stability

of the system. To gain a better understanding of channel capacity temporal variations,

capacity dynamic range was observed as illustrated in Chapter 6. In this study, 90% of

the capacity dynamic range, was calculated for ten hours within two measurement days.

Out of the six measurement days, Day 5 and Day 6 had continuous data for most of the

measurement hours. Therefore, Day 5 and Day 6 were chosen in the analysis. Similar

capacity variations for all sub-carriers were observed in the analysis. During day 5, for a

single sub-carrier, the maximum and minimum capacity dynamic ranges observed were

0.28 bits/s/Hz and 0.21 bits/s/Hz, respectively. Moreover, for Day 5, small variations

in capacity dynamic range were observed, with an average hourly variation rate of

0.23 bits/s/Hz. It was a 0.5% variation from the mean capacity measured during 5 hour

measurement window. Compared to Day 5, Day 6 exhibited more variations in capacity

dynamic range. During Day 6, the maximum and minimum capacity dynamic ranges

observed were 0.84 bits/s/Hz and 0.53 bits/s/Hz, respectively. Also, Day 6 recorded


an average hourly variation rate of 0.68 bits/s/Hz which was a 1.5% variation from the

mean capacity measured during 5 hour measurement window. Reasons for different

capacity variations for Day 5 and Day 6 were further analysed accounting the weather

conditions, as high variations in wind conditions were observed during measurement

hours. Results have shown that the wind speed can introduce variations in the capacity

dynamic range. However, for these two days only 0.5% and 1.5% capacity variations,

from mean capacities, were experienced. Therefore, according to channel capacity

dynamic range analysis, MUSA-MIMO uplink channels deployed in the rural Smithton

area support stable channel capacities.

Question 6 is concerned about whether there is any capacity variation when users are

located close in angle around the AP. It is interesting to investigate how much capacity

variations does the system exhibits, when the users are restricted to a specific angle

around the AP. MU-MIMO systems have been considered to be immune to possible

performance degradation caused by the propagation channel, such as having a LoS

propagation, due to wide physical separation between the users [83]. However, to the

best of author’s knowledge, capacity variation of MUSA-MIMO-OFDM systems due to

different UT positions, especially in rural areas with dominant LoS propagation remains

as an open problem. To find the relationship between the channel capacity and the angle

of user distribution (θ), a number of deterministic simulations were performed, by em-

ploying the validated deterministic channel model, while increasing θ from 10° to 360°.

Two studies were conducted to identify the relationship between capacity variation

and user distribution. In the first study, UTs were randomly distributed within the

boundaries of two concentric circles (5km and 25km radii) located around the AP and

the distributions were restricted at angles θ ranging from 10° to 360°. Results showed a

capacity increment as θ increased from 10° to 360°. A significant capacity improvement

was observed when θ increased from 10° to 180°. However, a smaller increment in

capacity compared to 10°≤ θ ≤180°was observed than in 10° ≤ θ ≤ 180°.

The second study was conducted with more controlled user distributions to analyse

capacity variation with the angle of separation (θS ep). In this study , θS ep between the

users was kept constant and users were distributed at a similar distance from the AP.


Then θS ep was increased from 0° to 60° with 1° steps during the different realizations.

When θS ep=0°, the users were concentrated to a point and when θS ep=60°, all six users

were separated by 60° angle to spread around the 360° coverage area. As the angular

separation between UTs (transmitters) was increased, the capacity also increased as each

AP antenna (receivers) sees more uncorrelated UT channels. When θS ep=0° the capacity

was recorded as 8.25 bits/s/Hz. As the θS ep was increased, the capacity also increased

and reached the maximum at θS ep=30°. Recorded capacity value when θS ep=30° was

43.9 bits/s/Hz. As θ was increased from 30° to 60°, no additional capacity improvement

was observed for the given AP antenna array.

The above variations were explained by analysing the eigenvalue distribution for

different θS ep values. As θS ep=0°, only one eigenvalue (out of 6 eigenvalues) was dom-

inant. This eigenvalue distribution related to a fully correlated channel matrix. As

θS ep was increased, the single dominant eigenvalue diminished and correlation between

sub-channels reduced. Therefore, a capacity increment was experienced when θS ep was

increased from 0° to 30°. As θS ep was increased from 30° to 60°, no significant change

in eigenvalue distribution was observed. This is due to the fact that when θS ep ≥ 30°,

each AP antenna saw an uncorrelated channel from each UT. Therefore, no additional

capacity improvement could be observed. This study fully answers question 6 which

intended to identify the relationship between capacity variation and user distribution

around the AP.

In order to answer question 7, a suitable user grouping method stated in Chapter 6

was employed. This method maximize the minimum angle separation among any neigh-

bouring UTs. In this study two user, four user, eight user grouping cases and capacity

without user grouping were investigated to identify the capacity improvement related to

user grouping. Several AP-UT antenna combinations, 4 AP × 2 UT, 8 AP × 4 UT, 16 AP

× 8 UT, 32 AP × 16 UT, 64 AP × 32 UT and 128 AP × 64 UT were used in the analysis.

Results showed that the capacity for a given antenna combination could be improved

using the grouping method stated in Chapter 6. Moreover, this capacity improvement

became significant as the number of AP and UT antennas were increased. Results of

this study answers question 7. Therefore, implementing a suitable user grouping method

as shown in Chapter 6 can minimize the detrimental effects imposed on capacity as


verified by this study. Users allocated to different groups may be assigned into different

frequency channels or time slots to ensure optimal performance of the system.

Results of this thesis have significantly benefited CSIRO scientists and MUSA-MUMO-

OFDM system developers to understand performance and capacity gains of such MUSA-

MUMO-OFDM systems in rural environments. Moreover, the deterministic model and

deterministic simulation results have already been used by CSIRO scientists to determine

optimum user distribution angles around the AP, and to further improve the performance

of this system in rural environments.

7.2 Research Outcomes

7.2.1 Publications

In the course of this doctoral research work, the following publications have submitted

or published in international conferences and refereed journals.

• Nisal L. Ratnayake, Karla Ziri-Castro, Hajime Suzuki, and Dhammika Jayalath,

“On the capacity of Rayleigh and free-space MIMO Communications”, expecting

to submit to IEEE Antennas and Wireless Propagation Letters, currently working

on this publication.

• Nisal L. Ratnayake, Hajime Suzuki, Karla Ziri-Castro, and Dhammika Jayalath,

“Analysis of rural MUSA-MIMO-OFDM uplink channel capacity”, IEEE Trans-

actions on Wireless Communications, will be submitted on 5th March 2013.

• Nisal L. Ratnayake, Hajime Suzuki, Karla Ziri-Castro, and Dhammika Jayalath,

“Measurement, Modeling and User Distribution Effects for Multiuser MIMO-

OFDM channels in Rural Environments”, Special Issue on Radio Wave Propa-

gation and Wireless Channel Modeling of International Journal of Antennas and

Propagation, under review.


“Effects of User Distribution on Multiuser MIMO-OFDM Channel Capacity in

7.2. RESEARCH OUTCOMES 197

Rural Areas”, Twelfth International Symposium on Communications and Informa-

tion Technologies (ISCIT), Australia, October 2012.

• Hajime Suzuki, David Robertson, Nisal L. Ratnayake, and Karla Ziri-Castro, “Pre-

diction and measurement of multiuser MIMO-OFDM channel in rural Australia”,

IEEE 75th Vehicular Technology Conference (VTC2012), Japan, May 2012.

• Nisal L. Ratnayake, Karla Ziri-Castro, and Hajime Suzuki, “Time variation effects

of weather conditions in rural MUSA-MIMO-OFDM channels”, Loughborough

Antennas and Propagation Conference, U.K, November 2011.


“Deterministic diffraction loss modelling for novel broadband communications

in rural environments” Proceedings of 2011 Australian Communications Theory

Workshop (AusCTW), Australia, February 2011.

• Nisal L. Ratnayake, Lakmali Atapattu, Karla Ziri-Castro, and Dhammika Jayalath,

“Efficient wireless broadband communications to rural area”. Ninth Annual Sym-

posium on Electromagnetic Compatibility, Australia, November 2010.

• Nisal L. Ratnayake,“Modelling the broadband wireless channel in rural Australia”.

Eleventh IEEE International Symposium on a World of Wireless, Mobile and Mul-

timedia Networks, Canada, June 2010.

7.2.2 Awards

• Awarded “2012 Netcom HDR student award for research excellence” award by

the discipline of Networks and Communications on 5th December 2012.

• Awarded “Outstanding higher degree research student of the month” award in

August, 2011 by the Faculty of Built Environment and Engineering, Queensland

University of Technology.

• Best student paper award for the paper titled “Efficient wireless broadband com-

munications to rural area”.


• Awarded $1000 travel grant for the paper titled “Efficient wireless broadband

communications to rural area”.

7.3 Future Research Topics

One of the objectives of this thesis is to develop a deterministic MU-MIMO channel

model for rural environments. This model is capable of predicting the channel matrices

for 1705 OFDM sub-carriers. Generating channel matrices for 1705 OFDM sub-carriers

introduce added computational complexity. Therefore, computers with high computa-

tional resources are required (more than 6 GB memory) to run this model. Computa-

tional complexity of generating MUSA-MIMO channels for 1,705 OFDM sub-carriers

independently, can be reduced by taking into account the coherence of MUSA-MIMO

channels in frequency. It will allow this model to run on resource limited computers

as well. This will be considered in a future work. Moreover, the applicability of this

model for performance prediction of Long Term Evolution (LTE) systems will also be

considered as future work.

As described in Section 6.6.2, variation of channel capacity was analysed using

random and controlled user distribution scenarios. In future, for a given rural area,

analysis of MUSA-MIMO performance using realistic UT distributions (for instance

many houses in rural areas are distributed along a road) is considered. In order to locate

the positions of rural houses, rural house location data are required. After obtaining these

locations for a given rural area, this data can me imported to the deterministic model for

performance prediction in realistic UT distributions.

Appendix A

A.1 Detecting LoS availability using terrain analysis algorithm

As stated in Chapter 5, obstructions to the LoS path can be detected using a terrain

analysis algorithm presented in Algorithm 1. It should be noted that only the main

steps related to terrain analysis are presented in Algorithm 1. Before terrain analysis

procedure, it accounts the earth curvature and introduces a correction to the terrain

heights. To determine the LoS path availability, the algorithm checks whether all first

Fresnel zone heights between the AP and UT are greater than the corrected terrain

heights. If this condition is satisfied, the algorithm detects no obstructions to the LoS

path. Else, obstructions to the LoS path are present.

A.2 Detecting diffraction edges

If the first Fresnel zone obstruction is detected by Algorithm 1, possible diffraction edges

are calculated by Algorithm 2. In order to detect diffraction edges, algorithm calculates

intersection points between the terrain profile and the LoS path. Algorithm 2 presents

the procedure of detecting the main diffraction edge. Then, v-parameter and the complex

Fresnel integral are calculated for the main edge. Since Deygout method is employed in

this research, diffraction loss due to other terrain obstructions are found with respect to

a line joining the main edge between the transmitter and the receiver. The total loss is

calculated as the sum of three components, the main edge and the subsidiary main edges

on either side. As an example, v-parameter and the complex Fresnel integral calculation

199

200 APPENDIX A. APPENDIXA

for only the main diffraction edge is presented in Algorithm 2.

Algorithm 1: Terrain analysis (Detecting LoS path availability)Data: DEM data, UT and AP locations

Result: LoS path available or not

dstep=resolution of the DEM

ntot=number of dstep from Ap to UT

for i=1:ntot do

d(i)=i × dstep;

dLoS (i)=i × dLoS step;

get terrain height h(i), for d(i) from DEMh(i)=

DEM data(longitude(d(i)),latitude(d(i)));

apply Earth curvature correction;

hest(dc) = h(dc) + ecrr

(cos

(∣∣∣∣ d2ecrr−

dcecrr

∣∣∣∣) − cos(

d2ecrr

) );

hest(i) = h(i) +

( ecrr cos(

dLoS2ecrr

)(ecrr−

ecrr cos( dLoS

2ecrr

)cos

(∣∣∣∣∣ dLoS2ecrr

−dc

ecrr

∣∣∣∣∣) )

ecrr cos( dLoS

2ecrr

)cos

(∣∣∣∣∣ dLoS2ecrr

−dc

ecrr

∣∣∣∣∣)

);

Tx height=hest(1)+ Tx antenna height;

Rx height=hest(ntot)+Rx antenna height;

derive LoS path equation (yLoS ) for Tx-Rx pathcalculate Fresnel radius at

distance d(i)r1(i) =

√(λdLoS (i)(dLoS−d(i))

dLoS

);

calculate lowest Fresnel zone path (Lower Fres(i)) closer to the ground

Lower Fresnal Path(i) = yLoS (i) − r1(i);

calculate terrain obstructions

if Lower Fresnal Path(i) − hest(i) ≥ 0 then

Terrain Obs Point(i) = 0;

else

Terrain Obs Point(i) = Lower Fresnal Path(i) − hest(i);

end

end

if all elements in Terrain Obs Point(i) == 0 then

LoS path available;

else

LoS path obstructed;

end

A.2. DETECTING DIFFRACTION EDGES 201

Algorithm 2: Terrain analysis (Detecting diffraction edges)Data: DEM data, UT and AP locations, Terrain Obs Point matrix

Result: Diffraction edges

detect value from Terrain Obs Point matrix, related to main diffraction edge

main diffraction val=i=ntotmaxi=1

[Terrain Obs Point]

find i index detect main diffraction edge

imain edge= f ind(Terrain Obs Point==main diffraction val);

calculate v-parameter for main edge

vmain = h√

2(dLoS )λi×dLoS step(dLoS−i×dLoS step) ;

F(vmain) = EE0

=(1+ j)

2

∫ ∞vmain

e− jπt2

2 dt;

202 APPENDIX A. APPENDIXA

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