Eﬀects of Multipath Interference on Radio …rmf25/papers/Effects of Multipath Interference on... · Eﬀects of Multipath Interference on Radio Positioning Systems Ramsey Michael

Effects of Multipath Interference

on Radio Positioning Systems

Ramsey Michael Faragher

Department of Physics

Churchill College, University of Cambridge

A thesis submitted for the degree of

Doctor of Philosophy

September 2007

ii

Declaration

This dissertation is the result of work carried out in the Astrophysics Group

of the Cavendish Laboratory, Cambridge, between October 2004 and June 2007.

The work contained in the thesis is my own except where stated otherwise. No

part of this dissertation has been submitted for a degree, diploma or other quali-

fication at this or any other university. The total length of this dissertation does

not exceed sixty thousand words.

Ramsey Faragher

September 2007

iii

This thesis is dedicated to my parents, Pauline and Brian, and to

my brother Paul.

iv

Acknowledgements

I would like to thank my supervisor, Dr. Peter Duffett-Smith, for his friendly

and expert guidance during the last three years, and for giving me the oppor-

tunity to work on such an interesting project. Cambridge Positioning Systems

sponsored this research and I am grateful for their support. I would like to

acknowledge James Brice for his invaluable help in understanding Viterbi decod-

ing and the GSM signal structure. I also want to thank my close friends for

keeping me sane(ish) - Stanislav Shabala, George Vardulakis, Michael Bridges,

Anna Scaife, Emily Curtis, Tom Auld, Jonathan Zwart, Huw Jones, Matt Raskie,

Max Holzner, Paul Rhatigan, David Singerman, Marisa Grillo, Iga Wegorzewska,

Kerry McCann, Vicky Lister, Priya Shah, Friederike Mansfeld, Kirstin Woody,

Avaleigh Milne, Liz Azzato, Alex Gillies and the rest of my basketball team. I

would especially like to thank my girlfriend Ally for her love, patience, and sup-

port during the writing of this thesis. Finally, and most importantly, I want to

thank my parents for their unconditional support, and for putting so much of

their time and money into my education. I could not have reached this point in

my academic career without them.

v

I do not think that the wireless waves I have discovered will have any

practical application.

Heinrich Rudolf Hertz

vi

Abstract

The effects of multipath interference on GSM signal timing stabilities and on ra-

dio positioning systems using the GSM network are examined. Two experimental

methods for accurately measuring signal arrival times are described - the inter-

ferometric technique and the network-synchronised technique. An experimental

apparatus capable of performing measurements on the GSM network to a reso-

lution of 24.5 nanoseconds or 7.35 metres is described. The results of a set of

experiments measuring the timing stability of the received signals from two net-

works suggest that Fine Time Aiding can be provided on one network over time

periods of 3 days or more and on the other over time periods of up to 5 hours.

A set of experiments measuring the positioning error associated with moving an

antenna slowly over sub-wavelength distances indoors is described. Examples of

errors in the region of hundreds of metres are noted for an antenna moving a few

millimetres. The errors are shown to be caused by corruption of the Extended

Training Sequence timing marker in the received signal. The raised-cosine model

is proposed and demonstrates the ability to accurately reproduce experimental

behaviour and determine probable propagation paths. Alternative methods of

determining signal arrival times using the ETS timing marker are proposed and

their accuracies are compared to the usual ‘peak-max’ technique. Finally, the

timing error distributions for rural, suburban, light-urban and mid-urban envi-

ronments are measured. A probability density function model derived from the

raised-cosine model is shown to reproduce the experimental results.

vii

Glossary of Abbreviations

3G. Third Generation.

AOA. Angle Of Arrival.

BCCH. Broadcast Control Channel.

BSIC. Base Station Identity Code.

BTS. Base Transceiver Station.

C/A code. Coarse Acquisition code.

CCH. Control Channel.

CDMA. Code Division Multiple Access.

DCM. Database Correlation Method.

ETS. Extended Training Sequence.

FCB. Frequency Control Burst.

FDMA. Frequency Division Multiple Access.

FH. Frequency Hopping.

FTA. Fine Time Aiding.

FRK-H. The model of Rubidium Oscillator used in this project.

GLONASS. GLObal NAvigation Satellite System.

GNSS. Global Navigation Satellite System.

GPIB. General Purpose Interface Bus.

GPS. Global Positioning System.

GSM. Group Speciale Mobile

ILS. Instrument Landing System.

LORAN. LOng RAnge Navigation.

LOS. Line Of Sight.

MCXO. Microprocessor Controlled Crystal Oscillator.

viii

NAVSTAR. NAVigation Satellite Timing And Ranging.

OCXO. Oven Controlled Crystal Oscillator.

P code. Precise code.

PN code. Pseudorandom Number code.

RbO. Rubidium Oscillator.

RDF. Radio Direction Finder.

RFS. Rubidium Frequency Standard.

SA. Selective Availability.

SCB. SynChronisation Burst.

SCH. SynChronisation Channel.

SNR. Signal to Noise Ratio.

TCXO. Temperature Controlled Crystal Oscillator.

TDOA. Time Difference Of Arrival.

TDMA. Time Division Multiple Access.

TOA. Time Of Arrival.

TOF. Time Of Flight.

TTFF. Time To First Fix.

UMTS. Universal Mobile Telecommunications System.

UPS. Uninterruptible Power Supply.

VHF. Very High Frequency.

VLF. Very Low Frequency.

VOR. Very High Frequency Omni-directional Radio Ranging.

XO. Crystal Oscillator.

ix

x

Contents

1 Introduction to radio positioning 1

1.1 Local radio positioning . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Cell-phone positioning . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2.1 Cell-ID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.2.2 Database Correlation . . . . . . . . . . . . . . . . . . . . . 12

1.2.3 Enhanced Observed Time Difference . . . . . . . . . . . . 13

1.2.4 Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.2.5 Enhanced GPS . . . . . . . . . . . . . . . . . . . . . . . . 14

1.2.5.1 Autonomous start . . . . . . . . . . . . . . . . . 17

1.2.5.2 Cold start . . . . . . . . . . . . . . . . . . . . . . 18

1.2.5.3 Warm and hot starts . . . . . . . . . . . . . . . . 18

1.2.5.4 Fine Time Aiding . . . . . . . . . . . . . . . . . . 18

1.3 Multipath interference . . . . . . . . . . . . . . . . . . . . . . . . 19

1.4 Contributions to this field of research . . . . . . . . . . . . . . . . 20

1.5 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2 Timing stability 23

2.1 Allan Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.2 Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.2.1 Crystal oscillators . . . . . . . . . . . . . . . . . . . . . . . 34

2.2.2 Temperature-compensated crystal oscillators . . . . . . . . 37

2.2.3 Oven-controlled crystal oscillators . . . . . . . . . . . . . . 37

xi

CONTENTS

2.2.4 Microcomputer-controlled crystal oscillators . . . . . . . . 38

2.3 Atomic oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.3.1 Rubidium oscillators . . . . . . . . . . . . . . . . . . . . . 40

2.3.2 Caesium beam oscillators . . . . . . . . . . . . . . . . . . . 44

2.3.3 Hydrogen masers . . . . . . . . . . . . . . . . . . . . . . . 45

2.3.4 Caesium fountains . . . . . . . . . . . . . . . . . . . . . . 47

2.3.5 Optical atomic clocks . . . . . . . . . . . . . . . . . . . . . 48

2.4 Measurements with two Rb frequency standards . . . . . . . . . . 48

2.5 Measurements of the stabilities of FRK-H Rb oscillators . . . . . 49

2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3 Time of flight measurements on cellular networks 55

3.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.1.1 Interferometric method . . . . . . . . . . . . . . . . . . . . 55

3.1.2 Network-synchronised method . . . . . . . . . . . . . . . . 56

3.2 The Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.2.1 Radio frequency digitiser . . . . . . . . . . . . . . . . . . . 59

3.2.2 Triggering and synchronisation . . . . . . . . . . . . . . . 59

3.2.3 Uninterruptible power supplies . . . . . . . . . . . . . . . . 60

3.3 Data storage and analysis . . . . . . . . . . . . . . . . . . . . . . 60

3.3.1 Sampling theory . . . . . . . . . . . . . . . . . . . . . . . 61

3.3.2 MATLAB driven data capture . . . . . . . . . . . . . . . . 63

3.3.3 Cross correlation . . . . . . . . . . . . . . . . . . . . . . . 66

3.3.3.1 The ambiguity function . . . . . . . . . . . . . . 66

3.4 Anatomy of a GSM signal . . . . . . . . . . . . . . . . . . . . . . 68

3.4.1 GSM digital encoding . . . . . . . . . . . . . . . . . . . . 71

3.5 Anatomy of a CDMA signal . . . . . . . . . . . . . . . . . . . . . 72

3.6 The Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

3.6.1 Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . 73

3.6.2 Surveying . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

xii

CONTENTS

3.6.3 Post-processing . . . . . . . . . . . . . . . . . . . . . . . . 74

4 GSM Network Stability 85

4.1 Method and apparatus . . . . . . . . . . . . . . . . . . . . . . . . 85

4.1.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.2 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . 88

4.2.1 900 MHz Network . . . . . . . . . . . . . . . . . . . . . . . 93

4.2.2 1800 MHz Network . . . . . . . . . . . . . . . . . . . . . . 98

4.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5 The effects of indoor multipath environments on timing stability103

5.1 Method and apparatus . . . . . . . . . . . . . . . . . . . . . . . . 103

5.2 Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . 104

5.2.1 Roof experiment . . . . . . . . . . . . . . . . . . . . . . . 105

5.2.2 Roof Laboratory Tests . . . . . . . . . . . . . . . . . . . . 110

5.2.3 Electronics Laboratory tests . . . . . . . . . . . . . . . . . 117

5.2.3.1 Spatial and temporal variations . . . . . . . . . . 120

5.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

6 Modelling the effects of indoor multipath environments on tim-

ing stability 127

6.1 Modelling cross-correlation peak distortions . . . . . . . . . . . . 127

6.1.1 Received Signal Interference model . . . . . . . . . . . . . 128

6.1.2 Cross-Correlation Peak Interference model . . . . . . . . . 128

6.1.3 Results of simulations . . . . . . . . . . . . . . . . . . . . 129

6.2 Determining signal arrival times . . . . . . . . . . . . . . . . . . . 138

6.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

7 A study of the timing errors encountered when performing radio-

location using the GSM network 147

7.1 Definitions of environment . . . . . . . . . . . . . . . . . . . . . . 148

7.2 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

xiii

CONTENTS

7.2.1 GPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

7.2.2 GPS accuracy and errors . . . . . . . . . . . . . . . . . . . 150

7.3 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

7.3.1 Indoor mapping accuracy . . . . . . . . . . . . . . . . . . 155

7.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

7.4.1 Error analysis . . . . . . . . . . . . . . . . . . . . . . . . . 159

7.5 Modelling the timing error distributions . . . . . . . . . . . . . . 161

7.5.1 Fitting the free parameters . . . . . . . . . . . . . . . . . . 166

7.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

8 Summary and further work 175

8.1 The experimental apparatus . . . . . . . . . . . . . . . . . . . . . 175

8.2 The experimental methods . . . . . . . . . . . . . . . . . . . . . . 175

8.3 GSM network timing stabilities . . . . . . . . . . . . . . . . . . . 176

8.4 GSM network timing stabilities in indoor multipath environments 176

8.5 GSM radio location timing error distributions in various environ-

ments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

8.6 Further work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

A Distributions of A, φ and α 181

A.1 Distribution of φ . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

A.2 Distribution of α . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

A.3 Distribution of A . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

References 199

xiv

List of Figures

1.1 Sketch showing the geometries involved with the Angle Of Arrival,

Time Of Arrival and signal strength positioning methods. . . . . . 2

1.2 Sketch showing the hyperbolic geometry involved with the TDOA

positioning method. . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Plot showing the variation in candidate locations for a GPS re-

ceiver position using the weak-signal method as the satellites move

through their orbits. . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.4 Plot showing the cross-correlation function resulting from search-

ing a frequency range for a given PN code . . . . . . . . . . . . . 15

1.5 Sketch demonstrating the benefit of having accurate estimates of

the positions of the PN codes in the received satellite broadcasts . 17

2.1 Sketch showing the types of error affecting an oscillator’s frequency 25

2.2 Plot of a series of phase samples versus time. . . . . . . . . . . . . 27

2.3 Idealised Allan deviation Plot . . . . . . . . . . . . . . . . . . . . 30

2.4 Allan deviation plot for various oscillators. . . . . . . . . . . . . . 31

2.5 Plot showing a simple electrical circuit which displays oscillatory

behaviour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.6 Plot showing the transfer of energy in a tank circuit during its

oscillatory cycles. . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.7 Plot showing nomalised resonance curves for oscillators with dif-

ferent Q values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

xv

LIST OF FIGURES

2.8 The equivalent electrical circuit for a crystal resonator . . . . . . 35

2.9 A circuit diagram for a crystal oscillator . . . . . . . . . . . . . . 36

2.10 Plot showing the frequency variations with temperature for three

crystal oscillator systems. . . . . . . . . . . . . . . . . . . . . . . 38

2.11 Schematic diagram of a Rubidium frequency standard. . . . . . . 42

2.12 Schematic diagram of a Caesium beam frequency standard. . . . . 45

2.13 Schematic diagram of a Hydrogen maser frequency standard. . . . 47

2.14 Schematic diagram of the apparatus used to measure the stability

of an FRK-H Rb oscillator. . . . . . . . . . . . . . . . . . . . . . . 50

2.15 Allan deviation plots for an Efratom FRK-H Rb oscillator and for

an OCXO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

2.16 The phase differences between the 10MHz outputs of two Rubid-

ium oscillators in four experiments. . . . . . . . . . . . . . . . . . 53

3.1 The experimental apparatus . . . . . . . . . . . . . . . . . . . . . 58

3.2 A sample of data showing the signal-to-noise ratio . . . . . . . . . 63

3.3 Sampling theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.4 The ETS ambiguity function . . . . . . . . . . . . . . . . . . . . . 67

3.5 GSM Framing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.6 GSM Bursts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.7 Post-processing flowchart . . . . . . . . . . . . . . . . . . . . . . . 75

3.8 A description of the GSM modulation and encoding techniques,

and the BSIC and frame number decoding process . . . . . . . . . 77


and the BSIC and frame number decoding process (continued) . . 78





3.12 A cross-correlation profile generated using the interferometric method 82

xvi

LIST OF FIGURES

3.13 A cross-correlation profile generated using the network-synchronised

method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.1 A picture showing the antenna above the roof of the Cavendish

Laboratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.2 Sketch showing the experimental setup used to produce the cali-

bration Allan Deviation curves . . . . . . . . . . . . . . . . . . . . 88

4.3 Plot showing the Allan deviation curves produced by an internally-

and externally-locked Racal GSM signal generator. . . . . . . . . 89

4.4 Plots showing the variation in relative signal arrival times from a

GSM base station broadcasting in the 900 MHz waveband. . . . . 90

4.5 Plot showing the variation in signal arrival times from a GSM base

station broadcasting in the 1800 MHz waveband. . . . . . . . . . 91

4.6 The Fourier transform of the data given in Figure 4.4. . . . . . . . 92

4.7 The Fourier transform of the data given in Figure 4.5. . . . . . . . 92

4.8 The Allan deviation plots for the base stations on the 900MHz

network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4.9 Map of Cambridgeshire showing the positions of the base stations

studied and the Cavendish Laboratory . . . . . . . . . . . . . . . 95

4.10 The timing data and Allan deviation curves from the 900 MHz

GSM base station represented by Curve ‘C’ in Figure 4.8 . . . . . 97

4.11 The Allan deviation plots for the base stations on the 1800MHz

network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

4.12 Plot comparing the timing errors for three base stations. . . . . . 100

5.1 A view of the BTS from the roof of the Rutherford building . . . 106

5.2 A view of the BTS from the first position of the antenna during

the initial experiment on the roof of the Rutherford building . . . 107

5.3 Diagram illustrating the first Fresnel zone for a transmitter-receiver

separation of 1,200 metres and operating with a wavelength of 30

centimetres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

xvii

LIST OF FIGURES

5.4 Plot showing the data from the roof experiment. . . . . . . . . . . 109

5.5 Plot showing sample SCB peaks from the roof experiment . . . . 110

5.6 Plot showing multipath behaviour recorded inside the Roof Labo-

ratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112


ratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114


ratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

5.9 Sketch demonstrating how sharp spikes in timing error can be pro-

duced by SCB peaks deformed by multipath interference . . . . . 116

5.10 Plot showing the signal stability recorded inside the Rutherford

Building during the night . . . . . . . . . . . . . . . . . . . . . . 117

5.11 Plot showing the consistency of the multipath behaviour recorded

inside a room in the Rutherford building. . . . . . . . . . . . . . . 119

5.12 Plot showing the multipath behaviour recorded inside the Ruther-

ford building over a small area. . . . . . . . . . . . . . . . . . . . 120

5.13 Plot showing the moduli of ten consecutive SCB peaks recorded

during an indoor survey . . . . . . . . . . . . . . . . . . . . . . . 121

5.14 Scatter plots showing the correlation between temporal and the

apparent spatial multipath variation. . . . . . . . . . . . . . . . . 123

5.15 Plot showing multipath behaviour recorded inside the Rutherford

building by a slow moving antenna. . . . . . . . . . . . . . . . . . 124

5.16 Plot showing the timing variations recorded in the main corridor

of the Rutherford building for a slow moving antenna. . . . . . . . 125

6.1 Plot showing a simulation of the Roof Laboratory experiment . . 130

6.2 Plot showing a simulation of the Roof Laboratory experiment . . 131

6.3 Picture showing the view from the Roof Laboratory window . . . 132

6.4 Plot showing a simulation of the Roof Laboratory experiment. . . 133

6.5 Plot showing a simulation of the Electronics Laboratory experiment.134

xviii

LIST OF FIGURES

6.6 Plot showing a simulation of the Electronics Laboratory experi-

ment with random phases on reception. . . . . . . . . . . . . . . . 136


ment with random amplitudes on reception. . . . . . . . . . . . . 137


ment with random amplitudes and measurement noise on reception.138

6.9 Plot showing methods of determining a signal arrival time using

the SCB peak. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

6.10 Plots showing tests of the three signal-arrival techniques using sim-

ulated data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

6.11 Plots showing tests of the three signal-arrival techniques using two

sets of data gathered using an indoor receiver. . . . . . . . . . . . 142

6.12 Plot showing tests of the three signal-arrival techniques using the

data from the initial roof experiment. . . . . . . . . . . . . . . . . 143

7.1 Plot showing the effects of good and bad satellite geometry on the

accuracy of a GPS position . . . . . . . . . . . . . . . . . . . . . . 151

7.2 Plot showing the distribution of GPS positions recorded in a fixed

position on the Cavendish Laboratory roof at 2 pm and 5 pm over

many days and weather conditions. . . . . . . . . . . . . . . . . . 153

7.3 Plot showing the use of Pythagoras’ theorem in calculating the

distance from a base station using the signal flight time. . . . . . 154

7.4 Plots of the normalised histograms of the timing error for each

environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

7.5 Diagram showing the floor plan of the indoor environment used in

the survey. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

7.6 Comparison of the modulus of the GSM ETS auto-correlation peak

and a truncated raised-cosine function . . . . . . . . . . . . . . . 162

7.7 Plot showing how the superposition of two displaced and out-of-

phase cross-correlation peaks can result in a distorted function. . . 163

xix

LIST OF FIGURES

7.8 Plot showing the effect of varying σy in the model . . . . . . . . . 167

7.9 Plot showing the effect of varying R in the model . . . . . . . . . 167

7.10 Plot showing the effect of varying p in the model . . . . . . . . . . 168

7.11 Plot showing the characteristic delays in the outdoor environments 169

7.12 Plots showing the rural data set with the multipath model overlaid 170

7.13 Plots showing the suburban data set with the multipath model

overlaid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

7.14 Plots showing the light-urban data set with the multipath model

overlaid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

7.15 Plots showing the mid-urban data set with the multipath model

overlaid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

7.16 Plots showing the indoor data set with an adjusted multipath

model overlaid . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

A.1 Diagram showing the parameters for considering Fresnel diffraction

at a knife edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

A.2 Plots of the signal amplitudes after diffraction down to points of

interest from a single knife edge for various distances from a 15

metre tall BTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

A.3 A plane wave incident onto a plane boundary . . . . . . . . . . . 187

A.4 Plots of the reflection coefficients for vertically polarised 900MHz

GSM signals incident on brick and concrete surfaces . . . . . . . . 188

A.5 Plots showing the received signal amplitude (relative to the unob-

structed signal) for two propagation mechanisms. . . . . . . . . . 190

A.6 Plots showing the correlation between S1 and S2 for the four po-

tential distributions of A and the distributions of α and φ. . . . . 192

xx

Chapter 1

Introduction to radio positioning

This thesis examines the effects of multipath interference on radio positioning

techniques, specifically those that can be employed on the GSM cellular network

using signal arrival time measurements. The ability to locate a person or object

using radio waves holds great appeal for many applications such as safety and

security applications, personal navigation, the provision of location-based services

and the tracking of people or goods. All cellular radio-positioning systems require

a method of determining a user’s position relative to a set of signal sources at

known locations. This position can be determined using one or more of the

following basic methods:

Angle Of Arrival (AOA). The user’s position can be determined by considering

the direction to each source (triangulation).

Time Of Arrival (TOA). The user’s position can be determined by calculating the

distance (or difference in distances) to each source, inferred from measurements

of the signal arrival times (or differences in arrival times). The distance to a

source is directly proportional to the signal flight time for a signal propagating

in a given medium.

Signal strength. Signal strength decreases predictably in free space with distance

from the source. The received signal strengths from a number of sources can be

used to establish estimates of the distances to the sources.

1

1. INTRODUCTION TO RADIO POSITIONING

Figure 1.1: Sketch showing the geometries involved with the Angle Of Arrival (left),Time Of Arrival (right) and signal strength (also right) positioning methods. The AOAmethod measures the angular separation between pairs of sources, or between a sourceand a reference direction. Two sources are sufficient to provide a unique solution.The TOA method involves measuring the signal flight times from a set of sources tothe receiver. Each measurement defines a circle around the source which intersectsthe receiver’s position. Three sources can provide a unique two-dimensional position.The signal strength method also defines circles around each source which must intersectwith the receiver, and so three sources are also required for a unique solution using thistechnique.

All of these techniques work best with line-of-sight (LOS) paths to the sources.

If the LOS paths are obstructed then the relative accuracies of the three methods

can vary considerably. The signal-strength method is highly variable, for example

moving from just outside to just inside a building can reduce the signal strength

by an amount that corresponds to moving a much greater distance from the signal

source in open space. If the strongest signal arrivals at a receiver are reflected

or diffracted signals, then the accuracy of the angle of arrival method can be

reduced significantly since the signal arrival directions can differ from their true

bearings. The angle-of-arrival technique also requires an antenna system capable

2

1.1 Local radio positioning

of measuring the direction of a signal’s path, a feature which is neither simple

nor inexpensive in a hand-held device. Time-of-arrival methods are therefore the

most robust techniques for difficult, non-LOS environments as the slight increase

in path length caused by a complicated propagation path will result in a smaller

error compared to the corresponding angular and signal strength changes.

Every positioning method has an inverse, i.e. a mobile receiver can measure

the signals from a network of transmitters, or alternatively, a network of receivers

can measure the signals from a mobile transmitter. In both cases, the position

of the mobile device is determined. Radio positioning can therefore either be de-

scribed as ‘local’ or ‘remote’. Local positioning involves a mobile unit calculating

its own position, whereas remote positioning involves the network determining

the location of the mobile units.


The first local radio navigation system was the radio direction finder (RDF). This

method has been used by ships since the early twentieth century and has been

used extensively by aircraft since about 1930 [1]. RDF uses a highly-directional

antenna to determine the bearing of a signal source. A single signal can be used as

a directional aid while two or more signals can be used to determine a position by

triangulation. A system employing narrow intersecting RDF beams was used by

German bombers during World War II to trace a flight path along a certain route

to a target. The modern instrument landing system (ILS) employed by airports

uses RDF to guide aircraft along the correct glide slope to land on a runway in

low visibility [2]. A number of signals are broadcast on different frequencies and

in diverging, narrow beams along and around the correct glide path. The pilot

can determine his glide path relative to the ideal by monitoring the frequency of

the strongest signal receipt.

The next development in radio navigation came in the 1950s with very high

frequency omni-directional radio ranging (VOR) [2]. This system allows an air-

3


craft to determine the bearing to the VOR source without needing a dedicated,

movable, and highly-directional antenna. The VOR source broadcasts two 30

Hz modulations on Very High Frequency (VHF) carriers (VORs are assigned fre-

quencies in the range 108–117.95 MHz). These two signals are, (i) a frequency

modulated reference which is identical in all directions and (ii), an amplitude

modulated navigation broadcast which has a direction-dependant phase differ-

ence compared to the reference. The navigation signal is broadcast by a direc-

tional antenna rotating at 30 Hz in order to generate the relationship between

signal phase and broadcast direction. An aircraft receiving these signals using

an omni-directional antenna can measure their phase difference and so determine

the bearing of the VOR source.

Systems that measure a signal’s arrival angle but cannot employ the VOR

technique require a highly-directional antenna. Positioning systems which mea-

sure the arrival time of a signal are not limited by these requirements. The

difficulty encountered when measuring signal flight times is in determining the

times that the signals were broadcast relative to the times they were received. Ra-

dio navigation systems can avoid this problem by measuring the Time Difference

Of Arrival (TDOA) of the signals from pairs of synchronised sources (see Figure

1.2 below). Each time-difference measurement then corresponds to a hyperbolic

surface which must intersect the user. The different arrival times recorded from

different pairs of sources define different hyperbolic surfaces and the common re-

gion in space where these surfaces intersect or overlap gives the user’s position.

Three signal sources are required to determine a two-dimensional position.

The first radio positioning system to use signal arrival times was the British

GEE system employed in World War II to aid bombers [3]. The system incor-

porated three 30 Hz transmitters (a ‘master’ and two ‘slaves’) all broadcasting

precisely-timed, 6 microsecond pulses. The master transmitted a single pulse

followed 2 milliseconds later by a double pulse. The first slave broadcasted a

single pulse 1 millisecond after it received the master’s single pulse. The sec-

ond slave broadcasted a single pulse 1 millisecond after it received the master’s

4


Figure 1.2: Sketch showing the hyperbolic geometry involved with the TDOA position-ing method. The difference in arrival times of the signals received from synchronisedtransmitters define hyperbolic surfaces in space upon which the receiver must lie. Threesignal sources are required to provide a unique two-dimensional position.

double pulse. The procedure repeated in a 4 millisecond cycle. The receiving

unit measured the relative arrival times of the pulses from all three transmitters

and used hyperbolic geometry to calculate its own location. The receiver could

achieve a timing resolution of 1 microsecond, representing an error of ±150 me-

tres on each hyperbola and a resulting error on the overall position calculation of

around ±210 metres. At the maximum range of about 650 kilometres, this error

increased both because of the reduction in signal strength and the geometry of

the system1. The error at this distance was roughly ±1.5 kilometres along a line

toward the midpoint of the GEE transmitters, and roughly ±10 kilometres per-

pendicular to this direction. Although poor by modern standards, the precision

1For a discussion of how source geometry affects positioning accuracy see the description ofdilution of precision in Section 7.2.2 of Chapter 7.

5


of the system was revolutionary at the time. The system was also much more

flexible than the German RDF technique which was limited to guiding aircraft

along a particular route. The GEE system allowed an aircraft to determine its

own position anywhere within the operating range of the transmitters.

The GEE technique led to the development of the American LORAN (LOng

RAnge Navigation) system, which is typically accurate to around half a kilometre

[2]. The modern surviving version, LORAN-C, makes use of a number of trans-

mitters worldwide to provide coverage over the majority of the USA and North

Western Europe, including coastal waters.

The first fully global radio positioning system was OMEGA, which became

operational in 1971 [4]. It was developed for aviation purposes and used eight

transmitters located around the globe to provide position calculations to an ac-

curacy of 4 miles. The system broadcasted Very Low Frequency (VLF) signals

(10-14 kHz) using large antennas on masts 400 metres high or more. Each trans-

mitter emitted a unique pattern of four tones and the location of a receiver was

calculated using the TDOA method.

A major advance in global radio navigation was made with the development

of Global Navigation Satellite Systems (GNSSs) in the 1960s. The first oper-

ational GNSS system was the TRANSIT system (also known as NAVSAT) [5].

This system consisted of five active satellites in polar orbits with periods of 106

minutes. A number of backup satellites were also in orbit but were only used

when one of the active satellites failed. Each satellite broadcasted a precise tim-

ing signal and its own orbital characteristics. The Doppler shift of the received

frequency from the expected value was used by the receiver along with the or-

bital information to determine the range to the satellite. This range alone was

not enough to determine a unique position; fixes from another satellite or from

the same satellite at different points in its orbit were required. TRANSIT could

therefore not provide rapid and real-time positioning. However, the system was

adequate for its purpose of providing periodic corrections to submarine guidance

systems.

6


The American NAVSTAR GPS (NAVigation Satellite Timing And Ranging

Global Positioning System) is currently the only fully operational GNSS [5]. The

system’s constellation of thirty active satellites (as of April 2007) are in a medium

Earth orbit at a height of 20,200 kilometres and provide navigation assistance to

both military and civilian users using two different wave-bands.

GPS incorporates CDMA encoding (see Section 3.5 for a discussion of this

technique) to allow all of the satellites to broadcast on the same frequency and

to use the entire available bandwidth. Each satellite broadcasts data using two

spreading codes (PN codes), the 1023 bit (or ‘chip’) long Coarse Acquisition

(C/A) code at a bit-rate of 1.023 million chips per second, and the Precise code

(P code) at a bit-rate of 10.23 million chips per second, with the latter only

available for military purposes. The C/A code repeats every millisecond and

each code is unique to each satellite. The P code is a more complicated sequence,

being 2.35× 1014 chips (approximately 266.4 days) long but allocated such that

each satellite broadcasts a 6.182× 1012 chips (one week) long portion of the full

sequence.

The satellites carry atomic clocks which are kept in coarse alignment with

each other and with GPS time by signals from a ground-based control network.

The satellite timing references are allowed to drift away from GPS time by up

to a microsecond before their on-board frequency standards are corrected, but

these time offsets are continually monitored and updated in transmissions to the

satellite to be including in their own signal broadcasts.

The navigation information transmitted by the satellites contains three types

of data. The first is almanac data containing the status and coarse orbital in-

formation for every satellite in the constellation. The second is ephemeris data,

allowing the receiver to calculate the precise orbital position of the transmitting

satellite. The third is the clock information (including the offset of the on-board

clock from GPS time) used by a receiver to calculate the signal’s Time Of Flight

(TOF).

7


The relative position of the receiver to a given satellite is described by the

equation √(X0 −Xn)2 + (Y0 − Yn)2 + (Z0 − Zn)2 = c(T0 − Tn), (1.1)

where c is the speed of the radio waves, X0, Y0 and Z0 are the Cartesian coor-

dinates of the receiver, Xn, Yn and Zn are the Cartesian coordinates of the nth

satellite, Tn is the transmission time of the signal from the nth satellite and T0

is the reception time of this signal at the receiver. Each satellite broadcasts its

own Tn value at regular intervals. The orbital information broadcasted by the

satellites allow Xn, Yn and Zn to be calculated for a given Tn. When a GPS signal

is received and decoded from the nth satellite, the values of Tn, Xn, Yn and Zn at

the moment that the signal was transmitted are known. A set of four simultane-

ous equations of the form given above in equation 1.1 (and so signals from four

satellites) are therefore required in order to solve for the unknowns X0, Y0, Z0

and T0 and calculate the receiver’s position. As the equations are non-linear, the

solution is found via an iterative process. If an estimate of the receiver’s position

is available at the start of the process, then the time required to arrive at the

solution (or the best estimate of the solution) is reduced.

This technique is only available when the satellite signals are strong enough to

be fully decoded and when the hardware allows the precise timing of the leading

edge of a data sub-frame to be determined. Other techniques are available which

allow GPS navigation using weak signals and rely on the fact that when the

spreading code template is cross correlated with the received signal, the position

of the cross-correlation peak in the data stream can be determined even when the

signal is too weak to be decoded. The signal timings can be measured to a high

precision modulo one millisecond (the repeat rate of the C/A PN code), but the

integer number of millisecond units that have passed between transmission and

reception is not known. The offsets in the arrival times of the PN codes from

each satellite can therefore be compared as they are measured, but the times of

flights of each signal are unknown. The time offsets then define a very large set of

8

1.2 Cell-phone positioning

possible locations for the receiver position, with a separation between candidate

locations of about 300 kilometres in three dimensions. However, as the satellites

move through their orbits, or as the receiver moves, the changes in the satellite

signal time offsets can be monitored and this reduces the number of candidate

locations for the receiver until there is only one possible receiver position (or in

the case of a moving receiver, only one set of receiver positions) that matches all of

the timing offsets that have been recorded (see Figure 1.3 below). Alternatively

the location of the recevier can be determined by using the the arrival times

of each signal to construct and solve a set of simultaneous equations (see the

discussion of the Matrix positioning technique below).

The range to a satellite can be measured to an accuracy of about 3 metres

using the civilian wave band (depending on the quality of the electronics used by

the receiver). The military signal is broadcast at a higher bit-rate and provides

a higher resolution by a factor of ten. These levels of precision are reduced

by a number of sources of error such as atmospheric effects, clock errors, the

accuracy of satellite orbital data, and the satellite geometry (see Section 7.2.2

in Chapter 7). The accuracy of absolute position calculations on the civilian

band is reduced to about 10–15 metres because of these errors. Various relative-

measurement techniques can achieve accuracies of 3–5 metres or better. Full

differential measurements can also be performed, yielding sub-metre precision,

by monitoring the phase of the carrier signal from each satellite.

The Russian GLONASS (GLObal NAvigation Satellite System) was a fully

functional GNSS in the mid 1990s but has now fallen into disrepair and is only

partially operational. The system is currently being renovated with the help of

the Indian government. Further GNSSs are being planned by Europe and China.


Many local radio positioning systems require a network of transmitters, a po-

sitioning technique, and a user with an appropriate receiver. Cell phones have

9


Figure 1.3: Plot showing the variation in candidate locations for a GPS receiver po-sition using the weak-signal method as the satellites move through their orbits. Thegreen markers represent an initial set of candidate locations, the red markers representthe set of candidate locations a few tens of seconds later as the satellites have movedthrough their orbits. As time passes, only one candidate location will be common to allsets for a stationary receiver, and this gives the receiver’s position.

become very popular portable radio receivers, with an estimated 2.5 billion hand-

sets in use the world as of 2006 [6], and so the idea of providing a radio positioning

system via cell phone networks is very attractive. A cell-phone positioning sys-

tem would allow networks and handset manufacturers to provide location-based

services, navigational aid, and the position of a user during an emergency call.

10


1.2.1 Cell-ID

The most basic form of cell-phone positioning is called Cell-ID, and is an inherent

feature of all cell phone systems [7]. In order to route calls to and from a hand-

set, the network provider must keep a constantly updated record of which Base

Station Transceiver (BTS) is “serving” the cell phone. Since every BTS has a

limited range and serves a certain area, a cell phone’s position must therefore be

confined to that region at that time. BTS antennas are either omni-directional

or directed into sectors. The most common arrangement is a tri-sectored BTS

with three transceivers, each covering a 120 degree swath. In GSM, the maxi-

mum range of a high-powered BTS (macrocell) is roughly 35 kilometres, but some

smaller transmitters (microcells) used to boost coverage in cluttered areas have

a range of a few kilometres [8]. Picocell transmitters have a range of about 100

metres, and are used in areas with dense phone usage but poor coverage, such

as train stations, shopping centres, etc. The positioning accuracy of this tech-

nique therefore depends on the type of BTS serving the cell phone and is highly

variable. For a cell phone known to be served by a high-powered and directional

BTS, the position is only known to be somewhere within a sector with a radial

length of roughly 35km and an arc length of roughly 73 km.

An improvement can be made to Cell-ID by also considering the Timing Ad-

vance (TA) value when determining a cell phone’s position [7]. Since electro-

magnetic radiation propagates at a finite speed, signals to and from distant cell

phones have longer flight times than those nearby. The GSM network uses Time

Division Multiple Access, allowing a number of users to share the same radio

frequency channel without interfering with each other by carefully synchronising

their transmissions (see Section 3.4). This level of synchronisation can only be

maintained if the signal flight times are known to an adequate precision. Timing

markers in the signals are monitored by the receiver and the signal flight times

are stored as TA values to enable propagation-delay compensation. The TA value

is a number between 0 and 63 and represents signal flight times in units of 3.69

11


microseconds (the GSM symbol period). This in turn corresponds to increments

of about 1,100 metres in the round-trip signal propagation path. The TA value

therefore increments for every 550 metre change in range between a mobile and

BTS and allows propagation-delay compensation for handsets up to about 35.2

kilometres away. Since the TA value only represents the radial distance from the

BTS the improvement to the positioning accuracy only applies to this aspect of

the cell phone’s position. The position estimate provided by TA with a direc-

tional high powered BTS antenna is an arc in space 550 metres wide which can

be between a few hundred metres and 73 kilometres long depending on the cell

phone’s distance from the BTS.

A further improvement to this technique can be made by forcing the cell

phone to register with other base stations within range and repeating the TA

measurements. Depending on the geometry and number of available base stations,

this can improve the positioning accuracy to around ±275 metres in all directions.

1.2.2 Database Correlation

A technique called the Database Correlation Method (DCM) can also be used to

position cell phones [9]. This system relies on the assumption that each position

in a given region has a unique ‘signal fingerprint’ defined by the set of signal

strength measurements from all nearby BTSs. A database containing the signal

strengths measured at every position in an area is first created either by surveying

or by computer simulation. The handset can then compare a given set of BTS

signal strengths to the values in this database and look up the corresponding

location. Accuracies of 100 metres or better have been demonstrated for outdoor

positioning using a database generated with signal propagation models [9, 10].

Signal propagation models are inadequate for simulating the complicated signal

environments found indoors, but the system has been shown to determine indoor

receiver positions to an accuracy of 5 metres or better using a database generated

12


with previously recorded data [11]. However, the signal strength at a given loca-

tion can vary due to changes in the local environment, atmospheric conditions,

and variations in the output from the BTS. A given ‘fingerprint’ is therefore not

necessarily constant and reliable over time.

1.2.3 Enhanced Observed Time Difference

The TDOA technique discussed above can be also be applied to cell phone posi-

tioning, however, the TDOA technique relies on synchronised base station trans-

missions, which are not a feature of the GSM network. This can be accounted

for in a central processing node called a Serving Mobile Location Centre (SMLC),

which constantly monitors the relative transmission times of the BTSs on the

network using measurements made by Location Measurement Units (LMUs) dis-

tributed throughout the network at known locations. The time offsets of the

BTS broadcasts are then taken into account during the TDOA calculations when

positioning a given handset (using the same timing marker used for TA). This

method is called Enhanced Observed Time Difference (E-OTD). The positioning

accuracy depends on the distribution of the BTSs, the use of interpolation tech-

niques (see Section 3.3.1 in Chapter 3), and signal degradation caused by noise

and multipath, but is typically quoted as being in the range of 50–150m [12].

1.2.4 Matrix

The Matrix positioning system, invented and developed by Cambridge Positioning

Systems, is a technique that provides the high accuracy associated with E-OTD

without requiring any LMUs distributed throughout the network [13, 14, 15].

Matrix calculates receiver positions by constructing, and then solving, a set of

simultaneous equations of the form

ctij = |ri − bj|+ εi + αj, (1.2)

13


where c is the speed of the radio waves, the vector ri is the position of the

ith receiver, and the vector bj is the position of the jth BTS. The value of tij

represents the arrival time of the timing marker from the jth BTS at the ith

receiver. The ε value is the timing offset of a given receiver and the α value is the

timing offset of a given BTS. The values of t, ε and α are all expressed relative

to an imaginary universal uniform clock.

The set of simultaneous equations cannot be solved for a single stationary

handset, but for a distribution of handsets sharing information, or a single moving

handset, enough data can be gathered to solve the set of equations. For a system

with ‘M ’ receivers and ‘B’ BTSs, the set can be solved when M×B ≥ 3M+B−1.

As more receivers join the distribution, or as any of the current set move, the

extra data continues to be used to improve the accuracy of previous and current

positions by improving the estimates of the ε and α values. Consequently, the

accuracy of the entire track of a single moving cell phone can improve steadily

as the cell phone (or others around it) move around the network. The typical

accuracy of the Matrix method is in the range of 50–150 metres.

1.2.5 Enhanced GPS

E-GPS is a cell phone positioning technique pioneered by Cambridge Positioning

Systems that incorporates both the Matrix system and an integrated, low-power

and low-cost GPS receiver [16]. In E-GPS, the GPS receiver is aided in acquiring

the satellite signals rapidly. In principle, a GPS device could acquire a satellite’s

signal immediately if it had knowledge of both the expected time offset and

frequency offset. The broadcast frequencies appear to be shifted because of the

Doppler effect as the satellites move through their orbits, and the time offsets

of the transmissions depend on the unknown distances to the satellites and the

unknown current value of GPS time. An unassisted GPS device therefore needs

to scan through a large range of frequency and time offsets searching for signals.

This two-dimensional search consists of cross-correlating a known code sequence

14


with a section of data received at a given time on a given frequency (see Figure

1.4) in order to ‘lock on’ to the satellite.

Figure 1.4: Plot showing the cross-correlation function resulting from searching a fre-quency range for a given PN code. Estimates of the frequency and of the position ofthe PN code within the received signal allow this search window to be reduced. Thisreduces the time required to find the correct frequency and the exact position of thecross-correlation peak

The receiver attempts to acquire the signal in time by determining the cur-

rent chip position of the C/A code broadcast. This is performed by setting the

receiver’s internal clock to one of the 1023 possible chip offsets and integrating

over hundreds of milliseconds1 before performing the cross correlation. This is

repeated for each offset value in sequence until the cross-correlation peak exceeds

1These long integration times are required since the satellite signals are weak by design toincrease security

15


a given threshold, indicating that the signal has been found. If all of the possible

offset values are exhausted before a signal is found, then another frequency must

be searched. Since the C/A code repeats every millisecond, the minimum coher-

ent integration time is a millisecond and therefore the coarsest frequency steps

that a receiver can make during an initial acquisition stage is 1 kHz without risk-

ing ‘missing’ the signal. The combination of the maximum possible Doppler shift

and the possible error on the receiver’s frequency reference results in a total fre-

quency error of up to about ±10 kHz, meaning that there are about 10 frequency

channels to test.

The search time can be reduced by increasing the number of correlators in the

device to allow parallel searching, but this increases its cost. If the GPS device

can estimate the time offset and frequency offset, the signal acquisition time and

required number of correlators can both be greatly reduced. These estimates

can be made using data from a recent position fix by the GPS device itself, or

using data from an external source. This ‘assistance’ data usually includes the

satellite orbital data, an estimate of the GPS receiver location, and an estimate

of the current GPS time. The GPS device can use these pieces of information

to calculate a narrow range of frequency offsets over which to search for each

satellite. The search window is also reduced by estimating the time offsets (i.e.

the code-phase offsets of the PN code sequences in each satellite broadcast) so

that the cross correlations can be performed over smaller time-offset ranges (see

Figure 1.5 below).

GPS devices can perform ‘hot’, ‘warm’, ‘cold’ and ‘autonomous’ starts de-

pending on the accuracy and content of the assistance data they are given or the

amount of time that has passed since their last satellite acquisition. The Time To

First Fix (TTFF) for each of these conditions varies considerably. TTFF refers

to the time taken for a GPS device to return a position calculation after it has

been requested.

16


Figure 1.5: Sketch demonstrating the benefit of having accurate estimates of the po-sitions of the PN codes in the received satellite broadcasts. With no knowledge of thelocation of the spreading code, a cross-correlation over all possible code-phase offsets isneeded (as shown in the picture marked (a) above). If the position of the PN code isknown with some degree of accuracy, then fewer code-phase offsets need to be tested,reducing the processing time required (as shown in the picture marked (b) above).

1.2.5.1 Autonomous start

A GPS device will perform an autonomous start if it has no information about

the GPS time, receiver location, or satellite orbits. In this case, the GPS receiver

simply sweeps the entire code-phase offset range and entire frequency offset range

attempting to decode strong signals. The TTFF is dependant on the number of

correlators in the GPS device, the number of visible satellites and the time taken

to download the full data content from a satellite. The time taken to download

the ephemeris data is up to 30 seconds, but the time taken to download the

almanac data is at least 12.5 minutes. Each satellite broadcasts only its own

ephemeris data, and the data is only valid for a few hours. The almanac data is

valid for 6 months or more and for this reason it is typically stored on the GPS

device in non-volatile memory to allow the device to perform cold starts.

17


1.2.5.2 Cold start

A GPS device performs a cold start if it only has valid almanac data available.

The TTFF then depends on the time required for the GPS device to acquire

each satellite and then download its ephemeris data. The TTFF is therefore

governed by the number of correlators, the number of available satellites, their

signal strengths and the ephemeris download times. A cold start usually takes at

least 30 seconds.

1.2.5.3 Warm and hot starts

Warm and hot starts are possible if the GPS receiver has the almanac data, valid

ephemeris data for one or more satellites, an estimate of the receiver location

(within 100km or better) and an estimate of GPS time (within a few microseconds

or better). Depending on the accuracy of these estimates and the age of the

ephemeris data, the TTFF range is about 1–15 seconds. A hot start refers to a

TTFF of a few seconds or less.

1.2.5.4 Fine Time Aiding

As discussed above, a GPS device can either store data in order to perform future

warm or hot starts, or be provided with the data from an external source when

required. The device would need to search for (and acquire) satellites every few

hours in order to maintain warm starts independently, which would result in an

unwanted drain of its power supply. This approach would also rely on the device

being in a suitable environment at each ‘update time’ in order to receive the

signals. If the data is provided externally however, then the GPS device only

needs to be powered when a position calculation is required by the user. Every

fix can be then be a warm or hot fix with a low TTFF value, even for a GPS

device which has never been used before.

Assistance data can be categorised into an estimate of the receiver’s position,

an estimate of GPS time, the satellite orbital information, and estimates of the

18

1.3 Multipath interference

Doppler shifts. The accuracy of each of the pieces of assistance data determines

the TTFF. For a cell phone with a built-in GPS device, the receiver’s position

can be provided to an accuracy of 150 metres or better via the Matrix positioning

system. Almanac and ephemeris data can be provided via the cell phone network

to the highest accuracy possible. The estimate of GPS time can be provided by

using the Matrix positioning system to calibrate measurements of GPS time to

the frame number (which increments at a known rate) broadcast by a given BTS

on the cell-phone network at that moment. By comparing the current BTS frame-

number value with the calibration value, the current GPS time can be calculated.

The Matrix technique measures the timing offsets between base stations (the

values of α in Equation 1.2 above), and so this calculation can be performed

using a different base station from the one used to record the calibration values

if necessary. The cell phone’s reference oscillator (and the reference oscillator in

a GPS device) are only stable1 enough to hold GPS time accurately for a short

period. Cell-phone networks use more stable frequency references, which can be

used to provide this timing assistance (Fine Time Aiding) over much longer time

periods (as shown in Chapter 4 of this thesis).

1.3 Multipath interference

Multipath interference describes the phenomenon of multiple copies of the same

signal interfering with each other at the point of reception. The effect occurs

whenever there is more than one propagation path for a signal to follow from

transmitter to receiver. The propagation paths can be different lengths and so

superimposed signals can have relative delays and phase differences. Multipath

interference effects can be negligible in situations where one signal path results in

a much stronger signal than the others, but in general it is possible for multipath

signals to cause significant corruption of the desired communication.

1See Chapter 2 for a discussion of the meaning of “clock stability”.

19


Signal path losses can be classed as slow fading and fast fading effects [17].

Slow fading is a large-scale effect caused by the clutter between the transmitter

and receiver such as buildings and trees. The signals arriving in different places

are attenuated by different amounts due to penetrating different media along

their propagation paths. As the receiver is moved short distances, variations in

the received signal due to these effects are gradual. Fast fading is a small-scale

effect which is caused by multiple signals interfering at the point of reception. As

the receiver moves short distances, the phases and number of interfering signals

at the point of reception change and the effects on the signal strength can be

large and vary rapidly. The full fading environment consists of the fast fading

variations superimposed on the overall large scale slow fading variations.

Multipath interference, and so fast fading effects, can cause errors on cell-

phone positioning techniques by corrupting the signal timing marker. For radio

systems broadcasting high-bandwidth signals, the coherence length is short and

cross correlation with the timing marker produces a narrow peak. Multipath

interference can therefore appear as separately resolved timing markers if the

signal coherence length is shorter than the typical signal delays. For narrow-

band networks such as GSM, the signal coherence length is much longer than

the typical delay lengths (the coherence length is about 2 kilometres for GSM

signals and the delay lengths are typically up to several hundred metres). The

multipath signals cannot be resolved separately for signals on the GSM network

and they superimpose to create a single distorted cross-correlation peak. This

effect, and its impact on positioning systems utilising this timing marker, are

studied in detail in this thesis.

1.4 Contributions to this field of research

Most authors working on GSM multipath interference have been concerned with

the effects of this phenomenon on received signal strength [17, 18] and decoding

[19]. Most research on the effects of multipath interference on cellular positioning

20

1.5 Thesis outline

systems has previously involved either (a) ray-tracing computer simulations [20],

or (b) studying a radio signal created specifically for the research, which cannot

be broadcast in the cellular frequency bands and is not structured in the same

way as the cell phone signals [21]. Some research has been performed using real

cellular signals to produce empirical models of the effects of multipath interference

on positioning systems [22].

The work I present here consists of accurate and high-resolution measurements

of the GSM signals using an atomic reference, the first absolute measurements

of signal flight times on GSM networks, models that reproduce the observed

multipath interference effects, and two new methods of determining GSM signal

arrival times which remove the largest errors caused by multipath interference.

1.5 Thesis outline

Chapter 1 - Introduction to radio positioning

This chapter provides a summary of local radio positioning techniques and their

history. A discussion of radio positioning techniques specific to the GSM network

is included, followed by a description of multipath interference, signal fading, and

the content of this thesis.

Chapter 2 - Timing stability

This chapter describes the importance of timing stability to the experimental

stages of the project and discusses various frequency references. The concept of

Allan variance as a measure of timing stability is included. An experiment was

performed to determine the timing error associated with the experimental appa-

ratus used for this research and the results are presented here.

Chapter 3 - Time of flight measurements on cellular networks

This chapter presents two methods for measuring signal arrival times on the GSM

network along with a discussion of the apparatus and experimental techniques

21


used during the research presented in this thesis.

Chapter 4 - GSM network stability

This chapter presents the results of a series of experiments which measured the

temporal stabilities of a number of cell phone base stations from two different

network providers at a stationary receiver.

Chapter 5 - Effects of indoor multipath environments on GSM tim-

ing stability


degradation of the apparent temporal stability of received signals on the GSM

network caused by moving a receiver slowly over sub-wavelength distances in-

doors.

Chapter 6 - Modelling the effects of indoor multipath environments

on GSM timing stability

A model based on multipath interference is presented and shown to reproduce

the behaviour observed in the experiments described in Chapter 5.

Chapter 7 - A study of the timing errors encountered when performing

radio location using the GSM network


distributions of the errors on signal arrival times in various environments. A

model based on multipath interference is proposed and is shown to reproduce the

experimentally-obtained distributions.

Chapter 8 - Summary and further work

This chapter presents a summary of the results obtained from the work carried

out in this thesis and suggests further work.

22

Chapter 2

Timing stability

The aim of the research described in this thesis was to study the effects of multi-

path interference in various environments on the apparent arrival times of signals

radiated by GSM base stations. There were four main stages in this investigation:

a) designing and building a set of apparatus to gather data;

b) determining the signal stabilities of the base station transmissions;

c) determining the signal stabilities on reception in varying environments; and

d) modelling the signal stabilities.

There were three limiting aspects to making timing measurements. The first was

the resolution with which any measurement was made. The signals being mea-

sured were continuous but the apparatus sampled the signals at discrete instances

with a fixed sampling period. Fluctuations on time scales shorter than twice this

period were not resolved and contributed only to noise.

The second was the accuracy with which each measurement was made. The

effect of the quantisation of the analogue measurements by the digital apparatus

is considered in the next chapter. Here, the calibration of the reference oscillator

against which the measurements were compared is considered. In this sense, the

accuracy of the frequency reference is defined as the difference between its output

frequency averaged over a given time interval and its nominal frequency.

23

2. TIMING STABILITY

The third limiting aspect was the frequency stability of the reference oscillator.

Frequency stability refers to the repeatability of frequency measurements and is

determined by the distribution of error around the average value for a given set

of measurements. An oscillator can be stable but not accurate and it can be

accurate but not stable (i.e. stability and accuracy are independent attributes).

These lead to the concepts of frequency bias error and frequency bias rate error

(see Figure 2.1 below). The instantaneous frequency ω of an oscillator can be

modelled using a power series expansion,

ω = ω0 + ω′t+ ω′′t2 + ... (2.1)

where ω0 is the frequency at t = 0, ω′ is the first-order frequency variation with

time, ω′′ is the second order frequency variation with time, etc. The frequency

bias error is given by ∆ωb = ω0 − ωn, where ωn is the nominal frequency. The

frequency bias rate error is given by ω′. The higher order terms are not usually

named. The instantaneous frequency error is given by

∆ω(t) = ω0 − ωn + ω′t+ ω′′t2 + ... (2.2)

2.1 Allan Variance

The stability of a test oscillator can be determined by analysing its phase fluc-

tuations when compared to a reference oscillator [23]. A perfect oscillator would

produce a pure sine wave,

V (t) = V0 cos (2πf0t) , (2.3)

but in reality there is always some phase noise associated with the output signal.

A more realistic model is therefore given by

V (t) = V0 cos [2πf0t+ φ (t)] , (2.4)

24

2.1 Allan Variance

Figure 2.1: Sketch showing the types of error on the output signal from a frequencyreference (reproduced from Thompson, Moran and Swenson [23]). For an oscillatordesigned to operate at a frequency f0, there may be some bias-rate error, leading tovariation of the actual output frequency with time (the green line). This variation withtime is dependent on the stability of the oscillator. The oscillator may also suffer abias error, such that its mean frequency is displaced from the intended value (fb ratherthan f0). When the output signal is sampled and used as a timing reference there isalso a quantisation error associating with the sampling period tmin, which defines theresolution of the timing measurement.

where φ (t) represents the phase departure from the pure sine wave. The resultant

frequency variation with time is given by,

f (t) = f0 + δf (t) , (2.5)

where

δf (t) =1

2π

dφ (t)

dt. (2.6)

The fractional frequency deviation at a given instant can then be defined as

y (t) =δf (t)

f0

=1

2πf0

dφ

dt. (2.7)

This definition allows the performance of oscillators of different frequencies to be

compared. A measure of frequency stability based on measurements in the time

25

2. TIMING STABILITY

domain can be made by considering a set of frequency measurements recorded

with sampling period τ and the average fractional frequency deviation given by

yk =1

τ

∫ tk+τ

tk

y (t) dt. (2.8)

Combining this with equation 2.7 gives

yk =φ (tk + τ)− φ (tk)

2πf0τ. (2.9)

Measurements of yk are made at the repetition interval T , where T ≥ τ and such

that tk+1 = tk +T . The value of φ represents the phase of the test oscillator with

respect to the reference. The values of t and τ are also measured with respect to

the reference oscillator. A measure of the test oscillator’s frequency stability can

then be formed as the sample variance of yk given by

⟨σ2y (N, T, τ)

⟩=

1

N − 1

⟨N∑n=1

(yn −

1

N

N∑k=1

yk

)2⟩, (2.10)

where N is the number of time intervals of length T . As N → ∞ the above

quantity becomes the true variance. In many cases, however, equation 2.10 does

not converge because of the low-frequency behaviour of the power spectrum of

y, and then the true variance is not defined. This occurs because the long term

behaviour of an oscillator is determined by a random walk process and the timing

error at any point is the accumulation of all the past timing errors. This phe-

nomenon results in the true variance being unbounded. To avoid this problem, a

particular case of equation 2.10 is more commonly used with N = 2 and T = τ .

This two-sample variance is referred to as the Allan variance [24] and is given by

σ2A(τ) =

⟨(yk+1 − yk)

2⟩2

, (2.11)

or from equation 2.9,

σ2A(τ) =

⟨[φ (t+ 2τ)− 2φ (t+ τ) + φ (t)]2

⟩8 (πf0τ)

2 . (2.12)

26

2.1 Allan Variance

The estimate of an oscillator’s Allan variance for a dataset of M samples, sampled

with time interval τ is given by

σ2A(τ) =

1

2(M − 1)

M−2∑k=1

[φ (tk+2)− 2φ (tk+1) + φ (tk)]2

(2πτf0)2 . (2.13)

The accuracy of this estimate [25] is

σ (σA) ≈K√MσA, (2.14)

where K is a constant of order unity. The exact value of K is dependent on

the power spectrum of y. When the Allan deviation of an oscillator is being

Figure 2.2: Plot of a series of phase samples versus time (reproduced from Thompson,Moran and Swenson [23]). The Allan variance is calculated by considering the averageof all of the values of (δφ) 2, where δφ is the deviation of a given phase sample fromthe mean of its two adjacent samples.

determined, a perfect oscillator is required as a reference to ensure that the value

of τ is perfect and consistent. In practise this is unachievable, and therefore the

Allan variance measured by experiment is actually a joint variance of the reference

and test oscillator combined. If the oscillators are independent then their joint

variance is given simply by the sum of their individual variances,

σ2y = σ2

y1 + σ2y2. (2.15)

27

2. TIMING STABILITY

Three approaches can be used to determine a test oscillator’s Allan variance. If

the test oscillator is known to be much less stable than the reference oscillator

(such that σ2y1 σ2

y2), then the joint variance will be a close estimate of the test

oscillator’s variance. Alternatively, if an oscillator similar to the test oscillator can

be used for the reference (σ2y1 ≈ σ2

y2), then the Allan variance of the test oscillator

can be estimated as half of the measured Allan variance. In reality, however, two

oscillators of the same design will not be identical, and so an alternative estimate

is given by comparing three oscillators simultaneously. The three joint variances

are given by σ2ij, σ

2jk and σ2

ik where the individual variances are σ2i , σ

2j and σ2

k. Each

individual variance can then be calculated using the following set of equations

[26],

σ2i =

1

2

(σ2ij + σ2

ik − σ2jk

), (2.16)

σ2j =

1

2

(σ2jk + σ2

ij − σ2ik

), (2.17)

σ2k =

1

2

(σ2jk + σ2

ik − σ2ij

). (2.18)

For calculations of the Allan variance at time periods approaching half the length

of the experiment it is possible to find a negative sample Allan variance using this

approach. This occurs because of the lack of data for that time period resulting

in significant errors on the values of the joint variances (see equation 2.14 above).

Allan variances cannot be negative by their definition and so caution must be

exercised for long time periods with few data points.

Allan deviation plots of the logarithm of σA(τ) versus the logarithm of τ

are useful in analysing the stability of a test oscillator and are more conven-

tional in the literature than Allan variance plots. Allan deviation plots often

exhibit behaviour which can be categorised into four regimes as shown in Fig-

ure 2.3 below. These regimes are determined by a number of different processes

[27, 28], and are separable because of the distinct power-law dependencies of these

processes. Noise with a flat power spectrum independent of frequency is called

28

2.1 Allan Variance

white-frequency noise. Noise with a power spectrum inversely proportional to the

frequency is called flicker-frequency noise or “pink” noise. Noise with a power

spectrum proportional to the inverse square of the frequency is called random-

walk-of-frequency noise. White-phase noise has a power spectrum dependent on

the square of the frequency, and flicker-phase noise has a power spectrum pro-

portional to the frequency.

White-phase noise (region 1). This region has slope −1 on an Allan deviation

plot and is usually caused by random noise added to the measurement by the

system outside the oscillator. Sources of this noise include amplifiers and other

electronic components, and receiver noise when using an off-air frequency refer-

ence. This process dominates at short time periods. For time periods inside this

regime the oscillator can be considered to be behaving ideally, with the stability

of the reference signal being dominated by the externally added noise level.

Flicker-phase noise (region 1). This also contributes to the region with a −1 slope

on an Allan deviation plot, and may be caused, for example, by diffusion pro-

cesses in transistor junctions. For time periods inside this regime, the oscillator

can be considered to be behaving ideally, but with the stability being dominated

by the noise level.

White-frequency or random-walk-of-phase noise (region 2). This region has a

slope of −0.5 and is caused by additive noise within the oscillator, such as ther-

mal noise within its resonance cavity. The oscillator cannot be considered to be

perfectly controlled in this regime and beyond.

Flicker-frequency noise (region 3). This region has no time dependence, and its

physical source is not easily determined for a given system. It is usually attributed

to the physical resonance method of an active oscillator, or to the design or choice

of parts in the oscillator’s electronics [28].

Random walk of frequency (region 4). This region begins with a slope of +0.5

but eventually the plot meanders as the errors on the Allan deviation values over

long timescales increase (see Equation 2.14). It is caused by slow environmental

29

2. TIMING STABILITY

Figure 2.3: This plot shows the regions on an idealised Allan deviation curve. Overshort time periods, the plot exhibits a slope of −1 (region 1). The standard deviation ofthe frequency variation is constant for all time periods in this regime and is determinedby the level of white noise in the signal. The stability of the oscillator in this regime isdominated by this noise (as shown by the cutout labelled A), with less noise resultingin a lower Allan deviation for a given time period. Over longer time periods the Allandeviation decreases at a slower rate (region 2) and can become roughly constant (region3). Over these time scales the variation in the oscillator’s output frequency is domi-nated by the frequency-drift-rate error of the oscillator rather than the signal noise level(cutout B in the sketch). This frequency-drift-rate error is determined by the “physicspackage” and electronic components used to produce the oscillating signal. For longertime periods the Allan deviation typically increases with period length (region 4). Thisis where the frequency-drift-rate error of the oscillator executes a random walk. Theoscillator is uncontrolled and its frequency is influenced by long-term environmentalvariations such as changes in temperature, magnetic fields, pressure, etc (cutout C inthe sketch).

30

2.1 Allan Variance

changes such as temperature, pressure and magnetic field variations. This be-

haviour is sometimes referred to as the “ageing” of the oscillator and is reduced

by isolating it as best as possible from the external varying environment.

Some typical Allan deviations for various oscillator types are given in Table

2.1 and Figure 2.4 below. The large variation in the stabilities of crystal oscilla-

Figure 2.4: Allan deviation plot for various oscillators. The largest region representsthe range of stabilities of crystal oscillators. Rb represents Rubidium oscillators; CsB represents Caesium beams; H represents Hydrogen masers [29]; Cs F representsthe approximate stability of Caesium Fountains [30, 31, 32]; and Opt represents theestimated stability of optical atomic clocks [33, 34, 35] (currently being researched).

tors given in Table 2.1 is because of the various mechanisms that can be used to

control and stabilise them (see Section 2.2.1). The stabilities of controlled crystal

oscillators can be better over short time periods than those of atomic references.

This is typically because of the signal-to-noise ratio of the atomic frequency mea-

31

2. TIMING STABILITY

surement and the time required to perform it. For example, Caesium fountain

frequency measurements each take approximately half a second to perform [30].

Practical atomic clocks therefore consist of a crystal oscillator with excellent

short-term stability which is regularly corrected by an atomic “physics package”

in order to combine the excellent short-term stability of the controlled crystal

oscillator with the more stable long-term behaviour of the atomic oscillator.

Oscillator τ = 1 second τ = 1 day τ = 1 month

Quartz [27] 10−6–10−13 10−6–10−11 10−5–10−11

Rubidium [27] 10−11 10−12–10−13 10−11–10−12

Caesium Beam [36] 10−12 10−13–10−14 10−13–10−15

Hydrogen Maser [29] 10−13 10−14–10−15 10−13–10−15

Caesium Fountain [30, 31, 32] 10−12 10−15 10−16

Optical (proposed) [33, 34, 35] ∼ 10−15 ∼ 10−17 ∼ 10−18

Table 2.1: Comparison of typical Allan deviations

2.2 Oscillators

There are many ways to design an electrical circuit which produces an oscillating

signal. The simplest of these uses a tank circuit [37], consisting of a capacitor

connected in parallel with an inductor (see Figure 2.5 below). If the capacitor, of

capacitance C, initially carries a charge, then as current flows from the capacitor

through the inductor, the energy that was stored in the electric field between

the plates of the capacitor is transferred into the magnetic field of the inductor

(see Figure 2.6 below). Once the capacitor is fully discharged the magnetic field

of the inductor begins to collapse, maintaining the current flow in the circuit in

the same direction as before and so charging up the capacitor with the opposite

polarity. Once the magnetic field has completely collapsed and the capacitor has

become charged again, it will discharge once more through the inductor, this time

with current flowing in the opposite direction.

32

2.2 Oscillators

Figure 2.5: A simple electrical circuit which displays oscillatory behaviour.

Figure 2.6: Plot showing the transfer of energy in a tank circuit during its oscillatorycycles.

This process continues in an oscillatory cycle with a frequency of

ω =

√1

LC. (2.19)

When a capacitor and inductor are connected in series with an oscillating volt-

age, then as the oscillation frequency is increased from a low value, the inductive

reactance increases whilst the capacitive reactance decreases. At the frequency

given by equation 2.19 the capacitive and inductive reactances are equal in mag-

nitude and opposite in phase, resulting in zero impedance and infinite current

flow. The circuit therefore behaves as a filter, suppressing frequencies away from

the resonant frequency.

33

2. TIMING STABILITY

In practise, there is always some resistance in the circuit, which results in

dissipation of the energy. This can be described in terms of the quality factor Q,

defined by

Q = 2π × energy stored

energy lost per cycle. (2.20)

When an oscillatory system is driven at a given frequency, its response is depen-

dant on Q and the driving frequency. As the driving frequency is moved away

from the system’s resonant frequency, the amplitude of driven oscillations for a

high Q system will decrease more rapidly than for a low Q system (see Figure

2.7 below). The width of the resonance peak, defined as the range of frequencies

between the half-power points of the resonance peak, is given by

∆f =f0

Q. (2.21)

The narrower the frequency response of the oscillatory element, the more stable

the oscillator can be. A perfect oscillatory element with an infinite value of Q

could, in theory, be used to make a frequency reference that would have only one

frequency component in its output.

2.2.1 Crystal oscillators

A piezoelectric crystal responds mechanically to an externally applied electric

field, and can also be used to generate a voltage by physically deforming it. This

behaviour allows the crystal to store and release energy, and when placed in an

electrical circuit it is equivalent to the system of electrical components shown

below in Figure 2.8. The section of the circuit with a capacitor, inductor and

resistor in series corresponds to the electrical properties of the vibrating crystal

itself. The capacitance (C0) in parallel with them corresponds to the capacitance

between the electrodes connecting the crystal to the circuit and any stray capac-

itance due to the crystal enclosure. This circuit can oscillate in two ways. The

series section containing C1 and L1 becomes resonant when the impedances of

the capacitor (ZC1 = 1iωC1

) and inductor (ZL1 = iωL1) are equal in magnitude

34

2.2 Oscillators

6.98 6.985 6.99 6.995 7 7.005 7.01 7.015 7.02 7.025 7.03

x 106

0

0.2

0.4

0.6

0.8

1

frequency (Hz)

normalisedresponse

Q = 300 Q = 98,000

Figure 2.7: Plot showing normalised resonance curves for the two oscillators describedin Table 2.2 below. The blue curve represents a system with a low Q value of 300built from electronic components. The green curve shows the response for a crystaloscillator with a Q value of 98,000.

Figure 2.8: The equivalent electrical circuit for a crystal resonator.

35

2. TIMING STABILITY

and out of phase by π radians (this occurs at ω = 1√L1C1

). The result is a sharp

minimum in the impedance of the series section, with the magnitude of this min-

imum dependant on the value of R1. Alternatively, the circuit can resonate in

parallel when ω = 1√L1C0

(see the discussion of the tank circuit above). The reso-

nant frequencies of the system can be finely adjusted by placing it in series with

another capacitor or inductor. The advantage of a crystal resonator is that it has

much higher value of Q than is possible to achieve with inductors and capacitors

(see Table 2.2) below.

A crystal oscillator (XO) consists of a piezoelectric quartz crystal resonator in

a feedback circuit with an amplifier, often supplemented by a variable capacitor

to provide fine frequency tuning. Figure 2.9 below shows a simple circuit diagram

for a crystal oscillator. The natural frequency of a crystal oscillator is determined

by both the crystal’s physical characteristics and the environmental conditions

(temperature, pressure, vibration, gravity, etc).

Figure 2.9: A circuit diagram for a simple crystal oscillator.

The short-term stability of an XO is limited by noise from electronic compo-

nents in the oscillator circuits. Long-term stability is limited by the environmen-

tal factors and any changes in the stiffness of the crystal caused by impurities,

36

2.2 Oscillators

Parameter 7 MHz crystal 7 MHz LC

L1 42.5 mH 12.9 µH

C1 0.0122 pF 40 pF

R1 19 Ω 0.19 Ω

Q 105 – 107 300

Table 2.2: Parameters of a crystal compared to an LC circuit [38]

friction, wear, and other structural effects in the crystal or its mounting [39].

While the environmental conditions and the physical properties of the crystal

remain constant, the XO resonates at an exact frequency. Temperature varia-

tion has a large effect on the stability of crystal oscillators and there are sev-

eral XO-based devices designed to reduce this problem. The most common are

temperature-compensated crystal oscillators (TCXO), oven-controlled crystal os-

cillators (OCXO) and microcomputer-compensated crystal oscillators (MCXO).

2.2.2 Temperature-compensated crystal oscillators

For a typical XO the variation in resonance frequency with temperature in the

range−55 C to 85 C is as shown in Figure 2.10(a). In a TCXO, the output signal

from a thermistor is used to generate a voltage that is applied to a varactor in

the crystal network in order to correct the resonance frequency [41] (see Figure

2.10(b)). This technique can improve the stability with respect to temperature

by a factor of 20.

2.2.3 Oven-controlled crystal oscillators

In an OCXO, the crystal unit and other temperature-sensitive components of the

oscillator circuit are maintained at a constant temperature, typically 70− 90 C

[42], where the slope of the crystal’s frequency-temperature variation is near zero

(see ‘A’ in Figure 2.10(a)). The crystal is also manufactured by slicing along a

certain crystal axis to have a minimum frequency-temperature dependence around

37

2. TIMING STABILITY

Figure 2.10: Plot showing the frequency variations with temperature for three crystaloscillator systems (reproduced from Vig [40]).

the oven temperature. This improves the temperature stability of the crystal by a

factor of 1000 or more (see Figure 2.10(c)). The frequency variation under these

conditions is around 1 part in 10−9, but OCXOs require more power, are larger,

and cost more than TCXOs or MCXOs.

2.2.4 Microcomputer-controlled crystal oscillators

The MCXO uses a “self-temperature sensing” method [43] rather than using a

thermometer that is external to the crystal unit. This allows for a more accurate

38

2.3 Atomic oscillators

measurement of the temperature of the crystal to be made than in a TCXO. Two

vibrational modes of the crystal are excited simultaneously and are combined such

that the resulting beat frequency is a monotonic (and nearly linear) function of

temperature. The crystal therefore senses its own temperature and a correction

voltage is applied to the varactor. The frequency variation with temperature of

an MCXO in the range −55 C to 85 C is around 1 part in 10−8.


The principle of an atomic oscillator (also known as an atomic clock) is to use

an atomic resonance frequency as a reference. This can be achieved in two ways.

In an active atomic clock, the photons released during the quantum transition

between two known energy levels can be used directly to provide the reference

frequency. In a passive atomic clock, a feedback circuit is used to match the

frequency of an OCXO or a laser to the transition frequency. In each case, the

reference frequency is provided via photon interaction with a quantum transition

on the atomic scale, and so can be less affected by environmental factors than the

mechanical vibration of a crystal. The two key requirements for a highly-stable

atomic reference are (i) a narrow atomic resonance (corresponding to a high Q

value) and (ii) a high signal-to-noise ratio. Heisenberg’s uncertainty principle

indicates that the narrowest resonance is obtained with the longest interaction

time (∆E∆t & ~ where ∆E = 2π~∆f). The stability of an atomic reference

is therefore typically poorest for very small time periods. In a passive atomic

clock such as the Rubidium standard used in this project, an OCXO provides the

output frequency signal and is continuously corrected to match the frequency of

the atomic absorption resonance, combining the excellent short-term stability of

an OCXO with the excellent long-term stability of an atomic oscillator.

The main types of atomic clocks utilise atomic transitions in Rubidium, Cae-

sium or Hydrogen gases and are discussed briefly below.

39

2. TIMING STABILITY

2.3.1 Rubidium oscillators

Rubidium is an alkali metal with a single valence electron. The spatial distribu-

tion of electrons in an atom depends on their values of n (the principal quantum

number), and l (the orbital angular-momentum quantum number). If an electron

has l 6= 0, then there is also some magnetic moment associated with it. Further-

more, electrons all have an intrinsic magnetic moment, or spin. The interaction

between the orbital magnetic moment and the intrinsic magnetic moment is called

spin-orbit coupling, or LS coupling, and is largely responsible for the complexity

of atomic spectra.

The electronic configuration of the ground state of Rubidium [44] is

1s22s22p63s23p63d104s24p65s.

There are four fully-filled shells (numbers 1− 4) and a single electron in the 5th

shell. The spectroscopic notation uses capital letters and so the electron in the

5s shell has the spectroscopic state given by 52S1/2 [44]. In this convention, the

upright letter S indicates that the total orbital angular momentum of the electron

is zero (l = 0), the upright letters P,D and F correspond to the total orbital

angular momentum quantum numbers 1, 2 and 3 accordingly. The superscript

value in the spectroscopic notation is given by (2S + 1) where italic S is the

total electron spin angular momentum quantum number. Since Rubidium only

has one valence electron, S = 12

and (2S + 1) = 2. The subscript value in the

spectroscopic notation indicates the total electronic angular momentum J . The

vectors of the total orbital angular momentum L and the electron spin S give

rise to the total angular momentum vector J = L + S. J (the modulus of J) can

therefore take any values given by J = |L + S|, |L + S − 1|, ..., |L − S|. For the

electron in the 5s orbit, L = 0 and S = 12

and so the only possible value of J is

12.

For an electron with one unit of orbital angular momentum (L = 1), such as

one excited to the 5p shell, J can take the values J = |1+ 12| = 3

2or J = |1− 1

2| = 1

2.

40


These correspond to the first two excited states of Rubidium and are denoted by

52P3/2 and 52P1/2. The P state is therefore split into a doublet. The splitting of

energy levels in this way is referred to as the fine structure of the atomic spectra.

Atomic nuclei also carry angular momentum I (I = 32

for Rb87). The total

angular momentum for an atom is given by F = I+J. The situation is analogous

to the spin-orbit coupling described above with the possible values of quantum

number F being F = |I+J |, |I+J−1|, ..., |I−J |. The coupling between electronic

and nuclear momenta is very weak, unlike spin-orbit coupling. If F 6= 0 then the

electronic state can be split into several further hyperfine levels. These levels are

quantised and take on the values mF = F, F − 1, ...,−F . If a magnetic field is

imposed on the atom in the direction of this angular momentum vector then a

torque is exerted on the atomic magnetic moment. The energy associated with the

interaction between the external field and the magnetic moment is proportional

to the value of mF for weak magnetic fields (. 1mT ). The result is that the

atomic states at zero magnetic field are split into 2F + 1 states when a magnetic

field is applied (see Figure 2.11 below). This hyperfine splitting of the electronic

states into these magnetic sub-levels is called the Zeeman effect [45].

In the case of Rubidium, the electronic ground state (52S1/2) is split into

two fine structure levels, determined by whether the spin of the unpaired valence

electron is aligned parallel or anti-parallel to the nuclear spin. The total quantum

angular momentum for these states is F = 2 and F = 1 respectively (see Figure

2.11 below). The frequency of the spin-flip transition between these states for a

87Rb atom is 6,834,682,614 Hz. This transition is used to provide the reference

frequency in a Rubidium oscillator [46] via a technique known as optical pumping

[47].

Optical pumping is used to drive all of the atoms in a cell containing Rubidium

vapour into the F = 2 state via an intermediate excited state. Circularly polarised

photons carry either +~ or −~ of angular momentum, and are labelled σ+ and σ−

accordingly. When an electron spontaneously relaxes from an excited state it can

emit a photon of either polarisation and drop into the corresponding fine-structure

41

2. TIMING STABILITY

energy level. However, in order to excite an atom selectively into one particular

energy level from a lower energy level, a photon with the correct energy and

the correct angular momentum is required. The Rubidium atoms are optically

pumped into the F = 2 state by first subjecting them to a magnetic field in order

to align the atoms according to their spins and to split their energy levels. If σ−

photons with energy matching the 52P1/2 → 52S1/2 transition propagate along

the magnetic axis then each photon carries an angular momentum of −~ and

so only the 52S1/2 (F = 1) → 52P1/2 transition can be excited. Once promoted

to the excited state, re-emission occurs and the electron relaxes into either the

F = 1 or F = 2 state. However, since only the 52S1/2 (F = 1) state is excited by

the σ− photons, the set of atoms are all pumped into the 52S1/2 (F = 2) state.

Figure 2.11: Schematic diagram of a Rubidium frequency standard (a) reproduced fromThompson, Moran and Swenson [23]. The energy levels of the 52P1/2 excited state and52S1/2 ground state involved in the process are shown in (b). The energy levels of theground states can be split further by an applied magnetic field (Zeeman effect, (c)) andso the cell must be magnetically shielded. The filtered light is strongly absorbed by thegas in the microwave cavity when it is emitting photons at the ground state hyperfinetransition frequency (d).

42


The frequency of a Rubidium oscillator is controlled by the following mech-

anism. A heated cell containing 87Rb vapour is subjected to an RF plasma

discharge which promotes the atoms to the 52P1/2 excited state. The excited

states relax into both the F = 2 and F = 1 states, and the resulting photons are

then passed through a filter. This consists of a cell of 85Rb vapour, whose energy

levels are slightly different from those of 87Rb. The photons from the F = 2

87Rb transition are absorbed by the 85Rb gas, but the photons from the F = 1

87Rb transition are not. This filtered light is then used in another cell inside a

microwave cavity to drive a set of 87Rb atoms into the F = 2 52S1/2 state via

optical pumping. The microwave cavity is resonant at the transition frequency

between the F = 2 and F = 1 52S1/2 states. This transition is not spontaneous

but can be stimulated by the application of microwaves of the same frequency.

With the microwave field applied, the atoms are forced into the F = 1 ground

state.

Whilst the microwave field is at the correct frequency, controlled by an OCXO,

the 87Rb gas absorbs a maximum amount of filtered light. A photo detector

beyond the microwave cavity detects changes in the intensity of the filtered light

and corrects the OCXO frequency in order to maintain maximum absorption in

the microwave cavity. The hyperfine transition frequency of the ground state of

87Rb is therefore used as the reference to control the OCXO.

The microwave cavity contains a buffer gas of inert atoms as well as the 87Rb

atoms. This has two purposes:

(i) If the buffer gas were not present, then collisions between the 87Rb atoms

and the walls of the cell would overwhelm the optical pumping effect by causing

transitions between the hyperfine ground state levels. Collisions with atoms of a

suitably inert buffer gas, such as nitrogen, do not have this effect as they do not

interfere with the magnetic hyperfine energy states [48, 49].

(ii) Doppler broadening of the hyperfine transition caused by collisions with

the buffer gas atoms is smaller than for collisions with the walls of the cell [50].

The absorption resonance line-width is about 100Hz at the centre frequency of

43

2. TIMING STABILITY

6,834,682,605 Hz, and corresponds to a Q of 6.834× 107, a factor of nearly 1000

times greater than for a quartz crystal.

The microwave cavity is magnetically shielded to reduce the effects of stray

external magnetic fields on the Zeeman splitting [51]. A weak magnetic field

is maintained in the cavity to maintain spin alignments. The shot noise of

individually-arriving photons leads to white-frequency noise which dominates the

frequency error at short timescales.

2.3.2 Caesium beam oscillators

Caesium is an alkali metal with a single valence electron like Rubidium. A Cae-

sium beam atomic clock uses a technique similar to that used in a Rubidium

atomic clock in order to generate a reference frequency [36], but uses inhomoge-

neous magnetic fields to filter atoms of the required electronic state instead of

using optical pumping.

The ground electronic state of 133Cs is split into two levels (F = 4 and F = 3),

depending on whether the spin of the unpaired valence electron is aligned parallel

to or anti-parallel to the nuclear spin. The transition frequency between these

states is 9,192,631,770 Hz and is used as the primary reference defining the length

of the SI second [52].

Atoms of Caesium are evaporated by an oven and move in a beam along a

confining cell through a number of stages (see Figure 2.12 below). They are first

filtered by a magnet according to their energy configurations, with the higher-

energy atoms (F = 4) following a different path through the magnetic field than

the lower-energy atoms. Only the beam of F = 3 atoms is directed into the

interaction region. The higher-energy beam is discarded. An OCXO driving a

dual microwave cavity (known as a Ramsey cavity [53]) tuned to 9,192,631,770

Hz is used to excite the F = 3 atoms into the F = 4 energy state. The Ramsey

cavity consists of two short microwave interaction regions of length l, separated

by a relatively large distance L, the microwaves in each cavity having almost

44


the same phase. The atoms are exposed to the microwave fields in the two

cavities in sequence, which results in interference causing Ramsey fringes [53] in

the resonance feature. These narrow the resonance peak by a factor of the order

of Ll. At the next stage of the process, another magnet separates the atoms that

have been excited into the higher energy state from those which have not and

directs them onto a detector. The beam current is used to correct the frequency

of the OXCO such that the current is maintained at its maximum value.

Caesium beam standards have poor signal-to-noise ratios which limits their

short-term stabilities, but they provide excellent long-term stabilities.

Figure 2.12: Schematic diagram of a Caesium beam frequency standard.

2.3.3 Hydrogen masers

Hydrogen is the simplest element, consisting of one electron bound to a proton.

The electronic ground state has two energy levels (F = 1 and F = 0) determined

by the orientation of the electronic and nuclear spins. The transition frequency

between these states is 1,420,405,752 MHz and is used as the frequency refer-

ence in a Hydrogen maser (microwave amplification by stimulated emission of

radiation) [29].

45

2. TIMING STABILITY

A schematic diagram of the Hydrogen maser is given in Figure 2.13 below.

Hydrogen from a storage tank is excited by an RF discharge and passes through

a state-selecting magnet which separates the F = 1 and F = 0 states. The atoms

in the upper state are directed into a microwave cavity resonant at 1,420,405,752

MHz. The cavity is shielded from external magnetic fields, and a solenoid provides

a weak homogeneous magnetic field inside the cavity. This field slightly splits the

hyperfine levels and allows the microwave radiation injected into the cavity to

stimulate transitions from the F = 1,mF = 0 state to the F = 0,mF = 0 state

while minimising transitions from the F = 1,mF = 1 state. Transitions with

∆mF = 0 have frequencies independent of applied weak magnetic fields to a first

approximation, and so slight variations in local magnetic field do not change the

reference frequency.

The maser oscillates if (a) the cavity is tuned close to the transition frequency

and (b) the power applied to the cavity is greater than the power lost inside

it. In an active maser, the stimulated emissions of the atomic medium are self-

sustaining and the addition of microwaves at the resonant frequency from an

external source is not required. In a passive maser, this injection of energy is

required. In an active maser, a probe in the cavity measures the frequency of

the radiation emitted by the atomic transitions and the measurement is used to

phase lock an OCXO. In a passive maser, the OCXO controls the frequency of the

microwave radiation injected into the cavity to stimulate the maser process. A

feedback circuit is used to adjust the OCXO frequency to maintain the maximum

level of stimulated emission.

Active masers are inherently more stable than passive ones, but are also more

expensive because of the quality of the cavity required in order to maintain self-

sustained stimulated emission. Active Hydrogen masers provide very stable fre-

quencies over periods of 1 second to 1 day. In a 1 hour averaging time, active

Hydrogen masers exceed the stabilities of the best known Caesium beam oscil-

lators by up to a factor of 100, with typical Allan deviations of about 2× 10−15

[54].

46


Figure 2.13: Schematic diagram of a Hydrogen maser frequency standard.

2.3.4 Caesium fountains

Caesium fountain clocks are the latest generation of atomic frequency standards

and are currently the primary standards at NPL and other research facilities

[30]. The accuracy with which the frequency of radiation emitted during changes

in atomic state can be measured limits the stability of an atomic clock. This

accuracy is determined, among other things, by Doppler effects associated with

the temperature and bulk motion of the gas, and also by the time over which

the measurement can be averaged. The atomic resonance frequency can be tuned

more accurately in a passive atomic clock by restricting the movements of the

atoms and so allowing them to interact with the applied microwave field for longer.

In Caesium fountains, lasers are used to cool and trap a cloud of Caesium atoms

resulting in an interaction time of about half a second (roughly 100 times longer

than the interaction time in the best Caesium beam standards). This longer

interaction time results in a much narrower resonance peak and more accurate

47

2. TIMING STABILITY

OCXO tuning, hence higher frequency stability. Caesium fountain frequency

standards out-perform Hydrogen masers on timescales longer than about one

month [30].

2.3.5 Optical atomic clocks

Optical atomic clocks are expected to provide much higher frequency stabilities

than current atomic standards [33, 34]. Since the frequency of optical radia-

tion is five orders of magnitude higher than microwave frequencies, 105 optical

oscillations can in principle be counted and averaged in the same time as one

microwave oscillation. An optical standard therefore should be roughly 105 times

more stable. Optical transitions usually have narrower line-widths too, resulting

in a further improvement in stability. However, optical frequencies are difficult

to measure accurately using standard electronic techniques [35] and optical tran-

sitions are also often ‘forbidden’ transitions, so are weak.

2.4 Measurements with two Rb frequency stan-

dards

The experiments discussed in this thesis involved measuring the signal flight time

along a path from a transmitter to a receiver. Efratom Rubidium frequency

standards were used in the apparatus, and tests were performed to characterise

their performance.

It is best to measure the signal flight time along a path from a transmitter to a

receiver using the same timing reference for the apparatus at each end. However,

this would at least require very long cables, which would be impractical and which

would, in any case, introduce further problems. In practise, two references must

be used. Frequency references of the same design should, in principle, output

identical frequencies, but in reality one drifts relative to the other so that at

any time there is a phase difference φ(t) between them. This varies over time

48

2.5 Measurements of the stabilities of FRK-H Rb oscillators

according to

φ(t) = φ0 + φt+ higher order terms, (2.22)

where φ0 is the phase difference at time t = 0 (corresponding to a synchronisation

point). Two clocks attached to these free-running frequency references would not

record identical times at the same instant (for t > 0), but if the value of φ(t)

is known in full (i.e. not just modulo 2π), then the time according to one clock

can be corrected to match the time according to the other. Therefore, if the two

clocks are used to gather data in separate locations, the data streams can be

aligned such that the corrected recordings represent simultaneous measurements.

The correction process is straightforward if the higher-order terms in equation

2.22 can be ignored, i.e.

φ (t2)− φ (t1) = φ (t2 − t1) , (2.23)

where φ (t1) and φ (t2) are measurements of the phase difference of the two clocks

at the beginning and end of the recording period. These measurements can then

be used to determine the value of φ and so the full phase difference between the

clocks at any point during the experiment can be calculated.

The accuracy of this method is limited by (a) the size of the frequency differ-

ence between the oscillators and (b) the assumption that the phase drift during

the experiment is linear. The frequency difference needs to be small enough such

that the sampling windows of the two sets of apparatus overlap in time for all

of the measurements during the experiment. The linearity of the phase drift,

and hence the accuracy of the phase correction technique, is determined by the

stabilities of the oscillators.

2.5 Measurements of the stabilities of FRK-H

Rb oscillators

The cumulative phase difference between two FRK-H Rb oscillators was measured

using the apparatus shown in Figure 2.14 below. Each unit was mounted inside

49

2. TIMING STABILITY

Figure 2.14: Schematic diagram of the apparatus used to measure the stability of anFRK-H Rb oscillator.

a large cardboard box in order to provide additional thermal stability during the

experiment. The oscillators were switched on for a month before measurements

began. The phase difference between the 10-MHz output of each unit was mea-

sured using a Hewlett-Packard HP497B digital vector voltmeter over a number of

days. The entire experiment was repeated four times, with one experiment last-

ing for 6 days and the other three lasting for 14 days. The samples were taken

at a frequency of 1kHz and averages over either 5 or 30 seconds were recorded

by a computer. The experiment was also performed with an OCXO compared to

an FRK-H oscillator to compare the stability of the FRK-H units to a particular

OCXO.

The Allan deviation plots for the four RbO experiments are shown below in

Figure 2.15, and the corresponding phase-difference plots are shown in Figure

2.16. The Allan variances of the two FRK-H oscillators are assumed to be equal

(see Section 2.1 above), and so the RbO Allan deviations given here are calculated

using equation 2.15. The Allan variance in the OXCO experiment was assumed

to be dominated by the OXCO and no correction for the instability of the RbO

was made. The large difference in the recorded Allan deviations (shown on the

50

2.6 Conclusions

plot below) supports this assumption.

The longest survey experiment measuring absolute signal flight times between

a BTS and a receiver, discussed in Chapter 7, lasted three hours. The Allan

deviation of the FRK-H oscillator for this time period is 6 × 10−13 according to

the data of Figure 2.15. This corresponds to an average error on the assumption of

a linear phase drift of 9 nanoseconds, or about 2.6 metres. The timing resolution

of the apparatus was 24.5 nanoseconds, and the measurement noise typically

contributed 50 nanoseconds of error or more (see Figure 4.4 in Chapter 4). The

error arising from the assumption of a linear phase drift was therefore acceptable.

2.6 Conclusions

1. Reviews of timing stability and oscillators were presented in this chapter.

2. A technique was described to allow data gathered simultaneously in separate

locations to be corrected for any linear phase drift between the reference oscilla-

tors during the data gathering process.

3. An analysis of the stability of an FRK-H Rubidium frequency reference was

performed in order to determine the errors associated with using this equipment

for this technique. The associated error was shown to be acceptable and smaller

than the errors from other sources in the experiments discussed in this thesis,

such as timing resolution and receiver noise.

51

2. TIMING STABILITY

Figure 2.15: Plots of the Allan deviations for an Efratom FRK-H Rubidium oscillatorand for an OCXO. The error bar associated with each individual Allan deviation valuecan be estimated using Equation 2.14 in Chapter 2. Data corresponding to timescaleslarger than about 25,000 seconds have been removed and the error bars for the remainingdata are smaller than the thickness of the lines used in the plot. Each Allan deviationvalue plotted here is an average over at least 10,000 measurements. The three FRK plotsgenerated using a digital vector voltmeter are similar, but the differences between them atlong time periods suggests that even a two-week sample is not entirely representative ofthe typical behaviour of an oscillator in a stable environment. The FRK plot generatedusing an analogue vector voltmeter (the green line) exhibits a lower stability over the first2000 seconds than the tests using a digital voltmeter, but this is caused by the increasedmeasurement noise associated with the analogue voltmeter and is not a feature of theFRK-H. Over the longest time periods the RbO is about 1000 times more stable thanthe OCXO.

52

2.6 Conclusions

0 2 4 6 8 10 12 14

x 105

−15

−10

−5

0

5

10

15

20

25

30

time (seconds)

phasedifference

(wavelengths)

2005 test2007 test (i)2007 test (ii)2007 test (ii)

Figure 2.16: The phase differences between the 10MHz outputs of two Rubidium os-cillators in four experiments. The variation in the plots demonstrates that even a twoweek data sample is still not entirely representative of the typical behaviour of an RbO

53

2. TIMING STABILITY

54

Chapter 3

Time of flight measurements on

cellular networks

3.1 Methods

Two methods can be used to measure the signal flight times between a GSM

transmitter and a receiver. They can be described as the interferometric method

and the network-synchronised method.

3.1.1 Interferometric method

Two identical sets of apparatus are used in the interferometric method to gather

data simultaneously at a reference position and at a position of interest. A

synchronised pair of highly-stable clocks is required to ensure that the recordings

occur simultaneously. The difference in signal arrival times at the two locations

is determined by cross-correlating the sampled data sets. The maximum absolute

value of the cross-correlation function (referred to as ‘the peak’) is at the centre, or

zero-offset point, of the cross-correlation function for two locations with identical

signal flight times. For a peak at any other position, the difference in arrival

times may be calculated by dividing the number of samples between the peak

and the centre of the cross-correlation function by the sampling frequency. The

55

3. TIME OF FLIGHT MEASUREMENTS ON CELLULARNETWORKS

time of flight (TOF) of a signal from the BTS to the position of interest can be

estimated directly from this offset if one set of apparatus is at the BTS itself.

Different methods of estimating the TOF from measurements of the cross-

correlation function are discussed in Chapter 6. In the experiments presented

in this thesis, the maximum absolute value of the cross-correlation function was

used as the estimator.

An advantage of the interferometric technique is that it filters out all common-

mode variations, such as oscillations and drifts in the signal caused by the base

station’s electronics or its frequency standard. Any variations caused by the

propagation path and multipath interference can therefore be studied directly. A

disadvantage of this technique is that it requires two sets of expensive apparatus

and two operators.

3.1.2 Network-synchronised method

The network-synchronised method relies on the transmission of a known code

word at regular intervals from each BTS. On GSM networks, the code word

is called the Extended Training Sequence (ETS) and it is transmitted during a

synchronisation burst (SCB) on the logical broadcast control channel (BCCH).

The measuring equipment is programmed to record data at a multiple of the

same regular interval so that the ETS appears at the same position in the data

stream every time for a stationary receiver. This position can be found by cross-

correlating the data stream with a copy of the ETS. The maximum value of the

modulus of the cross-correlation function marks the position of the ETS in the

signal, and is referred to here as the SCB peak.

For a stationary receiver, variations in the position of the SCB peak are caused

by (a) instabilities of the frequency references in the BTS or the measuring ap-

paratus, (b) transmitter based errors such as maintenance work at the BTS, (c)

changes in the propagation path, and (d) signal interference effects at the receiver.

As the receiving equipment is moved relative to the base station, the signal TOF

56

3.1 Methods

changes and the position of the SCB peak in the data recordings varies accord-

ingly. The SCB peak position corresponding to zero distance from the BTS can

be calibrated by making a recording at the base station itself during the exper-

iment. The number of samples between this calibration SCB peak and an SCB

peak recorded in a position of interest, divided by the sampling frequency, gives

an estimate of the TOF of the signal from the base station to the position of

interest.

The SCB peak position is only expected to be stationary with time for a

stationary receiver if the frequency references in the BTS and the measuring

apparatus both remain exactly on their nominal frequencies, or drift in exactly

the same fashion such that their difference remains the same. In practise neither

of these are situations are likely, but the systematic error caused by a relative drift

between the oscillators can be corrected. A constant offset in the frequencies of the

two references results in the SCB peak position drifting at a constant rate. Such

a linear drift can be corrected easily by performing calibration measurements at

the BTS at the beginning and end of an experiment. These measurements define

a linear slope across the recordings which can then be removed from the data set

(see Section 2.4 in Chapter 2 above).

An advantage of this method over the interferometric approach is that only

one set of apparatus and one operator are needed. A disadvantage is that this

technique does not filter out any slight variations, oscillations, non-linear drifts,

or other unwanted behaviour affecting the base station’s transmission times, but

instead relies on the BTS frequency reference being highly stable. A set of exper-

iments was performed to test the viability of the network-synchronised approach

(see Chapter 4 below). For base stations with highly-stable and consistent sig-

nals, the network-synchronised method can be as accurate as the interferometric

approach but without the need for as much equipment and manpower.

The signal stabilities of BTSs with highly-stable frequency references are dom-

inated by the level of measurement noise in the system over periods of a few hours

57


or less. This noise affects the accuracy of the measurements, including the cali-

bration measurements. However, since measurement noise is a random variation,

the accuracy is improved by averaging over many samples.

3.2 The Apparatus

The apparatus used to gather the data for this project is shown in Figure 3.1

below.

Figure 3.1: Schematic diagram showing the apparatus used to measure signal flighttimes. Accurate synchronisation was a vital part of the experimental process, and thiswas achieved by using a timer driven by a Rubidium frequency standard (Rb) to triggerthe digitiser’s (Rx) recording process, rather than triggering the digitiser via softwarecommands. The digitiser was controlled by the laptop via a General Purpose InterfaceBus (GPIB).

The apparatus consisted of a radio-frequency digitiser phase-locked to an

FRK-H Rubidium frequency standard. The timing of the data recordings was

controlled by the same frequency standard via a programmable counter. A set

of MATLAB scripts were developed by the author to control the digitiser and

data transfer process, to resample and filter the data, and to perform the cross-

58

3.2 The Apparatus

correlation processes. The digitiser’s recording process was not triggered by soft-

ware commands, but was controlled directly by the output from the Rubidium

atomic frequency reference via the timer. At the end of each timing period, the

timer output a pulse which triggered the digitiser’s capture sequence.

Each part of the apparatus and each stage of the MATLAB processing are de-

scribed in more detail below. One set of apparatus was required for the network-

synchronised approach, and two sets were required for the interferometric ap-

proach.

3.2.1 Radio frequency digitiser

The digitiser used was an IFR 2319E model [55], capable of recording a maximum

of one million complex samples at rates of 2.04 MHz, 4.08 MHz, 8.16 MHz or 16.32

MHz, over a frequency range of 500 MHz to 2 GHz, and with a bandwidth of up

to 10 MHz. The maximum length of an individual recording was therefore 0.49

seconds (one million samples at 2.04 MHz). The bandwidth of a GSM signal is

140kHz, and so any of these sampling frequencies satisfied the Nyquist-Shannon

sampling criterion [56]. The lowest sampling frequency was chosen in order to

maximise the amount of data that could be recorded in one measurement. The

original signal could therefore be fully reconstructed from the sampled data before

a time-of-flight calculation was performed. Timing resolution was improved using

interpolation, and averaging the values from a number of recordings at a given

position reduced the error caused by system noise. The digitizer output data in

the form of I and Q complex samples, such that the magnitude and phase of a

given sample were stored in cartesian coordinates rather than polar coordinates.

3.2.2 Triggering and synchronisation

The most important factor in gathering useful data was timing the recordings with

the highest accuracy possible. An FRK-H Rubidium Frequency Standard (RFS)

controlled the timing of the data captures via the counter and also provided the

59


reference frequency for the digitiser. This reduced the sampling and digitisation

error of the digitiser and also locked its internal digital transitions to the counter

transitions. For the interferometric method, synchronisation of the two sets of

apparatus was achieved by sending a signal via a split cable to both counters to

start them simultaneously. The two digitisers were connected to the same input

at the beginning and end of an experiment in order to measure the drift away

from the synchronisation over the period of the experiment. For the network-

synchronised technique, the counters were programmed to trigger recordings at

a multiple of the GSM ETS repeat rate (see Section 3.1.2 above and Section 3.4

below). Calibration recordings were performed at the BTS at the start and end

of each experiment in order to correct for the difference between the frequencies

of the RFS and of the frequency standard in the BTS.

3.2.3 Uninterruptible power supplies

The RFS was powered continuously from the start of its warm-up procedure to

the calibration measurements at the end of a survey in order to guarantee its

stability and synchronisation. This was achieved with an uninterruptible power

supply (UPS) such that whenever the RFS was disconnected from mains power

supply, it remained powered by a lead acid battery. During the mobile tests

the entire apparatus was powered using a large lead acid battery and a power

inverter, allowing for many hours of portable operation.

3.3 Data storage and analysis

A laptop running MATLAB was used to control the digitiser and counter. The

process of measuring signal arrival times was similar for the the network-synchronised

and interferometric techniques, the major difference being the cross-correlation

process. For the interferometric approach, two simultaneous measurements made

by the two sets of apparatus were cross correlated. For the network-synchronised

60


method, each recording was cross correlated with a copy of the ETS. In both

methods the position of the resulting cross-correlation peak was compared with

the positions of the cross-correlation peaks in the calibration measurements to

determine the signal flight time.

The research presented in Chapter 4 examined the base-station signal sta-

bilities using the network-synchronised method. During this work, the data was

transferred from the digitiser after each recording via a General Purpose Interface

Bus (GPIB) to the laptop. This transfer mechanism was slow, with a data rate

of around 3,000 samples per second. Each recording needed to contain at least

104,000 samples in order to ensure that it captured at least one ETS. The result-

ing read-out time of 40 seconds was the initial limiting factor in the number and

frequency of recordings. A faster data-acquisition interface was obtained later

and data was extracted at a much-higher rate of 2,000,000 samples s−1 to a ded-

icated data storage machine. This equipment was used during the experiments

discussed in Chapters 5 and 7, allowing much more data to be recorded in the

available time. The limiting factor for data gathering then became the size of the

hard disk in the data-storage machine.

3.3.1 Sampling theory

The Nyquist-Shannon sampling theorem [56] states that a band-limited signal

can be reconstructed fully from a set of samples if the sampling frequency used

is at least double the bandwidth of the signal. The original signal is retrieved by

convolving the sampled sequence with a sinc function. This is explained pictori-

ally in Figure 3.3 below. When using this form of reconstruction with real data,

there were a number of problems that affected the quality of the interpolated

signal.

(i) Each sample was quantised such that its magnitude could only take certain

discrete values. This quantisation error provided an injection of white noise into

the reconstructed signal.

61


(ii) Errors on the sample times (jitter) resulted in samples being recorded at in-

correct times.

(iii) The filter used by the digitiser to remove frequencies outside the intended

bandwidth was not hard edged, and so extra (unwanted) frequencies were sam-

pled. This caused aliasing of the original signal, adding noise into the signal band.

The timing error caused by jitter was limited to half of the time period of the

digitiser’s 65.28 MHz internal oscillator, i.e. 7.5 nanoseconds, and with digital

electronics the error was expected to be much lower than this value (and so neg-

ligible). The sampled data were filtered using a hard-edged function during post

processing (see Section 3.6.3 below) to remove the problems with the digitiser’s

filter. The digitiser provided 12-bit quantisation and so 4096 digitisation levels

over the measurement range, giving a dynamic range of 72 dB. This digitisation

noise was much lower than the receiver noise (see Figure 3.2). The receiver noise

was the main source of error on the measurements and resulted in an imperfect

reproduction of the original signal. This in turn resulted in an error on the po-

sition of the peak in the interpolated cross-correlation function. However, since

the receiver noise was a white-noise source, averaging over many results reduced

this effect.

A further complication lies in the fact that the sinc function extends from

-∞ to +∞ and the full function is required to reconstruct the signal exactly. A

very long truncated sinc function was used here (with 25 side lobes either side of

the main lobe) since integrating numerically over an infinite extent is impossible.

The extreme side lobes were much smaller than the main lobe (less than 1% in

amplitude), and so the error associated with using a truncated sinc function was

insignificant compared to the sources of error discussed above.

62


Figure 3.2: This sample of data is taken from a frequency control burst (FCB) recordedat a base station. The FCB is a single frequency broadcast, which allows a mobilehandset to correct its frequency reference to match that of the base station. The signalto noise ratio is roughly 20:1, or 26 dB, and provides a lower bound on the amount ofreceiver noise associated with the apparatus.

3.3.2 MATLAB driven data capture

A set of MATLAB programs was written (i) to control the digitiser and counter

card, (ii) to read the IQ data from the digitiser, and (iii) to perform the post

processing and cross correlations. The counter card was configured to send pulses

to the digitiser at the required recording rate. The only restriction on this rate for

the interferometric method was the time taken to read out a recording of adequate

length. The width of a cross correlation peak is approximately equal to 2∆f

where

∆f is the bandwidth. For GSM signals (with a bandwidth of 140 kHz) the width

of the cross-correlation peak is about 15 microseconds, and since the sampling

63


Figure 3.3: This diagram demonstrates the use of Fourier theory to fully reconstructa complete cross-correlation pattern from the cross correlation of two suitably sampleddata sets. Sampling a wave function corresponds to convolving its Fourier transformwith an array of delta functions. The result is an array of functions in Fourier space.Multiplying this array with a top-hat function of the correct width recreates the originalfunction’s Fourier transform, and this corresponds to convolving the sampled data inreal space with a suitably scaled sinc function.

64


rate used was 2.04 MHz, a minimum of 30 samples were needed to capture a full

cross-correlation peak. Further samples were then needed to allow for any drift

between the oscillators in the apparatus, and to measure the displacement of the

peak caused by path length differences between the two recordings. Each sample

corresponded to a distance of about 150 metres and the oscillator drift only

accounted for a few tens of samples over the course of a few hours, so recordings

of 1000 samples were more than adequate in the interferometric technique and

were transferred by GPIB in less than a second.

The network-synchronised approach required the recordings to capture at least

one synchronisation burst without any prior knowledge of their positions in the

data stream. In order to guarantee this the minimum number of samples per

recording was 104,000 as the maximum separation between SCBs is 51 millisec-

onds (see Section 3.4 below). The GPIB readout time for recordings of this length

was 40 seconds. The fast data acquisition interface could extract a full buffer of

one million complex samples containing 10 or 11 SCBs in half a second. The trig-

gering period used for the network synchronised method needed to be a multiple

of the multiframe repeat period of 3.0613

seconds (see Section 3.4 below).

The digitiser captured a preprogrammed number of samples each time it re-

ceived a pulse from the counter, and then attempted to transmit the samples to

the data-capture machine. The digitiser remained in transfer mode only for a

certain length of time before clearing its memory ready for the next recording.

The data transfer process on both the GPIB and fast data interfaces involved

handshaking, meaning the digitiser did not transmit any data packets until it

received a signal from the data receiving device confirming that the latter was

ready. This prevented any corruption of the data, or missing samples in a data-

set. The times of each recording were stored on the laptop via a readout from

the counter.

65


3.3.3 Cross correlation

The analogue cross-correlation operation between two continuous functions f and

g is defined as

f ? g =

∫ ∞

−∞f ∗(τ)g(t+ τ) dτ. (3.1)

This cross correlation can also be evaluated by performing a series of Fourier

transforms. The Fourier transform of f and the complex conjugate of the Fourier

transform of g are first determined. The cross correlation is then given by the

inverse Fourier transform of the complex product of these two functions, as shown

below in equation 3.2.

f ? g = F[F ∗(ν)G(ν)] (3.2)

3.3.3.1 The ambiguity function

The interferometric and network-synchronised methods described above both

make use of a matched filter to detect the arrival of a signal at the receiver.

If the receiver or transmitter are moving then the received signal will be Doppler

shifted accordingly. This can in turn have a detrimental effect on the cross-

correlation function and the ability to determine the signal arrival time correctly.

The receiver and transmitters remained stationary during all measurements in

this project, but the sources of any multipath interference, such as vehicles, tree

branches, people, etc could have been moving, resulting in a Doppler-shifted-

multipath signal. The ambiguity function is a two-dimensional function of time

delay and Doppler frequency and is given by

χ(τ, f) =

∫ ∞

−∞s(t)s∗(t− τ)e−i2πftdt. (3.3)

where τ is the time delay, f is the Doppler-frequency shift and s is the complex

function under test. The ambiguity function reveals how the cross-correlation

profile of a matched filter varies as the received signal is Doppler shifted. Figure

3.4 below is a plot of the ambiguity funtion for the GSM ETS. The strong central

66


Figure 3.4: The ETS ambiguity function. The Doppler shifts associated with the typicalvelocities encountered during these experiments (movements of vehicles within cities,pedestrians, tree branches, etc) are much lower than the width of the central peak ofthe ambiguity function in the frequency domain. The effect of Doppler shifts on themultipath signals under study here is therefore expected to be small.

peak is about 600 Hz wide in the frequency domain. A Doppler shift of 300 Hz

corresponds to a relative radial velocity between source and receiver of about

90 metres per second for a 900 MHz GSM signal. With this degree of relative

motion, the correct temporal alignment of the ETS template and the Doppler-

shifted ETS within the received signal would result in a central null in the cross-

correlation plot rather than a central peak. However, this velocity is an order

of magnitude higher than the velocities of typical moving objects during these

experiments such as vehicles moving within a city and pedestrians moving around

67


the local environment. The Doppler effect was therefore not expected to have any

significant effect on the multipath interference under study here.

3.4 Anatomy of a GSM signal

Data transmitted on the GSM network is encoded using both Time Division

Multiple Access (TDMA) and Frequency Division Multiple Access (FDMA). The

network is allocated two 25 MHz regions of the electromagnetic spectrum in

the microwave band, both around either 900 MHz or 1800 MHz. One of these

regions is used for transmissions by the BTSs and one for transmissions by the

cell phones. Both of these regions contain 124 200 kHz-wide discrete channels

to allow FDMA. The GSM bit rate is precisely 13,000,00048

bits per second, and

1250 bits define one GSM frame. Data on each channel are transmitted in these

4.615 millisecond frames, which are divided up into 8 bursts of equal length (see

Figure 3.5 below) to allow TDMA. The bursts are allocated to logical channels,

such that up to 8 logical channels can share a single frequency channel at once.

Each logical channel (with the exception of the BCCH) may be switched to a

new radio-frequency channel with each frame in order to provide higher signal

integrity (frequency hopping). If a user communicates using a fixed frequency,

multipath interference can corrupt the signal (see the discussion of fast fading

in Section 1.3 of Chapter 1 above). One solution to this problem is to switch

frequencies, as fades are uncorrelated on channels separated by a wide enough

frequency difference.

Multiple users sharing a single channel need to synchronise their transmis-

sions so that they each only broadcast data to the base station during their own

allocated burst period. The same level of synchronisation is required in order for

each handset to receive the correct burst from the BTS. The handsets use infor-

mation broadcast from the BTS during the synchronisation burst on the BCCH

to coordinate their transmissions and receipts (see Figure 3.6). A timing marker

is established by cross correlating a template of the ETS stored in the handset

68


Figure 3.5: The format of GSM data broadcasts is shown above. Up to 8 logicalchannels can share a single radio frequency channel by each being allocated a burstwithin a TDMA time frame. Each burst period (BP) contains a short training sequence(different from the ETS) which is used to estimate the channel impulse response toprovide coarse filtering of multipath effects and allow optimum detection of the databits transmitted on either side of it.

69


Figure 3.6: The formats of GSM bursts are shown above. Normal bursts are used totransmit data packets. Frequency correction bursts are used by the handset to synchro-nise the frequency of its internal oscillator with that of the BTS and so correct for anydrifts or Doppler shifts. Synchronisation bursts are used by the handset to coordinatethe transmissions and receptions of its normal bursts. Access bursts are transmitted bythe handsets when they are requesting channels to broadcast and receive data bursts on(i.e. when the user is trying to make a call).

70


with the data in the SCB, allowing the time that the ETS was received in the

data stream from the BTS to be determined with a precision of roughly ±12bit.

This is used as a reference point to calculate when the phone should transmit or

expect to receive its data packets1.

The synchronisation bursts occur in a semi-regular sequence on the BCCH.

An SCB is broadcast once every ten frames (46.15 milliseconds), four times in

succession, and then broadcast again after eleven frames (50.765 milliseconds).

The sequence then repeats. This irregular sequence defines a fifty-one-frame-long

multiframe, which contains five SCBs.

Each communication burst is 148 bits long, consisting of 114 data bits, 2 flag

bits, 26 equaliser training bits (a short training sequence), and 6 tail bits. A

further 8.25 bit periods of guard time are allowed between the bursts. The 26

training bits allow an adaptive equaliser to estimate the channel impulse response

to provide coarse filtering of multipath effects and allow optimum detection of

the 57 data bits and 2 flag bits either side of it to be performed.

3.4.1 GSM digital encoding

The communication data on the GSM network are encoded digitally using Viterbi

encoding and then are modulated for transmission using Gaussian Minimum Shift

Keying (GMSK). Viterbi encoding is a type of convolution coding which provides

error-correction capabilities. The original data sequence is used to generate a

much longer sequence for transmission, but one which is created in such a way

that any parts that are missing or corrupted due to noise in the system can be

redetermined (probabilistically) using the surrounding parts of the sequence (see

Figures 3.8 to 3.11 in the post-processing section below).

1See the discussion of timing advance in Section 1.2.1 of Chapter 1

71


3.5 Anatomy of a CDMA signal

The British Third Generation (3G) cellular network uses the Universal Mobile

Telecommunications System (UMTS) standard, which is in turn built on the Code

Division Multiple Access (CDMA) encoding technique. The 3G network was not

researched in the work described in this thesis, but this summary of CDMA is

provided for completeness and to complement the discussions of GPS (which also

uses the CDMA method).

CDMA uses Pseudorandom Noise codes (called the spreading codes or PN

codes) to encode each signal, and the key to the system is that all of the PN

codes are mutually orthogonal. This allows multiple users to transmit and receive

using the entire available bandwidth, but when filtering through all of the data

with a certain PN code, only the data encoded using the same PN code will be

retrieved, the rest will be filtered out. For example, a typical 3G call proceeds as

follows:

The mobile and BTS ‘handshake’ on a standard control channel to confirm

the PN code they will use for the rest of the communication. Once the code is

chosen the entire bandwidth can be used to transmit with large data rates. For

this example, consider a PN code v = (1,-1) (but note that a real PN code is much

longer - up to 38400 digits for the UMTS system) and a data vector (1,0,1,1). To

encode the data, a ‘1’ relates to the vector v and ‘0’ relates to the vector -v, so

this data stream becomes encoded as (1,-1,-1,1,1,-1,1,-1). Now consider another

mobile using the PN code u = (1,1) to send (0,0,1,1) to the same BTS at the

same time. This data stream is therefore (-1,-1,-1,-1,1,1,1,1). At the base station,

this is all received as the sum of the transmission vectors, i.e. (0,-2,-2,0,2,0,2,0).

In order to decode the two data streams, the BTS takes the dot product of each

PN code with the total data stream a chunk at a time. So for the v code, the

decoding process is: (1,-1).(0,-2); (1,-1).(-2,0); (1,-1).(2,0); (1,-1).(2,0). The data

stream (2,-2,2,2) is retrieved, which relates to (1,0,1,1) using the same logic as

before where positive = 1 and negative = 0. Performing the same operation

72

3.6 The Experiments

with the u code results in retrieving the u data stream. The statistical properties

of PN codes are very similar to those of white noise, and crucially they do not

correlate with each other or a delayed copy of themselves. This behaviour also

allows the data transmissions to be asynchronous, which reduces the complexity

of the network.

3.6 The Experiments

There were two types of experiment performed for this research, (a) static tests

and (b) mobile tests. For static tests, the equipment remained in a fixed position

and the antenna either remained stationary or moved short distances. The appa-

ratus was powered via the mains supply and could be run continuously. Mobile

tests involved loading all of the equipment onto a trolley or into a car and moving

the entire apparatus between measurement points. In this case, the equipment

was powered via a large lead-acid battery and a power inverter. The battery

held enough charge for more than a day of continuous use, but in practise mobile

experiments lasted three hours or less.

Each experiment consisted of three parts: preparation, surveying, and post

processing.

3.6.1 Preparation

The preparation for each set of experiments consisted of the following stages:

(a) The Rubidium frequency standard was allowed at least forty eight hours of

warm-up time in order to maximise its stability. It was powered via an unin-

terruptible power supply and so this requirement was easily met. The digitiser

was also powered for at least a day before any experiments to allow its internal

components to reach a stable temperature.

(b) The survey route and rough positions of measurement points were planned in

advance of the experiment. This minimised the time spent gathering data and so

73


minimised the time between calibration measurements. This in turn minimised

the errors on the timing measurements caused by clock drift (see Section 2.5 in

Chapter 2).

(c) The digitiser was tuned to the BCCH broadcast frequency of the BTS under

investigation. The Base Station Identity Code (BSIC) number was then decoded

from the data stream to verify that data was being recorded from the correct

BTS.

3.6.2 Surveying

The details of the survey methods used for each set of experiments are discussed

in Chapters 4, 5 and 7.

3.6.3 Post-processing

Each survey produced a set of BCCH recordings from a known BTS and the data

were processed to calculate the signal arrival times. The processing consisted of

the following stages (see also Figure 3.7):

(a) Each recording was first filtered using a top-hat function to remove all fre-

quencies except those inside the expected bandwidth of 140 kHz. This filtering

was performed by generating the Fourier transform of the data, deleting any

information at unwanted frequencies, and then generating the inverse Fourier

transform. This step was needed because the filter used by the digitiser to set a

recording bandwidth did not have a rectangular frequency transfer response. The

digitising process also applied a small DC offset to the data. This was measured

by averaging over a reasonable proportion (5%) of the data in a given recording

and then removing the resulting value from every sample.

(b) Next, each recording was searched for large spikes in amplitude so that they

could be removed. Large spikes were not common, but consisted of a single sam-

ple with a value 10–100 times larger than the next largest sample in the data.

They may have been a feature of the digitiser or of interference during the data

74

3.6 The Experiments

Figure 3.7: Flowchart describing how the raw data was processed to generate a list ofcross-correlation peak positions.

transfer process but could not have been true samples of the GSM signal based on

the values of the surrounding samples. A large spike in the sampled data would

have resulted in a corresponding large spike in the cross-correlation profile which

could have caused an error in the peak position of the cross-correlation function.

(c) The recordings were then resampled to match the GSM bit rate, allowing all

75


of the BSICs and frame numbers to be decoded (see Figures 3.8 to 3.11 below).

The BSIC was decoded to confirm that a given recorded signal had come

from the correct base station and was not excessively corrupted. Incorrect BSIC

numbers or frame numbers could have been caused by co-channel interference,

corruption by noise, or corruption by multipath interference. Recordings with

incorrect BSIC numbers or frame numbers were examined manually and then

discarded if the error was judged to have been caused by co-channel interference

or very poor signal strength.

(d) The cross-correlations were then performed, with the number of synchronisa-

tion bursts per measurement dependent on the number of samples recorded. For

the interferometric measurement technique, the cross-correlation profile of a full

recording of a million samples contained a strong central peak (corresponding to

the correct alignment of the two data sets), with many subsidiary peaks either

side (see Figure 3.12 below). These subsidiary peaks were caused by all of the

possible alignments within the two data streams of the regular features such as

the ETSs within each SCB and the short training sequences within each burst.

For the network-synchronised technique, each recording was cross-correlated with

a copy of the ETS. The positions of the synchronisation bursts in the recorded

signals were marked by clear peaks (‘SCB peaks’) in the cross-correlation profile,

as demonstrated in Figure 3.13 below.

The signal-to-noise ratio (SNR) in both of these plots appears to be relatively

low, but this is caused by the degree of cross-correlation noise and is not repre-

sentative of the SNR of the original received signals. The cross-correlation noise

is high because of a large number of training sequences and data bursts in the

recorded GSM signals which correlate with the ETS and each other.

(e) The resolution of each SCB peak was increased using the interpolation tech-

nique described above in Section 3.3.1 and Figure 3.3. The sampling rate of

2.04MHz provided an inherent timing resolution of 490 nanoseconds, correspond-

ing to a spatial resolution of 147 metres. The original signal was reconstructed

76

3.6 The Experiments

Figure 3.8: A description of the GSM modulation and encoding techniques, and theBSIC and frame number decoding process [57, 58].

77


Figure 3.9: A description of the GSM modulation and encoding techniques, and theBSIC and frame number decoding process (continued).

78

3.6 The Experiments


79



80

3.6 The Experiments

from these samples, then resampled at 40.8 MHz, providing a new timing resolu-

tion of 24.5 nanoseconds and a spatial resolution of 7.4 metres. This new sampling

frequency was chosen as a suitable compromise between increased resolution and

increased data storage and processing requirements.

(f) The data set was then corrected for a systematic error caused by the frequency

offsets between the frequency standards used in the experiments (see Section 2.4

in Chapter 2). The offset was measured by performing calibration recordings at

the start and end of an experiment and comparing them. For the interferometric

method, these calibrations were performed by connecting both sets of measuring

apparatus to the same signal source and waiting for them to record data. The

phase drift between the two sets of apparatus could be determined and corrected

by comparing the pairs of recordings at the beginning and end of the experiment.

For the network-synchronised method, these calibration measurements consisted

of data gathered at the BTS itself in order to determine the position of the SCB

peak corresponding to “zero” distance from the BTS. By comparing the change in

this position at the beginning and end of the experiment, the phase drift between

the RFS and the oscillator in the BTS could be estimated and the data corrected

accordingly.

(g) The SCB peak positions were then used to determine signal stabilities, rel-

ative signal arrival times, or absolute signal flight times (see Chapters 4, 5 and

7 respectively). Each SCB peak position was considered independently for the

experiments discussed in Chapters 4 and 7, and for most of the measurements dis-

cussed in Chapter 5. For the other measurements in Chapter 5, an average SCB

peak position was determined along with an error. This was possible because the

time delay between synchronisation bursts was a known quantity, and therefore

all of the SCB peaks in a set could be shifted backward in time accordingly and

so all compared directly with the first recorded SCB peak.

81


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 106

0

1

2

3

4

5

6

7

8

9

10x 10

11

absolutemagnitude

of thecross−

correlationvalue

sample

An example cross−correlation profile generated using the interferometric method

(a) Full cross-correlation profile.

0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05

x 106

0

1

2

3

4

5

6

7

8

9

10x 10

11

absolutemagnitude

of thecross−

correlationvalue

sample

An example cross−correlation profile generated using the interferometric method

(b) Detail around the cross-correlation peak.

Figure 3.12: A plot of the cross correlation of one million samples recorded at 2.04MHz from a base station’s control channel using the interferometric method. The profilecontains a strong peak corresponding to the correct alignment of the two data streams(a). The many subsidiary peaks (b) are caused by correlations between repetitive struc-tures in GSM broadcasts, such as TDMA frame tail bits and short training sequences(see section 3.4 above).

82

3.6 The Experiments

0 200000 400000 600000 800000 10000000

0.5

1

1.5

2

2.5

3

3.5

4x 10

5

sample

absolutemagnitude

of thecross−

correlationvalue

An example cross correlation profile generated using the network−synchronised method

(a) Full cross-correlation profile.

1.4 1.42 1.44 1.46 1.48 1.5 1.52 1.54 1.56 1.58 1.6

x 106

0

0.5

1

1.5

2

2.5

3

3.5

x 105

sample

absolutemagnitude

of thecross−

correlationvalue

An example cross correlation profile generated using the network−synchronised method

(b) Detail around two cross-correlation peaks.

Figure 3.13: A plot of one million samples recorded at 2.04 MHz from a base station’scontrol channel cross correlated with the GSM ETS using the network-synchronisedmethod. The profile (a) contains ten strong peaks, each marking the position of asynchronisation burst in the transmission. Each frame containing an SCB is preceededby a frame containing a frequency control burst (seen here as the small gaps to the leftof each SCB peak in (b)). The fine-scale subsidiary peaks are caused by correlationsbetween the ETS and the short training sequence within each normal burst.

83


84

Chapter 4

GSM Network Stability

A series of experiments was performed to determine the temporal stability of

the received signals on two GSM networks and to determine the viability of the

network-synchronised measurement technique discussed in the previous chapter.

Several base stations were studied using a stationary outdoor antenna on the

Cavendish Laboratory roof. The variation in signal arrival times from a given

BTS were compared to an RFS over elapsed times of many hours. The results

are presented here as Allan deviation plots. Allan deviation plots were discussed

in Chapter 2.

4.1 Method and apparatus

The equipment was prepared for the network-synchronised method as described

in the previous chapter. The signal stabilities were measured using the varia-

tions in the positions of the SCB peaks with time. Measurements of the absolute

signal TOFs were not needed and so the equipment did not need to be moved

at the start and end of each experiment to record calibration data at the BTS.

This reduced the measurement errors associated with moving the experimental

apparatus since the equipment remained fixed in one place with reduced changes

in temperature, pressure, humidity, vibration, etc. A fixed omni-directional an-

tenna positioned 10 metres above the above the roof of the Cavendish Laboratory

85

4. GSM NETWORK STABILITY

Figure 4.1: A picture showing the antenna above the roof of the Cavendish Laboratory.The 2dBi dipole highlighted by the green ellipse in the image was placed on top of a Yagiantenna mounted on a pole roughly 10 metres above the roof and roughly 25 metres abovethe ground.

(see Figure 4.1) was used to gather the data. Data were recorded at a multiple

of the multiframe repeat rate when using the network-synchronised method, cal-

culated as follows. The GSM bit rate is 13,000,00048

bits per second and 1250 bits

make up a frame. Multiframes contain 51 frames each and repeat in an unbroken

continuous sequence. A simple multiple of the multiframe period is 3.06 seconds

(48×1250×51×1313,000,000

) and this is also the smallest multiple used when recording data

during the work discussed in this thesis. For the work presented in this chapter,

tests lasting a day or less were recorded at a rate of 1 measurement every 61.2

seconds. For longer tests, data were recorded every 306 seconds because of re-

strictions on data storage capacity. The aim of the experiments was to determine

the stabilities of the received signal from various base stations over many hours,

86


and recording a measurement every few minutes was an adequate sampling period

for this purpose. Since the antenna remained stationary and in an open, high

environment, any variation in the SCB peak position was expected to be caused

by (i) measurement noise, (ii) the stability of the BTS’s transmitting equipment

and frequency reference, (iii) the stability of the signal’s propagation path, and

(iv) the stability of the RFS.

4.1.1 Calibration

A Racal 6104 Digital Radio Test Set [59] (a GSM signal generator), was connected

directly to the digitiser’s input with a short cable and phase-locked to an FRK-H

Rubidium oscillator identical to the one being used as the frequency reference by

the measurement apparatus (see Figure 4.2). The RACAL generated a BCCH

signal and the resulting Allan deviation plot is shown below as the red curve in

Figure 4.3. This red curve can be regarded as the base-line for the measurement

apparatus, as the signal was phase locked to a Rubidium atomic standard and

there was no propagation channel. The green curve in the same figure was gen-

erated with the Racal locked to its internal OCXO, with all other aspects being

the same. The curves in Figure 4.3 show that the measurement noise was the

dominant feature in the calibration data for short time scales. Both curves are

initially straight with a gradient of −1 and lie along the same line, showing that

the stabilities in these regions were dominated by random white noise on the

signal rather than by the stabilities of the frequency references (see Section 2.1

in Chapter 2). The vertical positions of these ‘-1’ regions with respect to the

axes were determined by the noise level. The signal stabilities over longer time

scales were determined by the respective stabilities of the frequency references,

as shown by the regions where the curves flatten off and the gradients become

positive.

The red curve has not been corrected for the Allan deviation of the FRK-

H used as the reference in the measurement apparatus and therefore represents

87


Figure 4.2: Sketch showing the experimental setup used to produce the calibrationAllan deviation curves. The Racal GSM signal generator was initially phase locked toan FRK-H standard identical to the one used to phase lock the measurement apparatus(a). In a second experiment, the Racal signal generator was locked to its own internalOCXO (b). The full measurement apparatus is given in Figure 3.1 in Chapter 3.

the combined Allan deviation of the whole system (the GSM broadcast and the

measurement apparatus combined). An estimate of the required correction can

be made using Equation 2.15 from Chapter 2, and the Allan deviation values for

the FRK-H shown in Figure 2.15in Chapter 2. However, applying this correction

adjusts all of the plots in this set of experiments in the same way, and so it does

not affect their relative behaviour or positions, nor the conclusions drawn by

comparing the position of the reference curve to the data curves. The correction

was therefore not applied.

4.2 Results and discussion

Base stations transmitting on both the 900MHz (“Network 1”) and 1800MHz

(“Network 2”) wavebands were studied. On both networks, the distances from

the Cavendish Laboratory to the base stations were between 300 metres and 8

kilometres. Networks 1 and 2 were controlled by different companies, and proba-

88


Figure 4.3: Plot showing the Allan deviation curves produced by an internally- andexternally-locked (green and red lines respectively) Racal GSM signal generator.

bly comprised equipment bought from different manufacturers at different times.

A section of the timing data gathered from a BTS on Network 1 is shown in Fig-

ure 4.4 below. The transmitting antenna of this base station was 1.2 km from the

receiver’s antenna and the variations in SCB arrival times rarely exceeded 0.1 mi-

croseconds from the average value over the whole test, with a standard deviation

of 46 nanoseconds. It is apparent from the detail (Figure 4.4(b)) that there was

a slow, quasi-periodic, variation with a period of several hundred seconds, and

this may have been an artifact of a frequency control loop in the BTS electronics.

Adjacent samples would have been uncorrelated if the fine scale structure was

dominated by white noise. The quasi-periodic nature of the data suggests that

the effective bandwidth of the variations was of order 10−3 Hz. Further evidence

for this can be seen in the Fourier transform shown in Figure 4.6 The spike at

about 3 mHz corresponds to the quasi-periodic behaviour noted above.

An example of data gathered from Network 2 is shown in Figure 4.5. This

89


(a) Variation in signal arrival times over 15 hours.

(b) Detail over 5 hours.

Figure 4.4: Plots showing the variation in relative signal arrival times at a stationaryoutdoor receiver from a GSM base station broadcasting in the 900 MHz waveband.

90


(a) Variation in relative signal arrival times over 65 hours.

(b) Detail over 5 hours.

Figure 4.5: Plot showing the variation in signal arrival times at a stationary outdoorreceiver from a GSM base station broadcasting in the 1800 MHz waveband.

91


0 1 2 3 4 5 6 7 8 9

x 10−3

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

frequency (Hz)

power (arbitraryunits)

Figure 4.6: The Fourier transform of the data given in Figure 4.4.

0 1 2 3 4 5 6

x 10−4

0

10

20

30

40

50

60

frequency (Hz)

power(arbitrary

units)

Figure 4.7: The Fourier transform of the data given in Figure 4.5.

92


base station was 8 km from the receiver’s antenna and appeared to be less stable

than the BTS on Network 1. The signal arrival times also show quasi-periodic

behaviour but on the longer timescale of about 40 minutes. The frequency control

loop associated with this equipment was presumably of a different design from

that of the BTS previously discussed. The slower variation on a timescale of

about 40 hours may have been caused by network control fluctuations, or effects

on the frequency reference in the base station such as temperature and pressure

changes. The standard deviation of this data set is about 0.9 microseconds. The

Fourier transform of the data is given in Figure 4.7. The large spike near the

origin corresponds to the 40-hour time variation. The quasi-periodic behaviour

with a timescale of about 40 minutes manifests itself in significant power around

0.26 and 0.48 mHz.

Variations on these timescales were not observed in the data measured on

Network 1, suggesting that they were associated with the BTS on Network 2 and

not with the measurement apparatus.

It should be noted at this point that each BTS has its own local frequency

reference, which under GSM specifications [60] has to maintain a frequency ac-

curacy (corresponding to the bias error discussed in Chapter 2) of 5× 10−8. The

most common method of maintaining this accuracy involves using the commu-

nications backbone to compare the frequency reference at the BTS to a stable

central reference which may be trained by GPS. Different manufacturers use dif-

ferent correction techniques, with some allowing the BTS to drift until a certain

threshold is reached before applying a correction, and others using a control loop.

4.2.1 900 MHz Network

Figure 4.8 shows the Allan deviation plots for four base stations on the 900MHz

network and two reference curves.

The black curve labelled ‘Ref’ represents a Racal GSM generator phase locked

to an FRK-H Rubidium oscillator (reproduced from Figure 4.3), and corresponds

93


Figure 4.8: The Allan deviation plots for the base stations on the 900MHz network

to the performance floor of the apparatus. The black curve marked ‘M’ is a line

representing the Allan deviation of a white-noise signal with a standard deviation

of 2 microseconds. This reference line is discussed further below.

The error bar associated with each individual Allan deviation value can be

estimated using Equation 2.14 in Chapter 2. Data corresponding to timescales

larger than 20,000 seconds have been removed and the error bars for the remaining

data are smaller than the thickness of the lines used in the plot. Each Allan

deviation value plotted here is an average over at least 150 measurements.

The other curves in Figure 4.8 represent the Allan deviations measured on

a number of base stations on the 900 MHz network. Curves ‘E’, ‘F’ and ‘G’

represent data gathered from a single BTS on different days. These three data

sets demonstrate a high degree of consistency. The pronounced wiggles in these

curves suggest that a quasi-periodic behaviour with a timescale of about 1,000

seconds appeared in this particular data set (the cause is unknown but is probably

associated with the BTS rather than the measurement apparatus). The curves

94


labelled ‘A’, ‘E’, ‘D’ and ‘C’ represent data from base stations that were 1.2,

2, 4 and 8.1 kilometres from the receiver’s antenna respectively (see Figure 4.9

below). The curve labelled ‘B’ represents data from the same BTS as curve ‘A’,

but the data was gathered using an antenna inside the laboratory rather than

the external antenna. The higher noise level associated with the decreased signal

strength accounts for the vertical shift between curves ‘A’ and ‘B’.

Figure 4.9: Map of Cambridgeshire showing the positions of the base stations studiedand the Cavendish Laboratory. The Laboratory is marked with a blue circle, the basestations on Network 1 are marked with a red triangle, and the base stations on Network2 are marked with a yellow triangle.

95


Curves ‘A’ to ‘G’ do not come close enough to the reference curve (‘Ref’)

to be affected by the behaviour of the RFS. All of the curves show that the

base stations studied on Network 1 were highly stable and that their frequency

references were approaching the stability of the FRK-H atomic reference. This

suggests that the crystal oscillators in the BTSs were locked to a central network

frequency reference of high stability using an underlying network-wide stabilising

mechanism as mentioned above. It also suggests that the network-synchronised

method discussed in the previous chapter will be as accurate as the interferometric

method when studying these base stations.

Curve ‘C’ exhibits a deviation from its initial −1 gradient over time periods

of 100–600 seconds before settling back to a −1 gradient. This is not typical for

a free running oscillator (see Section 2.1 in Chapter 2). This behaviour can how-

ever be caused by a perturbation with a characteristic timescale superimposed

on an otherwise highly stable signal. The variation is not an oscillation with a

fixed frequency, as this would result in a oscillation on the Allan deviation plot

marking out the period and sub-harmonics of the oscillation. Figure 4.10 shows

the sampled data gathered from this BTS and it can be clearly seen that there is

both a fine scale regular structure showing variations of around 1.5 microseconds

over roughly 20 minutes, and a smooth wander of a microsecond over timescales

of around 10 hours or more. Comparing these time periods to the Allan devi-

ation plot, the fine scale structure is responsible for the unexpected deviation

between 100 and 600 seconds. The BTS represented by curve ‘C’ was the oldest

base station studied on Network 1. The short term perturbations and long term

wander evident in Figure 4.10 are not seen in the other data sets for this network,

suggesting that this base station is not locked to a highly stable oscillator like the

newer transmitters on that network. The fact that the signal from this old BTS is

still highly stable over long time periods does however suggest that there is some

degree of frequency correction or control in operation. The finer-scale structure

is similar to the structure seen in the data from Network 2 in Figure 4.5 and may

be a feature of older base station technology. An Allan deviation plot generated

96


(a) Variation in relative signal arrival times

(b) Allan deviation plot comparisons

Figure 4.10: The timing data (a) and Allan deviation curves (b) from the 900 MHzGSM base station represented by Curve ‘C’ in Figure 4.8. The Allan deviation plotgenerated using data gathered at the base station is similar to the plot generated usingdata gathered at the Cavendish Laboratory over 8 kilometres away (b).

97


with data gathered at the base station is compared to curve ‘C’ in Figure 4.10.

The two curves exhibit the same behaviour and are positioned closely, supporting

the hypothesis that the short term perturbations noted previously are a feature

of the transmissions from the base station and not a feature of the propagation

path or interference effects at the receiver.

Curve ‘M’ in Figure 4.8 is a line representing a white noise signal with a

standard deviation of 2 microseconds. Duffett-Smith and Tarlow [16] have shown

that a GPS device can be assisted using FTA (see Section 1.2.5.4 above) if the

estimate of GPS time provided is within an accuracy of 2 microseconds. The

work presented here shows that the base stations on Network 1 can be used to

provide FTA with time periods of at least three days between calibrations.

4.2.2 1800 MHz Network

The Allan deviation curves for a set of base stations on the 1800 MHz GSM

Network are shown in Figure 4.11. The same reference curves (‘Ref’ and ‘M’)

are also displayed as before. The base stations vary in range from about 300

metres to about 8 kilometres from the Cavendish Laboratory (see Figure 4.9),

and the same general relationship holds between signal strength and vertical

position on the plot as for the 900 MHz data. The data exhibit varied behaviour

and demonstrate that the signals from the base stations on this network are not

as stable as those from Network 1. The lowest curves on the plot (labelled ‘P’,

‘Q’ and ‘R’) exhibit initial ‘−1’ slopes followed by smooth upward turns, and are

characteristic of Allan deviation plots for oven controlled crystal oscillators (see

Figure 2.15 in Chapter 2). Curves ‘P’ and ‘Q’ are both data from the same BTS

gathered a week apart to test for consistency and there is a noticeable difference

in the long term behaviour for t & 1000 seconds, possibly due to variations in the

environmental conditions or corrections at the BTS during the two tests.

The upper plots (labelled ‘S’, ‘T’ and ‘U’) display greater long term stability

with overall trends following −1 slopes, but all have significant oscillations super-

98


Figure 4.11: The Allan deviation plots for the base stations on the 1800MHz network

imposed on this trend. These are caused by oscillations in the timing data (see

Figure 4.12 below) which are most likely to be a feature of the equipment and pro-

cesses used by the base stations to generate the signals rather than being caused

by propagation effects or interference. These two distinct groups of curves suggest

that there are at least two groups of base stations on Network 2: (a) those with

unregulated or infrequently-regulated crystal frequency references and (b) those

with more stable or regularly-corrected reference sources but a further source of

inherent instability producing an oscillation in the signal transmission times. The

oscillation could be caused, for example, by the BTS’s frequency reference being

strongly over-corrected each time it deviates away from its nominal frequency by

a certain amount.

The position of the curves relative to the two-microsecond line shows that this

network can be used to provide FTA, but the method can only be guaranteed for

time periods between calibrations of about 5 hours or less. Curves ‘S’ and ‘T’ are

both data from the same BTS gathered a week apart, and they are reasonably

99


Figure 4.12: Plot comparing the timing errors for three base stations. The blue linerepresents the timing data from a BTS on Network 1 (curve ‘A’ in Figure 4.8). Thepink line represents the timing data from a BTS on Network 2 (curve ‘P’ in Figure4.11). The frequency reference may be controlled over long time scales or once it hasdrifted far enough from its nominal frequency, but the shape of curve ‘P’ in Figure4.11 and the very gradual changes in the drift exhibited above suggest that there areno corrections made over the time scale of this dataset (45 hours). The orange linerepresents the timing data from another BTS on Network 2 (curve ‘U’ in Figure 4.11)and demonstrates a higher stability than seen for the pink line, but also exhibits adistinct oscillation. This oscillation may be caused by the BTS’s frequency being over-corrected by the network’s frequency control mechanism each time it drifts a certainamount from its nominal frequency.

consistent. The timing data from Curve ‘S’ is given above in Figure 4.5 and

exhibits similar short term systematic variations to those seen in the timing data

from curve ‘B’ (Figure 4.10) in the Network 1 Allan deviation plot. A test at

that BTS suggested that the variations were a feature of the transmission, and

100

4.3 Conclusions

so may be a feature of older base-station technology.

It should be noted that if a given network uses GPS to train its central tim-

ing reference, then the whole network can be a stable repository of GPS time,

extracted using the E-GPS technique. However, if the central timing reference is

not trained by GPS, the network may gradually drift relative to GPS, degrading

its E-GPS performance.

4.3 Conclusions

1. A calibration experiment was performed to determine the Allan deviation plot

that would be measured for a base station locked to a Rubidium oscillator. This

provided a reference to compare with the BTS signal stabilities.

2. The stabilities of the signals from the four base stations studied on the 900

MHz network were all very high. The stabilities were dominated by the level

of receiver and measurement noise for the full length of the tests and were all

approaching the levels expected from atomic frequency standards. This suggests

that the base stations were all locked to highly stable frequency references, such

as GPS time, or a highly stable central frequency reference. It is unlikely that

there is an expensive atomic frequency standard in every base station on the net-

work.

3. The oldest macro cell transmitter tested on the 900 MHz network exhibited a

systematic variation in its synchronisation burst transmission times over a period

of roughly ten minutes. This variation reduced the overall stability of the sig-

nal, but the data still suggested that the base station’s frequency reference was

highly stable over the full time period of the test. A test performed at the base

station suggested that the variation was a feature of the transmission and not a

propagation or interference effect.

4. The four base stations studied on the 1800 MHz network displayed lower signal

stabilities than those on the 900 MHz network. There also appeared to be two

101


types of base stations on the 1800 MHz network - those controlled by oven con-

trolled crystal oscillators and others controlled by more stable reference sources

but with an unwanted oscillation or semi-periodic variation superimposed on the

signal reducing the stability.

5. The studies of the two networks suggest that Fine Time Aiding can be pro-

vided on Network 1 over time periods of 3 days or more and on Network 2 over

time periods of up to 5 hours.

6. The base stations on the 900 MHz network exhibiting signal timing stabilities

close to the timing stability of the FRK-H Rubidium atomic standard can be

used to perform experiments using the network-synchronised method described

in Chapter 3.

102

Chapter 5

The effects of indoor multipath

environments on timing stability

A series of experiments was performed to investigate the temporal stability of the

signals received from GSM base stations at a slowly-moving indoor antenna.


The experimental method for recording and analysing data was the same as de-

scribed in Chapter 4. A conveyor belt was added to the apparatus to move the

antenna smoothly and continuously across the measurement space at speeds rang-

ing from a millimetre per minute to a centimetre per second. The experiments

were performed on a grid marked out on a table top in three different areas -

outside on the flat roof of the Rutherford building of the Cavendish Laboratory,

inside a small fully-enclosed room on the roof itself (the Roof Laboratory), and

inside a room on the second floor of the Rutherford building (the Electronics

Laboratory).

The maximum distance sampled in each experiment was restricted by the sizes

of the desks and work surfaces available to 60–70 centimetres. Various recording

rates and conveyor belt speeds were tested in order to find a balance between

sampling as finely as possible in space to provide a high spacial resolution, and

103

5. THE EFFECTS OF INDOOR MULTIPATH ENVIRONMENTSON TIMING STABILITY

gathering the data as quickly as possible to reduce uncertainties in the results

caused by unknown factors such as movements of people or objects. Ideally, a

large array of antennas and digitisers would have been used to gather all the data

simultaneously but this was impossible in practise. These temporal variations

during the experiments reduced the ability to draw firm conclusions about the

signal stability as a function of position in a static multipath environment. The

experiments did, however, allow realistic (i.e. varying and uncontrolled) multi-

path environments to be studied. A set of calibration measurements was recorded

at the beginning and end of every data set in order to correct for the linear slope

caused by the frequency offset between the BTS reference and the Rubidium

reference (as described previously). These measurements consisted of recording

data in the same fixed position. The conveyor belt was transparent and ran over

a fixed grid, allowing the antenna to be placed at the calibration position to an

accuracy of a millimetre before and after each experiment.

5.2 Results and discussions

The mean position of the SCB peaks recorded in the calibration measurements

defined a reference point used to examine the relative positions of the other SCB

peaks in a given experiment. All of the experiments were performed over distances

much smaller than the effective spatial resolution of the recording apparatus of

7.4 metres (see Section 3.6.3 in Chapter 3). If the experiment had been performed

in free space, the apparatus would not have been able to resolve the effects of the

changes in the positions of the antenna. In practise variations much larger than

the resolution limit were recorded, corresponding to timing errors caused both by

measurement noise and multipath interference. These findings support an anec-

dotal report by Duffett-Smith who found in an early GSM cell phone positioning

experiment that a change of 10 centimetres in the position of a receiving antenna

altered the apparent receiver position relative to the BTS by 90 metres.

104


5.2.1 Roof experiment

An experiment was performed over a distance of 30 centimetres on the roof of

the Rutherford building with a visible line of sight to a BTS 1.2 kilometres away.

It was not possible to use the conveyor belt on the roof and so the antenna

was moved in a line toward the BTS manually in 2 centimetre steps with 5

measurements recorded at each position. Each measurement consisted of 105,000

samples recorded at a rate of 2.04 Ms s−1, which was enough to guarantee at

least one SCB peak captured per recording. The aim of this first experiment was

to determine if there were any spatial multipath variations in a small region of

this LOS environment. The roof itself was not entirely flat, with a number of

‘sky lights’ protruding a metre from the surface in various places. There were

also several other buildings within 200 metres of the experiment. Both of these

features could have caused significant multipath effects.

The view of the BTS from the roof of the Rutherford building can be seen in

Figures 5.1 and 5.2 below. This base station was used for all of the experiments

described in this chapter and was the most stable BTS studied in Chapter 41.

Figure 5.1 gives the clearest view, with the BTS indicated with a green ellipse.

Figure 5.2 gives the view of the BTS from the location of the first position of the

antenna during the roof experiment. The base station has been highlighted again

with a green ellipse. The Fresnel theory of diffraction introduces the concept of

Fresnel zones between transmitters and receivers, such that reflections or scat-

tering from objects within odd-numbered zones interfere constructively with the

LOS signal, and objects within even numbered zones generate multipath signals

which interfere destructively [61]. The Fresnel zone radius at a given point p

along the line-of-sight path within a communication link is given by

Fn =

√nλd1d2

d1 + d2

, (5.1)

1The BTS on the 900 MHz network represented by curve ‘A’ in Figure 4.8

105


Figure 5.1: This picture shows the view from the roof of the Rutherford building ofthe base station used in all of the experiments in this chapter. The base station ishighlighted with a green ellipse.

where Fn is the nth Fresnel zone radius in metres, d1 is the distance between the

transmitter and p, d2 is the distance between the receiver and p, and λ is the

wavelength of the signal. The first Fresnel zone contains the strongest reflected

signals (since it contains the shortest propagation paths and shallowest reflec-

tion angles compared to the other zones) and therefore in order to reduce the

destructive interference effects of even numbered Fresnel zones, the first Fresnel

zone must be as clear of obstacles as possible in order to maximise its construc-

tive contribution to the LOS signal. Figure 5.3 below is a diagram showing the

region enclosed by the first Fresnel zone for this system. The skylights, rooftop,

and nearby building visible in Figure 5.2 were blocking roughly 50% of the first

Fresnel zone and therefore the effect of multipath interference at this receiver was

expected to be high. The skylights visible on the left side of Figure 5.2 were a

106


Figure 5.2: This picture shows the view of the base station from the first position ofthe antenna during the initial experiment on the roof of the Rutherford building. It ishighlighted with a green ellipse.

metre high and are just off the bottom of the picture in Figure 5.1.

The data from this experiment is shown in Figure 5.4 below. Each point on the

plot is the average SCB position of the 5 values recorded at each antenna position.

The error bars on each point are given by the standard deviation of each set of

5 values and they give an estimate of the measurement noise for the experiment.

The large timing error recorded 10 centimetres from the starting position suggests

that the antenna was moved 450 metres toward the base station. The standard

deviation of the 5 samples recorded at this position is only 75 metres, and so

measurement noise alone could not account for such a large error. These five

measurements were recorded over 30 consecutive seconds, suggesting that this

anomaly was present over at least half a minute. As shown later, this apparent

shift in position was caused by the effects of multipath interference distorting

107


Figure 5.3: Diagram showing the first Fresnel zone for a transmitter-receiver separationof 1,200 metres and operating with a wavelength of 30 centimetres

the shape of the SCB?ETS cross-correlation peak. This distortion displaced the

position of the maximum value of the peak (used to mark the arrival of the signal)

and so displaced the apparent position of the receiver. The maximum values of

the cross-correlation peaks for these samples are also the lowest for the whole

data set (given by the pink line in Figure 5.4). This quantity is related to both

the signal quality and the signal strength - the peak height will be low for either

a weak signal or a signal corrupted by interference, or both. The open-sky, line-

of-sight environment of this experiment suggests that the cross-correlation peak

value was low here because of signal cancellation from multipath interference.

Figure 5.5 below shows some sample cross-correlation peaks for this data set and

supports the hypothesis that the large timing error was caused by distortion of

the SCB peaks. This initial experiment demonstrated that multipath interference

could cause a large error even in a line-of-sight environment. It also showed that

108


Figure 5.4: Plot showing the data from the roof experiment. The blue line gives thetiming error associated with the relative position of the SCB peaks in each measurementand is plotted against the left-hand axis. Each microsecond of timing error correspondsto an error of about 300 metres in the estimated distance of the receiver along a lineaway from the BTS. The pink line represents the maximum absolute value of each SCBpeak and so gives a measure of the signal strength and quality. The pink line is plottedagainst the right hand vertical axis. The horizontal axis gives the distance from theinitial position. Five recordings were taken at each position, then the antenna wasmoved 2cm toward the base station. The last 5 measurements were recorded back at theinitial position in order to correct the data for any unwanted slope.

the multipath behaviour could vary on a finer scale than the wavelength of the

radiation carrying the signal (about 30 centimetres).

The first five and last five measurements in the data set were recorded at

the calibration point and the data was corrected for a slight slope as discussed

previously. Even after this correction was carried out, there remained a small but

significant slope in the data (note the offset in the SCB position between the data

at position 28 and the data at the calibration point, position 0). This difference

represented a displacement of 60 metres, whereas the real change in antenna

109


1.7987 1.7987 1.7988 1.7988 1.7989 1.7989 1.799 1.799

x 105

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

x 104

position in cross correlation function (samples)

magnitudeof thecross−

correlationvalue

Figure 5.5: Plot showing sample SCB peaks from the roof experiment shown in Figure5.4 above. In order of peak height (largest first) the SCB peaks correspond to samplenumbers 1,24,31,27 and 26. It is clear from this plot that the large position error seen10 centimetres from the starting position in Figure 5.4 (i.e across samples 26 to 30) iscaused by distorted SCB peaks, which are in turn most likely to be caused by multipathinterference.

position was only 30 centimetres. The measurement noise level in this region of

the graph accounts for an error of around ±10 metres (one standard deviation),

so this timing error was likely to have been caused by another multipath effect

varying smoothly over a larger length scale than the previous effect.

5.2.2 Roof Laboratory Tests

Several tests were performed on a grid inside the Roof Laboratory of the Ruther-

ford building. A brick wall with a large glass window separated the antenna from

110


the open space of the roof. The outside wall of the Roof Laboratory was clad

in corrugated iron, which would have been a significant barrier to radio waves.

The strongest signals inside the room were therefore likely to have entered via

the window after scattering toward it from nearby objects or by diffraction at

the window’s edge. There may also have been slot-antenna effects at the edges

of the sheets of cladding, which were electrically connected with bolts every 50

centimetres along the vertical edge of each sheet. The window did not face the

base station but its plane was approximately parallel to a line from the room to

the BTS.

The first test inside the Roof Laboratory consisted of moving the antenna

along a line running parallel to the window using the conveyor belt, then repeat-

ing the same test 4 hours later along the same line to check for consistency in

the multipath behaviour. The results are shown in Figure 5.6 below. The dark

blue line represents the results of the first test. The first 10 recordings were made

using the external antenna mounted on a mast about 10 metres above the roof of

the Cavendish Laboratory (see Figure 4.1 in the previous chapter). Recordings

11–20 were then made using the internal antenna positioned outside the Roof

Laboratory window with LOS to the BTS. This antenna was then placed on the

conveyor belt inside the Roof Laboratory and recordings were made every 3.06

seconds with the conveyor belt moving at 20 millimetres per minute. Measure-

ments 701–710 were then recorded using the indoor antenna placed outside in

the LOS position again, and the final recordings (711–720) were made using the

external antenna on the mast. The red line represents the second test. In this

case the first 10 and final 30 samples were recorded at the LOS position outside

the Roof Laboratory using the internal antenna; the mast-mounted antenna was

not used. These initial and final recordings in both tests were used to remove the

overall slope on the data, but also to check for any large variation in SCB position

between points just inside and just outside the Roof Laboratory. In fact, such

differences were small enough to ignore. The cyan and pink lines represent the

maximum value of the cross-correlation peak for each data set as before. Note

111


Figure 5.6: This plot shows the data gathered over a 70 cm length in the Roof Labora-tory in a non-LOS environment. The antenna moved along a line toward the BTS andparallel to the window. The blue and red lines represent the SCB positions recorded at10 a.m. and 2 p.m. on the same day along the same line. The cyan and pink linesrepresent the maximum absolute values of the SCB peaks at 10 am and 2 pm.

the very large signal strengths at the external, mast-mounted positions in the

first test, as expected.

There are marked similarities between the red and blue plots, but the two are

not identical. The variation in the wavelength of the standing wave structures

in both plots represents a change in frequency of about 5 parts in a million per

second over 4 hours. The data gathered in Chapter 3 showed that the BTS was

more stable than this by about four orders of magnitude, and so this feature is

unlikely to have been caused by a change in either the BTS frequency reference

or the RFS. It could have been caused by movements of nearby objects, but all

of the objects in the Roof Laboratory and out on the roof of the laboratory were

112


static during the experiments. The movements of objects and people on the lower

floors of the building could have been partially responsible, but it was difficult

to see how they could have caused the whole effect. It is also unlikely that the

strongest signals in the Roof Laboratory would come from the lower floors of

the building. The antenna was placed at the initial position on the grid to an

accuracy of a millimetre, much less than the apparent shift between the red and

blue plots (about 5 centimetres around sample 100). The most likely cause was

that the conveyor belt may not have drawn the antenna along exactly the same

line to within a millimetre. The conveyor belt consisted of a roll of thin paper that

could be drawn out across a desk and then wound back by an electric motor. The

belt was driven at one end and the paper was free at the other end. During the

experiments, there may have been some slight variation in the path followed by

the antenna as the conveyor belt’s mechanism removed any slack or twist in the

paper. The right hand sides of the plots represent the region where the antenna

was closest to the winding mechanism, and so errors would be smallest here. This

is the region with the closest agreement between the two plots. Both plots also

exhibit a smooth oscillation in timing error with a wavelength of approximately

30 centimetres. The timing error varies across a range of about 3 microseconds

for the first test, and about 1.5 microseconds for the second test, corresponding

to apparent peak-to-peak variations in signal path lengths of about 900 metres

and 450 metres respectively.

A second experiment was performed along the same line the next day, but

with 20 samples recorded per antenna position at a rate of 3.06 seconds between

samples. The antenna was moved in 1 centimetre increments by hand and only

covered the first 50 centimetres of the line compared to the previous tests. The

first twenty and final twenty measurements were recorded with the antenna placed

at a reference position outside the Roof Laboratory window with line-of-sight to

the BTS. The resulting plot is shown below in Figure 5.7. The overall variation

in timing error was very similar to the variation seen in Figure 5.6 even though

the experiments were performed on different days, supporting the hypothesis

113


Figure 5.7: This plot shows the data gathered over a 50 centimetre length in the RoofLaboratory. The antenna was moved along the same line as used in Figure 5.6, andwith the same starting position.

that the spatial multipath environment in the Roof Laboratory was stable and

dominated by fixed nearby objects. The error bars on the blue line represent

the standard deviations of the timing errors for each set of 20 recordings per

position and provide estimates of the levels of measurement noise in the system

for this experiment. The error bars are greatest when the SCB peak values are

smallest, and this is caused by the measurement noise having a greater effect on

the positions of the SCB peak when the peaks have been distorted by multipath

interference. When an SCB peak is significantly distorted, it is shallower than

an undistorted peak (see Figure 5.5). Measurement noise has the greatest effect

when the rate of change of the gradient is smallest, so a sharply-peaked cross-

correlation peak (e.g. the purple line in Figure 5.5) is less affected than a shallower

cross-correlation peak (e.g. the green line in Figure 5.5).

114


A further experiment inside the Roof Laboratory consisted of recording data

along 5 parallel lines on the work surface, each 5 centimetres apart. The results

of the previous experiment suggested that the multipath environment had been

oversampled spatially, and so this time recordings were taken 6.12 millimetres

apart every 6.12 seconds. The results of the experiment are given below in Figure

5.8. The plot shows a number of regions with a smooth variation in timing error

Figure 5.8: This plot shows the data gathered along 5 parallel lines in the Roof Labo-ratory. Each measurement path was separated by 5 cm and the corresponding lines inthe plot have been artificially offset to allow a clear comparison of the behaviour alongand across the paths. The top line in the plot represents the path closest to the RoofLaboratory window.

over approximately 30 centimetres, as observed in the previous experiment. There

are also two discontinuous ‘double spikes’ along the yellow line. The first double

spike represents a peak-to-peak timing error of 7 microseconds, corresponding to

an uncertainty in position of 2.2 kilometres. Figure 5.9 demonstrates the cause

115


of these spikes. As multipath rays interfere, they can create a ‘double-peaked’

SCB peak (see Figure 5.5 above). The maximum value of the overall SCB peak

is used as the timing marker, and when the two peaks are very similar in height

slight variations in the receiver position can result in the relative heights of these

two peaks varying smoothly. The apparent position of the timing marker can

therefore suddenly snap from the crest of one of the peaks to the other, producing

these characteristic large and discontinuous spikes. The correlations between the

measurement lines in Figure 5.8 highlighted by the dotted grey lines demonstrate

that the smooth variations observed along a given line also exist along other

directions in the Roof Laboratory.

Figure 5.9: This sketch demonstrates how sharp spikes in timing error can be producedby SCB peaks deformed by multipath interference. As the receiver moves the corruptedSCB peak can consist of two peaks which vary smoothly with receiver position. As onepeak becomes higher than the other, a large discontinuity is produced in the timing errorplot.

116


5.2.3 Electronics Laboratory tests

A set of experiments was performed in the Electronics Laboratory, a cluttered,

windowless room on the top floor of the Rutherford building. A calibration

experiment was performed first in order to determine the noise level inside the

room. The antenna remained in a fixed position and measurements were recorded

every 61.2 seconds from 6 pm. to 9 am. For the majority of the data set (i.e.

times from about 7 pm to 7 am) there were few movements of people or objects

within the building and no movement at all within the room. The results are

given below in Figure 5.10. The standard deviation of the timing error over small

Figure 5.10: This plot shows the data from the calibration experiment performed duringthe night in the Electronics Lab. The noise level corresponds to a timing error of 83nanoseconds.

sections of the plot (about 100 samples) was 83 nanoseconds, or an error on a

distance calculation of 25 metres. There are some moderate systematic deviations

of around 300 nanoseconds over timescales of a hundred minutes. The timing error

caused by drift in the RFS over 200 minutes is about 12 nanoseconds according

to the data shown in Figure 2.15 in Chapter 2, and so cannot explain these

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large deviations. Similarly, the data presented in Figure 4.8 suggests that the

BTS cannot be responsible for this systematic drift either (curve ‘A’ in Figure

4.8 represents the BTS used here, and the data suggests a timing error of 50

nanoseconds or better over this time period). This variation may be a result

of changes at the BTS or corrections to the BTS control loop put into effect

by network personnel. Changes in the local thermal environment may also have

contributed, although the RFS was contained within a large, sealed, cardboard

box.

An experiment was performed to investigate the consistency of the multipath

environment in the Electronics Lab over an hour. Data were recorded over the

same line 4 times in succession. A recording was taken every 6.12 seconds with a

conveyor belt speed of 1 millimetre per second. The experiment was performed in

the middle of the day and so may have been affected by people moving in the room

and in the corridor outside. The results are shown below in Figure 5.11. There

is a noticeable correlation between the four plots, and the small-scale variation

in timing error is much higher than the noise level determined in the previous

experiment. The rapid changes in timing error shown in the first half of all four

tests suggest a much denser and more complicated multipath environment than

the one observed in the Roof Laboratory, with multipath interference varying

on a much finer scale than the size of the central wavelength of the radiation.

The typical variations in timing error in the first half of each data set (±1.5

microseconds) correspond to an error of ±440 metres when the receiving antenna

is moved by approximately 3 centimetres. This is a characteristic of a deep,

random interference pattern in which the rays contributing at any point differ by

many radians of phase.

A test was performed in the Electronics Lab along 4 parallel lines each sep-

arated by 10 centimetres, similar to the one described above in Figure 5.8. The

results of this test are given below in Figure 5.12. A recording was made ev-

ery 6.12 seconds with a conveyor belt speed of 1 millimetre per second, and the

first line tested was the same line as used in the consistency test above (Figure

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Figure 5.11: This plot shows the data from an experiment performed in the ElectronicsLaboratory. Data was recorded along the same line 4 times in succession to check forconsistency in the multipath environment over an hour. The 4 coloured lines in theupper part of the figure represent the timing errors of each test and are plotted againstthe left axis. The line with error bars in the lower part of the figure represents theaverage SCB peak maximum value at each antenna position and is plotted against theright hand axis. The error bars are given by the standard deviation of the SCB peakmaximum values recorded at each antenna position.

5.11). It should be noted, however, that the first line is not similar to the lines

generated in the consistency test. The cause for this may have been that the

two experiments were performed on different days and so different positioning or

movements of people and objects in the lab had a major effect on the multipath

environment. When comparing Figures 5.8 and 5.12 it is apparent again that the

multipath environment is much denser and more complex in the Electronics Lab

than in the Roof Laboratory. Large spikes surrounded by areas with relatively

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Figure 5.12: This plot shows the data gathered along 4 parallel lines in the ElectronicsLaboratory. Data was recorded every 6.12 seconds and the antenna moved along eachline at a rate of 1 mm/sec.

little variation in timing error are a noticeable feature. There is little coherence

between the measurement lines in Figure 5.12 when compared to those in Figure

5.8, but this may be explained by both an increased complexity in multipath

environment and the increased spacing between measurement lines compared to

the previous experiment.

5.2.3.1 Spatial and temporal variations

An experiment was performed in the Electronics Lab in an attempt to distinguish

between the effects of spatial and temporal multipath interference on an indoor

receiver. The apparatus was programmed to capture 10 consecutive SCB peaks

within 0.5 seconds while stationary before the receiver was moved to the next

position. The standard deviation of an individual data set provided a measure

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of the variation in timing error caused by temporal multipath effects over about

half a second. Figure 5.13 below shows an example of the trajectory of the peaks

of the cross-correlation functions from one of these measurement sets. The figure

shows a large, but smooth and systematic change in position of the maximum

value of the SCB peak over the recording time of 0.5 seconds, as indicated by

the grey arrowed lines. The distortions were most likely to have been caused by

the movement of one or more objects in the propagation path of one or more

of the multipath signals. This movement changed the phases and delays of the

Figure 5.13: Plot showing the moduli of ten consecutive SCB peaks recorded duringa single measurement during an indoor survey. The peaks have all been shifted by anappropriate amount to allow their direct comparison. The solid blue curve representsthe earliest measurement in the set, and the grey arrows mark the movement of thepeak across subsequent measurements.

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signals at reception and so altered the effect of the superposition of the signals

on the resulting SCB peak. The positions of the 10 peaks vary over a range

of approximately 7 microseconds, corresponding to a range of approximately 2

kilometres on the calculations of the corresponding distances from the BTS.

In the Electronics Laboratory experiment, the antenna moved at 0.04 mil-

limetres per second and could be regarded as being stationary for the half-second

period over which each set of 10 SCB peaks were recorded. Figure 5.14 demon-

strates how the temporal and spatial variations depend on each other.

The diagrams are scatter plots of the standard deviations within a given mea-

surement set of 10 SCBs (vertical axis), against the standard deviations of the

average of each measurement set taken over a moving window of ten samples

(2.5 centimetres). The largest values of temporal variation correspond with the

largest values of spatial variation. However, it is unlikely that temporal multipath

variations should be correlated with spatial multipath variations in this way, as

temporal multipath is caused by moving objects or instabilities in frequency ref-

erences, whereas spatial multipath is caused by the location and number of fixed

objects in the environment. The apparent correlation is more likely to be caused

by the rapidly varying temporal multipath effects overpowering the spatial mul-

tipath effects and dominating the timing error variation for both stationary and

moving receivers. Some of this variation is also caused by measurement noise,

but it is clear from the correlation that the fastest temporal variations correspond

with the most complex multipath regions.

The data of Figure 5.14(a) are also plotted in Figure 5.15 in time order. The

error bars correspond to the standard deviations of each set of 10 SCB peaks and

give a measure of the temporal variations. The blue line connects the average

value of each set and gives a measure of the spatial variations. The magnitudes

of the errors bars in the first half of the data are comparable with the noise

level in the calibration experiment described above (see Figure 5.10), suggesting

that there were no significant changes in the temporal multipath environment

over 0.5 seconds. The variation in the timing error across consecutive samples is

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(a)

)

(b)

Figure 5.14: These scatter plots demonstrate the correlation between the timing errordue to temporal (σt) and spatial (σs) multipath variations. The upper figure (a) rep-resents the data from Figure 5.15 and lower figure (b represents the data from Figure5.16.

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Figure 5.15: This plot shows the data gathered along a line using the fast capturemachine to record 10 SCB peaks per antenna position. The mean value at each position(blue upper line) is plotted against the left axis, with the standard deviation plotted asan error bar on each point. The mean maximum value of the SCB peak at each position(pink lower line) is plotted against the right axis. The antenna moved at a speed of 0.04millimetres per second, with recordings made every 6.12 seconds such that 100 sampleson the plot corresponds to a distance of approximately 2.5cm.

not random but exhibits a structure, suggesting that there is a spatial multipath

structure in the data. However, the second half of the data exhibits larger and

more rapid variations in the timing error which were probably caused by either a

very dense and complicated spatial multipath environment, or by rapid temporal

variations caused by people and objects moving around nearby. The error bars in

this regime are much larger than in the first half of the data, suggesting that these

large variations in timing error are occurring over a timescale of 0.05 seconds or

faster.

The data of Figure 5.14(b) are also plotted in Figure 5.16 in time order.

These correspond to a test in the corridor outside the Electronics Laboratory

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next to a large window. The window ran along a line toward the BTS but the

line-of-sight was blocked by a large building. The antenna was moved manually

along a small grid such that it was stationary during each recording and moved

2 millimetres away from the window between each sample. The data exhibits

rapid and correlated variations in the timing errors across consecutive samples,

as in the first experiment, suggesting that the variation was caused by multipath

interference on a fine scale rather than by measurement noise. There is little

variation in the size of the error bars, suggesting that the temporal multipath

variation over 0.5 seconds was reasonably consistent in this environment. A

number of people walked along the corridor toward the end of the experiment, and

this may explain the larger error bars, and so the increased temporal variations,

for samples 89, 94 and 97.

Figure 5.16: This plot shows the data gathered along a short distance in the maincorridor of the upper floor of the Rutherford building. The antenna was moved manuallyin 2 millimetre intervals such that it was stationary during each recording process ratherthan moving continually on a conveyor belt. Ten consecutive SCB peaks were recordedper position. The mean value at each position is plotted with the standard deviationplotted as an error bar on each point.

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5.3 Conclusions

1. Significant timing errors (greater than a microsecond) can be measured in all

environment types - indoors and outdoors, and even with a line of sight to the

source. These large errors are not caused by measurement noise but by multipath

interference distorting the SCB peak.

2. These timing errors can vary over length scales much shorter than the central

wavelength of the radiation carrying the signal. Using the positions of the max-

imum absolute values of the SCB peaks as timing markers can result in errors

on position calculations as large as many kilometres, and with the error varying

with receiver position on a millimetre scale.

3. There is an apparent positive correlation between the degree of spatial and

temporal multipath interference in indoor environments, but it is more likely that

when the temporal multipath variations are large and rapidly varying they domi-

nate the overall multipath environment for both stationary and moving receivers.

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Chapter 6

Modelling the effects of indoor

multipath environments on

timing stability

A series of simulations based on multipath interference were performed to in-

vestigate the temporal stability of the signals received from GSM base stations

at a slowly-moving indoor antenna. Three methods of measuring a GSM sig-

nal’s arrival time are also considered and compared using the simulations and

experimental data.

6.1 Modelling cross-correlation peak distortions

The experiments described in the previous chapter demonstrated that multipath

interference has a large effect on the shape of the SCB?ETS cross-correlation

peak (see Figure 5.5 above), which in turn has a large effect on the ability to use

this feature as a reliable and consistent timing reference marker. Two approaches

can be taken when modelling these distortions - a Received Signal Interference

model (RSI) and a Cross-Correlation Peak Interference model (CCPI).

127

6. MODELLING THE EFFECTS OF INDOOR MULTIPATHENVIRONMENTS ON TIMING STABILITY

6.1.1 Received Signal Interference model

The RSI model closely reproduces the experimental technique. A band-limited

sample signal is created in MATLAB by superimposing a large number of monochro-

matic waves, each with random initial phase and unique frequency, such that the

bandwidth and central frequency of the final signal matches that of the GSM

signal used for the indoor experiments (a central frequency of 953MHz with a

bandwidth of 140 kHz). A section of this signal is then selected to be used as the

training sequence, with the requirement that the cross correlation of the selected

section with the whole signal results in a single, strong, symmetrical peak.

This approach was used in a computer program to simulate many signal rays

propagating from a source into a room, reflecting off surfaces and then interfering

with other reflected copies of itself at the points of reception. The resulting

superposition of delayed and attenuated signals was then cross correlated with

the training sequence and the peak of the cross-correlation function recorded.

The position of the cross-correlation peak as a function of receiver location in a

multipath environment could then be simulated. The limitations of this model

were (a) the ‘quality’ of the training sequence was inferior to the real ETS (for

example, the ETS is perfectly symmetrical and has low subsidiary maxima in

its auto-correlation function), and (b) a large amount of computation time was

required.

6.1.2 Cross-Correlation Peak Interference model

This approach makes use of the associative behaviour of the cross-correlation pro-

cess. Superimposing a number of signals and then cross correlating the result with

the ETS gives the same result as cross correlating each signal separately first be-

fore superimposing the results (this is shown explicitly in Equation 7.2 in Chapter

7 below). It is therefore possible to model the SCB?ETS cross-correlation peak

using a suitable function and then to consider the effect of superimposing ver-

sions of this function to model multipath interference. A truncated raised-cosine

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function can be used to represent the GSM cross-correlation peak with a high

accuracy (as shown in Figure 7.6 in Chapter 7 below) and delayed signals can be

modelled by displacing, phase shifting, and attenuating this function accordingly.

In the CCPI model, the path length, phase, and amplitude of each component

is calculated according to each propagation path and the corresponding raised-

cosine function is created. These raised cosines can all then be superimposed

and the peak position of the resulting shape recorded. The major advantage of

this technique is that simulations run very quickly, allowing for high resolution

simulations to be run over large distances.

6.1.3 Results of simulations

Simulations based on the RSI and CCPI models were tested using identical signal

parameters to verify that they both produced the same results. Having estab-

lished that the CCPI model was satisfactory, the RSI model was discarded. The

CCPI model was run under various conditions in an attempt to recreate some of

the features seen in the Roof Laboratory and Electronics Laboratory experiments.

The strongest signals in the Roof Laboratory were likely to have arrived in the

room by propagating through its large window after scattering from objects on the

roof or nearby buildings. The LOS signal would have had to penetrate a brick wall

clad with corrugated iron to enter the lab directly and would therefore have been

strongly attenuated. The simulations were two dimensional, with movement along

the x-axis in the simulations representing the movement of the antenna in the

experiments. Any signals arriving from the positive-y region represented signals

arriving through the window, and any from the negative-y region represented

signals reflecting inside the lab from the wall opposite the window.

The smooth oscillatory behaviour observed in the Roof Laboratory experi-

ments was the first feature considered with the CCPI model. The first mech-

anism considered was a signal interfering with itself after a normal reflection.

A path difference of 5 metres and an amplitude ratio of 0.4 was used (Figure

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A.4 in Appendix A gives the reflection coefficients for GSM signals interacting

with brick and concrete surfaces). Figure 6.1 below shows a plot for this simple

two-signal interference with the receiver moving along a line perpendicular to the

signal paths. It is clear that there are no noticeable effects at all on the estimated

position of the peak over this distance with this combination of parameters and

direction of motion. This is because with this frequency (953 MHz) and geometry

(the receiver moving along a line perpendicular to the directions of signal prop-

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simulation of indoor multipath effects on cross correlation peak position

plot showing the direction of and distances to the signal sources in the simulation

Figure 6.1: This plot shows the result of using the CCPI model to simulate a signalentering the Roof Laboratory and interfering with itself after reflecting from the facingwall inside the lab. The top diagram shows the arrangement of the sources used inthe simulation (reflections are simulated by placing sources along the direction of thereflection path with a distance determined by the overall path length).

130


agation), the relative phase of the interfering signals varies over a much larger

length scale than seen in the real experiment.

An alternative scenario for the Roof Laboratory signal environment involves

multiple signals with similar amplitudes scattering into the room through the

window from various surfaces on the roof of the Rutherford building or from

nearby buildings. Figure 6.2 shows an oscillation with similar period and ampli-

tude to those seen in Figure 5.6 created using a two-ray interference simulation.

The period of the oscillation is determined by the angular separation of the sig-

nal propagation paths on arrival at the receiver and the direction of motion of

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Figure 6.2: This plot shows the signal requirements to reproduce the oscillations ob-served in the Roof Laboratory experiments, using two signals with similar amplitudes(1 and 0.7), a 200 metre path difference and an angular separation of 90 degrees. Theangular separation determines the period of oscillation, and the relative amplitudes andpath difference both determine the amplitude of the oscillation. Note that a timing errorequivalent to more than 300 metres can occur.

131


the receiver. The period decreases as the angular separation increases or as the

direction of motion moves toward either of the sources. The amplitude of the

oscillation is determined by the relative amplitudes of the signals and the path

difference between the sources. Signals with similar amplitudes produce larger

oscillations, as do large path length differences, with the latter variable having

the greater effect.

The results of this simulation therefore suggest that the behaviour observed

in the the Roof Laboratory could have been caused by the superposition of a

reflection from an object outside the Roof Laboratory window, and a reflection

with 200 metres of delay from a nearby building. Figure 6.3 shows a panoramic

view of the Roof Laboratory window from the position of the experiments inside

the room. The structure in the centre of the image and the sky lights on the roof

are possible candidates for causing the first reflection, and the buildings on the

left of the image are likely causes of the second reflection.

Figure 6.3: This picture shows a panoramic view of the Roof Laboratory window fromthe position of the antenna during the Roof Laboratory experiments.

A reasonable approximation to the behaviour seen in Figure 5.8 is shown in

Figure 6.4. The behaviour was simulated by considering the same signals used to

produce Figure 6.2 and including another strong signal from the upper y-plane

(representing another signal arriving through the Roof Laboratory window) and

three weak signals from the lower y-plane representing reflections from inside the

Roof Laboratory.

The behaviour observed in the Electronics Laboratory was more complicated

than the behaviour observed in the Roof Laboratory. Figure 6.5 below shows the

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Figure 6.4: This plot shows the signal requirements to reproduce some of the behaviourobserved in the Roof Laboratory experiments. Smooth variations in timing error andlarge, rapid deviations can both be recreated in the same simulation. The signals fromthe upper plane all have similar amplitudes (0.7, 0.8, 1) and represent signals scatteredfrom nearby buildings and objects on the roof. The three signals from the lower planerepresent reflections from inside the lab and all have lower amplitudes accordingly (0.2,0.3, 0.4)

effect of simulating a random distribution of sources within a medium-sized room

such as the Electronics Laboratory (12 metres by 7 metres), each with a similar

amplitude and with the signal phase on receipt determined by the path length.

The figure shows that the very rapid and large variations in SCB peak position

observed for a moving receiver in the Electronics Laboratory cannot be modelled

without introducing further factors.

The Electronics Laboratory was a much more cluttered and much more active

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Figure 6.5: This plot shows the variation in timing errors as a result of a randomdistribution of a number of sources with the same amplitude and similar path lengths.Comparing this plot with the data from the Electronics Laboratory tests shows that thevery rapid and large variations in the timing errors seen in the experiments cannot berecreated with the signal phases determined by the path lengths alone and the amplitudesfixed.

environment than the Roof Laboratory, with a number of people moving around

inside the room and surrounding areas. The Electronics Laboratory had no ex-

ternal windows except for a row of skylights in the ceiling angled at 45 degrees

to the horizontal plane and facing away from the BTS. Any signals reaching the

receiver must have either entered the room via these skylights, other parts of the

ceiling, or by passing through other rooms and corridors in the building. Signals

entering via other rooms in the building may have interacted with many mov-

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ing objects during their propagation. The movement of other objects along the

propagation path, such as tree branches, could also have produced variation in

the multipath environment measured inside the Electronics Laboratory. In order

to model these additional variations, the signals in the simulation were allocated

some random phase variation, random amplitude variation, random path length

variation, or a combination.

The phase of a 900MHz GSM signal changes over 2π radians for a movement

of around 30cm (i.e. the wavelength). Phase changes can occur on refractions,

reflections, diffractions and scattering events, and so a random phase value was

tested first to account for the movement of any people or objects interacting with

the signals before they reached the receiver.

Figure 6.6 below shows the effect of randomising the phase of each signal on

receipt. The signal amplitudes were fixed and their path lengths determined by

the coordinates of the sources and receiver. The figure shows rapid variations in

timing errors but the distribution of these variations does not accurately simulate

that observed in the experiments. The variation is relatively uniform and ran-

domising the phase effectively just increases the overall noise level on the SCB

position measurements. This method does not produce any regions with very

little variation in timing error next to regions with very large variations, which

were common features in the real experiments (see Figure 5.15 for example).

Allowing the signal path lengths and directions to vary randomly within the

range of a few metres and a few degrees respectively (to account for the movement

of people, trees, etc interacting with the propagation paths) produces very sim-

ilar results to those seen when randomising the phase as described above. This

is because these very small changes in signal delay (corresponding to roughly

0.1% of the width of the SCB peaks) are insignificant compared to the effects of

phase and amplitude variations. The random phase fluctuations resulting from

randomising the signal path lengths dominate the effect on the timing error plots

for randomised signal path lengths.

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Figure 6.6: This plot shows the variation in timing error as a result of allowing thephases of the signals from each source to be random rather than determined by thepath length. This produces rapid variations in the timing errors for small receivermovements, but the variations are not large enough and are too uniform to simulatethe structure seen in the Electronics Laboratory experiments.

Figure 6.7 below shows the effect of allowing the signal amplitude to vary ran-

domly within an order of magnitude (0.1 to 1) for each signal on reception. The

distribution of the sources is the same as for the previous test. This simulation

produces similar behaviour to the Electronics Laboratory tests, with regions of

consistent SCB position next to regions with very large and rapid variation in

SCB position, and with large systematic variations across a number of consec-

utive samples. The scales of the timing error variations in the simulations are

dominated by the magnitudes of the path length differences between different

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Figure 6.7: This plot shows the variation in the timing errors as a result of allowing theamplitudes of the signals to be randomly assigned between 0.1 and 1 on reception. Thisproduces behaviour similar to that seen in the Electronics Laboratory experiments, withregions of consistent timing errors next to regions with very large and rapid variationin timing errors.

sources rather than the scale and range of the amplitude variations.

Figure 6.8 below shows the effect of adding white noise to the previous simu-

lation in an attempt to reproduce more closely the behaviour seen in figures such

as 5.11. Figure 6.8 is a reasonable reproduction of the behaviour seen in Figure

5.11, with a region where the timing error varies by the measurement noise level

next to a region with large, rapid and systematic variations.

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Figure 6.8: This plot shows the same simulation as in Figure 6.7 but with measurementnoise included in order to reproduce the behaviour seen in Figure 5.11 more closely.

6.2 Determining signal arrival times

The work presented here has demonstrated the large errors caused by multipath

interference that are associated with determining signal arrival times by recording

the position of the maximum absolute value of the SCB?ETS cross-correlation

peak. Figure 5.5 shows the distortions to the SCB peak caused by multipath in-

terference and demonstrates the large error associated with this simple method.

The bandwidth of a GSM broadcast is about 140 kHz, corresponding to a coher-

ence length of about 2km and a coherence time of about 7 microseconds. The

cross-correlation peaks are therefore approximately 14 microseconds wide, and

any corruption or distortion of the peak can result in timing errors on a scale

of hundreds of metres or worse. This error can be reduced by increasing the

138


bandwidth, but this option is not a viable solution for a well-established network

and is only feasible when designing new communication networks. It might be

possible to reduce the error by processing the SCB peak in a different way. Three

methods of determining signal arrivals using the SCB peak are suggested here

and shown in Figure 6.9 below.

Figure 6.9: Plot showing three methods of determining a signal arrival time using theSCB peak: (a) finding the maximum absolute value of the SCB peak, (b) finding theposition where the SCB peak first exceeds a threshold value, and (c) finding the midpointof the SCB peak. The upper set of figures demonstrate the three methods applied toan uncorrupted SCB peak. The lower set demonstrate the three methods applied to acorrupted SCB peak (the grey curve represents the peak for the line-of-sight signal, theblack curve represents the peak after corruption by multipath interference). The lowerset of figures demonstrate that method (a) can result in significant errors, and methods(b) and (c) can result in reduced errors, apparently showing a greater resistance to peakdistortion.

(a) Peak-max position. This technique involves finding the maximum absolute

value of the cross correlation function. It is the simplest and quickest technique,

and the technique used by some current cell-phone positioning systems. The er-

rors associated with this technique are studied in detail this thesis and can be

139


very large due to distortion of the shape of the SCB peak.

(b) Peak-rise position This technique involves finding the earliest position in the

cross-correlation function where the ‘early side’ of the SCB peak exceeds a thresh-

old value. The distortion of the SCB peak by multipath interference is reduced

near its base but in practise, the peak-rise position required to guarantee minimal

distortion is so early that it is usually buried in noise on the cross correlation plot.

This method is only useful therefore if the noise level can be reduced by using a

highly sensitive receiver or by averaging over many recordings.

(c) Midpoint position. This technique involves finding the midpoint of the full

SCB peak by considering the average position of the early and late sides of the

peak. The accuracy is determined by the threshold value chosen to represent the

width of the SCB peak. If the full width is chosen, then errors caused by measure-

ment noise dominate the accuracy since the gradient of the SCB peak is shallow

at its base (see the discussion of measurement noise and the shape of the SCB

peak in Section 5.2.2 above). As the threshold width is reduced then the accuracy

of the method becomes dependent on the level of multipath interference, since

the distortion of a corrupted SCB peak increases with height. A suitable compro-

mise may be dependent on the level of receiver noise and the signal strength. If

the multipath signals are significantly delayed, then the resulting corrupted SCB

peak is wider than for the uncorrupted case, and so this also increases the error

associated with the technique.

These three techniques were tested first using simulated data and the results

are shown in Figure 6.10 below. The upper plot shows a small section of the

simulated data, and the lower plot shows a histogram of the timing errors for the

three techniques over the full simulation. The peak-rise technique performed best,

followed by the midpoint technique, then the peak-max technique. It must be

noted however that the simulated cross-correlation peaks are less realistic toward

the edges of the peak, as the effects of cross-correlation noise and of information

either side of the ETS are not incorporated. The peak-rise technique therefore

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frequency

peak−max positionmid−point positionpeak−rise position

(b) Histograms of the timing errors for each tech-nique.

Figure 6.10: Plots showing tests of the three signal-arrival techniques using simulateddata. The short section of data demonstrates that the midpoint and peak-rise methodsare more consistent than the peak-max method, and that the midpoint and peak-maxmethods correlate strongly except in the case of significantly corrupted SCB peaks. Thehistogram suggests that the peak-rise technique is the best, although the simulated datais unrealistic near the edges of the SCB peak (see the main text above).

141


performs very well here, but is expected to perform less well for real data where

the edges of the cross-correlation peak meet cross-correlation noise.

The three techniques were then tested using some data gathered by an indoor

stationary antenna. The plots are shown below in Figure 6.11. The peak-rise

and midpoint methods display slightly better accuracy than the traditional peak-

max position method, and greatly reduce large errors in the cases of significantly

corrupted SCB peaks. The peak rise and midpoint techniques were however

highly sensitive to the threshold values used, as expected. The plots shows the

best results for both methods and were generated using a threshold width of 75%

of the full SCB peak width for the midpoint method, and a threshold of 20% of

(a) Timing errors over a short section ofdata

(b) Histograms of the timing errors for thedata shown in (a).

(c) Timing errors over a short section ofdata.

(d) Histograms of the timing errors for thedata shown in (c).

Figure 6.11: Plots showing tests of the three signal-arrival techniques using two setsof data gathered using an indoor receiver. The peak-rise and midpoint methods displayslightly better accuracy than the traditional peak-max position method.

142


the full peak height for the peak-rise method.

As a final test with real data, the three techniques were compared using the

data from the initial experiment on the roof (see Figures 5.4 and 5.5) and the

results are given in Figure 6.12 below. In this case, the ability of the peak-

rise and midpoint techniques to reduce large timing errors is clear. The peak-

rise method shows some improvement over the normal peak-max method, but

the midpoint method can be used to reduce large errors caused by corrupted

SCB peaks significantly. However, both the peak-rise and midpoint methods

require more processing power than the peak-position method. A GSM cell phone

samples the incoming signal at 270.833kHz, and so records a sample every 3.7

Figure 6.12: Plot showing tests of the three signal-arrival techniques using the datafrom the initial roof experiment. The peak method results in a large timing error whenthe SCB peaks are significantly corrupted (see Figure 5.5). The peak-rise techniquereduces this error slightly, and the mid-rise technique can be used to minimise theerror.

143


microseconds. The SCB peak is about 14 microseconds wide, and so is only

sampled 3 times by a cell phone. In this project, by comparison, the SCB peaks

were sampled 28 or 29 times and then this resolution was increased by a factor of

20 using interpolation. In a cell phone, a simple computation can be performed

to estimate the maximum value of the SCB peak using 3 values, whereas the

improved accuracy of the peak-rise and mid-position techniques are dependent

on either a much higher sampling rate or a processor-intensive interpolation. As

modern cell phones become more sophisticated it is possible that the interpolation

process, and therefore the midpoint technique, may become a feasible solution to

the problem of large timing errors.

The effect of SCB peak corruption on timing errors can also be reduced by in-

creasing the bandwidth of the signal, such that the SCB peak narrows. The third-

generation cell phone networks broadcast signals with 5MHz of bandwidth. The

coherence time of these signals is 0.2 microseconds, and so the cross-correlation

peak of a timing marker is about 0.4 microseconds wide. The timing errors on

the third-generation networks are therefore expected to be noticeably lower than

those experienced on GSM networks, with the main problem being estimating

the earliest arrival from a number of individually resolved timing markers.

6.3 Conclusions

1. Two models are considered in order to simulate the experiments studied in

Chapter 5, a model based on cross correlating signal waveforms (RSI) and a model

based on superimposing truncated raised-cosine functions in order to represent

the superposition of SCB?ETS cross-correlation peaks (CCPI). The two models

produce identical results but the CCPI model requires much less processing time

than the RSI model.

2. Simulations presented here using the CCPI model suggests that smooth vari-

ations in the SCB peak positions can be accounted for by a sparse multipath

144

6.3 Conclusions

environment consisting of a small number of significant signals with similar am-

plitudes, phase differences determined by their path lengths, and some angular

separation all interfering at the receiver.

3. Simulations presented here using the CCPI model suggests that the rapid and

large variations in timing errors indoors cannot be accounted for by signals with

fixed amplitudes interfering at the receiver. If the amplitudes of the signals vary

randomly at each position, then the behaviour seen in the Electronics Laboratory

can be simulated. Randomly varying the phase or path lengths (within reason-

able limits) alone cannot reproduce this behaviour.

4. The rapid variations in signal amplitude proposed can be accounted for by

movement of people and small changes in receiver position. As the receiver posi-

tion varies, the exact path each signal takes to reach that point changes and so

do the densities and exact structures of walls and objects along those paths. If

the path involves scattering or diffraction then slight changes in receiver position

will also result in different receiver amplitudes due to the exact polar pattern at

the diffracting or scattering object. A given signal path may also be temporarily

attenuated or scattered by the movement of people and objects in the local envi-

ronment.

5. Two methods are proposed to increase the accuracy when determining signal

arrival times, the peak-rise method and the midpoint method. Both methods

demonstrate an improvement in accuracy by reducing, and in some cases remov-

ing, the most extreme errors in a given data set. However, both methods require

more intensive computation than the simple peak-position technique.

145


146

Chapter 7

A study of the timing errors

encountered when performing

radio-location using the GSM

network

A series of experiments was performed in order to study the accuracy of position-

ing systems in various environments using the signals radiated by the transmitters

of the GSM network. The distances between a receiver and a reference GSM base

station were measured by considering the synchronisation burst on the base sta-

tion’s control channel (see Section in Chapter 3). These distances were then

compared to those determined using a GPS device or accurate mapping. Ru-

ral, suburban, light urban, mid urban, and indoor environments in and around

Cambridge were surveyed.

Whenever SCB signals are used to calculate a position, it is usually under two

assumptions. The first of these is that an unbiased and consistent measurement

of the signal’s arrival time can be made using a feature of the cross correlation

between the incoming signal and the ETS. The simplest feature is the maximum

absolute value, but there are many other possibilities. This property is used

here because (a) it is the feature currently used Cambridge Positioning Systems’

147

7. A STUDY OF THE TIMING ERRORS ENCOUNTEREDWHEN PERFORMING RADIO-LOCATION USING THE GSMNETWORK

products, and (b) it illustrates very well many of the effects which are common

to the use of all features. The second assumption is that the resulting estimate

of a signal’s time of flight is the same as the line of sight time of flight and so is

representative of the linear distance between the base station and receiver. These

assumptions are tested in this chapter.

7.1 Definitions of environment

A simple set of rules was formulated to determine the general nature of a given

outdoor environment.

Rural: A rural area has well-spaced, one- or two-storey buildings, many trees, and

narrow roads through farmland, fields and small villages. Grantchester village and

its surrounding farm tracks were used for this survey.

Suburban: A suburban area is located on the edges of a city, with one- and

two-storey detached and semi-detached housing. The spacing between buildings

across roads is larger than the height of the buildings. Trees are also a dominant

feature of this environment.

Light-urban: A light-urban environment features two-storey terraced housing and

terraced rows of shops or businesses. The distances between buildings across a

road are often comparable with, or less than, the heights of the buildings.

Mid-urban: A mid-urban area has larger buildings (exceeding two storeys) and

they are typically offices, stores and apartment blocks. The distances between

buildings across roads are less than their heights. Lamp posts and traffic signs

are also a major feature of this environment.

Dense-urban: A dense-urban environment is usually found in the central areas

of large cities and consists of urban canyons with very tall buildings in every

direction, very few trees but an appreciable density of lamp posts and traffic

signs. There was not an area fitting this definition (e.g. central London) close

enough to the Cavendish Laboratory for a feasible survey to take place.

148

7.2 Apparatus

7.2 Apparatus

The network-synchronised method was used as discussed in Chapter 3. The

experiments discussed in Chapter 4 had identified a number of base stations with

stable enough signals for use with this method. The experiments lasted 4 hours

or less, with roughly 1 hour of that time used for preparation before data was

gathered. Transferring the equipment into the test vehicle took half an hour,

and everything was powered for an hour before any measurements were made.

This allowed the internal temperatures of each piece of equipment to stabilise

and provided some time for the survey to be planned. The test vehicle used

was a large car, and a 2 dBi antenna was attached to the roof. The digitiser

was programmed to record a million samples at 2.04 MS s−1 each time it was

triggered, resulting in 10 or 11 SCB peaks captured per measurement (depending

on how close to the start of the million samples the first SCB peak was recorded).

Three of these measurements recorded every 6.12 seconds defined a measurement

set consisting of 30 or 33 SCB peaks. A survey was defined as a collection of

measurements recorded during one day in a single environment type. Although

increasing the number of measurements in a measurement set would have been

possible, a balance was found between good statistics and the time and resources

required to process and store all the data. At the beginning and end of each

survey a calibration measurement set was recorded at the base-station. These

two calibration measurement sets allowed the unwanted linear slope in the data

to be corrected (see the discussion of this correction in Chapter 2).

7.2.1 GPS

A SiRFstar III GPS receiver, built into a Mio A201 hand-held computer, was

used to determine the reference positions during each survey. This 20-channel

GPS device used the Coarse Acquisition (C/A) code on the L1-band (1575.42

MHz) and had a tracking sensitivity of -143 dBm [62]. The positioning accuracy

149


provided by the GPS receiver was maximised by setting it to use the signals from

all available satellites when calculating a position.

7.2.2 GPS accuracy and errors

The accuracy of a GPS position calculation is determined by a number of factors

including the geometry of the satellite constellation, the code type, random er-

rors and systematic errors. For a modern GPS device using the C/A signals, the

timing resolution is about 10 nanoseconds, and for a military receiver using the

Precise code (P code) it is about 1 nanosecond, corresponding to distances of 3

metres and 30 centimetres respectively. The position accuracy is usually worse

than this because of the geometry of the satellite constellation, objects obstruct-

ing the sky, and because of noise and multipath interference. The reductions

in positioning accuracy caused by geometrical effects are calculated by the GPS

receiver in the form of a Horizontal Dilution of Precision factor (HDOP) and a

Vertical Dilution of Precision factor (VDOP). The expected positioning accuracy

for a given satellite constellation geometry is then given by the measurement

error multiplied by the HDOP and VDOP values. For example, using the mea-

surement resolution given above for C/A code signals and in the absence of noise

or multipath, an HDOP value of 3 will result in an expected accuracy of 9 me-

tres on the calculated horizontal position, and a calculation using P-code signals

with a VDOP of 1.5 will result in an accuracy of 45 centimetres in calculating

the receiver’s altitude. The HDOP and VDOP values are calculated using the

diagonal elements of the covariance matrix of the least-squares position solution

considering all available satellites. The HDOP value is determined by consider-

ing the variance in the Latitude and Longitude solutions for each combination

of four satellites, and the VDOP value is determined using the variance in the

height solutions [63, 64].

The random errors caused by receiver noise and rapid temporal multipath can

be reduced by averaging over a large number of position calculations. The receiver

150

7.2 Apparatus

Figure 7.1: This figure shows the effects of good and bad satellite geometry on theaccuracy of a GPS position. The sketch is shown in two dimensions, but the principleis easily extended to three. The curved pink lines represent the possible position of areceiver that has measured a certain arrival time from a given satellite. The thicknessof the lines represents the error on the measurement. The sketch on the left representsa good satellite geometry, with three satellites evenly distributed and well spread outacross the measurement plane. The black area highlighting the region intersected by allthree signals represents the region of uncertainty in the receiver position. The figure onthe right represents a poor signal geometry, with all three sources lying roughly along aline. The intersecting region is much larger for this geometry, leading to a reduction inthe positioning accuracy.

noise and multipath constitute, in effect, “dither noise” and usually dominate over

the timing resolution of the receiver. In these circumstances, the average position

of a stationary receiver can result in a higher positioning accuracy. However,

static multipath interference represents a systematic error at a stationary receiver

and its effect cannot be reduced by averaging.

The systematic errors as a result of daily changes in the atmospheric conditions

such as tropospheric effects (±0.7 metres), ionospheric effects (±4 metres), errors

in ephemeris data (±2 metres) and drifts in the satellite clocks (±3 metres) cannot

just be averaged out of the system. However, since the errors are systematic,

the relative distances between a set of points will still be determined to a high

151


accuracy by a static GPS receiver although their absolute positions may all be

systematically displaced from their true value. The surveys performed here used

relative measurements (a calibration GPS reading was taken at the BTS at the

start and end of the experiment), and so in principle the GPS error was expected

to be dominated by the random errors and therefore reduced by averaging (each

GPS position recorded in the surveys was actually an average of 50 values).

However, since each survey took a number of hours to complete, the factors which

affected the systematic errors may have varied in that time. In order to account

for this possibility the difference between calibration measurements recorded three

hours apart was considered. An averaged GPS position was recorded in a fixed

location on the roof of the Cavendish Laboratory twice a day for 12 days. The

experiment was performed at 2 pm and 5 pm each day since these were typically

the times of the calibration measurement sets during the surveys. The satellite

availability and geometry were always good from the laboratory roof, with at

least 8 satellites available and an HDOP of 1–1.2 for each data point. This was

also a feature of the real calibration experiments as the base stations were in open

areas. The data had a standard deviation of 4 metres as shown below in Figure

7.2. This standard deviation was used as the error on each GPS position in the

surveying experiments.

The horizontal distances from the BTS (according to GPS measurements) and

the measured GSM signal flight times are being compared in these experiments,

so the error associated with VDOP was not considered. The horizontal distance

according to the GSM flight time was determined by using Pythagoras’ theorem

and the knowledge of the heights of a given BTS and the GSM receiver (see

Figure 7.3 below).

7.3 Method

The method used to gather data was similar to that used for the experiments

described in Chapter 4, with the digitiser being triggered continuously every 6.12

152

7.3 Method

Figure 7.2: Plot showing the distribution of GPS positions recorded in a fixed positionon the Cavendish Laboratory roof at 2 pm and 5 pm over many days and weatherconditions. There is no clear correlation between pairs of points measured on the sameday.

seconds, a multiple of the hyper-frame repeat period. However only a fraction

of these measurements were useful - the ones recorded whilst the equipment was

stationary at a point of interest. The data acquisition software was programmed

to accept an arming command from the user, then to read out just one measure-

ment set from the digitiser before disarming itself. The digitiser’s display panel

advised the user whether the device was recording a measurement or waiting for

the next trigger. The data capture and readout process took just under a second

153


Figure 7.3: Plot showing the use of Pythagoras’ theorem in calculating the distancefrom a base station using the signal flight time. The lengths B and h are known,corresponding to the base station height and the height of the receiver’s antenna. Thepath length L can be calculated using the signal flight time and the known value of the

speed of the radio waves. The distance D is then given by√

L2 − (B − h)2. For themajority of measurements, L B, and so D = L to a good approximation. Howeverthe full calculation is required for the calibration measurements at each BTS, and forany other measurements near the BTS.

and the digitiser was programmed to clear its memory 3 seconds after each trigger

event in order to prevent any corruption of data in the next measurement. The

user therefore had 3.12 seconds to arm the data acquisition apparatus from the

moment the digitiser display message changed, and in practise this was plenty of

time. A typical outdoor measurement-set recording proceeded as follows:

1. The vehicle was parked at a survey-point.

2. The GPS device was triggered to record the position. A position was calcu-

lated every second and the average of 50 values recorded. In all of the outdoor

environments, the HDOP was always less than 1.5 with at least 8 satellites used

in each position calculation.

3. The data acquisition apparatus was manually armed during one of the inter-

vals when the digitiser’s display message had changed from ‘capturing data’ to

154

7.4 Results

‘waiting for trigger’.

4. The position was recorded on the high-resolution map used to plan the surveys

for both reference purposes and also as a backup position measurement method

if the GPS device’s automatic data storage process was found to have failed after

the survey. In practise this backup was never required.

5. Once the GSM and GPS recording sequences had ended, the vehicle was moved

on to the next position.

7.3.1 Indoor mapping accuracy

The method used to determine the survey-point positions indoors was slightly

different since the GPS device could not be used directly. Instead, an accurate

floor plan was used, which was calibrated externally by using the GPS to deter-

mine the positions of the four corners of the building. A grid was then drawn up

on the floor plan and positions were marked on this map as data were gathered.

Positions could be recorded within an accuracy of 2–3 metres. The dimensions

of the building according to the floor plan agreed with the dimensions according

to the GPS positions of the corners of the buildings to within a metre.

7.4 Results

The distributions of the timing errors in each environment are shown below in

Figure 7.4. Each dataset is presented as a histogram with 50 nanosecond bins and

with lines connecting the values in each bin rather than using bars. This allows

all five datasets to be presented together for comparison without any dataset

obstructing the view of others. A 5-bin moving average was performed on each

histogram before graphing in order to smooth the data. Each histogram has

been created using multiple surveys and contains over 1,000 data points. It

should be noted that all five plots contain a significant portion of data with

negative values, corresponding to SCB peaks which give time of flight values

155


Figure 7.4: Plots of the normalised histograms of the timing error for each environment

shorter than the LOS time. These values are not caused by receiver noise (an error

of around ±80 nanoseconds indoors (see Figure 5.10 and around ±50 nanoseconds

in an open environment (see Figure 4.4)) or by systematic errors (the calibration

measurement sets minimised systematic error on the overall position of the plots

to within 16 nanoseconds 1). They are the result of a real effect of multipath

interference on the shape of the cross-correlation peak, as discussed in Chapter

5 (see Figure 5.5), and are explained in the modelling section below when the

effect of superimposing delayed copies of the same signal and performing a cross

correlation is considered.

1This value is given by combining the GPS error and the error associated with assuming alinear phase drift between the reference oscillators - see Section 7.4.1 for details

156

7.4 Results

The histograms show that the timing error distributions for rural and subur-

ban environments were narrower than for the urban and indoor environments as

expected. The majority of the rural and suburban values (66%) lie in the range

-0.33 to 0.33 microseconds, corresponding to errors of ±100 metres. The urban

and indoor environments have a similar proportion of values within the range

-0.5 to 0.8 microseconds, corresponding to errors in the range of -150 metres to

240 metres. All of the environment types contain a small number of values with

errors of ±600 metres or more. The urban and indoor distributions are also not

symmetrical about zero, but contain more positive timing error values than neg-

ative. This suggests that there is either a mean, non-zero signal delay in these

environment types, or that moderate and dense multipath interference results

in a bias towards positive timing errors. The modelling performed in Chapter

6 suggests that the latter may be true (see the peak-max position histograms

in Figures 6.10 and 6.11), but in either case, the result is an effective mean or

‘typical’ signal delay value in these environments.

The indoor data set also exhibits three distinct and equally spaced peaks,

which may have been caused by resonance with the particular dimensions and

layout of the building’s interior. The building used for the indoor tests (The

Rutherford building of the Cavendish Laboratory) contained a number of small

rooms connected by long corridors. The short corridors were approximately 26

metres long, and the long corridors were approximately 63 metres long. The spac-

ing between the first two peaks in the data corresponds to a difference of about 50

metres and the spacing between the first and last peaks in the data correspond to

a difference of about 120 metres. These extra peaks may have been caused by the

strongest received signal propagating along the corridors before scattering to a

receiver, or alternatively by signals entering the building from different directions

after reflecting or scattering from other nearby buildings. Figure 7.5 below shows

a sketch of the floor plan of the building used for the survey. The ground floor

and first floor were both included in the survey, and the layout of both floors

is identical apart from a glass walkway connecting the first floor of the building

157


Figure 7.5: Diagram showing the floor plan of the indoor environment used in the sur-vey. Shaded areas represent offices, the corridors are white, solid lines represent wallsand doors and whereas dashed lines represent windows. Possible signal propagationpaths to a receiver point are marked A, B, C and D and are discussed in the text above.

to an adjacent building. The windows on the first floor and ground floor facing

the direction of the BTS did not have visible lines of sight to them, but the roof

of the building did, and it is assumed that signals either penetrated through, or

diffracted over, the building blocking the line of sight and then approached along

vectors similar to those marked ‘A’, ‘B’, ‘C’ and ‘D’ in the figure. ‘A’ represents

a signal that travelled in a straight line through brick, concrete, office partitions,

windows, doors, people and furniture and would have been considerably attenu-

158

7.4 Results

ated. ‘B’ represents a signal that entered the glass walkway and propagated down

the corridor before diffracting or reflecting toward reception points. ‘C’ shows a

possible mechanism which could have increased the delay of a given signal con-

siderably by including reflections from metal filing cabinets and cupboards in the

corridors in order to allow a signal to reverberate in a corridor before reaching

a reception point. ‘D’ shows another possible mechanism involving propagation

along the corridors. It is also possible that signals reflected from the buildings

beyond the Cavendish Laboratory (not shown in the diagram, but off the bottom

of the sketch) and entered the surveyed building from the far side, propagating

back toward the BTS. These signals would have then had an extra path length of

roughly 150 metres. However, there was no clear correlation between these dis-

tinct peaks and any general areas within the building, suggesting that the indoor

signal environment is complex and varies on a fine spatial scale.

7.4.1 Error analysis

The error in the determination of an individual SCB peak position was affected by

a number of factors including the stabilities of the frequency standards used by the

measuring equipment and the BTS, errors in the reference positions determined

by GPS or accurate mapping, and the error introduced by up-sampling noisy

data.

The stability of the RFS was measured in an experiment discussed in Chapter

2 which showed that the average error associated with the assumption of a linear

phase drift between two identical RFS oscillators over a 3 hour test was about

9 nanoseconds. It was also shown in Chapter 4 that the long-term stabilities

of certain local base stations on Network 1 were similar to that of the FRK-

H Rubidium oscillator, and those particular base stations were the only ones

used in the experiments described in this chapter. The results from Chapter 2

therefore provide an approximation to the error associated with the linear-phase-

drift corrections for these experiments. The full value of this error only applied to

159


measurements performed toward the end of a three hour test, with measurements

closer to the beginning of the test having a proportionately lower error.

The timing error due to measurement noise for a stationary indoor receiver

was shown in Figure 5.10 to be about ±80 nanoseconds, and the measurement

noise at an outdoor receiver was shown to be about ±50 nanoseconds (see Figure

4.4),

The error associated with GPS positioning was shown in the discussion above

to be 4 metres, corresponding to a 13 nanoseconds timing error on each GPS

measurement. Although averaging improved the GPS accuracy, the work above

demonstrated that there was an upper bound of approximately 4 metres on the er-

ror when performing relative measurements over the course of about three hours.

The resolution of an SCB peak position after up-sampling was 24.5 nanosec-

onds, giving a measurement resolution error of 12.25 nanoseconds.

Combining all of these independent errors in quadrature (and noting that two

GPS and two SCB-peak measurements are used per time of flight calculation)

gave a total maximum error on an indoor measurement 3 hours after a cali-

bration measurement of 97 nanoseconds. With the error caused by drift in the

frequency standards discounted, the total error is 96 nanoseconds. For a short

outdoor test (such that the GPS errors can be ignored) this error drops to 73

nanoseconds. These errors were larger than the bin size used to produce the

histograms (50 nanoseconds) but the 5-bin moving average used to smooth the

data also reduced the error caused by any data points in the wrong bin. The

measurement noise clearly dominates the error in these recordings, and can be

reduced by averaging over many recordings. However, in producing these timing

error distributions, each recording was considered separately so that the effects

of rapid temporal multipath variations (which contribute randomly to the overall

error on a measurement) could be recorded and studied rather than averaged out.

160

7.5 Modelling the timing error distributions


In attempting to reproduce the timing-error distributions observed for each en-

vironment, the underlying cross-correlation process used to determine the arrival

time of a signal was first considered. The cross correlation of the continuous

functions f(x) and g(x) is defined as:

(f ? g)(x) =

∫f ∗(t)g(x+ t) dt. (7.1)

When considering the cross-correlation operations performed in the experiments

discussed here, the ETS is represented by the function g(x), and the function

f(x) is replaced with a sum of functions mi(x) representing the summation of

the multipath signal events. The cross-correlation process is associative, and so

cross correlating each individual signal with the ETS before superimposing them

produces the same result as superimposing all the signals before performing the

cross correlation:

(f ? g)(x) =

∫g(x+ t)

(N∑i=0

m∗i (x)

)dt =

N∑i=0

(∫g(x+ t)m∗

i (x) dt

). (7.2)

This simplifies the modelling process greatly. In addition to this, Figure 7.6

below shows that modelling the modulus of the ETS auto-correlation peak as

a truncated raised-cosine function is a very good approximation. The process

of superimposing a number of truncated raised-cosine functions can therefore

be used to model interfering cross-correlation peaks. This is more elegant than

modelling a number of interfering digital signals prior to performing a cross-

correlation and also allows the problem of multipath interference to be considered

analytically.

The position of a distorted SCB peak is determined by the phase differences,

displacements, and amplitudes of the interfering multipath signals. In the raised-

cosine model, the displacements of the peaks prior to their superposition rep-

resents the relative delays of the signals, and their initial relative amplitudes

represent both their phase differences and amplitudes (see Figure 7.7).

161


Figure 7.6: Comparison of the modulus of the GSM ETS auto-correlation peak and atruncated raised-cosine function

The width of the ETS autocorrelation peak is determined by the signal band-

width, fb Hz, and is approximately equal to 2fb

seconds. For a GSM channel with

a signal bandwidth of 140 kHz, this corresponds to a width of 14.3 microsec-

onds (equivalent to 4.29 kilometres). The modulus of the cross-correlation peak

associated with the earliest-arriving signal can therefore be modelled using the

following function:

H(z) =

1 + cos (πfb(z − α0)) if −1

fb< (z − α0) <

1fb

0 otherwise, (7.3)

where z corresponds to a position along the cross-correlation function in seconds

and α0 is the delay of the earliest significant arrival relative to the delay of the

LOS signal (i.e. if the earliest measurable arrival is LOS then α0 = 0).

A number of delayed SCB peaks corresponding to the multipath events are

162


Figure 7.7: Plot showing how the superposition of two displaced and out-of-phase cross-correlation peaks can result in a distorted function. The blue curve represents an SCBpeak; the green curve represents a delayed, phase rotated, and attenuated copy; and thered curve represents their superposition.

then superimposed:

ψ = H(z) +N∑i=1

Ai cos(φi)H(z − αi), (7.4)

where N is the total number of individual multipath events and Ai, φi, and αi

represent the relative amplitude, relative phase, and extra delay (total signal

flight time minus earliest significant signal flight time) of the ith multipath event

compared to the earliest arrival.

The position of the maximum value of this function (zmax) provides the esti-

mate of the signal arrival time and can be measured by solving dψdz

∣∣∣∣z=zmax

= 0.

The offset of zmax from zero represents the timing error associated with the as-

163


sumption that the peak of the function corresponds to the LOS arrival.

dψ

dz

∣∣∣∣z=zmax

=− πfb sin (πfb(zmax − α0))

− πfb

N∑i=1

Ai cos(φi) sin(πfb(zmax − α0 − αi)) = 0. (7.5)

Now using the trigonometric identity

sin(a− b) = sin(a) cos(b)− cos(a) sin(b), (7.6)

and rearranging gives

tan (πfb(zmax − α0)) =

∑Ni=1Ai cos(φi) sin(πfbαi)

1 +∑N

i=1Ai cos(φi) cos(πfbαi). (7.7)

The distributions of two new variables, x and y, can now be considered, corre-

sponding to the results of the two sums in Equation 7.7 above. According to

the central limit theorem [65], and on the assumption that the processes are ran-

domly distributed and uncorrelated, as the value of N increases, the distributions

of x and y tend to Gaussian distributions. This assumption can be verified by

using suitable values for N and suitable distributions for A, φ and α, as shown in

detail in Appendix A. The two probability densities functions (pdfs) for the new

variables are given by

pdf

(N∑i=1

Ai cos(φi) sin(πfbαi)

)=

1√2πσy

exp− y2

2σ2y (7.8)

and

pdf

(1 +

N∑i=1

Ai cos(φi) cos(πfbαi)

)=

1√2πσx

exp− (x−1)2

2σ2x , (7.9)

and can be used to determine the probability distribution of zmax. The joint pdf

for a function dependant on both of these distributions is given by the bivariate

Gaussian distribution:

pdf(x, y) =1

2πσxσy√

1− p2exp

− ξ

2(1−p2) , (7.10)

164


where, in this case,

ξ =(x− 1)2

2σ2x

− 2p(x− 1)y

σxσy+y2

σ2y

(7.11)

and p = correlation(x, y) = σx,y

σxσy.

In Equation 7.7, the two distributions are combined as a ratio, and the ratio

distribution described by Fieller [66] is now considered. For the ratio v = yx,

where x and y are distributed according to the joint pdf f(x, y), the pdf of v is

given by:

pdf(v) =

∫ ∞

−∞|x|f(x, vx) dx, (7.12)

which gives

pdf(v) =

∫ ∞

−∞|x|exp

−

(x−1)2

2σ2x

− 2p(x−1)vxσxσy

+(vx)2

σ2y

2(1−p2)

2πσxσy√

1− p2dx. (7.13)

The solution of this integral, given by Fieller, is

pdf(v) =σxσy

√1− p2

π(v2σ2x − 2pvσxσy + σ2

y)× exp

− 1

2σ2x(1−p2)

+σy(vpσx − σy)

π(v2σ2x − 2pvσxσy + σ2

y)32

× exp−v2

2(v2σ2x−2pvσxσy+σ2

y) ×∫ σy(vpσx−σy)

σxσy

√(1−p2)(v2σ2

x−2pvσxσy+σ2y)

0

exp−v2

2 dv. (7.14)

The probability density function of zmax can be determined using this equation

by noting from Equation 7.7 that

tan(πfb(zmax − α0)) = v. (7.15)

If the pdf of an independent random variable τ is given as f(τ), then the pdf of

µ, where µ = g(τ), is given by

pdf(µ) = |(g′(g−1(µ)))−1|f(g−1(µ)). (7.16)

Substitution of the parameters f(τ) = pdf(v) and µ = g(v) = arctan(v) gives

pdf(zmax) = |(1 + v2)

πfb|pdf(v). (7.17)

165


Noting that (1+v2)πfb

is positive for all v and using the standard error function via

the following substitution (given by Boas [67])∫ x

0

exp−t2

2 dt =

√π

2erf(

x√2), (7.18)

the full model can be given as:

pdf(zmax) =(1 + v2)

π2fb

(R√

1− p2

v2R2 − 2pvR + 1exp

− 1

2R2σ2y(1−p2)

+(vpR− 1)

√2πσy(v2R2 − 2pvR + 1)

32

× exp−v2

2σ2y(v2R2−2pvR+1) ×erf

((vpR− 1)

R√

2(1− p2)(v2R2 − 2pvR + 1)

)),

(7.19)

where v = tan(πfb(zmax − α0)) and R = σx

σy.

7.5.1 Fitting the free parameters

The model given in Equation 7.19 has four free parameters: p, R, σy and α0.

The figures below show how the curve described by the model changes as p, R

or σy are varied individually while holding the others constant. Variations in α0

just displace the curve left or right on the zmax axis. Changes in the dependant

variables R and σy affect the shape of the curve in similar ways, as expected.

The best fit values for each distribution using Chi-squared fitting with a 95%

confidence interval are shown below in Figures 7.12 to 7.16 and in Table 7.1. The

best-fit values of σy are within the range 20–100 for all of the environment types,

while the values of R are within the range 1–20. Figure 7.8 shows that the curve

described by the model is hardly affected by changes in the value of σy when it is

greater than the value of R. The value of σy is therefore not presented here as its

exact value in each set of best-fit values had little effect on the resulting curve.

The table of results demonstrates clear trends in the values of R and α0 as

the environment types become more cluttered, and therefore as the expected level

166


−3 −2 −1 0 1 2 3

x 10−6

0

0.005

0.01

0.015

0.02

0.025

delay in seconds

frequency

σy = 0.1

σy = 1

σy = 10

Figure 7.8: Plot showing the effect of varying σy in the model. For each curve, R = 1and p = 0.

−3 −2 −1 0 1 2 3

x 10−6

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

delay in seconds

frequency

R = 0.1R = 1R = 10

Figure 7.9: Plot showing the effect of varying R in the model. For each curve, p = 0and σy = 1.

167


−3−3 −2 −1 0 1 2

x 10−6

0

1

2

3

4

5

6

7

8x 10

−3

delay in seconds

frequency

p = −0.5p = 0p = 0.99

Figure 7.10: Plot showing the effect of varying p in the model. For each curve, R = 1and σy = 1.

Parameter R p α0

Rural 12.7± 1.1 0.03± 0.04 51± 5 ns

Suburban 13.0± 0.1 −0.04± 0.02 72± 6 ns

Light-urban 4.7± 0.3 0.20± 0.12 183± 24 ns

Mid-urban 3.5± 0.3 −0.46± 0.07 239± 23 ns

Indoor 16.0± 3.1 0.54± 0.18 30± 6 ns, 190± 6 ns, 425± 6 ns

Table 7.1: A table showing the best-fit parameters for each dataset.

of multipath interference increases. The values of α0 are useful in determining a

characteristic timing error for each environment, corresponding to the delay of the

earliest-arriving signal in the model. The relationship between these characteristic

delays and the environment types can be estimated using

α0 = 57× E, (7.20)

where E is an integer representing the environment type such that 0 corresponds

to free space, 1 corresponds to rural environments, and so on (see Figure 7.11).

The model fits the rural, suburban, light-urban and mid-urban datasets well,

and its ability to reproduce the experimental results supports the hypothesis

168


Figure 7.11: Plot showing the characteristic delays in the outdoor environments. Theerror bars do not represent standard deviations and are explained in the text.

that multipath interference dominates the timing error distributions. The indoor

dataset is not fitted well by the model because of the resonance peaks discussed

previously, but a good fit can be achieved by picking out its three distinct peaks

using three superimposed distributions with the same R, σy and p values but dif-

ferent α0 values. These three distributions probably correspond to three distinct

regions or environment types inside the building studied where distinct propaga-

tion paths dominate separately in different areas of the building (see discussion

above).

The error associated with each parameter was determined by finding the best-

fit set of values for a given environment, then varying one while holding the others

constant until the Chi-squared test statistic reached the 95% confidence limit in

each direction. In the case of the indoor data set, the three best-fit α0 values,

corresponding to the three peaks, were treated as one variable.

169


−4 −2 0 2 4

x 10−6

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07


norm

alis

ed f

requ

ency

−4 −2 0 2 4 6

x 10−7

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07


norm

alis

ed f

requ

ency

−15 −10 −5

x 10−7

0

1

2

3

4

5

x 10−3


norm

alis

ed f

requ

ency

0 5 10

x 10−7

0

0.005

0.01

0.015

0.02

0.025


norm

alis

ed f

requ

ency

rural datamodel

Figure 7.12: Plots showing the rural data set with the multipath model overlaid

−1 0 1

x 10−6

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07


norm

alis

ed f

requ

ency

−2 0 2 4 6 8

x 10−7

0

0.01

0.02

0.03

0.04

0.05

0.06


norm

alis

ed f

requ

ency

−1.5 −1 −0.5

x 10−6

0

1

2

3

4

x 10−3


norm

alis

ed f

requ

ency

0.5 1 1.5 2 2.5

x 10−6

0

1

2

3

4

5

6

x 10−3


norm

alis

ed f

requ

ency

suburban datamodel

Figure 7.13: Plots showing the suburban data set with the multipath model overlaid

170


−2 0 2

x 10−6

0

0.005

0.01

0.015

0.02

0.025


norm

alis

ed fr

eque

ncy

−4 −2 0 2 4 6 8

x 10−7

0.005

0.01

0.015

0.02

0.025


norm

alis

ed fr

eque

ncy

−3 −2 −1 0

x 10−6

0

2

4

6

8

10

12

x 10−3


norm

alis

ed fr

eque

ncy

1 1.5 2 2.5 3

x 10−6

0

1

2

3

4

5

6

7

x 10−3


norm

alis

ed fr

eque

ncy

light−urban datamodel

Figure 7.14: Plots showing the light-urban data set with the multipath model overlaid.

−2 0 2

x 10−6

0

0.005

0.01

0.015

0.02


norm

alis

ed fr

eque

ncy

−5 0 5 10

x 10−7

0

0.005

0.01

0.015

0.02

0.025

0.03


norm

alis

ed fr

eque

ncy

−2 −1.5 −1 −0.5

x 10−6

0

2

4

6

8

10x 10

−3


norm

alis

ed fr

eque

ncy

0.5 1 1.5 2 2.5 3

x 10−6

0

2

4

6

8

x 10−3


norm

alis

ed fr

eque

ncy

mid−urban datamodel

Figure 7.15: Plots showing the mid-urban data set with the multipath model overlaid.

171


−2 0 2

x 10−6

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035


norm

alis

ed f

requ

ency

−4 −2 0 2 4 6 8

x 10−7

0

0.01

0.02

0.03

0.04


norm

alis

ed f

requ

ency

−2.5 −2 −1.5 −1 −0.5 0

x 10−6

0

5

10

15

20x 10

−3


norm

alis

ed f

requ

ency

0.5 1 1.5 2 2.5 3

x 10−6

0

2

4

6

8

x 10−3


norm

alis

ed f

requ

ency

indoor dataadjusted model

Figure 7.16: Plots showing the indoor data set with the adjusted multipath modeloverlaid (see text)

7.6 Conclusions

1. The experimental results show that the errors on measurements of GSM signal

arrival times have a narrower distribution in rural and suburban environments

than in urban and indoor environments.

2. All of the timing error distributions exhibit both positive and negative errors,

but the negative errors are too large to be explained by noise alone. These are

dominated by multipath interference distorting the SCB?ETS timing marker, and

hence influencing the position of the peak.

3. The model proposed in Section 7.5 can be used to reproduce the experimental

distributions and has been used with experimental data to determine the typical

signal delay for a given environment.

4. The best-fit values of the model suggest that the typical signal delay for the

strongest receipt in rural and suburban environments is 50–70ns, corresponding

to 15–21 metres of extra path length.

172

7.6 Conclusions

5. The best-fit values of the model suggest that an extra signal delay of 180–240

nanoseconds is a feature of urban environments, corresponding to 55–72 metres

of apparent extra path length. However, the modelling performed in Chapter 6

suggests that moderate and dense multipath interference results in a bias toward

positive timing errors (see the peak-position histograms in Figures 6.11 and 6.10).

In either case, the result is an effective typical signal delay value of around 200

nanoseconds in these environments.

6. A simple ‘rule of thumb’ equation is proposed to allow the characteristic delay

for a given environment type to be estimated using a simple calculation.

7. The indoor environment showed a different error distribution from the outdoor

environments, and cannot be accurately modelled using the model as given by

Equation 7.19 above. However, a good fit can be achieved by superimposing 3

curves described by the model with different values of α0, the variable correspond-

ing to the delay of the earliest significant arrival. This would suggest a number

of different propagation mechanisms active in the environment and each domi-

nating in different areas depending on the exact nature of the local environment,

i.e. being near a window, or in a long corridor, etc.

173


174

Chapter 8

Summary and further work

8.1 The experimental apparatus

A set of apparatus was constructed in order to measure signal arrival times via the

SCB broadcasts on the BCCH channels of base stations on the GSM network. The

140 kHz-bandwidth GSM broadcasts were oversampled, allowing the signals to be

fully reconstructed using the Nyquist-Shannon sampling theory. The signals were

sampled at a rate of 2.04 MHz and interpolated to increase this resolution by a

factor of 20 to allow an effective timing resolution of 24.5 nanoseconds. In practise,

the accuracy of an individual recording was decreased by measurement noise and

temporal multipath interference, but averaging over many measurements reduced

the effect of these errors. Systematic errors from features such as the instabilities

of the frequency references were discussed and quantified. They were found to be

insignificant over short experiments lasting a few hours.

8.2 The experimental methods

Two experimental methods were proposed, the interferometric method and the

network-synchronised method. The interferometric method removed systematic

errors caused by fluctuations in the base station broadcasts, whereas the network-

175

8. SUMMARY AND FURTHER WORK

synchronised method required half as much equipment and only one operator.

The accuracy of the network-synchronised method approached the accuracy of the

interferometric approach as the stability of the base station frequency standards

increased.

8.3 GSM network timing stabilities

The temporal stability of the received signals on two GSM networks were mea-

sured. The signals broadcasted by the base stations on Network 1 all demon-

strated a very high level of stability, leading to the conclusion that the network-

synchronised method could be used with this network. The temporal stability

of a received signal was noted to reduce for an indoor antenna, demonstrating

that the received temporal stability was dependant not only on the base sta-

tion’s frequency standard, but also on the propagation path and signal strength.

The signals on Network 2 all demonstrated a reduced stability when compared

to Network 1. Three distinct signal qualities were observed during the exper-

iments, which were assumed to have been caused by the different technologies

and frequency-stabilising techniques used in base stations of different ages and

on different networks. The results of the experiments suggested that Network

1 could be used confidently to provide FTA to an E-GPS device with periods

of 3 days or more between calibrations, whereas Network 2 could only be used

confidently to provide FTA with periods of 5 hours or less between calibrations.

8.4 GSM network timing stabilities in indoor

multipath environments

The multipath behaviour over sub-wavelength distances indoors was studied. Sig-

nificant timing errors of a microsecond or more were recorded for antenna move-

176

8.5 GSM radio location timing error distributions in variousenvironments

ments on the millimetre scale. This behaviour was also noted during an experi-

ment with a visible line of sight to the base station in an outdoor but cluttered

environment, confirming that extreme errors due to multipath can still occur

even with a line of sight between a transmitter and receiver. A model based

on superimposing truncated raised-cosine functions was proposed to simulate the

superposition of the SCB peaks from interfering multipath signals. The model

was shown to reproduce features seen in the experimental results. Two methods

were proposed for increasing the accuracy of determining signal arrival times, the

peak-rise method and the midpoint method. Both methods improved the tim-

ing accuracy by removing the most extreme errors in a given data set, but both

required more intensive computation than the simple peak-max technique.

8.5 GSM radio location timing error distribu-

tions in various environments

The timing error distributions in various environments were determined by us-

ing the peak-max technique to measure signal flight times on the GSM network.

The timing error distributions in rural and suburban environments were narrower

than for urban and indoor environments, and were also reasonably symmetrical

about zero. The urban and indoor distributions were not symmetrical about zero,

containing more positive timing error values than negative. This suggested that

there is either a mean, non-zero signal delay in these environment types, or that

moderate and dense multipath interference results in a bias toward positive tim-

ing errors. The modelling performed during the indoor multipath experiments

suggested that the latter may be true, but in either case, the result was an effec-

tive mean or ‘typical’ signal delay value in these environments. A timing error

probability density function model was derived from the raised-cosine model and

was shown to reproduce the experimental distributions. The model reproduced

177


the urban datasets best when an extra path delay of 180–240 nanoseconds was

included, suggesting that the signals in these environments have a typical ex-

tra path length of 55-72 metres. The indoor timing-error distribution exhibited

three distinct peaks, corresponding to three distinct groups of signals with dif-

ferent mean propagation delays. This feature was possibly caused by signals

resonating in the building’s corridors, or by signals entering the test environment

after reflecting from different local buildings.

8.6 Further work

The network stability measurements discussed in Chapter 4 were only performed

on two networks, and only in Cambridge, England. This was adequate for the

purposes of determining whether the network-synchronised technique could be

used during this research, but further network stability tests are required to de-

termine more accurate figures relating to the capability of GSM networks to pro-

vide FTA. The degradation in timing stability experienced by a rapidly moving

receiver (such that Doppler effects are not negligible) should also be investigated

to determine the effect on providing FTA to a moving receiver. Further investi-

gations into new techniques for determining signal arrival times using the SCB

cross-correlation peak should also be carried out, as they can improve the accu-

racy of GSM radio positioning and as the processing power of handsets increase,

computation-hungry algorithms will become a viable option. The timing error

distribution for a dense urban environment such as the centre of London still

needs to be determined.

Finally, performing the experiments discussed in Chapters 4–6 of this thesis

on the 3G network would be an appropriate large-scale extension to this work.

The much shorter coherence length of these wide-band signals would yield a much

finer resolution and so provide much more information about the multipath envi-

ronment. The TOA estimation methods would therefore also be different and are

178

8.6 Further work

worth researching. The actual mechanisms of radio positioning on 3G networks

can also be researched, as this is not a simple task using CDMA signals. The

signals are all broadcast in the same waveband, and so strong local signals over-

power weaker distant signals. Radio positioning typically requires measurements

from at least three base stations, but it is difficult to perform measurements using

a number of base stations simultaneously using the 3G network. Techniques such

as Cumulative Virtual Blanking [68] need to be developed.

179


180

Appendix A

Distributions of A, φ and α

A model of the effects of multipath interference on the position of the maximum

value of the GSM SCB?ETS cross correlation peak was proposed in Chapter 7.

The model of the cross-correlation peak, ψ, involves superimposing truncated

raised-cosine functions in the following way:

ψ = H(z) +N∑i=1

Ai cos(φi)H(z − αi), (A.1)

where

H(z) =

1 + cos (πfb(z − α0)) if −1

fb< (z − α0) <

1fb

0 otherwise, (A.2)

and where:

z corresponds to a position along the cross-correlation function in seconds;

fb is the signal bandwidth in Hertz;

N is the total number of i individual multipath events;

Ai, φi, and αi represent the relative amplitude, relative phase, and extra delay

(total signal flight time minus earliest significant signal flight time) of the ith

multipath event compared to the earliest arrival; and

α0 is the delay of the earliest significant arrival relative to the delay of the LOS

signal.

181

A. DISTRIBUTIONS OF A, φ AND α

The model also involves the two summation terms,

S1 =N∑i=0

Ai cos(φi) sin(πfbαi) (A.3)

and

S2 = 1 +N∑i=0

Ai cos(φi) cos(πfbαi). (A.4)

The central limit theorem [65] states that any summation will tend toward a

normal distribution as N tends to infinity if the variables being summed are

all randomly chosen, independent, and are drawn from distributions with finite

variances. The values of A, φ and α fit these criteria, but the condition for N

being large enough needs to be determined. There is also a clear dependency

between S1 and S2, suggesting that their limiting Gaussian distributions will not

be independent.

The validity of applying the central limit theorem here can be determined by

using suitable distributions of A, φ and α to calculate many values of S1 and S2

to see if they are normally distributed. The distributions of A, φ and α cannot

be determined but they can be estimated.

A.1 Distribution of φ

The distribution of φ is dependant on two major features:

1. The reflection, diffraction, refraction, and scattering processes, which give rise

to many signals arriving at a given point via different paths, change a given sig-

nal’s phase such that it no longer depends on the path length alone.

2. For a GSM signal with a central frequency of around 900MHz and a band-

width of 140 kHz, the value of φ changes over its full range as the receiver is

moved about 30 centimetres along the line of propagation. The amplitude of the

individual signal (Ai) and the value of πfbαi will change negligibly by comparison

over this small distance.

182

A.2 Distribution of α

Taking these two features together suggests that modelling φ with a uniform dis-

tribution between −π and π independent of α is appropriate, i.e. the probability

density function (pdf) of φ can be given as:

pdf(φ) =1

2π, for − π ≤ φ ≤ π. (A.5)

A.2 Distribution of α

The distribution of α represents the signals which arrive at the receiver with

significant amplitudes, since delayed paths with negligible corresponding ampli-

tudes do not contribute to the multipath interference being modelled. Therefore,

α cannot be negative (since the LOS signal is always represented by α = 0) and

the probability density function must tail-off as the value of α increases, since

the likelihood of a significant signal decreases with increasing delay. A suitable

distribution based on these criteria is a Rayleigh distribution, given by:

pdf(α) =α

σ2α

exp−α2

σ2α , for 0 ≤ α ≤ ∞, (A.6)

where the parameter σα determines the modal value of the distribution.

A.3 Distribution of A

Estimating the distribution of signal amplitudes involves considering the signal

propagation mechanisms. At GSM frequencies, the signals can penetrate and

propagate through buildings and other objects such that even when the LOS

path is visibly obstructed the attenuated LOS signal could still be part of the

multipath environment, but possibly with a lower amplitude than one or more of

the multipath signals. In this model the value of A is defined such that the ampli-

tude of the LOS receipt or earliest significant signal arrival is always normalised

to 1. Therefore when modelling rural and suburban environment positions where

183


the LOS signal is often likely to be present, then the values of A will mostly be

below 1. For the city and indoor environments where the LOS signal is likely to

be heavily attenuated after penetrating buildings, the earliest significant arrival

may typically be a delayed multipath signal which has undergone less attenua-

tion, and therefore the values of A will mostly be distributed around and above

1.

A common signal propagation mechanism is likely to be diffraction over rooftops

and around building edges. A building’s rooftop or edge is assumed to be a sharp

edge and the following Fresnel analysis uses the parameters given in Figure A.1

below. Within the ‘shadow’ regime of Fresnel diffraction the following approx-

Figure A.1: Diagram showing the parameters for considering Fresnel diffraction at a

knife edge. The base station of height B is a distance D from a knife edge obstruction

(building) of height b. The receiver is a distance s beyond this, where s D.

imation given by Saunders [18] can be used for the diffracted signal intensity

relative to the unobstructed signal:

I = 20 log10

(1√2πv

)dB for v > 1, (A.7)

where the diffraction parameter v is given by

v = x

√2(D′ + s′)

λD′s′. (A.8)

184


The parameters x, D′ and s′ are given above in Figure A.1. It can also be shown

using the diagram that:

s′ = L cos(θ), (A.9)

D′ =√

(D + s)2 +B2 − s′, (A.10)

sin(θ) =x

L, (A.11)

and

L =√s2 + b2, (A.12)

and so

x =(√

s2 + b2)

sin

(arctan

(b

s

)− arctan

(B

D + s

)). (A.13)

The signal intensity, I (in dB), is converted to amplitude (in linear units) via the

relationship:

A = A010I10 . (A.14)

Plots of the resulting signal amplitude versus distance from the base of the point

of diffraction are given in Figure A.2 below. The signal amplitudes are given as

the value relative to the unobstructed free space amplitude at each point. In or-

der to generate a probability density function for this mechanism, the histogram

of the values given by one of these curves can be considered. The distribution

of A for a particular building size and BTS distance would then be given by a

function that fits this histogram. However, since a general distribution of A is

required, it is better to generate A values using the Fresnel diffraction model for

randomly drawn environmental parameters and therefore create a more general

histogram. This distribution of A will be valid for the case where a single diffrac-

tion over rooftops or around the edges of buildings can be argued to be a dominant

propagation mechanism, such as may be the case in urban environments.

185


Figure A.2: Plots of the signal amplitudes after diffraction down to points of interest

from a single knife edge for various distances from a 15 metre tall BTS

Reflections are another likely propagation mechanism, either on their own or

after a diffraction over rooftops and down toward the receiver. The GSM network

signals are generated with the electric field linearly polarised in the vertical plane

and can reflect from surfaces either in the same plane as this polarisation, or

perpendicular to it. The amplitudes of these reflected electric field components

are given by the Fresnel reflection and transmission coefficients [18] as follows:

Ereflected|| = R||Eincident =cos(θtransmitted)− Z1

Z2cos(θincident)

cos(θtransmitted) + Z1

Z2cos(θincident)

Eincident (A.15)

and

Ereflected⊥ = R⊥Eincident =cos(θincident)− Z1

Z2cos(θtransmitted)

cos(θincident) + Z1

Z2cos(θtransmitted)

Eincident. (A.16)

186


Figure A.3: A plane wave incident onto a plane boundary.

In these equations, R|| and R⊥ are the parallel and perpendicular reflection coef-

ficients, Z1 and Z2 are the impedances of the two media, such that Z =√

µrµ0

εrε0,

and

θtransmitted = arcsin

(n1

n2

sin(θincident)

). (A.17)

Figure A.4 below shows the reflection coefficients (and so the relative ampli-

tude after reflection for a given interaction) for concrete (εr = 6.1) and for brick

(εr = 5.1). These equations can be used to generate values for A if it is assumed

that a dominant propagation mechanism can be just one reflection from a brick

or concrete surface.

A combined reflection and diffraction process, such as that experienced by a

signal diffracting over a rooftop and then reflecting from a building before prop-

agating to a receiver, is also likely to be a dominant signal propagation mech-

anism. The resulting A values can be calculated by determining the diffraction

angle and reflection angle to reach a given receiver point based on the building

sizes and spaces, then multiplying the results of the Fresnel and reflection cal-

culations together. Figure A.5 below shows plots of the the calculated received

187


0 10 20 30 40 50 60 70 80 900

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

incident angle (degrees)

reflectioncoefficient

reflections in the vertical plane from concrete reflections in the vertical plane from brickreflections in the horizontal plane from concrete (dashed)reflections in the horizontal plane from brick (dashed)

Figure A.4: Plots of the reflection coefficients for vertically polarised 900MHz GSM

signals incident on brick and concrete surfaces

signal amplitudes for both a diffraction straight down to the receiver and for a

diffraction-reflection process for 6m tall buildings spaced 30 metres apart (typical

dimensions for 2 storey terraced housing). Both mechanisms result in signals

with the same order of magnitude for the building dimensions and spacings cho-

sen. The amplitudes of the resultant signals are around 3 orders of magnitude

lower than for an unobstructed signal, but the LOS signal itself would have been

attenuated before reaching the receiver, passing through appreciable thicknesses

of brick, concrete, slate, wood, plastic, plaster, metal, mortar etc. The average

attenuation at GSM frequencies through a concrete wall over all incident angles

is given by Latapyc [69] as 7 dB, with a loss caused by furniture given as 1 dB

188


per metre. Therefore for a typical small house, assuming one internal wall and

a few metres of furniture, a loss of around 25 dB might be expected for a path

through the building. This corresponds to a change in amplitude to a factor of

0.003 of its initial value, which is similar to the values for the other propagation

mechanisms.

Scattering processes from poles, posts, branches and rough surfaces will also

provide signal propagation mechanisms. When the scattering object has a dimen-

sion comparable to the wavelength of the radiation (which is true for poles, posts,

window ledges, branches, tree trunks, etc, at GSM frequencies.) the scattering

will be most effective. According to the “effective roughness” approach presented

by Esposti [70, 71], the adjusted Lambertian model for diffuse scattering from a

surface is given by

Es =K · Sri · rs

√√√√ 8 · dS · cos(θi)

4π + 3π · cos(θi) ·(1 + sin2 θi

4

)+ π

2· cos3 θi

·

(1− (sin θs · sin θi) · cos (φs − φi) + cos θi · cos θs

2

) 32

, (A.18)

where S is the scattering coefficient, dS is the surface element scattering radiation,

(ri, θi, φi) are the polar coordinates of the incident wave, Es is the amplitude of

the scattered wave at polar coordinate (rs, θs, φs), and K is a constant dependant

on the amplitude of the impinging radiation. Values can be drawn from this

model using random coordinates and coefficients in order to generate a probability

density function for this propagation mechanism as before.

Free-space path-loss is an important factor in attenuating the signal over a

long propagation path, but the attenuation caused by the slightly increased path

length due to a reflection, diffraction or scatter is negligible compared to the

attenuation caused by the signal deflection interaction. The effects of free space

path loss due to the slightly increased path lengths caused by these propagation

mechanisms is therefore ignored.

189


0 5 10 15 20 25 300

1

2

3

4

5

6

7x 10

−3

relativeamplitude

compared tounobstructed(LOS) signal

distance from rooftop (metres)

diffraction directly down from rooftop to receiverdiffraction followed by reflection from opposite brick building

(a)

(b)

Figure A.5: Plots (a) showing the received signal amplitude (relative to the unob-

structed signal) for two propagation mechanisms - diffraction over a rooftop, and a

shallower diffraction followed by reflection from a nearby facing building (b).

190


These four propagation mechanisms all result in different probability distri-

butions for A, but the aim of this exercise is to verify whether the sums S1 and

S2 described above tend to Gaussian distributions as the number of terms in

the sums increases, so checking this for all four potential distributions for A will

determine if the use of the Gaussian approximation is valid.

A large number of values for S1 and S2 were calculated using the distribu-

tions of α, φ and the four propagation mechanisms given above to represent four

possible distributions of A. The following figures show the resulting plots for

each distribution of A, assuming 10 multipath interactions per point of interest

(i.e. N = 10 in the sums S1 and S2) - a reasonable value considering the number

of surfaces and edges available in a typical multipath environment. Each plot

consists of 120,000 values of S1 and S2 and a bivariate Gaussian distribution is

overlaid for comparison. All four plots support the use of the central limit the-

orem approximation for these distributions and 10 multipath events per survey

point.

————————————————————————

191


1.25 1.5 1.75 2 2.25 2.5 2.75 30.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

S2

S1

(a) single diffraction mechanism

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

0.4

0.6

0.8

1

1.2

1.4

S2

S1

(b) single reflection mechanism

0 1 2 3 4 5

0.5

1

1.5

S2

S1

(c) combined diffraction and reflection

mechanism

(d) diffuse scattering mechanism

Figure A.6: Plots showing the correlation between S1 and S2 for the four potential

distributions of A. The distributions of α and φ remain the same for each test, and

N=10 in all of the sums. The solid coloured contours represent the distribution of

values and the overlaid black, dotted contour lines represent the best-fitting bivariate

Gaussian distribution. These overlaid contour lines show good fits to the solid contour

plots, supporting the use of the central limit theorem in approximating the distribution

of S1 and S2 with a bivariate Gaussian distribution

192

Bibliography

[1] K. B. Williams. Secret Weapon: US High-Frequency Direction Finding in

the Battle of the Atlantic. Naval Inst Pr, 1996. 1.1

[2] 2001 Federal Radionavigation systems. United States Department of De-

fense and Department of Transportation, DOT-VNTSC-RSPA-01-3.1/DOD-

4650.5, 2001. 1.1, 1.1

[3] A. Price. Instruments of Darkness: The History of Electronic Warfare.

Peninsula, 1977. 1.1

[4] J. A. Pierce. Omega: Facts, Hopes and Dreams. Harvard University of

Cambridge, Department of Engineering and Applied Physics, 1974. 1.1

[5] N. Bowditch. The American Practical Navigator. National Imagery and

Mapping Agency, 2002. 1.1

[6] Wireless Intelligence. www.cellular-news.com/story/19223.php. 1.2

[7] P. Solanki and H. Huosheng. Techniques used for location-based services: A

survey. Master’s thesis, University of Essex, 2005. 1.2.1

[8] PPS 10 Telecommunications. www.planningni.gov.uk. 1.2.1

[9] P. Kemppi. Database correlation method for multi-system location. Master’s

thesis, Helsinki University of Technology, 2005. 1.2.2

193

BIBLIOGRAPHY

[10] G. Wolfle, R. Hoppe, D. Zimmermann, and F. M. Landstorfer. Enhanced

localization technique within urban and indoor environments based on accu-

rate and fast propagation models. European Wireless 2002, Firence, Italy:7,

February 2002. 1.2.2

[11] V. Otsason. Accurate indoor localization using wide GSM fingerprinting.

Master’s thesis, University of Tartu, 2005. 1.2.2

[12] Location Based Services. GSM Association Permanent Reference Document

SE 2.3, ver 3.1.0:52, 2003. 1.2.3

[13] P. J. Duffett-Smith, J. P. Brice, and P. Hansen. Radio positioning systems.

US Patent Number 6,529,165, 4th March 2003. 1.2.4

[14] P. J. Duffett-Smith and J. P. Brice. Positioning systems and methods. US

Patent Number 6,937,866, 30th August 2005. 1.2.4

[15] C. Drane, P. J. Duffett-Smith, S. Hern, and J. P. Brice. Mobile positioning

using E-OTD without LMUs. proceedings of AeroSense 2003, SPIE’s 17th

Annual International Symposium on Aerospace/Defence Sensing, Simulation

and Controls, 2003. 1.2.4

[16] Duffett-Smith P. J. and B. Tarlow. E-GPS: indoor mobile phone positioning

on GSM and W-CDMA. Proceedings of the ION GNSS 2005, Long Beach,

September 2005. 1.2.5, 4.2.1

[17] N. Blaunstein and J. B. Andersen. Multipath phenomena in cellular networks.

Artech House, 2002. 1.3, 1.4

[18] S. R. Saunders. Antennas and Propagation for Wirelss Communication Sys-

tems. Wiley, 1999. 1.4, A.3, A.3

[19] J. Borkowski and J. Lempiainen. Geometrical transformations as an efficient

mean for reducing impact of multipath propagation on positioning accuracy.

194

BIBLIOGRAPHY

Proceedings of the IEE International Conference on 3G Mobile Communica-

tion Technologies, pages 368–372, October 2004. 1.4

[20] T. Rautiainen, G. Wolfle, and R. Hoppe. Verifying path loss and delay spread

predictions of a 3d ray tracing propagation model in urban environment.

Vehicular Technology Conference, 2002, IEEE VTC 56th, 4:2470–2474, 2004.

1.4

[21] M. J. Mughal, A. M. Street, and C. C. Constantinou. Detailed radio imaging

of buildings at 2.4 GHz. Vehicular Technology Conference, 2000, IEEE VTC

52nd, 1:57–63, 2000. 1.4

[22] G. Wolfle, R. Hoppe, D. Zimmerman, and Landstorfer F. Enhanced local-

ization technique within urban and indoor environments based on accurate

and fast propagation models. European Wireless, 2002. 1.4

[23] A. R. Thompson, J. M. Moran, and G. W. Swenson, Jr. Interferometry and

Synthesis in Radio Astronomy. Wiley, 1986. 2.1, 2.1, 2.2, 2.11

[24] D. W Allan. Statistics of atomic frequency standards. Proceedings of the

IEEE, 54:221–230, 1966. 2.1

[25] P. Lesage and C. Audoin. Characterization and measurement of time and

frequency stability. Radio Sci., 14:521–539, 1979. 2.1

[26] J. A. Barnes. Atomic time keeping and the statistics of precision signal

generators. Proc. IEEE, 54:207–219, 1966. 2.1

[27] D. W. Allan, N. Ashby, and C. C. Hodge. The science of timekeeping.

Hewlett Packard Application Note 1289. 2.1, 2.1

[28] R. F. C. Vessot. Frequency and time standards. Methods of Experimental

Physics, 12C:198–227, 1976. 2.1, 2.1

195

BIBLIOGRAPHY

[29] N. F. Ramsey. The Atomic Hydrogen Maser. Metrologia, 1:7–15, 1965. 2.4,

2.1, 2.3.3

[30] Clairon et al. The LPTF Preliminary Accuracy Evaluation of Cesium Foun-

tain Frequency Standard. Proceedings of Tenth European Frequency and

Time Forum, 1:218–223, 1996. 2.4, 2.1, 2.3.4

[31] D. Boiron, A. Michaud, P. Lemonde, and Y. Castin. Laser cooling of Cesium

atoms in gray optical molasses down to 1.1µk. Phys. Rev. A., 53:R3734–

R3737, 1996. 2.4, 2.1

[32] A. Di Stephano, D. Wilkowski, J. H. Muller, and E. Arimondo. Five-beam

magneto-optical trap and optical molasses. Applied Physics. B, Lasers and

optics, 69:263–268, 1999. 2.4, 2.1

[33] S. A. Diddams, Th. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger,

L. Hollberg, W. M. Itano, W. D. Lee, and C. W. Oates. An Optical Clock

based on a single trapped 199Hg+ ion. Science, 293:825–828, 2001. 2.4, 2.1,

2.3.5

[34] M. Takamoto, F. Hong, R. Higashi, and H. Katori. An optical lattice clock.

Nature, 435:321–324, 2005. 2.4, 2.1, 2.3.5

[35] S. T. Cundiff and J. Ye. Colloquium: Femtosecond optical frequency combs.

Rev. Mod. Phys., 75:325–342, 2003. 2.4, 2.1, 2.3.5

[36] E. Beehler, R., R. C. Mockler, and J. M. Rischardson. Cesium Beam Atomic

Time and Frequency Standards. Metrologia, 1:114–131, 1965. 2.1, 2.3.2

[37] K. C. A. Smith and R. E. Alley. Electrical Circuits. Cambridge University

Press, 1992. 2.2

[38] D. Biddulph. Radio Communication Handbook. Radio Society of Great

Britain, 1994. 2.2

196

BIBLIOGRAPHY

[39] J. C. Brice. Crystals for quartz resonators. Rev. Mod. Phys., 57:105–146,

1985. 2.2.1

[40] J. R. Vig. Introduction to Quartz Frequency Standards. Army Research

Laboratory EPSD, SLCETTR921, 1992. 2.10

[41] E. Frerking, M. Crystal oscillator design and temperate compensation. Van

Norstrand Reinhold, New York, 1978. 2.2.2

[42] OCXOs Oven Controlled Crystal Oscillators. Vectron International Appli-

cation Note. 2.2.3

[43] M. Bloch, M. Myers, and J. Ho. The microcomputer compensated crystal

oscillator (MCXO). Proceedings of the 43rd Annual Symposium on Frequency

Control, pages 16–19, 1989. 2.2.4

[44] B. H. Bransden and C. J. Jochain. Physics of Atoms and Molecules. Prentice

Hall, 1996. 2.3.1, 2.3.1

[45] P. Zeeman. On the influence of magnetism on the nature of light emitted by

a substance. Philosophical Magazine, 43:226, 1897. 2.3.1

[46] C. Audoin and J. Vanier. Atomic frequency standards and clocks. Journal

of Physics E: Scientific Instruments, 9:697–720, 1979. 2.3.1

[47] A. Kastler. Quelques questions concernant la production optique du inegalite

du population des niveaux qualification spatiale des atoms. Application a

l’experience de Stern et Gerlach et a la resonance magnetique. J. Phys.

Radium (France), 11:255–265, 1950. 2.3.1

[48] P. L. Bender, E. C. Beaty, and A. R. Chi. Optical detection of narrow Rb87

hyperfine absorption lines. Phys. Rev., 1:311, 1958. 2.3.1

[49] P. Davidovits and R. Novick. The optically-pumped Rubidium maser. Proc.

IEEE, 54:155, 1966. 2.3.1

197

BIBLIOGRAPHY

[50] R. H. Dicke. The effect of collisions upon the Doppler width of spectral lines.

Phys. Rev., 89:472, 1953. 2.3.1

[51] P. Forman. Alfred Lande and the anomalous Zeeman effect, 1919-1921.

Historical Studies in the Physical Sciences, 2:153–261, 1970. 2.3.1

[52] 13th General Conference of Weights and Measures. CGPM [Conference Gen-

erale des Poids et Mesures] Resolution 1). 2.3.2

[53] N. F. Ramsey. Molecular Beams. Oxford: Clarendon, 1956. 2.3.2

[54] http://www.quartzlock.com/resources/ANQL1 02.pdf. 2.3.3

[55] IFR 2319E data sheet. www.aeroflex.com. 3.2.1

[56] C. E. Shannon. Communication in the presence of noise. Proc. Institute of

Radio Engineers, 37:10–21, 1949. 3.2.1, 3.3.1

[57] Electromagnetic compatibility aspects of radio-based mobile telecommuni-

cations systems, appendix D. Link Collaborative Research, 1999. 3.8

[58] M. Bapat, D. Levenglick, and O. Dahan. GSM Channel Equalization, De-

coding, and SOVA on the MSC8126 Viterbi Coprocessor (VCOP). Freescale

Semiconductor Application Note, AN2943, 2005. 3.8

[59] Aeroflex. Racal instruments wireless solutions. Cellular Parametric Test.

4.1.1

[60] European Telecommunications Standards Institute. GSM 05.10. 4.2

[61] N. Born and E. Wolf. Principles of Optics. Cambridge University Press,

1999. 5.2.1

[62] SiRFstarIII specifications. www.sirf.com. 7.2.1

[63] R. B. Langley. Dilution of Precision. GPS World, pages 52–59, May 1999.

7.2.2

198

BIBLIOGRAPHY

[64] C. Rizos. Principles and Practice of GPS Surveying. SNAP Australia, 1999.

7.2.2

[65] H. Tijms. Understanding Probability: Chance Rules in Everyday Life. Cam-

bridge University Press, 2004. 7.5, A

[66] E. C. Fieller. The Distribution of the Index in a Normal Bivariate Population.

Biometrika, 24:428–440, 1932. 7.5

[67] M. L. Boas. Mathematical Methods in the Physical Sciences. John Wiley

and sons, 1983. 7.5

[68] Duffett-Smith P. J. and Macnaughtan M. D. Precise UE positioning in

UMTS using cumulative virtual blanking. Third International Conference

on 3G Mobile Communication Technologies, pages 355–359, May 2002. 8.6

[69] J. M. Latapyc. GSM mobile station locating. Master’s thesis, Norwegian

University of Science and Technology, 1996. A.3

[70] V. Degli-Esposti. A diffuse scattering model for urban propagation predic-

tion. IEEE Transactions on Antennas and Propagation, 49:1111–1113, July

2001. A.3

[71] V. Degli-Esposti. Measurement and modelling of scattering from building

walls. 14th IST Mobile and Wireless Communications Summit, 2005. A.3

199

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