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 qualification 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 opportunity 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 decoding 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 support 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.
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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 radio positioning systems using the GSM network are examined. Two experimental methods for accurately measuring signal arrival times are described - the interferometric technique and the network-synchronised technique. An experimental apparatus capable of performing measurements on the GSM network to a resolution 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 networks 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 environments 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 Sp´eciale Mobile
ILS.
Instrument Landing System.
LORAN.
LOng RAnge Navigation.
LOS.
Line Of Sight.
MCXO.
Microprocessor Controlled Crystal Oscillator.
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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.
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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
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
2.3
3 Time of flight measurements on cellular networks 3.1
55
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
3.1.1
Interferometric method . . . . . . . . . . . . . . . . . . . .
55
3.1.2
Network-synchronised method . . . . . . . . . . . . . . . .
56
The Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
3.2.1
Radio frequency digitiser . . . . . . . . . . . . . . . . . . .
59
3.2.2
Triggering and synchronisation . . . . . . . . . . . . . . .
59
3.2.3
Uninterruptible power supplies . . . . . . . . . . . . . . . .
60
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
Anatomy of a GSM signal . . . . . . . . . . . . . . . . . . . . . .
68
3.4.1
. . . . . . . . . . . . . . . . . . . .
71
3.5
Anatomy of a CDMA signal . . . . . . . . . . . . . . . . . . . . .
72
3.6
The Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
3.6.1
Preparation . . . . . . . . . . . . . . . . . . . . . . . . . .
73
3.6.2
Surveying . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
3.2
3.3
3.4
GSM digital encoding
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CONTENTS
3.6.3
Post-processing . . . . . . . . . . . . . . . . . . . . . . . .
4 GSM Network Stability 4.1
4.2
4.3
74 85
Method and apparatus . . . . . . . . . . . . . . . . . . . . . . . .
85
4.1.1
Calibration . . . . . . . . . . . . . . . . . . . . . . . . . .
87
Results and discussion . . . . . . . . . . . . . . . . . . . . . . . .
88
4.2.1
900 MHz Network . . . . . . . . . . . . . . . . . . . . . . .
93
4.2.2
1800 MHz Network . . . . . . . . . . . . . . . . . . . . . .
98
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
5.3
Spatial and temporal variations . . . . . . . . . . 120
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6 Modelling the effects of indoor multipath environments on tim127 ing stability 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 radiolocation using the GSM network 147 7.1
Definitions of environment . . . . . . . . . . . . . . . . . . . . . . 148
7.2
Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
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CONTENTS
7.3
7.2.1
GPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
7.2.2
GPS accuracy and errors . . . . . . . . . . . . . . . . . . . 150
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 7.3.1
7.4
Error analysis . . . . . . . . . . . . . . . . . . . . . . . . . 159
Modelling the timing error distributions . . . . . . . . . . . . . . 161 7.5.1
7.6
. . . . . . . . . . . . . . . . . . 155
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 7.4.1
7.5
Indoor mapping accuracy
Fitting the free parameters . . . . . . . . . . . . . . . . . . 166
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 environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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. . . . . .
1.2
Sketch showing the hyperbolic geometry involved with the TDOA positioning method. . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3
2
5
Plot showing the variation in candidate locations for a GPS receiver position using the weak-signal method as the satellites move through their orbits. . . . . . . . . . . . . . . . . . . . . . . . . .
1.4
Plot showing the cross-correlation function resulting from searching a frequency range for a given PN code . . . . . . . . . . . . .
1.5
10
15
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6
Plot showing the transfer of energy in a tank circuit during its oscillatory cycles. . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7
33
33
Plot showing nomalised resonance curves for oscillators with different Q values. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xv
35
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 . . . . . . . . . . . . . . . . . . . . . .
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
crystal oscillator systems.
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 Rubidium 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 . . . . . . . . .
3.9
77
A description of the GSM modulation and encoding techniques, and the BSIC and frame number decoding process (continued) . .
78
3.10 A description of the GSM modulation and encoding techniques, and the BSIC and frame number decoding process (continued) . .
79
3.11 A description of the GSM modulation and encoding techniques, and the BSIC and frame number decoding process (continued) . .
80
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 4.1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A picture showing the antenna above the roof of the Cavendish Laboratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2
89
Plots showing the variation in relative signal arrival times from a GSM base station broadcasting in the 900 MHz waveband. . . . .
4.5
88
Plot showing the Allan deviation curves produced by an internallyand externally-locked Racal GSM signal generator. . . . . . . . .
4.4
86
Sketch showing the experimental setup used to produce the calibration Allan Deviation curves . . . . . . . . . . . . . . . . . . . .
4.3
83
90
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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.9
94
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 Laboratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.7
Plot showing multipath behaviour recorded inside the Roof Laboratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.8
Plot showing multipath behaviour recorded inside the Roof Laboratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.9
Sketch demonstrating how sharp spikes in timing error can be produced 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 Rutherford 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 experiment with random phases on reception. . . . . . . . . . . . . . . . 136
6.7
Plot showing a simulation of the Electronics Laboratory experiment with random amplitudes on reception. . . . . . . . . . . . . 137
6.8
Plot showing a simulation of the Electronics Laboratory experiment 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 simulated 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-ofphase 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 unobstructed signal) for two propagation mechanisms. . . . . . . . . . 190 A.6 Plots showing the correlation between S1 and S2 for the four potential 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 AOA method measures the angular separation between pairs of sources, or between a source and 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 to the receiver. Each measurement defines a circle around the source which intersects the receiver’s position. Three sources can provide a unique two-dimensional position. The signal strength method also defines circles around each source which must intersect with the receiver, and so three sources are also required for a unique solution using this technique.
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 described 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.
1.1
Local radio positioning
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
1. INTRODUCTION TO RADIO POSITIONING
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 frequencies 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 difference compared to the reference. The navigation signal is broadcast by a directional 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 measure 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. Radio 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 region 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 incorporated 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 second slave broadcasted a single pulse 1 millisecond after it received the master’s
4
1.1 Local radio positioning
Figure 1.2: Sketch showing the hyperbolic geometry involved with the TDOA positioning method. The difference in arrival times of the signals received from synchronised transmitters define hyperbolic surfaces in space upon which the receiver must lie. Three signal 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 metres 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 perpendicular to this direction. Although poor by modern standards, the precision 1
For a discussion of how source geometry affects positioning accuracy see the description of dilution of precision in Section 7.2.2 of Chapter 7.
5
1. INTRODUCTION TO RADIO POSITIONING
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 transmitters 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 accuracy 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 transmitter 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 operational 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 timing 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 orbital 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
1.1 Local radio positioning
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 information 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
1. INTRODUCTION TO RADIO POSITIONING
The relative position of the receiver to a given satellite is described by the equation p (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 coordinates 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 simultaneous 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 relativemeasurement 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.
1.2
Cell-phone positioning
Many local radio positioning systems require a network of transmitters, a positioning technique, and a user with an appropriate receiver. Cell phones have
9
1. INTRODUCTION TO RADIO POSITIONING
Figure 1.3: Plot showing the variation in candidate locations for a GPS receiver position using the weak-signal method as the satellites move through their orbits. The green markers represent an initial set of candidate locations, the red markers represent the set of candidate locations a few tens of seconds later as the satellites have moved through their orbits. As time passes, only one candidate location will be common to all sets for a stationary receiver, and this gives the receiver’s position.
become very popular portable radio receivers, with an estimated 2.5 billion handsets 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 system 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 Cell-phone positioning
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 handset, 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 maximum 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 technique 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 Advance (TA) value when determining a cell phone’s position [7]. Since electromagnetic 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
1. INTRODUCTION TO RADIO POSITIONING
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 directional 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
1.2 Cell-phone positioning
with previously recorded data [11]. However, the signal strength at a given location 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 positioning, however, the TDOA technique relies on synchronised base station transmissions, 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) distributed 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 techniques (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 | + i + αj ,
13
(1.2)
1. INTRODUCTION TO RADIO POSITIONING
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 j th BTS. The value of tij represents the arrival time of the timing marker from the j th BTS at the ith receiver. The 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, 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 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
1.2 Cell-phone positioning
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 frequency range for a given PN code. Estimates of the frequency and of the position of the PN code within the received signal allow this search window to be reduced. This reduces the time required to find the correct frequency and the exact position of the cross-correlation peak
The receiver attempts to acquire the signal in time by determining the current 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 1
These long integration times are required since the satellite signals are weak by design to increase security
15
1. INTRODUCTION TO RADIO POSITIONING
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 coherent 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 risking ‘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 frequency 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 depending 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
1.2 Cell-phone positioning
Figure 1.5: Sketch demonstrating the benefit of having accurate estimates of the positions of the PN codes in the received satellite broadcasts. With no knowledge of the location of the spreading code, a cross-correlation over all possible code-phase offsets is needed (as shown in the picture marked (a) above). If the position of the PN code is known 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. INTRODUCTION TO RADIO POSITIONING
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 framenumber 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. 1
See Chapter 2 for a discussion of the meaning of “clock stability”.
19
1. INTRODUCTION TO RADIO POSITIONING
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 cellphone 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 narrowband 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 apparatus 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
1. INTRODUCTION TO RADIO POSITIONING
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 timing stability This chapter presents the results of a series of experiments which measured the degradation of the apparent temporal stability of received signals on the GSM network caused by moving a receiver slowly over sub-wavelength distances indoors. 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 This chapter presents the results of a series of experiments which measured the 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 multipath 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 measured 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 0 t + ω 00 t2 + ...
(2.1)
where ω0 is the frequency at t = 0, ω 0 is the first-order frequency variation with time, ω 00 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 0 . The higher order terms are not usually named. The instantaneous frequency error is given by ∆ω(t) = ω0 − ωn + ω 0 t + ω 00 t2 + ...
2.1
(2.2)
Allan Variance
The stability of a test oscillator can be determined by analysing its phase fluctuations when compared to a reference oscillator [23]. A perfect oscillator would produce a pure sine wave, V (t) = V0 cos (2πf0 t) ,
(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 [2πf0 t + φ (t)] ,
24
(2.4)
2.1 Allan Variance
Figure 2.1: Sketch showing the types of error on the output signal from a frequency reference (reproduced from Thompson, Moran and Swenson [23]). For an oscillator designed to operate at a frequency f0 , there may be some bias-rate error, leading to variation of the actual output frequency with time (the green line). This variation with time is dependent on the stability of the oscillator. The oscillator may also suffer a bias error, such that its mean frequency is displaced from the intended value (fb rather than f0 ). When the output signal is sampled and used as a timing reference there is also a quantisation error associating with the sampling period tmin , which defines the resolution 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)
1 dφ (t) . 2π dt
(2.6)
where δf (t) =
The fractional frequency deviation at a given instant can then be defined as y (t) =
δf (t) 1 dφ = . f0 2πf0 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 Z 1 tk +τ y¯k = y (t) dt. (2.8) τ tk Combining this with equation 2.7 gives y¯k =
φ (tk + τ ) − φ (tk ) . 2πf0 τ
(2.9)
Measurements of y¯k 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 y¯k given by
σy2 (N, T, τ ) =
1 N −1
* N X n=1
N 1 X y¯n − y¯k N k=1
!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 phenomenon 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 (¯ yk+1 − y¯k )2 = , 2
σA2 (τ )
(2.11)
or from equation 2.9,
σA2 (τ ) =
[φ (t + 2τ ) − 2φ (t + τ ) + φ (t)]2 8 (πf0 τ )2
26
.
(2.12)
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 σ ˆA2 (τ )
M −2 X 1 [φ (tk+2 ) − 2φ (tk+1 ) + φ (tk )]2 = . 2(M − 1) k=1 (2πτ f0 )2
(2.13)
The accuracy of this estimate [25] is K σ (ˆ σA ) ≈ √ σA , M
(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 average of all of the values of (δφ) 2 , where δφ is the deviation of a given phase sample from the 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, 2 2 σy2 = σy1 + σy2 .
27
(2.15)
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 2 2 (such that σy1 σy2 ), 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 2 2 be used for the reference (σy1 ≈ σy2 ), 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 2 2 are given by σij2 , σjk and σik where the individual variances are σi2 , σj2 and σk2 . Each
individual variance can then be calculated using the following set of equations [26], σi2 =
1 2 2 2 σij + σik − σjk , 2
(2.16)
σj2 =
1 2 2 σjk + σij2 − σik , 2
(2.17)
σk2 =
1 2 2 σjk + σik − σij2 . 2
(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 conventional in the literature than Allan variance plots. Allan deviation plots often exhibit behaviour which can be categorised into four r´egimes as shown in Figure 2.3 below. These r´egimes 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 randomwalk-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 proportional 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 reference. This process dominates at short time periods. For time periods inside this r´egime 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 processes in transistor junctions. For time periods inside this r´egime, 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 thermal noise within its resonance cavity. The oscillator cannot be considered to be perfectly controlled in this r´egime 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. Over short time periods, the plot exhibits a slope of −1 (region 1). The standard deviation of the frequency variation is constant for all time periods in this r´egime and is determined by the level of white noise in the signal. The stability of the oscillator in this r´egime is dominated by this noise (as shown by the cutout labelled A), with less noise resulting in a lower Allan deviation for a given time period. Over longer time periods the Allan deviation decreases at a slower rate (region 2) and can become roughly constant (region 3). Over these time scales the variation in the oscillator’s output frequency is dominated 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 “physics package” and electronic components used to produce the oscillating signal. For longer time periods the Allan deviation typically increases with period length (region 4). This is where the frequency-drift-rate error of the oscillator executes a random walk. The oscillator is uncontrolled and its frequency is influenced by long-term environmental variations such as changes in temperature, magnetic fields, pressure, etc (cutout C in the sketch).
30
2.1 Allan Variance
changes such as temperature, pressure and magnetic field variations. This behaviour 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 represents the range of stabilities of crystal oscillators. Rb represents Rubidium oscillators; Cs B represents Caesium beams; H represents Hydrogen masers [29]; Cs F represents the approximate stability of Caesium Fountains [30, 31, 32]; and Opt represents the estimated 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 Quartz [27] Rubidium [27] Caesium Beam [36] Hydrogen Maser [29] Caesium Fountain [30, 31, 32] Optical (proposed) [33, 34, 35]
τ = 1 second 10−6 –10−13 10−11 10−12 10−13 10−12 ∼ 10−15
τ = 1 day 10−6 –10−11 10−12 –10−13 10−13 –10−14 10−14 –10−15 10−15 ∼ 10−17
τ = 1 month 10−5 –10−11 10−11 –10−12 10−13 –10−15 10−13 –10−15 10−16 ∼ 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 oscillatory cycles.
This process continues in an oscillatory cycle with a frequency of r 1 ω= . LC
(2.19)
When a capacitor and inductor are connected in series with an oscillating voltage, 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 magnitude 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 dependant 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 capacitance 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 =
1 ) iωC1
and inductor (ZL1 = iωL1 ) are equal in magnitude
34
2.2 Oscillators
Q = 300 Q = 98,000
1
0.8
0.6
normalised response 0.4
0.2
0 6.98
6.985
6.99
6.995
7
7.005
7.01
frequency (Hz)
7.015
7.02
7.025
7.03 6
x 10
Figure 2.7: Plot showing normalised resonance curves for the two oscillators described in Table 2.2 below. The blue curve represents a system with a low Q value of 300 built from electronic components. The green curve shows the response for a crystal oscillator 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 ). L1 C1
The result is a sharp
minimum in the impedance of the series section, with the magnitude of this minimum dependant on the value of R1 . Alternatively, the circuit can resonate in parallel when ω =
√ 1 L1 C0
(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 components in the oscillator circuits. Long-term stability is limited by the environmental factors and any changes in the stiffness of the crystal caused by impurities,
36
2.2 Oscillators
Parameter L1 C1 R1 Q
7 MHz crystal 7 MHz LC 42.5 mH 12.9 µH 0.0122 pF 40 pF 19 Ω 0.19 Ω 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 variation has a large effect on the stability of crystal oscillators and there are several XO-based devices designed to reduce this problem. The most common are temperature-compensated crystal oscillators (TCXO), oven-controlled crystal oscillators (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 crystal oscillator 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 .
2.3
Atomic oscillators
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, Caesium 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 distribution 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. Furthermore, 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 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 5s. 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 52 S1/2 [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 =
1 2
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 =
1 2
and so the only possible value of J is
1 . 2
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+ 21 | =
40
3 2
or J = |1− 21 | = 12 .
2.3 Atomic oscillators
These correspond to the first two excited states of Rubidium and are denoted by 52 P3/2 and 52 P1/2 . 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 =
3 2
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 (52 S1/2 ) 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 87
Rb 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 52 P1/2 → 52 S1/2 transition propagate along the magnetic axis then each photon carries an angular momentum of −~ and so only the 52 S1/2 (F = 1) → 52 P1/2 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 52 S1/2 (F = 1) state is excited by the σ − photons, the set of atoms are all pumped into the 52 S1/2 (F = 2) state.
Figure 2.11: Schematic diagram of a Rubidium frequency standard (a) reproduced from Thompson, Moran and Swenson [23]. The energy levels of the 52 P1/2 excited state and 52 S1/2 ground state involved in the process are shown in (b). The energy levels of the ground states can be split further by an applied magnetic field (Zeeman effect, (c)) and so the cell must be magnetically shielded. The filtered light is strongly absorbed by the gas in the microwave cavity when it is emitting photons at the ground state hyperfine transition frequency (d).
42
2.3 Atomic oscillators
The frequency of a Rubidium oscillator is controlled by the following mechanism. A heated cell containing
87
Rb vapour is subjected to an RF plasma
discharge which promotes the atoms to the 52 P1/2 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 85 Rb vapour, whose energy levels are slightly different from those of
Rb. The photons from the F = 2
87
Rb transition are absorbed by the
87
Rb transition are not. This filtered light is then used in another cell inside a
microwave cavity to drive a set of
85
87
87
Rb gas, but the photons from the F = 1
Rb atoms into the F = 2 52 S1/2 state via
optical pumping. The microwave cavity is resonant at the transition frequency between the F = 2 and F = 1 52 S1/2 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
87
Rb 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 87
Rb is therefore used as the reference to control the OCXO. The microwave cavity contains a buffer gas of inert atoms as well as the
87
Rb
atoms. This has two purposes: (i) If the buffer gas were not present, then collisions between the
87
Rb 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 Caesium 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 inhomogeneous magnetic fields to filter atoms of the required electronic state instead of using optical pumping. The ground electronic state of 133 Cs 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 higherenergy 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
2.3 Atomic oscillators
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 reference 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 selfsustaining 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 selfsustained stimulated emission. Active Hydrogen masers provide very stable frequencies 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 oscillators by up to a factor of 100, with typical Allan deviations of about 2 × 10−15 [54].
46
2.3 Atomic oscillators
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 radiation 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 transitions are also often ‘forbidden’ transitions, so are weak.
2.4
Measurements with two Rb frequency standards
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 ˙ + higher order terms, φ(t) = φ0 + φt
(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 difference 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 an FRK-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 measured using a Hewlett-Packard HP497B digital vector voltmeter over a number of days. The entire experiment was repeated four times, with one experiment lasting 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 oscillators 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 oscillator and for an OCXO. 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 about 25,000 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 10,000 measurements. The three FRK plots generated using a digital vector voltmeter are similar, but the differences between them at long time periods suggests that even a two-week sample is not entirely representative of the typical behaviour of an oscillator in a stable environment. The FRK plot generated using an analogue vector voltmeter (the green line) exhibits a lower stability over the first 2000 seconds than the tests using a digital voltmeter, but this is caused by the increased measurement noise associated with the analogue voltmeter and is not a feature of the FRK-H. Over the longest time periods the RbO is about 1000 times more stable than the OCXO.
52
2.6 Conclusions
30 2005 test 2007 test (i) 2007 test (ii) 2007 test (ii)
25
20
15
phase 10 difference (wavelengths) 5
0
−5
−10
−15
0
2
4
6
8
time (seconds)
10
12
14 5
x 10
Figure 2.16: The phase differences between the 10MHz outputs of two Rubidium oscillators in four experiments. The variation in the plots demonstrates that even a two week 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 CELLULAR NETWORKS
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 crosscorrelation 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 commonmode 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 crosscorrelating 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 apparatus, (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 accordingly. 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 experiment. 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 experiments was performed to test the viability of the network-synchronised approach (see Chapter 4 below). For base stations with highly-stable and consistent signals, 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 dominated by the level of measurement noise in the system over periods of a few hours
57
3. TIME OF FLIGHT MEASUREMENTS ON CELLULAR NETWORKS
or less. This noise affects the accuracy of the measurements, including the calibration 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 flight times. Accurate synchronisation was a vital part of the experimental process, and this was achieved by using a timer driven by a Rubidium frequency standard (Rb) to trigger the digitiser’s (Rx) recording process, rather than triggering the digitiser via software commands. The digitiser was controlled by the laptop via a General Purpose Interface Bus (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 software 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 described in more detail below. One set of apparatus was required for the networksynchronised approach, and two sets were required for the interferometric approach.
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
3. TIME OF FLIGHT MEASUREMENTS ON CELLULAR NETWORKS
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 networksynchronised 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
3.3 Data storage and analysis
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 stabilities 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 resulting 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 dedicated 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 pictorially 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
3. TIME OF FLIGHT MEASUREMENTS ON CELLULAR NETWORKS
(ii) Errors on the sample times (jitter) resulted in samples being recorded at incorrect 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 sampled. 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 negligible). 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 position 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
3.3 Data storage and analysis
Figure 3.2: This sample of data is taken from a frequency control burst (FCB) recorded at a base station. The FCB is a single frequency broadcast, which allows a mobile handset to correct its frequency reference to match that of the base station. The signal to noise ratio is roughly 20:1, or 26 dB, and provides a lower bound on the amount of receiver 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
3. TIME OF FLIGHT MEASUREMENTS ON CELLULAR NETWORKS
Figure 3.3: This diagram demonstrates the use of Fourier theory to fully reconstruct a complete cross-correlation pattern from the cross correlation of two suitably sampled data sets. Sampling a wave function corresponds to convolving its Fourier transform with 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 original function’s Fourier transform, and this corresponds to convolving the sampled data in real space with a suitably scaled sinc function.
64
3.3 Data storage and analysis
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 milliseconds (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 triggering period used for the network synchronised method needed to be a multiple of the multiframe repeat period of
3.06 13
seconds (see Section 3.4 below).
The digitiser captured a preprogrammed number of samples each time it received 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 dataset. The times of each recording were stored on the laptop via a readout from the counter.
65
3. TIME OF FLIGHT MEASUREMENTS ON CELLULAR NETWORKS
3.3.3
Cross correlation
The analogue cross-correlation operation between two continuous functions f and g is defined as Z
∞
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)] 3.3.3.1
(3.2)
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 crosscorrelation 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-shiftedmultipath signal. The ambiguity function is a two-dimensional function of time delay and Doppler frequency and is given by Z ∞ χ(τ, f ) = s(t)s∗ (t − τ )e−i2πf t dt.
(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
3.3 Data storage and analysis
Figure 3.4: The ETS ambiguity function. The Doppler shifts associated with the typical velocities encountered during these experiments (movements of vehicles within cities, pedestrians, tree branches, etc) are much lower than the width of the central peak of the ambiguity function in the frequency domain. The effect of Doppler shifts on the multipath 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 Dopplershifted ETS within the received signal would result in a central null in the crosscorrelation 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
3. TIME OF FLIGHT MEASUREMENTS ON CELLULAR NETWORKS
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
13,000,000 48
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 transmissions 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 information 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
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3.4 Anatomy of a GSM signal
Figure 3.5: The format of GSM data broadcasts is shown above. Up to 8 logical channels can share a single radio frequency channel by each being allocated a burst within 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 to provide coarse filtering of multipath effects and allow optimum detection of the data bits transmitted on either side of it.
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Figure 3.6: The formats of GSM bursts are shown above. Normal bursts are used to transmit data packets. Frequency correction bursts are used by the handset to synchronise the frequency of its internal oscillator with that of the BTS and so correct for any drifts or Doppler shifts. Synchronisation bursts are used by the handset to coordinate the transmissions and receptions of its normal bursts. Access bursts are transmitted by the handsets when they are requesting channels to broadcast and receive data bursts on (i.e. when the user is trying to make a call).
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3.4 Anatomy of a GSM signal
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 ± 12 bit. 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). 1
See the discussion of timing advance in Section 1.2.1 of Chapter 1
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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
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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 apparatus 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 uninterruptible 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
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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 frequencies 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 sample 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
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3.6 The Experiments
Figure 3.7: Flowchart describing how the raw data was processed to generate a list of cross-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
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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 synchronisation 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 representative 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 technique 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, corresponding to a spatial resolution of 147 metres. The original signal was reconstructed
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Figure 3.8: A description of the GSM modulation and encoding techniques, and the BSIC and frame number decoding process [57, 58].
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Figure 3.9: A description of the GSM modulation and encoding techniques, and the BSIC and frame number decoding process (continued).
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3.6 The Experiments
Figure 3.10: A description of the GSM modulation and encoding techniques, and the BSIC and frame number decoding process (continued).
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Figure 3.11: A description of the GSM modulation and encoding techniques, and the BSIC and frame number decoding process (continued).
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3.6 The Experiments
from these samples, then resampled at 40.8 MHz, providing a new timing resolution 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, relative 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 discussed 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.
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11
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Figure 3.12: A plot of the cross correlation of one million samples recorded at 2.04 MHz from a base station’s control channel using the interferometric method. The profile contains 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 structures in GSM broadcasts, such as TDMA frame tail bits and short training sequences (see section 3.4 above).
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An example cross correlation profile generated using the network−synchronised method
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Figure 3.13: A plot of one million samples recorded at 2.04 MHz from a base station’s control channel cross correlated with the GSM ETS using the network-synchronised method. The profile (a) contains ten strong peaks, each marking the position of a synchronisation burst in the transmission. Each frame containing an SCB is preceeded by a frame containing a frequency control burst (seen here as the small gaps to the left of each SCB peak in (b)). The fine-scale subsidiary peaks are caused by correlations between the ETS and the short training sequence within each normal burst.
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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 variations 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 antenna positioned 10 metres above the above the roof of the Cavendish Laboratory
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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 Yagi antenna mounted on a pole roughly 10 metres above the roof and roughly 25 metres above the 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, calculated as follows. The GSM bit rate is
13,000,000 48
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 ( 48×1250×51×13 ) and this is also the smallest multiple used when recording data 13,000,000 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 restrictions 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,
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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 generated 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 FRKH used as the reference in the measurement apparatus and therefore represents
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Figure 4.2: Sketch showing the experimental setup used to produce the calibration Allan deviation curves. The Racal GSM signal generator was initially phase locked to an 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 internal OCXO (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-
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4.2 Results and discussion
Figure 4.3: Plot showing the Allan deviation curves produced by an internally- and externally-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 Figure 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 microseconds 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
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(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 stationary outdoor receiver from a GSM base station broadcasting in the 900 MHz waveband.
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4.2 Results and discussion
(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 outdoor receiver from a GSM base station broadcasting in the 1800 MHz waveband.
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0.018
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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 accuracy (corresponding to the bias error discussed in Chapter 2) of 5 × 10−8 . The most common method of maintaining this accuracy involves using the communications backbone to compare the frequency reference at the BTS to a stable central reference which may be trained by GPS. Different manufacturers use different 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
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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
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4.2 Results and discussion
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 studied and the Cavendish Laboratory. The Laboratory is marked with a blue circle, the base stations on Network 1 are marked with a red triangle, and the base stations on Network 2 are marked with a yellow triangle.
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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 however 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 deviation 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
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(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 MHz GSM base station represented by Curve ‘C’ in Figure 4.8. The Allan deviation plot generated using data gathered at the base station is similar to the plot generated using data gathered at the Cavendish Laboratory over 8 kilometres away (b).
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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-
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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 processes 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
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Figure 4.12: Plot comparing the timing errors for three base stations. The blue line represents the timing data from a BTS on Network 1 (curve ‘A’ in Figure 4.8). The pink line represents the timing data from a BTS on Network 2 (curve ‘P’ in Figure 4.11). The frequency reference may be controlled over long time scales or once it has drifted far enough from its nominal frequency, but the shape of curve ‘P’ in Figure 4.11 and the very gradual changes in the drift exhibited above suggest that there are no corrections made over the time scale of this dataset (45 hours). The orange line represents 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 a distinct oscillation. This oscillation may be caused by the BTS’s frequency being overcorrected by the network’s frequency control mechanism each time it drifts a certain amount 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
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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 timing 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 network. 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 signal, 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
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types of base stations on the 1800 MHz network - those controlled by oven controlled 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 provided 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.
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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.
5.1
Method and apparatus
The experimental method for recording and analysing data was the same as described in Chapter 4. A conveyor belt was added to the apparatus to move the antenna smoothly and continuously across the measurement space at speeds ranging 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
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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) multipath 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 anecdotal 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.
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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 scattering 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 r Fn = 1
nλd1 d2 , d1 + d2
The BTS on the 900 MHz network represented by curve ‘A’ in Figure 4.8
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(5.1)
5. THE EFFECTS OF INDOOR MULTIPATH ENVIRONMENTS ON TIMING STABILITY
Figure 5.1: This picture shows the view from the roof of the Rutherford building of the base station used in all of the experiments in this chapter. The base station is highlighted 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 reflection 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 constructive 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
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Figure 5.2: This picture shows the view of the base station from the first position of the antenna during the initial experiment on the roof of the Rutherford building. It is highlighted 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
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Figure 5.3: Diagram showing the first Fresnel zone for a transmitter-receiver separation of 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, lineof-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
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Figure 5.4: Plot showing the data from the roof experiment. The blue line gives the timing error associated with the relative position of the SCB peaks in each measurement and is plotted against the left-hand axis. Each microsecond of timing error corresponds to an error of about 300 metres in the estimated distance of the receiver along a line away from the BTS. The pink line represents the maximum absolute value of each SCB peak and so gives a measure of the signal strength and quality. The pink line is plotted against the right hand vertical axis. The horizontal axis gives the distance from the initial position. Five recordings were taken at each position, then the antenna was moved 2cm toward the base station. The last 5 measurements were recorded back at the initial 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
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4
x 10
2 1.8 1.6
magnitude1.4 of the cross− correlation1.2 value 1 0.8 0.6 0.4 0.2 0 1.7987
1.7987
1.7988
1.7988
1.7989
1.7989
1.799
position in cross correlation function (samples)
1.799 5
x 10
Figure 5.5: Plot showing sample SCB peaks from the roof experiment shown in Figure 5.4 above. In order of peak height (largest first) the SCB peaks correspond to sample numbers 1,24,31,27 and 26. It is clear from this plot that the large position error seen 10 centimetres from the starting position in Figure 5.4 (i.e across samples 26 to 30) is caused by distorted SCB peaks, which are in turn most likely to be caused by multipath interference.
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 Rutherford building. A brick wall with a large glass window separated the antenna from
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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 repeating 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. Measurements 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
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Figure 5.6: This plot shows the data gathered over a 70 cm length in the Roof Laboratory in a non-LOS environment. The antenna moved along a line toward the BTS and parallel to the window. The blue and red lines represent the SCB positions recorded at 10 a.m. and 2 p.m. on the same day along the same line. The cyan and pink lines represent 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
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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
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Figure 5.7: This plot shows the data gathered over a 50 centimetre length in the Roof Laboratory. The antenna was moved along the same line as used in Figure 5.6, and with 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 crosscorrelation 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).
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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 Laboratory. Each measurement path was separated by 5 cm and the corresponding lines in the plot have been artificially offset to allow a clear comparison of the behaviour along and across the paths. The top line in the plot represents the path closest to the Roof Laboratory 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
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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 produced by SCB peaks deformed by multipath interference. As the receiver moves the corrupted SCB peak can consist of two peaks which vary smoothly with receiver position. As one peak becomes higher than the other, a large discontinuity is produced in the timing error plot.
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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 during the night in the Electronics Lab. The noise level corresponds to a timing error of 83 nanoseconds.
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 separated 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 every 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 Electronics Laboratory. Data was recorded along the same line 4 times in succession to check for consistency in the multipath environment over an hour. The 4 coloured lines in the upper part of the figure represent the timing errors of each test and are plotted against the left axis. The line with error bars in the lower part of the figure represents the average SCB peak maximum value at each antenna position and is plotted against the right hand axis. The error bars are given by the standard deviation of the SCB peak maximum 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 Electronics Laboratory. Data was recorded every 6.12 seconds and the antenna moved along each line 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 during a single measurement during an indoor survey. The peaks have all been shifted by an appropriate amount to allow their direct comparison. The solid blue curve represents the earliest measurement in the set, and the grey arrows mark the movement of the peak 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 millimetres 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 demonstrates how the temporal and spatial variations depend on each other. The diagrams are scatter plots of the standard deviations within a given measurement 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 references, 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 multipath 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 error due to temporal (σt ) and spatial (σs ) multipath variations. The upper figure (a) represents the data from Figure 5.15 and lower figure (b represents the data from Figure 5.16.
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Figure 5.15: This plot shows the data gathered along a line using the fast capture machine 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 as an 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 0.04 millimetres per second, with recordings made every 6.12 seconds such that 100 samples on 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 r´egime 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 main corridor of the upper floor of the Rutherford building. The antenna was moved manually in 2 millimetre intervals such that it was stationary during each recording process rather than moving continually on a conveyor belt. Ten consecutive SCB peaks were recorded per position. The mean value at each position is plotted with the standard deviation plotted 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 maximum 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 dominate 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 investigate the temporal stability of the signals received from GSM base stations at a slowly-moving indoor antenna. Three methods of measuring a GSM signal’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).
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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 monochromatic 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 process. 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 before 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 versions 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 raisedcosine 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 established 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 experiments was the first feature considered with the CCPI model. The first mechanism 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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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 amplitude 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 signal 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 observed 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. The angular separation determines the period of oscillation, and the relative amplitudes and path difference both determine the amplitude of the oscillation. Note that a timing error equivalent to more than 300 metres can occur.
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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 from the 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 behaviour observed in the Roof Laboratory experiments. Smooth variations in timing error and large, rapid deviations can both be recreated in the same simulation. The signals from the upper plane all have similar amplitudes (0.7, 0.8, 1) and represent signals scattered from nearby buildings and objects on the roof. The three signals from the lower plane represent 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 random distribution 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 the very rapid and large variations in the timing errors seen in the experiments cannot be recreated with the signal phases determined by the path lengths alone and the amplitudes fixed.
environment than the Roof Laboratory, with a number of people moving around inside the room and surrounding areas. The Electronics Laboratory had no external 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 randomising 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 similar 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 the phases of the signals from each source to be random rather than determined by the path length. This produces rapid variations in the timing errors for small receiver movements, but the variations are not large enough and are too uniform to simulate the structure seen in the Electronics Laboratory experiments.
Figure 6.7 below shows the effect of allowing the signal amplitude to vary randomly 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 consecutive 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 the amplitudes of the signals to be randomly assigned between 0.1 and 1 on reception. This produces behaviour similar to that seen in the Electronics Laboratory experiments, with regions of consistent timing errors next to regions with very large and rapid variation in 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 simulation 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 measurement noise 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 interference and demonstrates the large error associated with this simple method. The bandwidth of a GSM broadcast is about 140 kHz, corresponding to a coherence 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
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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 the SCB peak: (a) finding the maximum absolute value of the SCB peak, (b) finding the position where the SCB peak first exceeds a threshold value, and (c) finding the midpoint of the SCB peak. The upper set of figures demonstrate the three methods applied to an uncorrupted SCB peak. The lower set demonstrate the three methods applied to a corrupted SCB peak (the grey curve represents the peak for the line-of-sight signal, the black curve represents the peak after corruption by multipath interference). The lower set 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 peak distortion.
(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 errors associated with this technique are studied in detail this thesis and can be
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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 threshold 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 measurement 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 compromise 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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Figure 6.10: Plots showing tests of the three signal-arrival techniques using simulated data. The short section of data demonstrates that the midpoint and peak-rise methods are more consistent than the peak-max method, and that the midpoint and peak-max methods correlate strongly except in the case of significantly corrupted SCB peaks. The histogram suggests that the peak-rise technique is the best, although the simulated data is unrealistic near the edges of the SCB peak (see the main text above).
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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 peakmax 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 of (b) Histograms of the timing errors for the data data shown in (a).
(c) Timing errors over a short section of (d) Histograms of the timing errors for the data. data shown in (c).
Figure 6.11: Plots showing tests of the three signal-arrival techniques using two sets of data gathered using an indoor receiver. The peak-rise and midpoint methods display slightly better accuracy than the traditional peak-max position method.
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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 peakrise and midpoint techniques to reduce large timing errors is clear. The peakrise 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 data from the initial roof experiment. The peak method results in a large timing error when the SCB peaks are significantly corrupted (see Figure 5.5). The peak-rise technique reduces this error slightly, and the mid-rise technique can be used to minimise the error.
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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 increasing the bandwidth of the signal, such that the SCB peak narrows. The thirdgeneration 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 variations in the SCB peak positions can be accounted for by a sparse multipath
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environment consisting of a small number of significant signals with similar amplitudes, 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 reasonable 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 position 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 environment. 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 removing, the most extreme errors in a given data set. However, both methods require more intensive computation than the simple peak-position technique.
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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 positioning 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 station’s control channel (see Section in Chapter 3). These distances were then compared to those determined using a GPS device or accurate mapping. Rural, 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’
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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.
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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
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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 errors 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 obstructing 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 measurement 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 metres 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 considering 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 the accuracy of a GPS position. The sketch is shown in two dimensions, but the principle is easily extended to three. The curved pink lines represent the possible position of a receiver that has measured a certain arrival time from a given satellite. The thickness of the lines represents the error on the measurement. The sketch on the left represents a good satellite geometry, with three satellites evenly distributed and well spread out across the measurement plane. The black area highlighting the region intersected by all three signals represents the region of uncertainty in the receiver position. The figure on the right represents a poor signal geometry, with all three sources lying roughly along a line. The intersecting region is much larger for this geometry, leading to a reduction in the 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
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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 position on the Cavendish Laboratory roof at 2 pm and 5 pm over many days and weather conditions. There is no clear correlation between pairs of points measured on the same day.
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 measurement 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
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7. A STUDY OF THE TIMING ERRORS ENCOUNTERED WHEN PERFORMING RADIO-LOCATION USING THE GSM NETWORK
Figure 7.3: Plot showing the use of Pythagoras’ theorem in calculating the distance from 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. The path length L can be calculated using the signal flight time and q the known value of the
speed of the radio waves. The distance D is then given by L2 − (B − h)2 . For the majority of measurements, L B, and so D = L to a good approximation. However the full calculation is required for the calibration measurements at each BTS, and for any 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 calculated 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 intervals 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 determine 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
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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. 1
This value is given by combining the GPS error and the error associated with assuming a linear phase drift between the reference oscillators - see Section 7.4.1 for details
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7.4 Results
The histograms show that the timing error distributions for rural and suburban 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 negative. 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 spacing 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
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Figure 7.5: Diagram showing the floor plan of the indoor environment used in the survey. Shaded areas represent offices, the corridors are white, solid lines represent walls and doors and whereas dashed lines represent windows. Possible signal propagation paths 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 considerably 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 distinct 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 FRKH 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-phasedrift corrections for these experiments. The full value of this error only applied to
159
7. A STUDY OF THE TIMING ERRORS ENCOUNTERED WHEN PERFORMING RADIO-LOCATION USING THE GSM NETWORK
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 error when performing relative measurements over the course of about three hours. The resolution of an SCB peak position after up-sampling was 24.5 nanoseconds, 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 calibration 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
7.5
Modelling the timing error distributions
In attempting to reproduce the timing-error distributions observed for each environment, 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: Z (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: ! Z N N Z X X ∗ ∗ (f ? g)(x) = g(x + t) mi (x) dt = g(x + t)mi (x) dt . i=0
(7.2)
i=0
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 crosscorrelation 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 raisedcosine model, the displacements of the peaks prior to their superposition represents the relative delays of the signals, and their initial relative amplitudes represent both their phase differences and amplitudes (see Figure 7.7).
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7. A STUDY OF THE TIMING ERRORS ENCOUNTERED WHEN PERFORMING RADIO-LOCATION USING THE GSM NETWORK
Figure 7.6: Comparison of the modulus of the GSM ETS auto-correlation peak and a truncated raised-cosine function
The width of the ETS autocorrelation peak is determined by the signal bandwidth, fb Hz, and is approximately equal to
2 fb
seconds. For a GSM channel with
a signal bandwidth of 140 kHz, this corresponds to a width of 14.3 microseconds (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: ( 1 + cos (πfb (z − α0 )) if −1 < (z − α0 ) < fb H(z) = 0 otherwise
1 fb
,
(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
7.5 Modelling the timing error distributions
Figure 7.7: Plot showing how the superposition of two displaced and out-of-phase crosscorrelation peaks can result in a distorted function. The blue curve represents an SCB peak; the green curve represents a delayed, phase rotated, and attenuated copy; and the red curve represents their superposition.
then superimposed: ψ = H(z) +
N X
Ai cos(φi )H(z − αi ),
(7.4)
i=1
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 dψ = 0. dz z=zmax
The offset of zmax from zero represents the timing error associated with the as-
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7. A STUDY OF THE TIMING ERRORS ENCOUNTERED WHEN PERFORMING RADIO-LOCATION USING THE GSM NETWORK
sumption that the peak of the function corresponds to the LOS arrival. dψ = − πfb sin (πfb (zmax − α0 )) dz z=zmax − πfb
N X
Ai cos(φi ) sin(πfb (zmax − α0 − αi )) = 0.
(7.5)
i=1
Now using the trigonometric identity sin(a − b) = sin(a) cos(b) − cos(a) sin(b),
(7.6)
and rearranging gives PN
tan (πfb (zmax − α0 )) =
i=1 Ai cos(φi ) sin(πfb αi ) . P 1+ N i=1 Ai cos(φi ) cos(πfb αi )
(7.7)
The distributions of two new variables, x and y, can now be considered, corresponding 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 randomly 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 X
! Ai cos(φi ) sin(πfb αi )
2
− y2 1 exp 2σy 2πσy
=p
i=1
and pdf 1 +
N X
! Ai cos(φi ) cos(πfb αi )
=√
i=1
(x−1)2 1 − exp 2σx2 , 2πσx
(7.8)
(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) =
2πσx σy
1 p
164
−
1 − p2
exp
ξ 2(1−p2 )
,
(7.10)
7.5 Modelling the timing error distributions
where, in this case, ξ= and p = correlation(x, y) =
(x − 1)2 2p(x − 1)y y 2 + 2 − 2σx2 σx σy σy
(7.11)
σx,y . σx σ y
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 =
y , x
where x and y are distributed according to the joint pdf f (x, y), the pdf of v is given by: Z
∞
|x|f (x, vx) dx,
pdf(v) =
(7.12)
−∞
which gives Z
∞
|x|
pdf(v) =
exp
−
(x−1)2 2p(x−1)vx (vx)2 + σx σy 2 − 2 2σx σy 2(1−p2 )
2πσx σy
−∞
p
1 − p2
dx.
The solution of this integral, given by Fieller, is p σx σy 1 − p2 − 2 1 2 2σx (1−p ) × exp pdf(v) = π(v 2 σx2 − 2pvσx σy + σy2 ) σy (vpσx − σy ) + 3 π(v 2 σx2 − 2pvσx σy + σy2 ) 2 Z √ σy2(vpσ2 x2−σy ) −v 2 2) v2 2 −2pvσ σ +σ 2 ) σx σ y (1−p )(v σx −2pvσx σy +σy 2(v 2 σx x y y × exp− 2 dv. × exp
(7.13)
(7.14)
0
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 0 (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 + v 2 ) |pdf(v). πfb
165
(7.17)
7. A STUDY OF THE TIMING ERRORS ENCOUNTERED WHEN PERFORMING RADIO-LOCATION USING THE GSM NETWORK
Noting that
(1+v 2 ) πfb
is positive for all v and using the standard error function via
the following substitution (given by Boas [67]) r Z x 2 π x − t2 exp dt = erf( √ ), 2 2 0
(7.18)
the full model can be given as: p − 2 21 R 1 − p2 (1 + v 2 ) 2R σy (1−p2 ) exp pdf(zmax ) = 2 2 2 π fb v R − 2pvR + 1 +√
(vpR − 1) 3
2πσy (v 2 R2 − 2pvR + 1) 2
× exp
−v 2 2 (v 2 R2 −2pvR+1) 2σy
(vpR − 1)
×erf
R
p
2(1 − p2 )(v 2 R2 − 2pvR + 1)
!! , (7.19)
where v = tan(πfb (zmax − α0 )) and R =
7.5.1
σx . σy
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
7.5 Modelling the timing error distributions
0.025 σy = 0.1 σy = 1 σy = 10
0.02 frequency 0.015
0.01
0.005
0
−3
−2
−1
0 delay in seconds
1
2
3 −6
x 10
Figure 7.8: Plot showing the effect of varying σy in the model. For each curve, R = 1 and p = 0. 0.035 R = 0.1 R=1 R = 10
0.03
0.025 frequency 0.02
0.015
0.01
0.005
0
−3
−2
−1
0 delay in seconds
1
2
3 −6
x 10
Figure 7.9: Plot showing the effect of varying R in the model. For each curve, p = 0 and σy = 1.
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7. A STUDY OF THE TIMING ERRORS ENCOUNTERED WHEN PERFORMING RADIO-LOCATION USING THE GSM NETWORK
−3
8
x 10
p = −0.5 p=0 p = 0.99
7
6
5 frequency 4
3
2
1
0
−3
−2
−1
0 delay in seconds
1
2 x 10
−6
Figure 7.10: Plot showing the effect of varying p in the model. For each curve, R = 1 and σy = 1.
Parameter Rural Suburban Light-urban Mid-urban Indoor
R p α0 12.7 ± 1.1 0.03 ± 0.04 51 ± 5 ns 13.0 ± 0.1 −0.04 ± 0.02 72 ± 6 ns 4.7 ± 0.3 0.20 ± 0.12 183 ± 24 ns 3.5 ± 0.3 −0.46 ± 0.07 239 ± 23 ns 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
7.5 Modelling the timing error distributions
Figure 7.11: Plot showing the characteristic delays in the outdoor environments. The error 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 different α0 values. These three distributions probably correspond to three distinct regions or environment types inside the building studied where distinct propagation paths dominate separately in different areas of the building (see discussion above). The error associated with each parameter was determined by finding the bestfit 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
0.07
0.07
0.06
0.06 normalised frequency
normalised frequency
7. A STUDY OF THE TIMING ERRORS ENCOUNTERED WHEN PERFORMING RADIO-LOCATION USING THE GSM NETWORK
0.05 0.04 0.03 0.02 0.01
rural data model
0.05 0.04 0.03 0.02 0.01 0
0 −4
−2
0 2 timing error (seconds)
4
−4
−6
x 10
−2 0 2 4 timing error (seconds)
6 −7
x 10
−3
x 10
0.025 normalised frequency
normalised frequency
5 4
0.02
0.015
3 2
0.01
0.005
1
0 0 −15
−10 −5 timing error (seconds)
0
5 10 timing error (seconds)
−7
x 10
−7
x 10
Figure 7.12: Plots showing the rural data set with the multipath model overlaid
0.07
0.06 normalised frequency
normalised frequency
0.06 0.05 0.04 0.03 0.02
suburban data model
0.05 0.04 0.03 0.02 0.01
0.01 0
0 −1
0 1 timing error (seconds)
−2 −6
x 10
0 2 4 6 timing error (seconds)
8 −7
x 10
−3
−3
x 10
x 10
4
normalised frequency
normalised frequency
6
3 2 1
5 4 3 2 1
0
0 −1.5
−1
−0.5
0.5 −6
timing error (seconds) x 10
1 1.5 2 timing error (seconds)
2.5 −6
x 10
Figure 7.13: Plots showing the suburban data set with the multipath model overlaid
170
7.5 Modelling the timing error distributions
0.025
light−urban data model
0.02
normalised frequency
normalised frequency
0.025
0.015 0.01 0.005
0.02 0.015 0.01 0.005
0 −2
0 timing error (seconds)
2
−4
−3
0 2 4 6 timing error (seconds)
8 −7
x 10
−3
x 10
x 10
12
7 normalised frequency
normalised frequency
−2
−6
x 10
10 8 6 4 2
6 5 4 3 2 1
0
0 −3
−2 −1 timing error (seconds)
0
1
1.5 2 2.5 timing error (seconds)
−6
x 10
3 −6
x 10
Figure 7.14: Plots showing the light-urban data set with the multipath model overlaid.
normalised frequency
normalised frequency
mid−urban data model
0.03
0.02 0.015 0.01 0.005
0.025 0.02 0.015 0.01 0.005 0
0 −2
0 timing error (seconds)
2
−5
0 5 timing error (seconds)
−6
x 10
10 −7
x 10
−3
−3
x 10
x 10
8
8
normalised frequency
normalised frequency
10
6 4 2
6 4 2 0
0 −2
−1.5 −1 −0.5 timing error (seconds) x 10−6
0.5
1
1.5 2 2.5 timing error (seconds)
3 −6
x 10
Figure 7.15: Plots showing the mid-urban data set with the multipath model overlaid.
171
7. A STUDY OF THE TIMING ERRORS ENCOUNTERED WHEN PERFORMING RADIO-LOCATION USING THE GSM NETWORK
indoor data adjusted model
0.04
0.03
normalised frequency
normalised frequency
0.035
0.025 0.02 0.015 0.01
0.03 0.02 0.01
0.005 0
0 −2
0 2 timing error (seconds)
−4
8 −7
x 10
x 10
x 10
8 normalised frequency
normalised frequency
0 2 4 6 timing error (seconds)
−3
−3
20
−2
−6
x 10
15
10
5
6 4 2 0
0 −2.5
−2
−1.5 −1 −0.5 0 timing error (seconds) x 10−6
0.5
1
1.5 2 2.5 timing error (seconds)
3 −6
x 10
Figure 7.16: Plots showing the indoor data set with the adjusted multipath model overlaid (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 corresponding to the delay of the earliest significant arrival. This would suggest a number of different propagation mechanisms active in the environment and each dominating 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
7. A STUDY OF THE TIMING ERRORS ENCOUNTERED WHEN PERFORMING RADIO-LOCATION USING THE GSM NETWORK
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 measured. The signals broadcasted by the base stations on Network 1 all demonstrated a very high level of stability, leading to the conclusion that the networksynchronised 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 station’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 experiments, 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. Significant timing errors of a microsecond or more were recorded for antenna move-
176
8.5 GSM radio location timing error distributions in various environments
ments on the millimetre scale. This behaviour was also noted during an experiment 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 timing 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 distributions in various environments
The timing error distributions in various environments were determined by using 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 timing errors. The modelling performed during the indoor multipath experiments suggested that the latter may be true, but in either case, the result was an effective 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
8. SUMMARY AND FURTHER WORK
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 extra path length of 55-72 metres. The indoor timing-error distribution exhibited three distinct peaks, corresponding to three distinct groups of signals with different 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 determine more accurate figures relating to the capability of GSM networks to provide 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 investigations into new techniques for determining signal arrival times using the SCB cross-correlation peak should also be carried out, as they can improve the accuracy 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 environment. 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 overpower 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
8. SUMMARY AND FURTHER WORK
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 X
Ai cos(φi )H(z − αi ),
(A.1)
i=1
where
( 1 + cos (πfb (z − α0 )) if −1 < (z − α0 ) < fb H(z) = 0 otherwise
1 fb
,
(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 X
Ai cos(φi ) sin(πfb αi )
(A.3)
i=0
and S2 = 1 +
N X
Ai cos(φi ) cos(πfb αi ).
(A.4)
i=0
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 signal’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 bandwidth 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 πfb αi 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 distribution between −π and π independent of α is appropriate, i.e. the probability density function (pdf) of φ can be given as: pdf(φ) =
A.2
1 , for − π ≤ φ ≤ π. 2π
(A.5)
Distribution of α
The distribution of α represents the signals which arrive at the receiver with significant amplitudes, since delayed paths with negligible corresponding amplitudes 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: −α2 α pdf(α) = 2 exp σα2 , for 0 ≤ α ≤ ∞, σα
(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 amplitude of the LOS receipt or earliest significant signal arrival is always normalised to 1. Therefore when modelling rural and suburban environment positions where
183
A. DISTRIBUTIONS OF A, φ AND α
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 attenuation, 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’ r´egime 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: 1 I = 20 log10 √ dB for v > 1, 2πv where the diffraction parameter v is given by r 2(D0 + s0 ) v=x . λD0 s0
184
(A.7)
(A.8)
A.3 Distribution of A
The parameters x, D0 and s0 are given above in Figure A.1. It can also be shown using the diagram that: s0 = L cos(θ),
D0 =
p (D + s)2 + B 2 − s0 ,
sin(θ) = and L=
√
x , L
s2 + b 2 ,
(A.9)
(A.10)
(A.11)
(A.12)
and so x=
√
s2 + b 2
b B sin arctan − arctan . s D+s
(A.13)
The signal intensity, I (in dB), is converted to amplitude (in linear units) via the relationship: I
A = A0 10 10 .
(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 order 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 diffraction 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
A. DISTRIBUTIONS OF A, φ AND α
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: Eref lected|| = R|| Eincident =
cos(θtransmitted ) − cos(θtransmitted ) +
Z1 Z2 Z1 Z2
cos(θincident ) cos(θincident )
Eincident
(A.15)
Eincident .
(A.16)
and Eref lected⊥ = R⊥ Eincident =
cos(θincident ) − cos(θincident ) +
186
Z1 Z2 Z1 Z2
cos(θtransmitted ) cos(θtransmitted )
A.3 Distribution of A
Figure A.3: A plane wave incident onto a plane boundary. In these equations, R|| and R⊥ are the parallel and perpendicular reflection coefq ficients, Z1 and Z2 are the impedances of the two media, such that Z = µrr µ00 , and θtransmitted = arcsin
n1 sin(θincident ) . n2
(A.17)
Figure A.4 below shows the reflection coefficients (and so the relative amplitude after reflection for a given interaction) for concrete (r = 6.1) and for brick (r = 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 propagating to a receiver, is also likely to be a dominant signal propagation mechanism. 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 calculations together. Figure A.5 below shows plots of the the calculated received
187
A. DISTRIBUTIONS OF A, φ AND α
1 reflections in the vertical plane from concrete reflections in the vertical plane from brick reflections in the horizontal plane from concrete (dashed) reflections in the horizontal plane from brick (dashed)
0.9
0.8
0.7
0.6 reflection coefficient 0.5
0.4
0.3
0.2
0.1
0
0
10
20
30
40 50 incident angle (degrees)
60
70
80
90
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 chosen. 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 Latapyˇc [69] as 7 dB, with a loss caused by furniture given as 1 dB
188
A.3 Distribution of A
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 dimension 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 v K · Su 8 · dS · cos(θi ) u Es = t ri · rs 4π + 3π · cos(θ ) · 1 + sin2 θi + i
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
A. DISTRIBUTIONS OF A, φ AND α
−3
7
x 10
6
5
relative amplitude 4 compared to unobstructed (LOS) signal 3
2
1 diffraction directly down from rooftop to receiver diffraction followed by reflection from opposite brick building 0
0
5
10
15 20 distance from rooftop (metres)
25
30
(a)
(b)
Figure A.5: Plots (a) showing the received signal amplitude (relative to the unobstructed signal) for two propagation mechanisms - diffraction over a rooftop, and a shallower diffraction followed by reflection from a nearby facing building (b).
190
A.3 Distribution of A
These four propagation mechanisms all result in different probability distributions 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 distributions 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 theorem approximation for these distributions and 10 multipath events per survey point. ————————————————————————
191
A. DISTRIBUTIONS OF A, φ AND α
1.2
1.4
1.15 1.1
1.2 1.05
S1
S1 1
1 0.95
0.8 0.9 0.85
0.6
0.8
0.4
0.75 1.25
1.5
1.75
2
2.25
2.5
2.75
3
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
S2
S
2
(a) single diffraction mechanism
(b) single reflection mechanism
1.5
S1 1
0.5
0
1
2
3
4
5
S
2
(c) combined diffraction and reflection
(d) diffuse scattering mechanism
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
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