Fingerprint Location Using Ray-Tracing

FINGERPRINT LOCATION METHODS USING
RAY-TRACING
A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF
MASTER OF PHILOSOPHY IN TELECOMMUNICATIONS
BY
Phillip Stephen Maher
SCHOOL OF ELECTRICAL ENGINEERING AND
TELECOMMUNICATIONS
UNIVERSITY OF NEW SOUTH WALES
NOVEMBER 2010

Abstract
Mobile location methods that employ signal fingerprints are becoming increas-
ingly popular in a number of wireless positioning solutions. A fingerprint is a spatial
database, created either by recorded measurement or simulation, of the radio envi-
ronment. It is used to assign signal characteristics such as received signal strength or
power delay profiles to an actual location. Measurements made by either the handset
or the network, are then matched to those in the fingerprint in order to determine a
location. Creation of the fingerprint by an a priori measurement stage is costly and
time consuming. Virtual fingerprints, those created by a ray-tracing radio propagation
prediction tool, normally require a lengthy o↵-line simulation mode that needs to be
repeated each time changes are made to the network or built environment. An open
research question exists of whether a virtual fingerprint could be created dynamically
via a ray-trace model embedded on a mobile handset for positioning purposes.
The key aim of this thesis is to investigate the trade-o↵ between complexity of the
physics required for ray-tracing models and the accuracy of the virtual fingerprints
they produce. The most demanding computational phase of a ray-trace simulation is
the ray-path finding stage, whereby a distribution of rays cast from a source point,
interacting with walls and edges by reflection and di↵raction phenomena are traced
to a set of receive points. Due to this, we specifically develop a new technique that
decreases the computation of the ray-path finding stage. The new technique utilises
a modified method of images rather than brute-force ray casting. It leads to the
creation of virtual fingerprints requiring significantly less computation e↵ort relative
to ray casting techniques, with only small decreases in accuracy.
Our new technique for virtual fingerprint creation was then applied to the devel-
opment of a signal strength fingerprint for a 3G UMTS network covering the Sydney
central business district. Our main goal was to determine whether on current mo-
bile handsets, a sub-50m location accuracy could be achieved within a few seconds
timescale using our system. The results show that this was in fact achievable. We also
show how virtual fingerprinting can lead to more accurate solutions. Based on these
results we claim user embedded fingerprinting is now a viable alternative to a priori
measurement schemes.

Chapter 1
Introduction
The ability to determine a location estimate of a mobile handset in a cellular system is
becoming increasingly important. Location-based advertising and information services
are becoming more popular with todays smart-phones and integrated mapping tools.
Network management can take advantage of a handsets location for more e cient
handling of calls and data services. For emergency services responding to distress calls,
determining the most precise position as possible of a mobile handset is of the utmost
importance (E-911) [1] [2] [3]. In the last few years, there has been an explosion in the
growth of location based applications for mobile handsets. These range from mobile
gaming, social networking collectives such as Facebook and Foursquare, to information
services that are location aware and provide suggestions on nearby restaurants, points
of interest and even the proximity of friends.
1.1 Positioning
Location computations can be done by the network, the handset itself or via a hybrid
process of the two. Common network based methods work on triangulation approaches
like Time of Arrival (TOA), Time Di↵erence of Arrival (TDOA), Angle of Arrival
(AOA) and Received Signal Strength (RSS). Each requires analysis of received signal
characteristics at three or more base stations to determine a position by Trilateration
[4]. However the accuracy of these location methods deteriorates under Non Line of
Sight (NLOS) conditions [5] [6] as well as requiring additional hardware at the base
station for AOA and accurate clock measurements for TOA/TDOA. Handset based
positioning solutions o↵er an alternative to network based approaches. For TOA
based approaches such as the Enhanced Observed Time Di↵erence (E-OTD) system
for 2G/GSM and the Observed Time Di↵erence of Arrival (OTDOA) method for
3G/UMTS systems, these o↵er similar Trilateration based positioning that also must
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deal with the same NLOS e↵ects as well as requiring changes made to the handset.
Modern smart-phones often come equipped with a GPS unit built in as Assisted-GPS
(A-GPS) capability, which can provide very precise location estimation. The drawback
with GPS is that it requires a clear unobstructed view of the sky for the satellite
signals which can be di cult in dense urban environments where buildings, bridges
and tunnels (as well as when the handset is taken indoors) can block the signals and
introduce multipath a↵ects that introduce errors. Other technologies such as Ultra
Wide Band (UWB), Wireless LAN (WLAN) and Bluetooth systems only o↵er short
range location estimation for mostly indoor environments [7].
1.2 Spatial Databases and Fingerprinting
Mobile location methods that employ signal fingerprints are becoming increasingly
popular in a number of wireless positioning solutions. A fingerprint is a spatial
database, created either by recorded measurement or simulation of the radio envi-
ronment. It is used to assign signal characteristics such as Received Signal Strength
(RSS) or Power Delay Profiles (PDP) to an actual location. Measurements made by
either the handset or the network are then matched to those in the fingerprint in order
to determine a location. Creation of the fingerprint by an a-priori measurement stage
is costly and time consuming. Virtual fingerprints, those created by a ray-tracing radio
propagation prediction tool, normally require a lengthy o↵-line simulation mode that
needs to be repeated each time changes are made to the network or built environment.
Fingerprint or Database Correlation Methods (DCM) look to o↵er improved
accuracy over triangulation methods in urban environments by their ability to take
into account NLOS propagation characteristics [8] [9]. Location estimates are made
with measured values observed by either the network or the handset, and the closest
match to the database is made by minimising some cost function. Virtual finger-
print databases have a series of advantages in being less time consuming to prepare
than manual measurements, are considerably less expensive to create and can be re-
simulated anytime there are changes made to the networks infrastructure. Virtual
fingerprinting is also more useful for addressing location estimation in mesh networks
where mobile routers can be moved every few days [10]. An open research question
exists of whether a virtual fingerprint could be created dynamically via a ray-trace
model embedded on a mobile handset for positioning purposes.
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1.3 Ray-Tracing
Ray tracing has been an important tool for modeling radio wave phenomena through
a variety of mediums. Not only is ray-tracing a reliable tool for simulating wireless
communications systems, but also for ocean acoustics, seismological modeling and
optical design for lenses. Ray-tracing is able to accurately model the wave like nature
of a radio signal by tracing the path of a set of narrow beams that approximate a
wave-front propagating through the environment. Ray-tracing can accurately model
interactions with surfaces such as reﬂection, transmission, di↵raction and scattering.
Being able to accurately model such propagation phenomena provides a powerful tool
for predicting the multipath propagation e↵ects that occur in wireless communication
systems.
Figure 1.1: A 2D ray-tracing example
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The use of ray-tracing models to produce a fingerprint database for location means
have been investigated in [11] [12] [13] [14]. By using detailed Computer Aided Design
(CAD) models for representing buildings and structures that influence the multipath
signal, the ray-trace model commonly runs in an o↵-line mode producing a large
database for a required city. The database stores at each grid point, accurate and
unique site specific signal characteristics, or a virtual fingerprint of the wireless sig-
nal at that location that should match actual measured signal properties. Location
methods that employ a ray-trace fingerprint database have been shown in principle
to be very robust in handling complex multipath environments with a good degree of
accuracy [11] [12] [13] [14]. The ability to predict signal characteristics in heavily built
up urban microcell areas, where most of the time the receiver locations are not within
Line Of Sight (LOS) of a transmitting antenna makes ray-tracing the ideal choice for
producing a virtual fingerprint.
1.4 Input Data for Ray-Trace Models
For wireless network planning, entire city three dimensional (3D) vector models are
often required for ray-trace analysis to be performed. A 3D vector model is a digital
representation of the city stored in a file format that lists the real world coordinates of
polygons that are used to represent buildings and other structures. The cost of these
models is often quite high due to the time and the methods required to create them.
Prices increase as the resolution of the vector data does, with some being accurate to
a few centimetres.
With the growth of geospatial mapping platforms such as Google Earth and
Microsoft Virtual Earth, these applications have begun incorporating 3D city models
along with aerial imagery, terrain topology and street maps. Extensive 3D city models
are available as a viewable feature layer in Google Earth for many cities. The vector
data is only accessible within the applications at the present time, however modeling
enthusiasts have been provided with tools to create and upload their own 3D models
via Google SketchUp. Similar tools have been developed that can trace over the
outlines of buildings in Google Earth for creation of a usable database such as the one
described in [15].
Augmented Reality (AR) applications have begun to emerge on smart-phones
which combine live real-world imagery captured by a camera which is augmented with
computer generated imagery. Location estimates can be made by detecting building
features from a live video stream which is then matched to a 3D building database.
This has led to location based services that allow the user to view a building via a
smart-phones camera and find what is nearby and even see what is behind it [16] [17].
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Central to these systems is the 3D building database used as reference data set for
localisation. With rising interest in utilising 3D city models for an increasing number
of applications and with a worldwide database that is expected to grow, it is likely
that this data will become freely available over time.
Figure 1.2: Google Earth
1.5 Processing Capability of Handsets
The processing power of mobile handsets (or terminals) is increasing at a rapid pace.
With the growth in smartphones, faster processors are required to increase the speed
and response of these multi-tasking operating systems. With the convergence of the
mobile handset with portable multimedia devices, mobile computing, gaming and the
growth of feature rich applications that all require more processing power, handset
makers are incorporating ever more powerful processors within these devices. Already
the growth in widescreen touch-phones and tablets has generated the need to display
high deﬁnition video content utilising processor speeds of 1GHz or higher. Handset
manufacturers look to be following the same trend as other mobile computing platforms
and moving to multi-core processing in order to reduce heat and power consumption
[18].
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1.6 Goals and Objectives
This research was conducted with the view that if access to this growing collection
of 3D vector model data is possible, the potential for creating a dynamic virtual
fingerprint on a handset, for location matching purposes with actual real-time signal
measurements is viable. Such a system would allow access to the most accurate,
up to date building database to be used on demand for location determination. As
stated earlier, this approach could be applied to mesh networks in which the networks
topology and environments are expected to change over time [10].
1.7 Thesis Structure
This thesis is outlined as followed. Chapter 2 describes the theory behind deterministic
radio propagation models and the various geometric methods used to approximate
radio propagation phenomena. Chapter 2 introduces a novel technique for identifying
object visibility within ray-trace models and the development of a ray-trace model for
use throughout this thesis. Chapter 3 describes the radio propagation theory applied
to ray-trace models, the calculation of radio propagation parameters and the various
signal metrics produced by the ray-trace model described in Chapter 2. Chapter 4
outlines the theory of positioning systems and the introduction of a new protocol for
determining location via a virtual fingerprint in near real-time, produced by the ray-
trace model described in Chapter 2. Through simulations and benchmarking tests,
the feasibility of this new protocol is validated. Chapter 5 concludes the thesis, with
comments on the findings from Chapter 4 and further research ideas.
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Chapter 2
Ray-Tracing
This chapter provides an introduction to the theory behind ray-trace models and
solving the associated geometric problems they present. Beginning with the simplest
approach of ray-casting, acceleration techniques and optimised methods are introduced
for faster and more e cient run-times. The chapter concludes with the development
of a novel solution to solving visibility issues for a non-optimised input vector dataset.
2.1 Introduction
Ray-trace algorithms have been used extensively to model wireless system parameters
in network planning stages, with the emphasis on high accuracy [19] [20]. With pre-
cise environment and network data, they can provide accurate site speciﬁc simulation
results. A major aspect of ray-trace models is the approach taken in representing the
geometric attributes of radio wave propagation. This chapter describes the various
types of ray-trace models common to many radio propagation prediction tools with
emphasis on the di↵erence in geometric calculations in each. It concludes with the de-
velopment of a novel visibility determination technique in a ray-trace model developed
for use in this thesis.
2.2 Ray-Tracing Inputs
Ray-trace models require a set of input data to describe as accurate as possible the
wireless network and the built environment. This includes information on the location
of the transmitting antennas, receive antennas and the radiation gain patterns of each.
For accurate modeling of radio wave phenomena interactions with the built environ-
ment (such as reﬂection and di↵raction), a digital representation of the buildings and
the terrain that exists within the area of study is necessary.
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2.2.1 Antenna Gain Patterns
Antenna manufacturers supply data files that provide a 360 degree gain patterns for
use in ray-trace models. Angular resolutions of 1o are usually provided for vertical and
horizontal radiation patterns as seen in Figure (2.1). With ray-trace algorithms being
deterministic in nature, a value for the antenna gain in any direction can be found by
linear interpolation from the vertical and horizontal gain pattern values.
Figure 2.1: Antenna gain patterns
2.2.2 Environment Data
Digitised environment data is required for all ray-trace modeling. Building data in the
form of a series of coordinates that provide an accurate representation of the vertices
of a building, are referred to as vector data and are contained within a Vector Data
File (VDF). Terrain data is commonly stored in a gridded array of data points that
have the same file structure as a raster file, which are two dimensional grid arrays of
terrain spot point values. These values can represent either height data or land usage
which are used in many empirical models for planning macrocells in cellular networks
or television and radio broadcast systems.
2.2.2.1 Building Vector Data
Building data is commonly stored in a vector file format where the real world coor-
dinates of the vertex points that make up each polygon feature of the building are
grouped in a hierarchical scheme. This data can be derived from a number of sources,
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with the most reliable often obtained from architectural CAD models. The vector
data in the Keyhole Markup Language (KML) file is stored in a tagged format, group-
ing together geographical values of longitude, latitude and altitude that make up the
polygons of a building object. The geographical coordinates require a conversion to
Universal Transverse Mercator (UTM) grid values for use in ray-trace model calcula-
tions.
2.2.2.2 Terrain Raster Files
Applications such as Google Earth and Microsoft Virtual Earth have access to a large
worldwide database of Digital Elevation Model’s (DEM) for use in accurately incor-
porating terrain e↵ects. The data stored within these files represent the height values
above mean sea level (ASL) of the earth’s surface excluding buildings, bridges and
naturally occurring vegetation. Terrain data has been made available by the NASA
Shuttle Radar Topography Mission (SRTM) which collected data ranging from lati-
tudes 56o S to 60o N. The data resolution is of one arc second (or roughly 30m) for
the United States of America and three-arc-second (⇠90m) for the rest of the world.
Figure 2.2: SRTM terrain tile
Raster file data is normally stored as a sequence of 8bit or 16bit values for a fixed
tile size, similar to that of a 1ox1o SRTM tile [21]. Terrain models are required for
either texture mapping surface imagery in applications such as Google Earth as well as
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an accurate 3D representation for the built environment, upon which building vector
models are added to. Digital Surface Model’s (DSM) di↵er from DEM’s in that the
data within represents a surface model of the earth, including the built environment
and naturally occurring terrain features like forest canopies.
2.3 Ray-Trace Models
There are a variety of approaches to implementing ray-tracing for wireless commu-
nication systems. This section discusses two common methods used for determining
ray-paths, the Brute Force and the Image Method. A variant of the Image Method
called Beam Tracing is also described, which borrows heavily from the Image Method
and approximates the launch of an inﬁnite number of rays.
2.3.1 Brute Force Method
Ray tracing methods involve determining the path of a propagating wave between a
source point and a receiver. The most basic implementation of ray-tracing is via the
Brute Force method, whereby rays are generated (or cast) from the source at discrete
angles which are then traced through the environment to interact with walls and
edges in a variety of electromagnetic wave phenomena such as reﬂection, transmission,
refraction and di↵raction.
Figure 2.3: The Brute Force method
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As shown in Figure (2.3), a source point labeled Tx is created along with a finite
number of rays that are cast out at a given angular separation to represent a propa-
gating wavefront traced to a receive point labeled Rx. Each ray is then tested to see
which wall it intersects with and if or not it has interacted with a reception sphere.
For reflection purposes the intersection point is then used to launch another ray at
an angle determined by Snell’s law and the model repeats the process of finding the
next wall that it interacts with. For di↵raction events, rays are often snapped-to a
wall edge point (if a minimum perpendicular distance between the ray and wall edge
is met) and the wall edge is treated as a new Tx source point of which a collection of
rays are then cast at a given angular resolution about the exterior wedge angle of the
wall. This recursive process is repeated until the ray fails to hit a target, a maximum
number of interactions is met or that the attenuation of the ray exceeds a threshold.
For calculating the field strength at a given receiver point, the simplest method
used is that of a reception sphere. For a given regular distribution of receive points, the
actual number of rays that will precisely intersect is quite small. A reception sphere is
used so that rays passing within a minimum distance are used to calculate the field at
that point. Determining the size of the sphere is di cult, for if the radius is too large
multiple rays from the same wavefront can be collected and create errors in the signal
metrics. If the reception sphere is too small, valid rays will not be detected. One
technique is to use a ray history that traces the origin of each reflected and di↵racted
ray such that errors with large reception spheres can be negated, but this comes at
the cost of an increased memory overhead. As rays belonging to the same wavefront
propagate, they diverge to the extent that the reception sphere is too small to capture
actual rays. Techniques such as ray splitting [22] can be used to counteract this and
maintain a minimal spatial resolution. Another approach to tackling this problem is
for having a variable sized reception sphere [19] [23] to reduce the error associated
with divergent rays.
2.3.2 Image Method
The Image Method takes a simplified approach to finding exact ray paths from the
transmitter to the receiver. It works by identifying potential reflecting surfaces and by
creating an “image” of the transmitter, as shown in Figure (2.4). A good description
of this image based technique can be found here [24]. For the transmitter labeled
Tx, after identifying Wall 2 as a potential reflection surface, a reflected image of the
transmitter is found and labeled as Tx Image Source 1. The process is then repeated by
treating Tx Image Source 1 as a virtual source, which identifies Wall 1 as a reflecting
surface and a mirror image of it is found and labeled as Tx Image Source 2.
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Figure 2.4: The Image Method
The Image Method does not require the use of a reception sphere as in the Brute
Force case. Once the maximum number of reflection iterations is met, the actual
ray path from the true Tx to Rx is determined in a reverse order, where a simple
intersection test is done to determine if a LOS case exists for the line segments Tx!P1,
P1!P2 and P2!Rx. This method allows for just a single ray to represent a spherical
wavefront arriving at a receive point, which negates the need for casting a large number
of rays like the Brute Force method to achieve the same result. The Image Method
avoids casting a large amount of rays which then need to be tested for intersections with
all the walls within the environment. As the Image Method provides exact ray paths,
it overcomes the errors associated with reception sphere problems. For di↵raction
purposes, wall vertex points are treated as similar virtual sources. A disadvantage of
the Image Method occurs in highly detailed environments, with increasing polygons
(building walls) this in turn increases search times for reflected sources. However many
optimisation techniques can be applied to reduce the search routines at run-time.
2.3.3 Beam Tracing
Beam Tracing is the name given to a variant of ray-tracing that relies heavily on
the Image Method. Instead of tracing infinitesimally thin rays, polygon regions are
created to represent an ensemble of rays belonging to a spherical wavefront between
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the transmitter and surfaces identified as reflectors [25] [26] [27]. From the example
shown in Figure (2.5), for the transmitter labeled Tx, a wall on Building 1 is found to
be a reflective source.
Figure 2.5: Beam Tracing
The mirror image of Tx is calculated and shown at the location of Tx’. The
illumination zone formed between Tx and Building 1 is found and highlighted in
yellow. The process is then repeated for Tx’ in which a green illumination zone is
created about Building 2 and its mirror image is determined at the location of Tx”.
This method improves on the Brute Force approach in determining transmitter to
receiver ray path tests, by reducing the number of computations for a large set of rays
cast and the required intersection tests with reception spheres. Polygons are created
for which a simple “inside polygon” test for receive points is performed to obtain
exact propagation paths without any of the errors associated with reception spheres.
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Building edges that are found within illumination zones are identified as di↵raction
sources and their illumination zone extends around the exterior angle of the two walls
of the building edge it lays on.
2.4 Ray-Trace Optimisation
For all ray-trace methods, optimisation techniques are applied to reduce to the compu-
tation time and make the algorithms more e cient. These techniques include Object
Space Partitioning, Visibility determination techniques and Di↵raction Tree creation
[28] [29] [30] [31]. Dimension reduction can be used when a full 3D ray-trace model
may not be needed. Dense urban environments made up of high-rise buildings can
benefit from a dimension reduction to either a 2D or 2.5D ray-trace rather than a
complex full 3D implementation. Pre-processing of environments provide the oppor-
tunity to implement these optimisations in which large data structures are created
and used at run-time to decrease simulation time. A key requirement of many image
and ray-beam based models is in knowing the exact back to front ordering of polygons
from a given viewpoint. Such techniques allow for quick determination of the Visible
Polygon Set (VPS).
2.4.1 Dimension Reduction
For site specific ray-trace results, a model that operates in 3D using high resolution
environment data is considered to provide the most accurate results possible. However
in cases such as urban microcell environments where both transmitters and receivers
are assumed to be lower than the height of buildings, a 2D or 2.5D model can be applied
with acceptable results as shown in [32] [33]. For a 2D model, building outlines are
used to represent buildings with infinitely tall walls and only include di↵raction e↵ects
in the horizontal plane. A 2.5D model uses a similar approach, except actual height
information of walls is taken into account, and the ray-path evaluation includes a z-
component for determining 3D ray-polygon intercepts [34]. Hybrid versions have been
developed which mix two separate 2D ray-trace results from analysis of the horizontal
and vertical planes [31]. The benefit of using either 2D or 2.5D ray-trace models is a
faster execution time when compared to 3D, at the expense of the accuracy [35].
2.4.2 Di↵raction Trees
As di↵raction edges can be treated as static sources, algorithms that model di↵raction-
reflection and di↵raction-di↵raction phenomena can benefit from a pre-processing stage
that identifies wall polygons and other building edges within di↵raction zones. This
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is only required to be run once, in order to create a tree like data structure linking
di↵raction edges with potential receiver locations, reflecting walls and other di↵raction
edges (if double di↵raction instances are to be modeled).
2.4.3 Object Space Partitioning
Object space partitioning is the term given to a variety of partitioning schemes in
which a data structure is created to enable fast spatial queries. Ray-trace algorithms
benefit from information about the objects that make up the environments regarding
placement in relation to others. Binary Space Partitioning (BSP) is a popular space
partitioning method for 2D and 3D ray-trace models.
Figure 2.6: BSP Tree creation
Developed by Fuchs et. al. [36], a root polygon is chosen to divide a region into
two halves by a hyperplane and a tree structure is created listing those objects in front
and behind. The subdivision is then repeated until all polygons have been accounted
for. The advantage of creating the BSP tree is such that at run-time, a fast tree query
can be done to find the front to back ordering of objects for a given viewpoint.
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The processing time of Image Based and Beam Tracing algorithms can be
reduced dramatically with a highly detailed BSP tree of an extensively analysed en-
vironment that provides a tree structure of view-dependent ordered polygons. Higher
dimension partitioning schemes involve the use of Quadtrees in which the environ-
ment is partitioned using two hyperplanes (into regions or quadrants) and thus 4 leaf
nodes in the tree. Octrees are applied to 3D models in which three hyperplanes are
used to partition the object space into octants and each node having 8 leaves. Ob-
ject space partitioning allows significant speed improvements at run-time for ray-trace
models, however it requires the creation of a large data structure in a lengthy o↵-line
pre-processing mode. The processing time is rated as being of order O(n2).
2.4.4 Visibility Determination
Visibility determination is a fundamental problem in computer graphics. As ray-trace
models deal with vector models, determining which portions of a polygon and what
lines are visible relies on classical computer graphics issues such as visible surface and
hidden line removal, first encountered with vector displays in the late 1960’s and early
1970’s [37]. Many algorithms have been developed for determining visible surfaces as
well as culling techniques for hidden surfaces [37] [38]. Modern raster based displays
which operate on a pixel level use fast z-bu↵er algorithms accelerated by powerful
Graphical Processor Units (GPU’s) found in PC video cards and newly emerging mo-
bile handsets with 3D graphics support.
Analytical Visibility refers to the exact determination of visible polygons and
portions of partly occluded polygons from a given viewpoint. Image based methods
such as Beam Tracing require a solution to Analytical Visibility in order to identify all
possible reflective sources. Visibility determination involves a number of processing
techniques such as Back Face Culling (BFC) and View Frustum Culling (VFC) to
reduce the set of known polygons in an environment to what is referred to as a Po-
tential Visible Set (PVS). The PVS is a data structure which is a table of information
regarding the visibility of each polygon before Analytical Visibility can be determined.
Back Face Culling is a technique which removes walls from search lists for ray-
polygon intersection tests, due to the fact that they are known to be facing away from
the transmitting source. All that is required is a single dot product check between
the normal vector belonging to the wall and that of a ray cast from the transmitting
source to a point that lies on the wall.
As shown in Figure (2.7), the red walls labeled [C,D,E,H,I,L] pass the BFC
test as their normal vectors make an acute angle with a ray cast from the view point.
The VFC removes those walls that are outside the region of the view frustum, which
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is the highlighted yellow and grey area subtended by the angle ↵ in Figure (2.7), of
which walls [C,E,I,L] lay either fully or partially inside.
Figure 2.7: The View Frustum
A Bounding Volumes test is one of the simplest culling techniques used for
removing objects outside of the view of the view frustum in which a simple ﬁltering
is applied on whether the coordinates that make a box surrounding a wall object lie
within the view frustum. Bounding Volumes tests are not only conﬁned to image or
beam tracing techniques but also ray-launching methods to evaluate if an intersection
test is required for a ray and a building/wall. For instance, walls [D,H] in Figure (2.7)
would be excluded from a Bounding Volume test and the view frustum. Occlusion
Culling is a term given to removing objects that are blocked or hidden by another
object due to the occluders geometry. In both 2D and 3D ray-tracing models, Shadow
Frusta culling [39] is a fast and e↵ective occlusion method.
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Figure 2.8: Shadow Frusta
As shown for the 2D/2.5D case in Figure (2.8), shadow frusta (grey regions) are
found for Walls [A,B,C,D]. As Wall B is found to reside entirely within the shadow
frustum of Wall A, it can be culled from the visibility list for the view point VP.
Partially occluded by Wall D is Wall C, and it requires clipping to determine its
portion visible from the view point VP. Determining if a wall lays inside a shadow
frusta can be done by Bounding Volumes test or Point In Polygon tests.
2.5 Ray-Trace Model Development
A 2.5D ray-trace model was developed for fast computation and accurate results for
the purposes of creating a virtual ﬁngerprint on a mobile handset. The model uses the
Beam Tracing method for determining ray-paths and 3D environment data (for both
buildings and terrain) in a non-optimised format. It employs a novel shadow frusta
culling technique for visibility determination of wall/polygon objects of buildings using
polygon algebra routines from The General Polygon Clipping (GPC) library.
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Figure 2.9: Ray-Trace algorithm ﬂow chart
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The ray-trace model was developed entirely in Matlab apart from the GPC library,
which was written in C/C++ and compiled into a Dynamic Link Library (DLL) with
a Matlab wrapper function to access its exported functions. The GPC was developed
by Manchester University and has been made freely available for academic use [40].
2.5.1 Data Import and Processing
The algorithm assumes that the building data source (in the form of a vector ﬁle
such as Google KML data) has not been pre-processed to provide ray-trace acceler-
ation techniques such as object space partitioning and di↵raction trees. Transmitter
location data and terrain data (such as SRTM height tiles) are also required inputs.
The environment import stage processes the incoming stream into a data structure of
building objects made up of facet structures, storing information regarding each walls
polygon points and information such as its 2D line equation, the 3D polygon normal
vector and the equation of the plane.
Figure 2.10: Matlab building data structure
As the algorithm is 2.5D, only rectangular polygons are used to represent the walls
that are perpendicular to the terrain. The terrain data is stored in a similar structured
format. Vertical di↵raction edges are identiﬁed by an inner product test to determine
the inner wedge angle and stored in a list, noting their location, wedge angle and
connecting walls. Receiver points are created at this stage of the algorithm and make
up a uniform grid outside building polygons with 10m resolution being adequate.
20

2.5.2 Novel Visibility Determination Method
The ray-trace algorithm creates a view frustum for a transmitter based on its antenna
properties, most importantly being its 3dB beamwidth for the angular width of the
frustum. For the example shown in Figure (2.11), the transmitter labeled Tx represents
a standard cellular 120o sector as highlighted in yellow.
Figure 2.11: The View Frustum of a transmitter
A search is then made to determine which buildings and walls lay either fully inside
the view frustum or are partially included. Those that are found to fall within this
region are passed through a BFC test to produce a list of walls that can be removed
from the visibility list. Shadow Frusta are then created by casting a ray from Tx to
each wall in the Potential Visible Set, and extending this to beyond the environment
space as shown in Figure (2.12).
These shadow frusta are then added together via the GPC library. The GPC is
based on the Vatti clipping method [41] which operates in a orderly fashion, whereby
21

Figure 2.12: Walls and associated Shadow Frusta
for the two polygons that are to be clipped, it identifies sweep lines of imaginary hor-
izontal lines through the two polygons at each vertex point. This creates scan beams
which are spaces between the scan lines that are processed sequentially from bottom
to the top to determine the new vertex points of the polygon. The Vatti algorithm
allows for clipping of complex shaped polygons that can include holes, those that are
convex, concave or self-intersecting. The GPC library allows boolean operations to be
performed on 2D polygons such as subtracting one polygon area from another, find-
ing the intersection of two polygons, union of polygons and an exclusive-or operation.
Union of each polygon in the ray-trace model is a linear process in which a combined
shadow frusta clips partially occluded wall polygons or fully occludes hidden polygons.
This novel method for finding the precise set of visible polygons, with the clip-
ping of partially occluded polygons included in the same operation o↵ers fast evaluation
of visibility determination. This approach avoids the need for a pre-processing stage
for object space partitioning or the creation of a visibility tree and the need to find
back to front ordering of polygons which must then be projected into a clipping plane.
22

Figure 2.13: General Polygon Clipper boolean operations
The resultant edges of the illumination polygon, shown in Figure (2.14) are then
matched to those lines associated with its outline, to walls on the buildings via bound-
ing volumes test and a 2D equation of line test. This provides a list of walls and
portions of walls that make up the visible polygons from the Tx view point.
Figure 2.14: Illumination Zone and LOS Region
23

2.5.3 Reflected Sources
The visible surfaces found within the illumination zone represent reflection sources
for the next iteration of the ray-trace algorithm. For each illuminated wall, the Tx
location is reflected about the wall via the method of images and a new reflected Tx’
source point is created with its own view frustum, extending from the walls outward
facing polygon to the environment as seen in Figures (2.14) and (2.15). The algorithm
is then repeated, by finding those walls within the new virtual Tx’ view frustums
and formation of shadow frusta which are then subtracted from the virtual Tx’ view
frustum.
Figure 2.15: First order reflection illumination zones
For each iteration of the algorithm, the illumination zones then check to see which
receiver points lay inside them. This is performed by a simple point in polygon test
(or Matlab’s “inpolygon.m” function). Di↵raction edges can also be identified in this
manner as they represent static receiver points.
24

2.5.4 Di↵raction Rays
Valid di↵raction events are determined by the same method used to identify receiver
points within illumination zones. When an illumination zone is found (either from a
transmitter or virtual source), an “inpolygon” test is applied to the list of di↵raction
edges in the environment. The di↵raction edge list is determined at the data import
stage. This pre-processing stage creates a data structure of di↵raction edges as well
as a linked list of known receiver points observable by each di↵raction edge. At run
time, whenever a di↵raction edge is found to reside within an illumination zone it is
recorded. A parent ray from the source to the di↵racting edge is created as well as
child rays from the di↵raction edge to the observed receiver points as shown in Figure
(2.16) .
Figure 2.16: Di↵raction rays associated with a single edge
The di↵raction loss associated with the child rays are determined during the ﬁeld
strength calculation stage, once all ray paths for that iteration have been determined.
Only single order horizontal plane di↵raction was implemented for this ray-trace model.
25

2.5.5 Comparison with Brute Force
For comparison checking, a Brute Force algorithm was developed to compare ray path
creation and processing speed. Rays were created at 0.1o resolution, which for a 120o
sectored initial view frustum area, equal to 1200 rays was cast into the environment.
A simulation was performed on the exact environment shown in Figure (2.16), having
receiver locations placed at 10m grid resolution within a 600m2 area and with 5 orders
of reflection. As shown in Figure (2.17), the green rays represent the initial launch
rays from the Tx (or 0th order) and the magenta rays the first order reflection from
the walls.
Figure 2.17: Rays cast using the Brute Force Method
The Beam Tracing method was found to run at almost half the time required for
this Brute Force method example. Each algorithm calculated its associated beam or
ray paths, reception at a receiver point and wall edges for di↵raction events. The Brute
Force method adopted a static reception sphere method and Beam Tracing applied its
point in polygon method. The Beam Tracing algorithm required just 8.65 seconds
whereas the Brute Force needed 15.92sec.
26

The limiting factor to the Brute Force method is the number of rays required to
be launched. Simulation times increase linearly with the number of rays cast. Given
the Beam Trace method approximates near infinite ray casting and perfect reception of
the propagating signal wavefront (with no double counting errors), validates its ability
to provide accurate and fast site specific propagation results.
2.6 Summary
This chapter has introduced a novel approach to the problem of determining the Visible
Polygon Set via the use of a polygon algebra library. Given the desired cities vector file
input dataset (without any pre-processing), the ray-trace model can quickly determine
the geometrical aspects of radio wave propagation. Its distinct advantages are
• Provides shadowing and polygon clipping in the one process.
• Does not require pre-processing stage like BSP tree creation and works as a single
pass operation of order O(n) due to the Vatti algorithm in the GPC library.
• The GPC library can remove redundant calculations by discarding polygons
found to lay fully within a shadowed region.
In line with the work in this thesis, this novel approach can take advantage of the
growing number of available 3D building datasets that are becoming available for use
with an embedded algorithm for determining radio propagation signal characteristics.
27

3.3 Multipath Propagation
Multipath propagation describes the di↵erent paths a radio wave travels from the
transmitter to the receiver due to it being reflected, di↵racted, refracted and scattered
in the radio environment. These di↵erent paths occur due to signals being either
reflected, di↵racted or scattered o↵ objects such as buildings, vehicles and mountains
in cellular systems. Due to the di↵erent paths that the waves travel, this results in
delayed arrivals of the signal at a receiver. Along with di↵ering arrival times, each path
would undergo its own separate phase change which results in a fluctuating received
signal. When waves are combined in phase they add constructively, and when out of
phase they add destructively and this results in fluctuations referred to as small scale
fading. The remainder of this chapter discusses reflection and di↵raction phenomena
and how they are implemented within the ray-trace model.
3.4 Reflection
For reflection phenomena, radio waves encounter an obstacle that is large compared to
the wavelength of the radio wave. As a result, part of the wave energy is reflected and
the remaining part is absorbed into the object. In cellular systems reflections primarily
occur at the ground surface and building walls. Radio waves can also be absorbed due
to atmospheric e↵ects or even by the human body. For vertically polarized waves
interacting with a partial conductor, a phase change of 180o occurs for the electric
field component Er shown in Figure (3.2). For horizontal polarized waves, the E field
component is parallel to the direction the wave travels.
The reflection coe cients are determined by the target objects electrical and mag-
netic properties and the angle of incidence. Following Snell’s Law, the incident angle
' is equal to the reflected angle as shown by in Figure (3.2). The following equations
determine the perpendicular Rs? and horizontal Rsk reflection coe cients of the re-
flected wave at the boundary of two mediums (in the case of the ray-tracing model,
being air and a smooth surfaced partial conductor)
Rs? =
"sin'
p
" cos2'
"sin' +
p
" cos2'
Rsk =
sin'
p
" cos2'
sin' +
p
" cos2'
(3.8)
where " is the complex permittivity such that " = "r - j60 , "r is the relative
permittivity and is the conductivity of the incident object. The reflected field at a
distance s away from the reflection point is given as
Er(s) = EiA(s)Rse jks
(3.9)
31

Figure 3.2: Reflection of vertically polarised plane wave incident on a conductor
where Ei is the incident electric field, k is the wave number 2⇡/ and A(s) is the
attenuation factor given by
A(s) =
1
s
(3.10)
For simplicity, each wall was treated as having the same value for "r = 15 and
= 0.012 S.m 1 and the ground having "r = 10 and = 0.005 S.m 1 [33]. As the
ray-trace model is considered 2.5D, wall reflection calculations are first determined
using the 2D beam method, and the actual ray intersect with the wall is performed in
3D, by an initial check to see whether the incident ray lies within the bounds of the
3D vertical wall.
32

3.5 Di↵raction
When a radio wave interacts with a conducting edge the wave undergoes di↵raction.
This causes the energy associated with the wave to bend about the object and its
e↵ects can be observed most notably when radio signals can still be received in NLOS
areas. The most common implementation of di↵raction is the Uniform Theory of
Di↵raction (UTD). To model this phenomena using ray theory, when a incident ray
hits an edge it is split into a multitude of di↵racted rays that propagate about the
edge in a cone like fashion as seen in Figure (3.3).
Figure 3.3: Di↵raction wedge side view
33

To determine the loss associated with di↵raction, the dyadic di↵raction coe cient
needs to be calculated for the vertical and horizontal components of the electromag-
netic wave. The coe cient D is a dyadic tensor for which
D(L, , 0
) =
e j⇡/4
2n
p
2⇡k

cot
✓
⇡ + ( 0)
2n
◆
F(kLa+
( 0
))
+cot
✓
⇡ ( 0)
2n
◆
F(kLa ( 0
))
+R?
k0cot
✓
⇡ ( + 0)
2n
◆
F(kLa ( + 0
))
+ R?
kncot
✓
⇡ + ( + 0)
2n
◆
F(kLa+
( + 0
)) (3.11)
where ’ is the incident ray angle with respect to the 0-face and is the departure
angle of the di↵racted ray with respect to the 0-face. The value s’ represents the
distance of the source to the di↵raction edge and s the distance from the edge to the
observation point. The wedge angle factor n lies within the range of 1<n2 such that
a value of n=3/2 for a 90o wedge [20] [43] as shown in Figure (3.4).
Figure 3.4: Top view of di↵raction wedge
34

The function F(x) is a transition function that contains a Fresnel integral.
F(x) = 2j
p
xejx
Z 1
p
x
e j⌧2
d⌧ (3.12)
This Fresnel integral can be approximated by the following equations found in [43].
For large values of X
F(X) '

p
⇡X 2Xej ⇡
4
2
3
X2
e j ⇡
4 · e[j(⇡
4
+X)] (3.13)
and smaller values of X
F(X) ⇠
✓
1 + j
1
2X
3
4
1
X2
j
15
8
1
X3
+
75
16
1
X4
◆
(3.14)
The resulting phase and magnitude of the transition function F(x) is as shown in
Figure (3.5).
Figure 3.5: Fresnel transition function
35

The values of a+ and a in Eq. 3.11 are a measure of the angular separation be-
tween the observed di↵racted field point and the Reflection Boundary (RB) or Shadow
Boundary (SB) as seen in Figure (3.4). These are given by the following
a±
( ± 0
) = 2cos2
✓
2n⇡N± ( ± 0)
2
◆
(3.15)
where N + and N are integer values that satisfy
2⇡nN+
( ± 0
) = ⇡ (3.16)
2⇡nN ( ± 0
) = ⇡ (3.17)
To visualize the value of N + and N , the following plots of N vs , in which =
( ± 0) are made use of in the actual ray-trace model and can also be found in [43].
Figure 3.6: The N+ function
The parameter L in Eq. 3.11 is a distance value that is dependent upon the type
of electromagnetic field wave type, be it plane, spherical, cylindrical or conical wave.
36

Figure 3.7: The N function
For the case of plane wave propagation used in the ray-trace model developed for this
work, L is given as
L = s · sin2
0 (3.18)
Finally the di↵racted ﬁeld Ed is calculated by
Ed(s) = EiD(L, , 0
)A(s0
, s)ejks
(3.19)
where the attenuation factor A, for a plane wave is given as
A(s0
, s) =
1
p
s
(3.20)
The di↵raction coe cient shown in Figure (3.8), has wedge angle of 2.513 rad. (or
144o), frequency f = 2100MHz, incident angles = 0.087 rad. (or 5o), = 0.262 rad.
(or 15o) with s0 = 500m and s = 500m.
37

Figure 3.8: Plot of di↵raction loss around a wedge
3.6 Field Strength Calculation
In the ray-trace algorithm described in Chapter 2, once the geometric calculations
for determining individual wavefronts (unique paths from transmitter to receiver) are
performed, calculations are made on a single ray inside each beam to determine the
value of the electric ﬁeld for the wavefront it represents. There are two methods which
can be used to calculate signal characteristics, these are the power-of-complex sum (PS)
where the total power is found by the sum of individual rays, or the sum-of-individual-
ray-powers (SP) method whereby the total signal power is obtained by summing the
individual ray powers [33] [44]. The following equation is used to determine the electric
ﬁeld Ei for the ith ray at a given location
Ei = E0ftifriLi(d)
2
4
Y
j
Rj
Y
k
Ak(s0
k, sk)Dk
3
5 e jkd
(3.21)
38

where E0 is the reference field strength value, fti fri are the field amplitude radia-
tion patterns for the transmit and receive antennas, Li is the loss component associated
with the distance of the ray path d, reflection loss Rj, di↵raction loss Dk with spread-
ing function Ak and the final exponential term being the associated propagation phase
factor due to path-length [23].
Figure 3.9: Ray-trace model output of Received Signal Strength
3.7 Channel Response
From the geometric results of the ray-trace model, many signal characteristics can
be determined in the electric field calculation stage. By adding the individual ray
paths together in superposition and taking into account each rays phase, this produces
realistic channel responses such as the Power Delay Profile which represents the delayed
39

arrivals of a signal from a single transmitted pulse. As the ray-trace model can work
in both uplink and downlink directions, a power delay profile can be created in which
the impulse response of a mobile handset is observed at the Base Station Transceiver
(BTS) of a cellular network and vice versa.
Figure 3.10: Unique wavefronts from a NLOS UE arriving at a BTS
Each ray in Figure (3.10) represents an independent wavefront, with the source
being the mobile handset or User Equipment (UE) in 3G/UMTS terminology, and the
receiver the BTS. Each ray-path has its own unique length and interactions with the
environment. The above simulation was performed with a maximum of 7 reflections
and a single order of di↵raction. The ray-paths have their length calculated which is
then translated into a time value. To theoretically model the multipath signals arriving
at the receiver, the equation first proposed in [45] for the band-limited complex impulse
response is given by
h(t) =
NX
n=1
An (t ⌧n)e j✓n
(3.22)
40

where the received signal ht is found by the vector sum of the time delayed multi-
path components in the form of the phase shifted Dirac function with amplitude An,
arrival time ⌧n and phase ✓n. In order to create realistic channel impulse responses
from a band-limited channel, the pulses created by Eq. 3.22 are convolved with a
raised cosine pulse of 260.4ns duration given that the WCDMA chip rate is given
as 3.84Mcps [46]. This pulse shape was chosen to approximate the frequency selec-
tive nature of a wireless channel (where high frequency components of a transmitted
pulse are attenuated and the observed pulse is distorted) and adding them together in
superposition, produces the power delay profile seen below in Figure (3.11).
Figure 3.11: Power Delay Profile observed at a BTS
Further signal metrics can be derived from the PDP, these being the Rician K factor
which is the ratio of signal power of the dominant multipath component over the mean
value of multipath components. The mean excess delay ⌧, can be derived from the
PDP, which is the average delay of multipath components after the first arrival. The
root mean squared time delay, or TRMS can also be derived from the PDP, in which
TRMS is the standard deviation of the delay of reflections, proportional to the energy
in the multipath components that make up the PDP. Calculating the TRMS allows
for further channel information such as the coherence bandwidth which represents the
frequency range over which the channel is considered a flat fading channel.
41

In a similar manner to the creation of the PDP, the Angle of Arrival (AOA)
can be determined from the multipath components of the ray-trace model. A similar
convolution of a theoretical distorted channel response cosine pulse with the width of
10o was performed on the delayed ray-paths as done in [42] for Power Angle Profiles
(PAP) arriving at the BTS and added using superposition to create the plot as shown
in Figure (3.12). The AOA (or PAP) represents an almost ideal case in which a
BTS was equipped with smart antenna with very high spatial resolution to distinguish
arrival angles less than 10o.
Figure 3.12: Angle of Arrival observed at a BTS
3.8 Summary
This chapter has described in detail the necessary radio propagation theory and calcu-
lations made on the geometric results of the ray-trace algorithm described in Chapter
2. With the signal characteristics provided by the ray-trace algorithm, the results
can be applied to higher layer communication system simulations and site specific
case studies. The signal metrics of Received Signal Strength, Power Delay Profile
and Power Angle Profile are used in Chapter 4 when applied to location estimation
systems.
42

Chapter 4
Location via Ray-Tracing and
Virtual Fingerprints
Using the ray-trace model developed in Chapter 3, simulations were performed on a
location method using virtual ﬁngerprints derived from ray-trace results. This chapter
describes a protocol that was created for this location method and investigates the
trade-o↵ between ray-trace model complexity and positioning accuracy, as well as
the feasibility of determining location using this ray-trace derived virtual ﬁngerprint
method on current generation mobile handsets.
4.1 Positioning Technologies
Positioning methods can be grouped by the means in which the signal is measured
and by which component makes the measurement in a wireless communication system.
They are either network centric, in which the wireless network analyses signal metrics
from the mobile handset and determines a position, or handset centric in which position
is determined by the handset alone. A hybrid method involves measurement and
location determination via a combination of both network and handset.
4.1.1 Network Based Positioning Methods
Network based methods used in cellular systems provide positioning estimates by
obtaining measurements at the BTS and in most cases, are sent to a location server
where they are processed and a position is determined. Mobile phone networks such as
2G/GSM and 3G/UMTS have a dedicated location server such as the Mobile Position
Center or Gateway Mobile Location Center (MPC/GMLC) as part of the networks
infrastructure. Many equipment vendors have their own positioning solution generally
43

referred to as a Location Measurement Unit (LMU) that can implement a number of
positioning technologies that report back to the MPC/GMLC.
4.1.1.1 Timing Methods
Time of Arrival (TOA) and Time Di↵erence of Arrival (TDOA) are methods in which
the signal from the handset is received by at least three BTS in order to determine a
position based on the signals arrival.
Figure 4.1: Time of Arrival positioning method
The TOA method works by determining a distance of the mobile handset from
each BTS that is directly proportional to the propagation time. The TOA method
requires accurate synchronisation of transmitters and receivers in the network and a
time stamp provided by the transmitter in order to calculate the time di↵erence and
distance. As shown in Figure (4.1), the one way propagation time is measured and
a range is calculated as [R1, R2, R3] and the intersection of the circles formed from
base stations [Tx1, Tx2, Tx3] provides a location. This method is often referred to as
Trilateration. The generalised location method for N base stations can be determined
by minimising a sum of squares algorithm in which a mobile handset at location (x0, y0)
transmits a time-stamp at t0 which is received at [t1, t2, ... tN ] by base stations located
44

at [(x1, y1), (x2, y2) ... (xN , yN )]. By minimising the following quadratic cost function
F(x) =
NX
i=1
↵2
i f2
i (x) (4.1)
in which ↵i is a coe cient related to the reliability of the signal received [7] [47]
at the ith measurement point and fi(x) is a distance value such that
fi(x) = c(ti t)
p
(xi x)2 + (yi y)2 (4.2)
where c is the speed of light. In cellular systems, it is often the case that the mobile
handset clock is not synchronized and the clock bias must be accounted for. Overall
accuracy depends upon the synchronisation which in turn is related to the systems
packet transfer and data rate. The TOA method su↵ers from multipath propagation
e↵ects, with NLOS propagation increasing the time delay of signals from the handset
to the BTS. Much research has been done on minimising the e↵ects of multipath
propagation errors [47] [48]. The TDOA method works on a similar principle, however
rather than observing the absolute time of arrival of the signal at a BTS, the time
di↵erence at which the signal arrives at three or more base stations is used. By
examining the di↵erence in time at which a signal arrives, removes the clock bias
error. Location estimates are found by the intersection of hyperbolic curves which are
formed by the comparing pairs of TOA circles [49].
In 3G/UMTS systems, the Observed Time Di↵erence of Arrival (OTDOA)
method can be implemented as a handset-based network assisted method or a network-
based handset assisted method. For the latter, the signal from a mobile handset is
required to arrive at 3 or more separate base stations where the di↵erence in the
arrival time is calculated. Increasing the number of base stations used in the location
estimation improves the accuracy and helps overcome the errors introduced by NLOS
propagating signals.
Built into the 2G/GSM systems, the Timing Advance (TA) value can be used to
determine location based on this parameter. As the mobile handsets are all at various
distances from the BTS and the multiple access scheme being TDMA, handsets must
be coordinated to transmit at certain times so as to not interfere with others. The TA
value is the variable parameter controlling when a mobile handset can transmit, and
it can be made use of as a measure of how far the handset is away from the BTS. The
accuracy of positioning by TA is quite poor due to its resolution, related to the TA
parameter being equivalent distance increments of ⇠550m [50]. A similar method in
3G/UMTS systems is the Round Trip Time (RTT) parameter. The round trip time is
45

determined to be the time di↵erence between the beginning of a transmitted downlink
Dedicated Physical Channel (DPCH) frame from the UMTS NodeB to the UE and
the beginning of a received corresponding uplink frame from the UE to the NodeB.
The minimum resolution obtained from this method is ⇠80m.
4.1.1.2 Angle of Arrival
The Angle of Arrival (AOA) method determines a mobile handsets location by the
use of directionally sensitive antennas. Signals from a mobile handset arriving at a
BTS have their angle of arrival estimated by steering the main lobe of an adaptive
phased array to the direction of arriving signal. This requires base stations within the
network to have complex phased array and an adaptive real time signal processing unit
to provide the beam steering capabilities. The network determines a location of the
handset by the intersection of two or more bearings. Multipath propagation e↵ects
can degrade position estimates, as the strongest signal arriving at the base station
may not have traveled along the bearing line, but via a misleading reﬂection from a
building or a moving vehicle for example. Typical location errors for AOA positioning
are within the range of 100m⇠300m.
Figure 4.2: Angle of Arrival positioning method
Further errors are incurred when positioning targets are located far from the BTS
which introduces angular error. The spatial resolution of two perfectly complement-
ing bearings is limited to 2Dsin(↵/2), where ↵ is the angular resolution, and D is
46

the distance between the target and the BTS [6]. Thus with increasing distance from
the BTS results in poorer spatial resolution as does increasing the minimum angular
resolution response of the phased array. This positioning method does not require any
additional changes made to a mobile handset, but the requirement of specialist direc-
tional antenna arrays and added signal processing units at the BTS which increases
the costs to implement for a network provider.
4.1.1.3 Cell-ID
The Cell Identification method (Cell-ID) is one of the simplest network based posi-
tioning methods. For mobile phone networks such as 2G/GSM and 3G/UMTS, the
coverage area of the networks is comprised of a number of cells, each with a unique
identification code. When a mobile handset moves within the networks coverage area,
it is connected to a serving cell which is often the BTS of the cell that provides the
strongest signal. For location accuracy, Cell-ID is considered the least accurate as a
mobile handsets position can only be assumed to be somewhere within the area of this
serving cell. For dense urban microcells, these cell sizes can be the order of 1km to
3km whereas in suburban or open rural areas, range from 10km to 30km. Cell-ID of-
fers a low accuracy location estimation that is proportional to the size of the networks
cell areas. It requires no modifications to the handset and no complex processing of
air-interface characteristics via the BTS or network [6]. Hybrid Cell-ID methods have
been proposed in which timing methods have been added such as RTT or TA [51].
Figure 4.3: Cell-ID positioning method
47

4.1.1.4 Fingerprinting
Is a method whereby a handset is located by matching various signal metrics to those
found in a spatial database. The database itself needs to be filled by various means and
this can involve either direct measurement or simulation using a radio network planning
tool. Fingerprints derived from radio propagation tool simulation can be referred to as
Virtual Fingerprints. Direct measurement methods require data collected from drive
tests in which precise location data is recorded (via GPS) and the various database
signal metrics are assigned to that location. The database values can be interpreted
as the radio environments signature at each of the coordinates.
Figure 4.4: Virtual Fingerprint created by a radio propagation tool
When a handset transmits from a given location, the signal is received at one
or more BTS units which then pass this information onto the network. The spatial
database is then searched to find the closest match to the signal(s) received at one
or more of the Base Stations. These signal metrics can vary from received signal
strength to spatial and temporal signal characteristics which can provide unique radio
fingerprints for a given location. Due to the unique site specific nature of fingerprint
methods, multipath propagation e↵ects can be exploited in identifying NLOS loca-
tions especially in the cases where a database is comprised of Power Delay Profiles [8]
48

[14]. Much research has been done in this area on the validity of Database Correla-
tion Methods (DCM). Measured database correlation methods like that described in
[11] require only a single BTS for matching of measured PDP’s. Virtual ﬁngerprint
methods that employ the matching of ray-traced derived PDP’s have been shown in
[13] [52]. Location via Virtual Fingerprints in 2G/GSM networks using the results of
planning tools and for RSS has also been extensively studied in [12], as well as hybrid
combinations of RSS and AOA for 3G/UMTS systems in [9]. Location error for many
of these methods has been estimated at being less than 100m [11] [52].
4.1.2 Handset Based Positioning Methods
These are positioning solutions that are performed by the handset itself. Handset
methods are limited by the types of measurements that can be made. For example, a
handset does not have the ability to implement spatial processing techniques such as
those that a BTS with a smart antenna array can. Most handset methods rely upon
signal measurements such as signal strength or time based approaches.
4.1.2.1 GPS and A-GPS
Since the use of the Global Positioning System (GPS) was made available to the
worldwide public in early 2000 after the removal of the Selective Availability feature
that made civilian use less accurate than military systems, an accurate positioning
system that o↵ers sub 10m accuracy has been quickly adopted as the most popular
method for determining ones location. GPS provides a 3D position as well as velocity
and time information provided the receiver has a clear unobstructed view of the sky.
It works by receiving time stamped coded data from 4 or more satellites and calculates
a position (in 3 dimensions) via Trilateration.
Di culties arise in dense cities, where tall buildings can obstruct or interfere
with signals from the satellite constellation and degrade accuracy due to multipath
propagation and shadowing. Location error in ideal circumstances can be as low as
⇠10m. Other environmental e↵ects include ionospheric disturbances for which the
GPS system can compensate for, except in extreme space weather events such as a
large coronal mass ejections and their associated solar radio burst which can result in
fadeouts in the HF, VHF and UHF ranges [53].
A common inclusion in many 3G handsets is Assisted GPS (A-GPS) technology,
which uses information obtained form the mobile phone network to assist the GPS
receiver in its start up phase. The network can provide information on the current
orbital data of satellites enabling the GPS receiver to acquire signal lock faster, rather
than searching from a cold start.
49

4.1.2.2 Observed Time Di↵erence Methods
Similar to the TOA method in which the handset, rather than the BTS, measures the
time di↵erences of signals sent from at least 3 BTS’s to calculate a range from each
and its overall position. The Enhanced Observed Time Di↵erence (E-OTD) system
for 2G/GSM networks operates by the handset observing information provided by
Base Stations and reference beacons or Location Measurement Units (LMU’s), which
are incorporated into some BTS sites across the network. The LMU contains an
accurate time source and computes clock di↵erences between Base Stations. When
3 or more E-OTD signals are received by a handset equipped to do so (by specialist
software installed on the phone) time di↵erences can be determined and location is
found by the intersection of hyperbolic curves [6]. The accuracy of this method is
around 50m⇠200m, is related to the number of observable LMU’s and is a↵ected by
NLOS propagation e↵ects.
The 3G/UMTS system equivalent is called Observed Time Di↵erence of Arrival
(OTDOA) method and operates in a similar manner to E-OTD method described in
section 4.1.1.1. Enhancements have been made to this method in which idle periods are
inserted into the NodeB transmissions in order for the handset to maximise the chance
that distant NodeB pilot signals can be observed [6]. This is due to the near far problem
which can occur in CDMA systems in which distant transmitters within the shared
channel cannot be heard due to stronger signals coming from closer transmitters.
4.1.2.3 Novel Handset Based Positioning Method
Proposed within this work is a novel method of handset based positioning. Novel
positioning methods involve measurements made either by the handset or the network
that are then compared with calculations made by the handset to estimate a position.
Some hybrid methods would require information from the BTS to be sent to the
handset which at this stage may not be part of the standards for current cellular
systems.
4.2 Virtual Fingerprint Protocol
A new protocol for location estimation based on creating a real time virtual ﬁngerprint
is proposed.
• Stage 1: Request made for location by the UE.
• Stage 2: The network reports back a UE location within 100m-500m of its actual
position using Cell ID or triangulation methods.
50

• Stage 3: The UE downloads vector model and base station data for area within
the initial error range.
• Stage 4: The UE executes a ray-trace algorithm to produce a virtual fingerprint.
• Stage 5: Location is found by optimal matching of UE measurements to those
in the virtual fingerprint.
Figure 4.5: The Virtual Fingerprint Location Protocol
To simulate this location protocol we first need an appropriate building database.
Since the Sydney Central Business District (CBD) was chosen as our area of interest,
the required building database for Sydney was derived from building outlines using
Google Earth satellite imagery in a similar method to that done in [15] and exported as
a Google KML file. The KML file contains a formatted structure that groups together
values of longitude, latitude and altitude to make up the polygons of a building object.
The geographical coordinates used in the KML file then need to be converted to UTM
grid coordinates for use in our ray-trace model. Such KML files would be suitable for
the building data that the handset could access in Stage 3 of the protocol.
To obtain base station locations (also required for Stage 3 of the protocol), a
search of the Australian Communication and Media Authority (ACMA) assignment
records provided the address or coordinates of actual sites and information on the
antennas used at each BTS [54] for the Three 2100MHz 3G network. Each cell of the
BTS was modeled from derived ACMA data with a directional antenna pattern with
output of 20W, which equated to an EIRP of 44.1dBm.
With this information in hand we could then test the protocol. To do this we set
up an environment in order to simulate live (handset) measurement data from which
the handset will derive a location. To simulate live measurements, a set of 34,485
grid points at 5m resolution was placed along city streets. These points were used to
51

represent UE locations placed 1.5m o↵ ground level. The RSS at each of these points
was modeled using a pathloss model based on log-normal shadowing
PL(d)[dB] = PL(d0) + 10n log
✓
d
d0
◆
+ ⌦ dB (4.3)
Here ⌦ dB is a zero-mean Gaussian random variable with variance 2
dB, d0 is a
reference distance from the transmitter in metres, d is the length of the path in metres
and n is the path-loss exponent. A value of n=3.3 was adopted, consistent with path-
loss models used in [3] [55]. The RSS at a distance d is then given by,
Pr(d)[dBm] = Pt(d)[dBm] PL(d)[dB] (4.4)
where Pt(d) is the transmitted power in dBm. Figure (4.6) shows the ray-trace sim-
ulation with 7 orders of reﬂection and 1 di↵raction order for the maximum RSS(dBm)
at 34,485 grid locations of 5m resolution with 27 Base Stations in the Sydney CDB
area of 1.2km x 1.7km.
Figure 4.6: Simulated RSS measured values
52

The live handset measurement data is used in Stage 5 of our protocol in order to
determine a location. The location at Stage 5 is determined using the following cost
function
⇠xy =
KX
k=1
RSSm
k RSSxy
k
2
(4.5)
where K is the number of Base Stations, RSSm
k is the live measurement (RSS from
Base Station k) and RSSxy
k is the ray-trace models derived RSS virtual ﬁngerprint
value at location xy from Base Station k. By minimising this cost function we can
ﬁnd a location estimate for the handset. Using Eq. (4.5) the mean value of localisation
error produced by the protocol for a range of environment parameters is determined,
the results of which are shown in Figure (4.7).
Figure 4.7: Mean localisation error for variable simulation parameters
53

The curves in Figure (4.7) show the mean localisation error versus number of ray-
trace reflections  ,for variable dB and Cell-ID location error (reported in Stage 2) of
R=100m and R=200m. The mean localisation error was averaged over the 34,485 grid
points, and Cell-ID error location radii of R=100m and R= 200m were probed. We see
that localisation error decreases with increasing orders of reflection, and mean location
error increases with dB. In terms of an optimum number of reflections required for
location estimate, the asymptotic behaviour of these curves suggests that no more
than 6 orders of reflection are needed. A value of 5 orders of reflection was chosen for
determining the UE system requirements.
4.3 System Requirements
In this section we investigate the handset system requirements for our new protocol.
As we are specifically interested in the protocols ability to produce an accurate loca-
tion estimate within a respectable time-to-fix, we define the term time-to-fix as the
time interval between the UE requesting an initial estimate at protocol Stage 1 and
the protocol delivering a location Stage 5. An accurate location estimate within 30
sec would be consistent with FCC requirements [1]. A 1km2 area KML file was found
to be less than 1MB in size. For an indication of the required download time, if the
downlink provided was a 3G UMTS 384 kbps service, this would be less than 5 sec.
Download times could be half of this time if the file was compressed in KMZ file format
(a zipped KML file).
The most time consuming and computational demanding phase of this protocol
is the ray-tracing. This can be separated into two distinct stages, 1) The ray-path-
finding stage and 2) the RSS calculation stage. The majority of the simulation time
is consumed by the ray-path-finding process. The speed at which the ray-trace model
can run is a function of the number of objects that make up the building database,
and the orders of reflection and di↵raction involved [24]. The RSS calculation stage
is where the individual ray paths arriving at a location are all summed together as
explained in the flow chart in Figure (2.9).
To approximate handset (or UE) processing times, the microprocessor found
inside many of todays smart-phones is the ARM11 processor, running at 369 MHz.
The chosen performance measure of ARM processors is the Dhrystone 2.1 benchmark
value representing Millions of Instructions Per Second (MIPS) per CPU clock speed
[56]. Source code and compiled versions of the Dhrystone benchmark tests can be
easily obtained for any operating system and used for comparison tests. Our simula-
tion test machine is a Dell Vostro 1500 with an Intel Core 2 Duo T7500 CPU running
at 2.2GHz with 3GB RAM (single core only used for processing tasks). Running
54

the Dhrystone 2.1 benchmark tests provided a Figure of 2.75 MIPS/MHz, giving an
approximate processing time ratio of the UE processor to the test machine of 2:1. Hav-
ing developed our ray-trace algorithm in Matlab, if the algorithm was to be written in
an optimised C/C++ code to run on an embedded system like a modern handset, a
notable speed performance would certainly be achieved. Twenty fold speed improve-
ments are achievable on translation from a Matlab environment to a fixed point C
environment [57].
A series of ray-trace simulations were run in order to quantify the time contri-
butions of the ray-path-finding and RRS calculations, with the total number of Base
Stations K set to K=15 for each time trial. To justify this number K, measurements
were conducted around Sydney CBD recording RSS and Cell-ID values on a handset
with a GPS unit using the CellPos [58] application to find the average number of
observable cells. The mean number of cells was found to be K=5 within a radius of
R=100m, and K=10 for R=200m. To gauge how this algorithm could perform on a
current UE, the number of Base Stations chosen was set to K=15, a value higher than
that anticipated observable in both the Active and Monitored set of a UE to demon-
strate the speed of the algorithm. A conservative value for the time factor divisor of
10 was applied, after taking into account the Dhrystone 2.1 benchmark test and opti-
mised C/C++ speed factor increase. The results are shown in the tables below, where
columns 2 and 3 represent Matlab performance time and column 4 is our approximate
handset processing time.
Simulation Matlab RSS Matlab Ray-Path Approx UE
Reflections calculation stage (sec) finding stage (sec) processing time (sec)
3 2.2 12.1 1.4
5 3.1 23.6 2.7
7 4.1 39.4 4.3
Table 4.1: Simulation times, 5m resolution, 15 BTS, Cell-ID location error R=100m.
3 0.7 11.3 1.2
5 1.1 22.6 2.4
7 1.6 38.2 4.0
Table 4.2: Simulation times, 10m resolution, 15 BTS, Cell-ID location error R=100m
55

3 8.0 31.0 4.0
5 13.0 68.6 8.2
7 18.0 124.0 14.2
3 2.2 29.7 3.2
5 10.4 65.0 7.5
7 16.7 117.7 13.4
From the last column of these tables we can see that UE processing times of
approximately a few seconds are expected for most location estimates. This confirms
that user embedded ray-tracing of the type discussed in this thesis is shown to be
feasible on todays handsets. It should also be noted that the number of Base Stations
a↵ects the processing time on the UE, where an extra Base Station adds an extra 5%
to processing time.
In the above tables, for a given ray-trace simulation with K=15 Base Stations
and initial search radius R=100m, high spatial resolution (Table 1 with grid size of
5m) results in longer simulation times when compared to low resolution (Table 2 with
grid size of 10m). These tests were repeated for K=15 Base Stations and initial search
radius R=200m, which exhibited the same behaviour of increased spatial resolution
resulting in increased simulation time. There was found to be a linear time increase
which applies to each transmitting antenna simulated, and the number of transmitters
required is a function of the initial search radius. From the results shown in Tables
4.1 to 4.4, in order to reduce the computation times, selection of an optimum number
of base stations is an important factor for the result within an acceptable time-to-fix.
The inclusion zone radius for the buildings and transmitters required for creation
of the virtual fingerprint was set as 50m away from the edge of the initial location
error circle. This distance was chosen in order to include transmitters that would
populate the virtual fingerprint with worthy NLOS contributions. If the number of
transmitters used for creating the virtual fingerprint was limited to those just found
within the initial search radius, this would have a notable e↵ect on the accuracy
of the location estimation. Building selection criteria was also an important factor in
determining accurate virtual fingerprints. The same inclusion zone for the transmitters
56

was applied to buildings. Any building with a vertex point found within this radius
was included in the virtual fingerprint calculation. This selection criteria avoided
the case where false LOS measurements of RSS values could corrupt the fingerprint
database for cases where a transmitter was modeled as having an unobstructed path.
Overall, with the Dhrystone CPU benchmarking ratio and optimised code speed factor
increase, supports the viability of the new location protocol described in section 4.2.
The accuracy and performance time will obviously improve as the processing power of
the UE increases.
4.4 Embedded Benchmarking Tests
In order to estimate the simulation time for the ray-trace algorithm to be performed
on a actual handset, benchmarking tests were done in parallel on both the Matlab
model and an application written in C/C++ Carbide and compiled into a Symbian
S60 application to test on di↵erent handsets.
Figure 4.8: Snap-shot of the console output for benchmarking tests
Using the profiling tool available for Matlab, this provides a complete analysis of
the number of function calls and the time required to execute each. By replicating
the same functions written in C/C++ Carbide and repeating them the same number
57

of times found in simulation of a single transmitting cell, this provided an estimate
of the actual run time of the ray-trace model if fully implemented on a handset. The
application was loaded onto 3 separate handsets, these being a Nokia 6120 (369Mhz
ARM 11 processor), Nokia E71 (369 MHz ARM11 Freescale MXC-300-xx processor)
and a Nokia E72 (600 MHz ARM11 processor). The following graph illustrates the
reduction in computing time as the processor speed increases and also supports the
proposed speed factor increase when Matlab code is translated to a ﬁxed point C
environment as mentioned in Section 4.3.
Figure 4.9: Embedded benchmarking results
4.5 Simulated and Measured Comparisons
Measurements of the Common Pilot Channel (CPICH) were taken using a handset
equipped with USIM Application Toolkit [59] to record Received Signal Code Power
(RSCP) values. The RSCP is reported to the SIM card as outlined in 3GPP TS-
31.111, Section 8.22 “Network Measurement Results” [60]. The CPICH is the downlink
channel from the UMTS NodeB to the UE, for phase synchronization and channel
estimation by the handset for Frequency Division Duplex (FDD) mode. Measurements
of the Received Signal Strength Indicator (RSSI), which is a common metric available
on most 3G mobile handsets provides the wideband RSS in a WCDMA system.
58

Figure 4.10: Measurement locations
The RSSI would not provide an indication of signal strength relative to a single
cell, due to the fact that all cells transmit a spread signal within the shared 5MHz
bandwidth and are separated in code domain. Recording the values of RSCP was
conducted at 153 precise locations within the Sydney CBD seen in Figure (4.10).
Exact coordinates were decided upon and measurements were taken for a few minutes
at each position to get a reliable sample set of data. This method of data collection
was necessary as it was found that logging paths with a GPS resulted in too many
errors associated with building shadowing as well as the aforementioned need for a
reliable sample set at each location to remove measured RSCP outliers. The mean
error between the ray-trace results versus measured was found to be 8.95dB and 68%
of results of the ray-trace were found to lie within 13.234dB of the measured results,
59

with a total sample size of 32394 individual RSCP measurements. It should be noted
that measurements close to the base station (i.e. directly under it or to the side) may
not lay within the main lobe of the radiated antenna pattern, as directional antenna
patterns with 3dB beam width of 60o are used on the majority of cells modeled for
the network (as determined from the ACMA database). This could account for some
of the larger di↵erences seen in the scatter plot. Measurement locations furthest from
the BTS and those in NLOS areas also contribute to the larger di↵erences found.
Figure 4.11: Scatter plot of measured vs. simulated RSCP
The above plot highlights a relatively high mean error when comparing the mea-
sured and simulated values for RSCP. Given the minimum location error achieved was
shown in Figure (4.7) to be just under 50m, the question exists, by using the ray-trace
algorithm can channel information such as spatial and temporal characteristics reduce
this error in location accuracy? The following section investigates the use of PDP and
AOA parameters derived from the ray-trace algorithm using similar orders of reﬂection
and hence, equivalent simulation times.
60

4.6 Novel Hybrid Positioning System Method
As demonstrated in Chapter 2, the ray-trace model can provide a wealth of information
regarding the channel characteristics, such that further signal metrics obtained from
ray-trace simulations could be used in a method that involved obtaining information
from both handset measurements and those from a 3G/UMTS NodeB. Section 4.2
discussed a five stage protocol for location estimation. With the NodeB’s ability to
perform enhanced signal processing techniques on arriving signals to determine Power
Angle Profiles (PAP) and Power Delay Profiles (PDP), provided a mechanism which
allowed the transfer of these metrics from the NodeB to a UE, the 5 stage protocol
could be amended such that
• Stage 1: Request made for location by the UE.
• Stage 2: The network reports back a UE location within 100m-500m of its actual
position using Cell ID or triangulation methods.
• Stage 3: The UE downloads vector model and base station data for area within
the initial error range.
• Stage 4: The UE executes a ray-trace algorithm to produce a virtual fingerprint.
• Stage 5: The NodeB reports back the measured signal metric (PDP/PAP) and
location is found by optimal matching of UE ray-trace derived virtual fingerprint.
In a similar manner to the ray-trace generated “measurements” that were
created for the RSS case, whereby various levels of Gaussian noise were added to the
ray-traced values, a similar approach was used to create realistic data sets that could
mimic measured data for the PDP and PAP metrics. For each multipath component
generated by the ray-trace algorithm, we added a zero-mean Gaussian random variable
⌦dB with variance 2
dB as done in section 4.2. Also added to the data were randomly
generated paths to take into account other multipath components that the 2.5D ray-
trace model would not be able to predict, such as local scattering of moving and small
objects that would be di cult to model. Random paths from simple Over Roof Top
(ORT) di↵raction rays that were determined by building heights and the direct path
to between the UE and NodeB were also included. Examples of PDP’s and PAP’s
created by adding noise and random paths are shown in Figures (3.11) and (3.12).
61

Figure 4.12: Ray-trace PDP vs. “measured” PDP
An example of the ray-trace model real and predicted PDP is shown in Figure
(4.12) in which the red line represents the ray-trace derived PDP (found by the UE)
and the blue line is that of the ray-trace created “measured” PDP (observed by the
NodeB). Figure (4.12) indicates notably di↵erent signal amplitudes for the two signals
due to added random paths and noise resulting for each. The multipath components
that appear before the strongest component are due to an estimated ORT di↵raction
path which was created for further realism in cases where the path of the UE to the
NodeB was not within LOS of the transmitter.
The PAP shown in Figure (4.13) is created from the same ray-trace simulation data
as the PDP case, where the red line represents the ray-trace derived result (for the
UE) and the blue line is that of the ray-traced model (with added noise and random
scattering multipath components) to be used as a measured PAP as observed at the
NodeB and reported back to the UE in the hybrid protocol.
In order to use both the PDP and PAP information for location purposes, a grid
of locations was devised based on the area covered by a NodeB initial error radius
62

Figure 4.13: Ray-trace PAP vs. “measured” PAP
with resolution of 10m. A grid of 8754 possible test locations based on the union of
the square coverage area of initial search radius condition R=200m for each NodeB
was created and is shown in Figure (4.14). Similar to the procedure for the creation
of the RSS measurements in section 4.2, for each of the 8754 test locations, a PDP
and a PAP from every grid point was generated and archived to represent the channel
response (as measured by the NodeB). For the case of R=100m this resulted in 2824
test locations while R=300m provided 13213 test locations.
Once the entire superset of ray-traced generated PDP’s and PAP’s to be used as
measured data was created, the hybrid positioning protocol could be simulated for
each test location. Given the NodeB measured PDP and PAP originating from a
single test location, the ray-trace simulation was performed (by the UE) for the grid
locations that reside within each observed cells initial error radius R (reported back
in Stage 2 of the protocol).
63

Figure 4.14: The 8754 test locations for hybrid location methods for R= 200m
The UE ray-trace results were then compared to the measured data via a cor-
relation function in order to determine the closest match. The higher the correlation
value, the closer the match was considered of the ray-trace and measured PDP or
PAP. The UE ray-trace simulations were repeated for varying orders of reﬂection and
varying initial error radius R = [100m,200m,300m] and the measured result data sets
were generated with added noise dB = [0,3,6,9,12,15] dB.
64

Figure 4.15: Plot of AOA correlation location tests
The result data from the hybrid protocol location method was then analysed to
observe the relation between the average location error versus the number of multipath
components. Figures (4.15) and (4.16) show the results for the location error associated
with the PAP and PDP metrics versus the number of multipath components.
As expected ray-trace simulations with higher orders of reﬂections were found to
produce proﬁles with the highest number of multipath components in the majority of
65

Figure 4.16: Plot of PDP correlation location tests
locations. Location errors for the PDP metric were shown to reduce to less than 50m
if a ray-trace model could produce a PDP of at least 5 multipath components or more
for either of the cases of variable initial search radius R. For PAP case, much higher
orders of reﬂection were needed to produce a PAP that was comprised of 15 or more
multipath components for location errors to be less than 50m. For both methods,
the addition of random added multipath components and noise to the measured data
66

had little e↵ect on the location error due to the behaviour of the correlation function
chosen as the matching function. This is in agreement with [14] in which the use of a
PDP fingerprint for location purposes had been investigated and found to be robust
to noise and multipath propagation e↵ects.
4.7 Summary
In this chapter we have introduced the di↵erent types of methods of mobile location
estimation via cellular networks. We then introduced a novel location protocol which
utilized the ray-trace algorithm described in Chapter 2 for creating virtual fingerprints
for location purposes. We investigated the performance characteristics of the location
protocol using the Received Signal Strength metric and the trade-o↵ found between
simulation time and location accuracy. We then determined the feasibility of this
protocol to work on an existing handset via benchmarking tests performed based
on simulation estimates as well as implementing the most time limiting routines on
an actual handset for further confirmation of the processing capabilities of todays
handsets. A detailed field measurement campaign was conducted to provide confidence
in the results of the ray-trace model outputs. Finally we concluded with the proposal
of a hybrid positioning protocol that takes into account more detailed channel result
information from the ray-trace model and the increase in location accuracy possible
from the use of this spatial and temporal channel information.
67

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