Estimating and mapping the Fresnel zone
clearance using digital terrain models
by
Filip Biljecki
A report submitted for the course Research Orientation (gm1100).
M.Sc. Geomatics programme
Supervisor: Hugo Ledoux
Department of GIS Technology
OTB Research Institute for Housing,
Urban and Mobility Studies
Delft University of Technology
The Netherlands
November 2009
Contents
Preface
3
1
Introduction
1.1 Radio propagation . . . . . . .
1.2 Fresnel zones . . . . . . . . . .
1.3 The Fresnel zone clearance . .
1.4 Radio links and their planning
1.5 Overview of this report . . . .
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2
Existing software solutions for radio link planning
2.1 Different types of software . . . . . . . . . . . .
2.2 Software review . . . . . . . . . . . . . . . . . .
2.3 Standard functionalities & conclusion . . . . .
2.4 Observed shortcomings . . . . . . . . . . . . . .
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Extending current software
3.1 Fresnel zone clearance map . . . . . . .
3.2 Export of link data to gis formats . . .
3.3 Automatic antenna optimal placement
3.4 Multi platform support . . . . . . . . .
3.5 tin support . . . . . . . . . . . . . . . .
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13
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4 Implementation and prototype development
4.1 Data used for testing . . . . . . . . . . . . . . . . . . .
4.2 Loading the data . . . . . . . . . . . . . . . . . . . . .
4.3 Estimation of the clearance of the first Fresnel zone .
4.3.1
ned example . . . . . . . . . . . . . . . . . .
4.3.2 ahn example . . . . . . . . . . . . . . . . . .
4.4 Point-to-multipoint assessment . . . . . . . . . . . .
4.5 Export of the data and integration in gis software . .
4.6 Import of the data in Google Earth . . . . . . . . . .
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Optimisation of the prototype
5.1 Minimisation of the number of segments . . . . . . . . . . . . . . .
5.1.1
Point-to-point analysis . . . . . . . . . . . . . . . . . . . . .
5.1.2
Point to multipoint analysis . . . . . . . . . . . . . . . . . .
5.2 Lower the resolution in the multipoint clearance computation . .
5.3 Lower the spatial extent of the multipoint clearance computation
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6 Conclusion
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References
29
1
List of Figures
1
2
3
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7
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14
15
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17
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19
20
21
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The first three Fresnel zones . . . . . . . . . . . . . . . . . . . . . . . . . .
An example of an obstruction of the first Fresnel zone . . . . . . . . . . .
The three general cases of the obstruction of a Fresnel zone . . . . . . . .
The terrain profile display from RadioLink . . . . . . . . . . . . . . . . . .
The signal strength prediction in the Radio Mobile application . . . . . .
A 3d view of the antenna coverage . . . . . . . . . . . . . . . . . . . . . . .
Terrain plot generated by Atoll Microwave with multiple repeater design.
Terrain plot generated by the Green Bay Professional Packet Radio . . .
The propagation of the k factor . . . . . . . . . . . . . . . . . . . . . . . .
Differences in computing the absolute height of the antenna . . . . . . .
A terrain plot (ned dataset) . . . . . . . . . . . . . . . . . . . . . . . . . .
A terrain plot (ahn dataset) . . . . . . . . . . . . . . . . . . . . . . . . . .
The first Fresnel zone clearance map (ned dataset) . . . . . . . . . . . . .
The three points of interest in the clearance map. . . . . . . . . . . . . . .
The generated viewsheds as additional plots . . . . . . . . . . . . . . . . .
The first Fresnel zone clearance map near the building of the ewi faculty
of TU Delft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The transparent clearance map exported to QuantumGIS and placed
above the dataset of the buildings . . . . . . . . . . . . . . . . . . . . . . .
A part of the clearance map exported to QuantumGIS and placed above
a satellite image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The clearance map exported to Google Earth . . . . . . . . . . . . . . . .
Decreasing the number of interpolations along the path significantly decreases the accuracy of the prediction. . . . . . . . . . . . . . . . . . . . .
Decreasing the number of interpolations along the path significantly decreases the accuracy of the predicted clearance map . . . . . . . . . . . .
The first Fresnel zone clearance map with the grid spacing of 25 m. . . . .
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Preface
The course Research Orientation (gm1100) is a 4 ects individual course in the curriculum of M. Sc. Geomatics with the objective of increasing the skill level of the participant
to execute research projects. The course serves as a preparation for the student’s forthcoming Master thesis research, and the student proposes an own topic.
The task of this project was to investigate the use of digital terrain models and gis
technologies in the planning and assessment of future radio links, and to develop my
own solution (a working prototype) to the problem for a better understanding of the
topic, and for practicing programming skills.
This project is divided in the following parts:
• Literature study – understand the basic theory behind radio wave propagation
and the planning of radio links (1 ects)
• Software study – assess existing software solutions (0.5 ects)
• Developing an own solution to the problem – programming a working prototype
(2 ects)
• Writing the final report (0.5 ects)
This project synthesised the following courses in the curriculum:
• ae4e04tu ⋅ Multivariate data analysis
• gm1020 ⋅ 3d geoinformation systems
• in4186gm ⋅ Datastructures, algorithms and databases
• ae4e05 ⋅ Digital terrain modeling
• gm1050 ⋅ gis principles
• gm1010 ⋅ Reference and coordinate systems
Various topics are studied beyond the Geomatics curriculum and some of them are
closely related to other courses found in other curricula of TU Delft:
• Computational Geometry
• Radio Wave Propagation
3
1
Introduction
1.1
Radio propagation
Radio waves are electromagnetic waves that occur in the radio frequency portion of the
electromagnetic spectrum in which waves can be generated by applying alternating current to an antenna [5]. The radio spectrum extends from as low as subhertz frequencies
to 30 000 GHz, and due to several reasons, it is divided in several bands by frequency.
One example of such band is the very high frequency band (vhf) from 30 to 300 MHz
in which fm radio and tv are broadcasted. However, not all bands can be used for an
efficient communication from one point on earth to another, which is the main focus of
this report.
Although the fundamentals of radio waves are equal regardless of the frequency, the
main difference between different spectra, or to be more precise — frequencies, is their
behaviour when they are transmitted to one point in space to another. Radio waves are
affected by the phenomena of reflection, refraction, diffraction, absorption and scattering. The scientific field of radio propagation deals with this problems.
The focus of this project is higher frequency waves, radio waves in the range from
300 MHz to 300 GHz, which propagate in a direct wave mode, in a path from the transmitter (Tx) to the receiver (Rx), which should be kept visible, i. e. free of obstacles. This
case of a clear radio path is often referred as the line of sight (los). In many applications,
such as gis, architecture and computational geometry the line of sight is considered to
be a straight line along which an observer has unobstructed vision [13]. However, in
radio propagation the definition is more loose. In lower frequency waves, due to several
radio behaviour properties, such as in vhf band, waves can travel through some objects,
and this is still considered as line of sight, although the visual view along the path might
be obstructed. In several cases, this does not apply to relief and large objects such as
buildings.
1.2
Fresnel zones
It is a common misconception that for a quality radio link it is required to keep only
the path connecting Tx and Rx free of obstacles, that is to achieve the a free los. Due
to the diffraction and the Huygens’ principle, for a quality link, an area close to the los
should be clear of obstacles too [14, 15], since the wave propagation from Tx to Rx is not
restricted to the vertical Tx-Rx plane but it includes contributions from scattered fields
off this plane [2, 10, 17]. Here the concept of Fresnel1 zones, which is essential in radio
propagation, is introduced.
Fresnel zones are a number of concentric ellipsoids which define the radiation pattern of a radio link. In theory there is an infinite number of ellipsoids, however, in most
applications only the first Fresnel zone is considered since the strongest signals lie in it.
The Figure 1 shows the two dimensional profile plot of the ellipsoids defining the first
three Fresnel zones. The dotted line represents the los. In this case the third Fresnel zone
is partially obstructed by the relief, while the first and second Fresnel zones are clear of
obstacles. This case is considered as fine for planning most of radio links.
Several sources claim that at least 60 of the first Fresnel zone should be kept free
of obstacles such as buildings, vegetation and relief, in order to have an efficient communication link [1]. However, the more of the Fresnel zones are clear, the better the
link.
1 Pronounced
as |freI"nEl|
4
Rx
Tx
Figure 1: The line of sight and the ellipsoids defining the first three Fresnel zones around
the transmitter and receiver of a radio path. The third Fresnel zone is partially obstructed
by the relief.
The radius of an n-th Fresnel zone at the distance d 1 from the transmitter and the
distance d 2 from the receiver for the wavelength λ of the transmission can be calculated
from the following relation
√
d1 d2
(1)
r n (d 1 , d 2 ) = nλ
d1 + d2
This relation is an approximation which is not valid very close to the endpoints [8].
For practical reasons, λ can be substituted with cf where c is the speed of light in the
medium and f the frequency, since c = λ f .
A Fresnel zone grows with increasing the distance d 1 from the near-end, reaching
its maximum halfway along the link [12], where d 1 = d 2 . Inserting this relation into (1)
we get
1√
nλd
(2)
r n max (d) =
2
where d = d 1 + d 2 , that is, the slant distance from Tx to Rx. For example, the radius
of the first Fresnel zone in the middle of a 10 000 m long 2.4 GHz link is 17.7 m.
We observe from (1) and (2) that a zone decreases with an increase of the frequency.
From now on we will concentrate on the case n = 1, i. e. the first Fresnel zone (ffz), since
the strongest signals lie in it, and for practical reasons we will use frequencies rather than
wavelengths.
1.3
The Fresnel zone clearance
A Fresnel zone can be obstructed several times along the path, by obstacles such as
a mountain, buildings, and vegetation. For assessing a radio link, in addition to the
information of the obstruction of the los and a Fresnel zone, it is mandatory to know
how much of a zone is obstructed, i. e. its clearance, since an obstruction of a Fresnel
zone automatically results in the signal degradation.
If we denote a path from the transmitter to the receiver with l, where l ⊂ R3 , we can
calculate the obstruction ω i of a Fresnel zone for all points along that path (∀l i ∈ l). This
means a function ω i which expresses the obstruction of a Fresnel zone on a particular
point between the Tx and Rx can be introduced, such that ω i ∶ l i ↦ [0, 1]. If o i ∈ R is
the distance from the los to the obstacle (perpendicular to the los), and r i ∈ R is the
5
radius of the Fresnel zone at the point l i , then the clearance of the Fresnel zone at that
point can be easily calculated from the following equation:
ωi =
oi
.
ri
(3)
The Figure 2 depicts the parameters from the Equation (3) with an example.
Figure 2: An obstruction caused by an object (in this case relief) at a point l i along the
radio path l, d 1 from the transmitter. The distance from the line of sight to the obstacle
is denoted with o i , while the Fresnel radius at that point is r i . The ratio between o i and
r i is the clearance of the Fresnel zone at the observed point l i .
Since the obstruction of a Fresnel zone can be in the range [0, 1] and the relation (3)
can give results outside of that range (e. g. when an obstacle is higher than the los), we
have to add few constraints:
⎧
ωi = 0
⎪
⎪
⎪
⎪
ω i (c i ) = ⎨ω i = c i
⎪
⎪
⎪
⎪
⎩ω i = 1
ci ≤ 0
0 < ci < 1
ci ≥ 1
Since the obstacle which causes the highest obstruction has the highest effect on
the link, only the minimum value of ω i along a path is taken into account, and can be
expressed as ω = min(ω i ). In other words, the higher the value of ω is, the better the
radio link is.
The Figure 3 shows the three general cases of ω. When the line of sight is obstructed,
the value of c i is 0 or smaller than 0, hence ω = 0. When the Fresnel zone is partially
obstructed, ω is in between 0 or 1, and in case the Fresnel zone is completely clear, then
ω = 1. By multiplying these values with 100 we can get the percentage of a Fresnel zone
clearance. As noted in the previous section, the recommended minimal value for ω for
the first Fresnel zone is 0.6, while it is optimal to keep any obstacle out of the ffz, and
few subsequent zones.
1.4
Radio links and their planning
In general, there are two types of radio links involving a transmitter and a receiver:
• point-to-point, often abbreviated to p2p, involving two antennas with fixed geographic position. For example, a wifi link between two buildings.
6
Rx
Tx
Rx
Tx
No Line of Sight
Line of Sight
Rx
Tx
Line of Sight
Figure 3: The three general cases of the obstruction of a Fresnel zone with the respective
values of ω. In the first case the line of sight and the Fresnel zone is obscured. In the
second case the line of sight is clear, but the Fresnel zone is partially obstructed. The last
case shows the best case for a radio link – a clear Fresnel zone.
• Mobile radio, a situation where the transmitter or receiver is capable of being
moved, whether it actually moves or not [15, 19]; for example a mobile phone
network. Radio propagation models are ubiquitous for mobile solutions [3].
Minimising the number of transmitters in order to reduce the costs of setting up
a communication link and at the same time maximise the performance of a network,
telecommunication companies, radio amateurs and other related parties carefully plan
new links. Nowadays this is done by using radio link planning software. In general,
these software solutions assess the feasibility of a radio link prior to any site survey. The
main questions that arise while planning a radio link are:
1. Are the two points visible?
2. What is the expected quality of the link and signal strength?
For answering these questions, a software for radio link planning consists of a radio
propagation prediction model derived from the user’s equipment and several additional
parameters, and a digital terrain model (dtm). The dtm is usually not included in the
software bundle and it should be acquired separately. By combining these two components, it is possible to get an estimate of the quality of the planned radio link. The use
of gis techniques is essential in radio planning, however, there is a number of software
which separate and concentrate only on the propagation prediction model, not taking
into account dtm. It is important to mention that these software serve as an estimation
only, while later site surveys are performed for more precise and reliable conclusions.
The intermediate step between 1. and 2. in the list above, is to calculate how much of
the first, or any else, Fresnel zone is obstructed, i. e. the value of ω. Since in practice there
are no obstructions above the los, only the lower hull of a Fresnel zone is considered.
For p2p applications, software solutions are designed to calculate the feasibility of
the link between two points, usually by returning the terrain profile along the path and
values such as the estimation of the signal loss. Mobile radio applications with a fixed
transmitter can be considered as an extension of the estimation for p2p links, since they
estimate the quality of the link for each point in a certain area, i. e. mobile coverage.
The main product of this analysis is a map representing estimated signal strength in a
geographic area (more on that in §2.2).
1.5
Overview of this report
A review of software solutions for radio link planning is made and is presented in §2. The
functionalities of representative software solutions are presented in §§2.2-2.3. There are
7
few noticed shortcomings which are listed in §2.4, that are further discussed in §3 for the
implementation in the prototype of this project. The programming implementation of
the working prototype with the implemented new functionalities is explained in §4. This
kind of software involves extensive computations, hence the optimisation techniques of
the prototype are discussed in §5. The report is concluded in §6.
Field measurements and in depth radio wave propagation integration is beyond the
reach of the Geomatics programme, hence it will not be discussed anymore. However,
the literature study was helpful to understand this topic.
8
2
Existing software solutions for radio link planning
2.1
Different types of software
There are three major categorisations of the software for radio link planning:
• Software categorised by the user group (radio amateurs, semi-professionals and
high-end professionals). High-end professional applications have advanced radio propagation algorithms, for example, they include land cover models, precise
climate models and calculate the clearance of multiple Fresnel zones.
• Based on frequency bands. Since bands have different radio behaviour and are
used for different purposes, a software often concentrate on a bounded frequency
range.
• Indoors/outdoors division. Indoor radio propagation software concentrates on
the coverage of a network in a building, hence they use building models, while
solutions for outdoor radio propagation use digital terrain models. This project
concentrates on the latter category which has more applications.
2.2
Software review
There is a high number of radio planning software solutions on the market. For the
purpose of reviewing them, I have chosen a limited number of applications. A notable
portion is listed in this section, while other reviewed solutions offer repetitive functionalities and are similar to the selected ones, hence they are not mentioned.
RadioLink2 is a Windows-based commercial application for planning point-to-point
radio links which supports usgs dem, sdts dem, srtm3, gt0po30, srtm30 and Ordnance Survey data formats. It can generate a terrain profile with the los and the first
and second Fresnel zones (see Figure 4).
Figure 4: The terrain profile display from RadioLink. It shows the antenna mast, los
and first and second Fresnel zones. The display scale is adjustable.
Radio Mobile3 is a free software which supports the prediction of performance of
point-to-multipoint radio systems. Figure 5 shows the prediction of the signal strength
of a vhf Omnidirectional system. It offers terrain plots as RadioLink, and a 3d perspective view of the terrain.
The spin-off company Afterimage GIS from Ball State University (Indiana, US) produced a solution with similar functionality [9]. It has a notable new functionality of a
3d view of an antenna coverage. An example is shown in Figure 6 [4].
2 http://www.radio-soft.co.uk/radiolink.html
3 http://www.cplus.org/rmw/english1.html
9
(Last access: 1 October 2009)
(Last access: 1 October 2009)
Figure 5: The prediction of the signal strength of a VHF Omnidirectional radio system
generated by the Radio Mobile application.
Figure 6: A three-dimensional view of the 900 MHz omnidirectional antenna coverage
in an urban area. Courtesy of Afterimage GIS.
Terrain Analysis Package4 offers a land cover module for importing the usgs Land
Use Land Cover (lulc) files. Land cover brings a more accurate analysis since surface
radio waves propagate differently on different land covers.
The solution Atoll Microwave5 by Forsk offers path profile analysis with multiple
antennas (as repeaters). An example prediction model is shown in Figure 7.
Green Bay Professional Packet Radio (gbppr)6 is an extensive set of free Perl cgi
utilities for radio propagation and radio link planning. The advantage of these utilities
is that they are available in the web browser, hence it is a multi-platform solution. The
Figure 8 depicts an example of a p2p radio link planning analysis. These utilities are
commonly used by radio amateurs.
4 http://www.softwright.com/tap6.html
(Last access: 1 October 2009)
(Last access: 1 October 2009)
6 http://www.qsl.net/n9zia/ (Last access: 1 October 2009)
5 http://www.forsk.com/web/EN/19-microwave-links.php
10
Figure 7: Terrain plot generated by Atoll Microwave with multiple repeater design.
Figure 8: The terrain plot generated by an utility in the Green Bay Professional Packet
Radio package. The terrain is shown in dark red, while the los and the ffz are shown
in dark blue and green, respectively. The plot considers the earth curvature, and shows
the boundary for the 60 of the ffz as the recommended clearance value.
tramps7 is different from the listed software since it is a backward solution. It uses
radio data from radio surveys of already set up radio links to generate a map of radio
coverage. Although it is different, it is interesting to mention that such software can be
used for assessing the radio link planning software solutions by comparing the theoretical (predicted) and empirical (surveyed) data.
2.3
Standard functionalities & conclusion
All software reviewed offer common functionalities, such as:
• A link budget analysis (e. g. calculation of the loss of the cable from the device to
the antenna).
7 http://www.macltd.com/products_tramps.php
11
(Last access: 1 October 2009)
• Pre-added antenna database with technical characteristics of several antenna types.
• Consideration of climate conditions for more precise prediction of the wave propagation.
• Link profile analysis — various plots showing the relief between the Tx and Rx
and the estimated los and ffz.
• Automatic antenna height optimisation; a functionality that calculates the difference between the input antenna height and the closest height of the antenna to
achieve the los and/or better Fresnel zone clearance.
• Map representing predicted signal strength (only point-to-multipoint oriented
software)
Virtually all applications run on Windows and the majority is commercial. Some
software can run on Linux exclusively through emulation such as Wine. Many products
have a disclosed price on their product websites and are available only via direct contact
(no trial download or resellers).
It is interesting to mention that all applications use raster data only. However, the
number of supported raster formats is usually high and some applications offer guidelines for obtaining the dtm, usually in form of web links with freely available data.
After reviewing these representative programs it can be concluded that this market
is relatively old and dense. Few software solutions date from the 1980s and are still in
use. The possibility for new major and breakthrough features is limited.
2.4
Observed shortcomings
During the overview of the existing software solutions, I have noticed five new major
functionalities that could be implemented in such applications:
• A first Fresnel zone clearance map, a point-to-multipoint geometric analysis similar to a viewshed and signal strength maps.
• Export to geodata formats and integration in gis software.
• Automatic calculation of the closest optimal antenna placement location in the
vicinity of the planned location for a receiver.
• Multi platform support (non-web based).
• Triangulated irregular network (tin) data support
These issues are further discussed in the next section (§3).
12
3
Extending current software
The new features listed in the previous section will be implemented in the prototype
of this project. The prototype offering these features could serve as a complement to
existing software products. This section gives the concept of these features, before the
programming implementation.
3.1
Fresnel zone clearance map
For mobile applications it is important to have a map with predicted signal strength in a
certain spatial extent. With such map it is possible to assess the feasibility of a transmitter
location for covering a certain space, and predict what areas will not have a good signal
reception. In addition, this prediction helps in point-to-point applications where it is
possible to see what is an optimal place of placing a receiver in a defined spatial extent.
Such feature is already shown in the Figure 5.
However, no software, that I know of, offers a first Fresnel zone (ffz) clearance map,
which could be useful in general application. Such map extends the viewshed into a general coverage map. The clearance map may be used without radio propagation models.
If we consider ∀n ∈ R3 this approach could produce a map representing the first
Fresnel zone clearance, similar to topographic maps with heights or air pressure maps.
This is important when one would like to estimate the coverage of the network in an
easy way, or in p2p applications for finding an optimal location for placing a receiver.
For the fixed Tx and Rx with a variable position, the argument l of the function ω
can be substituted with the point n i ∈ R3 , hence
ω ∶ n i ∈ R3 ↦ [0, 1]
(4)
If we calculate the value ω for every n in a spatial extent, a plot which represents the
ffz clearance in P can be generated.
This is similar to the concept of the viewshed. The viewshed is all the regions that
are visible from a viewpoint [11]. The viewshed returns a binary information - whether
a point is visible or not, while the ffz visibility would have the value of how much is
visible, i. e. how much the first Fresnel zone is obstructed.
From this data it would be also possible to create additional useful plots, as:
1. A standard viewshed, by truncating the value of ω for each point in the plot. In
case of ω = 0, there is no los, while for ω > 0 the point is visible.
2. A first Fresnel zone viewshed, i.e. only the points with a complete clear ffz. In
case of ω < 1 the Fresnel zone is obstructed, while for ω = 1 is clear.
By modifying the latter, it is possible to make a quality plot, i.e. to show points which
have a ffz above a certain threshold, for example only points with the clearance higher
than 60, that is ω > 0.6.
3.2
Export of link data to gis formats
The reviewed software solutions have limited gis capabilities and the export of the computed data to gis software is virtually non-existent. Obtained data, such as a clearance
or signal strength map, would be more useful when exported to gis software. Some of
the benefits are:
13
• It would be possible to perform additional (gis) analysis.
• The clearance map could be combined with a dtm or an aerial photo for a better
overview of the obstacles and surrounding area
• Land management applications. If a clearance or signal strength map is layered
over a cadastre map it would be possible to see the ownership boundaries for
placing an antenna.
3.3
Automatic antenna optimal placement
In p2p applications, the analysis returns the assessment information is the planned link
between two points feasible or not, often in the form of a terrain plot and ffz clearance
value. A new feature could be introduced to give a suggestion of another better (close)
location for placing the receiver.
With the feature described in §3.1, the data of the ffz clearance for each point near
the planned location of the receiver is already obtained. If the clearance at the planned
location is not satisfactory, the software could give the location of the closest point which
has a clearance higher than a certain threshold for a quality radio link.
However, there are many cases to consider in order to implement this feature in the
right way. For example, if the clearance of the ffz at the planned location x for the
receiver was 20, it would not make a good location to place an antenna. Therefore,
other points in the vicinity should be analysed as well, in order to find a better location
for the placement of the receiver. The closest point with the 100 clearance is a point a
which is 86 m away from the planned location x. But what if there was a location b 21 m
away from x with the clearance of 78? Although the clearance at the point a is better
than the clearance at this point, it may not be feasible to place an antenna at a location
which is 4x more distant, therefore we need to introduce weighting. Here we can define
a new dimension-less measure k for optimising the Rx location:
ω
k=√
d
(5)
where d is the distance between the initially planned location for the receiver and
currently considered location. A scalar could be added to the denominator to avoid very
ω
high weights for low clearance for very close points. Such example is k = √d+5
and the
behaviour of this function is shown in the Figure 9. From the plot, it is possible to see
that a point 10 m away with the clearance of 0.6 has approximately the same weight as a
37 m distant point with a clear ffz (ω = 1).
3.4
Multi platform support
With a multi platform support, a non-web based application would not be limited to a
certain operating system. As already mentioned, the majority of the existing software
is Windows based. A multi platform solution would enable the use of the program on
Linux and Mac OS. For this purpose, a multi platform programming language should
be used. Therefore, the prototype is implemented in Python, which has a powerful integration of gis, plotting and scientific libraries. The programming language, as the main
modules, are multi platform. The main modules that will be used in the prototype are:
14
k values
0
0.1
0.4
0.2
0.35
0.3
0.3
0.4
ω
0.25
0.5
0.2
0.6
0.15
0.7
0.1
0.8
0.05
0.9
1
0
10
20
30
40
50
60
Distance in [m]
70
80
90
100
Figure 9: The possible values of k for the points with the distance less than 100 m. The
abscissa shows the distance, while on the ordinate are the values of ω.
• Geospatial Data Abstraction Library (gdal)8 – a project of translation libraries
for raster and vector data formats.
• Computational Geometry Algorithms Library (cgal)9 – a library for easy access
to efficient and reliable geometric algorithms.
• NumPy10 , a fundamental package needed for scientific computing with Python.
It enables the storage of matrices and facilitates operations on them.
3.5
tin support
Although the availability of raster data is often high and the data can often be obtained
without costs, in some cases tin data has advantages: the data can include the vegetation
and other obstacles, which might be filtered out in raster data. For instance raw data obtained with airborne laser scanning could give better results than processed and filtered
raster data. Furthermore, gridding seen in raster often degrades the information, and
tin is adaptive to the relief of terrain. Therefore, such data should be supported by the
prototype as an alternative format.
8 http://www.gdal.org/
(Last access: 24 October 2009)
(Last access: 24 October 2009)
10 http://numpy.scipy.org/ (Last access: 24 October 2009)
9 http://www.cgal.org/
15
4
Implementation and prototype development
This section describes the development of the working prototype and the implementation of the features described in the previous section (§3) with the examples of the
computed results.
4.1
Data used for testing
The developed prototype was tested with different data in order to check the algorithms
and to ensure that the prototype can be used with any location. For this purpose two
datasets, one of an urban area and one of a uninhabited mountainous area, have been
used:
• ahn – the current elevation map of the Netherlands. A raster of 2011 × 1260 pixels
with the resolution of 5 m × 5 m, covering Delft. The buildings in the urban area
are not filtered, while the vegetation is.
• The National Elevation Data (ned) by the United States Geological Survey (usgs)
[7]. A raster of 1344 × 1736 pixels with the resolution of 8 m × 8 m. It represents a
10.7 km × 13.9 km extent in Colorado, with filtered buildings and vegetation.
A tin with 46 952 points was also used. It was obtained from the ned dataset (2
of random cells were selected from the grid and converted to a list of points). This also
served as a check between interpolations and different workflows between different type
of data.
For the raster data, the prototype is developed to analyse GeoTiff files. GeoTiff is a
de facto standard geoinformation format and most of dtm are available in it, and this
prototype is written to accept any georeferenced GeoTiff file. Some data is delivered
with no-data values or with grid size and heights which are not in metres (the prototype
is adjusted for metres only), hence these files should be processed beforehand.
4.2
Loading the data
The first step was to import the data: the frequency of the planned link in GHz, the
coordinates of the Tx and Rx, the antenna heights and the dtm. The coordinates are
transformed to the image coordinate system because of more efficient computations.
Different functions were written for this purpose.
Since antennas are usually placed on masts above ground or on a roof, the relative
height of the antenna to the dtm had to be correctly defined. In case of placing the antenna on a roof, the user has to be careful with the relative height. If the dtm contains
buildings, the height should be expressed relatively to the rooftop, while in case of the
filtered dtm the height is relative to the ground. The absolute height of the antenna is
calculated by adding the relative height to the value of the dtm at that point. The Figure 10 shows an example of this problem with an antenna placed on a roof of a building.
The dtm data is shown in brown colour. The elevation of the dtm is denoted with h, the
relative height of the antenna with r and the absolute height with a which is calculated
with the relation a = h + r. In Fig. 10(a) we see a dtm not filtered for buildings. The
relative height of the antenna is therefore the vertical distance from the antenna to the
roof, i. e. to the dtm. Fig. 10(b) shows a similar case with a filtered dtm. Now the relative height is the vertical distance from the antenna to the ground, since the building,
16
(a) dtm with buildings included
(b) dtm with filtered buildings
Figure 10: The relative height is different for filtered and non-filtered datasets. The absolute antenna height is denoted with a and the relative with r. The elevation of the dtm
is denoted with h. The green point shows the projection of the antenna to the dtm.
shown in grey, is not included in the dtm. From this example we can see that it is very
important to define the correct relative height for the antenna.
In case of raster the heights are interpolated with the bilinear interpolation, while in
case of the list of points (tin) the Delaunay triangulation was made with linear interpolation in triangles. The same operations in the prototype are performed on both raster
and vector data and they have the same functionality, only the interpolation routine is
different.
4.3
Estimation of the clearance of the first Fresnel zone
The prototype computes the los line from the absolute 3d coordinates of the two points
(Tx and Rx), and according to the frequency the absolute heights of the points in the
lower hull of the first Fresnel zone are estimated. For each point along the link the obstruction of the ffz should be computed. The line was discretised in n equal line segments, hence the height of n points was interpolated. Each point was compared to the
height of the corresponding point on the lower hull of the ffz ellipsoid and the los line
(as shown in Fig. 2). The user can define the number of points n. After the computation, the information about the estimated clearance and the profile plot is returned. The
clearance of the link is defined as the maximum obstruction along the link, although all
the values of the obstructions in the path are preserved and can be used to plot all or
a particular obstruction, for instance, all objects that cause the link to have a clearance
lower than 50.
4.3.1
ned example
The first example shows the assessment of a planned link in Colorado. The antenna
heights are 15 m above the ground, and the frequency 2.4 GHz. The number of interpolated points between the antennas was 100 (n = 100). The prototype returned the
following output:
The distance between the two points is 10604.3 m
The 1st Fresnel zone is partially obstructed. Its clearance is 39.4 %.
The clearance is not satisfactory for a quality link
(min. 60% of clearance is required).
17
The recommended clearance value of 60, mentioned in the introduction (§1.2),
can be changed according to the user’s needs. The terrain plot is shown in Figure 11.
Distance plot
2500
2400
Height [m]
2300
2200
2100
2000
19000
2000
4000
6000
Distance [m]
8000
10000
12000
Figure 11: The p2p terrain plot of the first example (ned data). The ffz clearance is 39.4.
The ground points of the antennas are marked with the green circles. The height scale
is exaggerated for a better overview.
The same parameters on the tin of the same dataset returned the same output and
assessment. However, due to the slower tin interpolations, the results were computed
slower than the raster, hence the use of raster data is advised when available.
4.3.2
ahn example
The second example is calculated in the urban area, in Delft. The frequency was the
same, while the antenna heights were 3 m relative to a roof. The prototype returned the
following output:
The distance between the two points is 7847.0 m
The LoS is blocked.
Fig. 12 shows the plot. It is visible that the link cannot be achieved due to the several
obstructions in between, mostly caused by the buildings. Since the heights in the urban
area are subject to more variations, the number of interpolated points (calculations) was
increased to 500.
If enabled, the prototype can compute and plot the clearance for the second Fresnel
zone for advanced applications. With smaller modifications any n-th Fresnel zone can
be calculated by this prototype, although the focus of this project is on the first Fresnel
zone.
4.4
Point-to-multipoint assessment
For mobile analysis, and for extended p2p analysis (e. g. suggesting a better location for
the antenna placement), the algorithm used in the first part of the prototype, was used to
estimate the clearance for multiple points, i. e. for each point in a defined spatial extent.
18
Distance plot
80
Height [m]
60
40
20
0
0
1000
2000
3000
4000 5000
Distance [m]
6000
7000
8000
Figure 12: The p2p terrain plot of the second example. The ffz is obscured by several
objects in the path. The ground points of the antennas are marked with the green circles.
The height scale is exaggerated for a better overview.
The spatial extent in the prototype is defined as a square, and the spacing between analysed points is defined with the resolution of the dtm. In the ahn dataset the resolution
is 5 m, and in the ned dataset 8 m.
The Figure 13 shows a clearance map generated by the prototype in the ned dataset.
The spatial extent is of size 1000 m × 1000 m. The planned location for the receiver (the
centre of the extent) is the same location as in the p2p assessment example shown in the
previous section (§4.3.1), therefore now we are estimating the clearance of nearby points
in order to find a better place for the receiver.
1800 +4.401e6
First Fresnel zone clearance
1.0
0.9
1600
0.8
0.7
1400
Y
0.6
0.5
1200
0.4
1000
0.3
0.2
800
0.1
600
473400 473600 473800 474000 474200 474400 474600
X
0.0
Figure 13: The first Fresnel zone clearance map in a spatial extent of 1000 m × 1000 m of
the ned dataset. The red circle is the planned receiver location, the yellow the suggested
location and the green the optimal location for the receiver.
19
The initially planned point for the receiver is located in the centre of the extent and it
is marked with a red circle. Each point in the plot shows the predicted value of the ffz
clearance from a user-defined fixed transmitter location. The prototype was run with
interpolating 50 points between the transmitter and each assessed location in the spatial
extent. The number of assessed points in the spatial extent is 15 625 (125 × 125), which
means that the p2p analysis described in the previous section was made 15 625 times.
However, this time the script was run without generating the profile plot for each point.
The colormap ranges from red to green, according to the clearance of each point,
with the dark green showing the full clearance of the ffz. The yellow circle marks the
suggested antenna location, i. e. the location with the most favourable (highest) value
of k. It is also useful to show the points with the maximum clearance value in the extent,
in this case ω = 1. If multiple points in the extent have a maximum clearance value, only
the closest point is shown. The closest maximum clearance is denoted with the green
circle. These three points are shown in the Figure 14 in more detail.
Figure 14: The three points of interest in the clearance map.
Along with the plot, the prototype returns the following information for the user:
The computation took 76.4 seconds.
The clearance of the first Fresnel zone at the planned location is 44.0 %.
This point is 10604.3 m away.
The best antenna site in the spatial extent is
( 473909.85198 , 4402105.9815 ) with the clearance of 100.0 %
This point is 64.6 m from the planned location.
The suggested antenna site is ( 473974.0 , 4402138.05551 )
with the clearance of 80.3 %
This point is 24.1 m from the planned location.
The total number of analysed points is 15625
In mobile applications, when the receiver is capable of being moved, this map can
be used to assess the signal coverage in a spatial extent.
As mentioned before, the obtained data can be also used for generating the viewsheds – the standard one for the los and the one only for points which have a clear ffz.
Both plots are shown in Fig. 15. The viewshed for the los is shown in the Figure 15(a),
and the viewshed for the clear ffz is shown in the Figure 15(b).
4.5
Export of the data and integration in gis software
Each generated clearance map is exported to a georeferenced GeoTiff upon each prototype execution, for usage in other gis software. This section shows an example.
20
Viewshed (LoS)
Viewshed (FFZ)
1800 +4.401e6
1600
1600
1400
1400
1200
1200
Y
Y
1800 +4.401e6
1000
1000
800
800
600
473400 473600 473800 474000 474200 474400 474600
X
600
473400 473600 473800 474000 474200 474400 474600
X
(a) los viewshed
(b) ffz viewshed
Figure 15: The generated viewsheds as additional plots. The red colour shows non visible
(obscured) points, while the green colour shows the visible points. The planned location
for the receiver is marked with the red circle.
A clearance map has been generated for a part of the TU Delft campus from the ahn
dataset. The planned location of the receiver was placed on the roof of the building of
the Faculty of Electrical Engineering, Mathematics and Computer Science (ewi) while
the location of the transmitter was placed 1200 m west of the building on another high
building. The prototype was run with interpolating 200 points between the transmitter
and each assessed location, and the spatial extent has the size 1000 m × 1000 m. The
obtained clearance map is shown in Figure 16. Since the planned location for the receiver
has already a ffz clearance of 100 which is the best possible result, no other locations
are suggested and marked on the map.
446600
1.0
First Fresnel zone clearance
0.9
0.8
446400
0.7
0.6
446200
Y
0.5
446000
0.4
0.3
445800
445600
84800
0.2
85000
85200
85400
X
85600
85800
86000
0.1
0.0
Figure 16: The first Fresnel zone clearance map near the building of the ewi faculty of TU
Delft. The location of the transmitter is placed 1200 m west of the building. The shaded
areas caused by the faculty building and other nearby buildings are visible towards the
east.
21
Each cell of the exported GeoTiff has the value of ω which ranges from 0 to 1. This
file can be imported in most of gis software for further analysis and processing.
For testing purposes I have used QuantumGIS11 . The transparent GeoTiff was placed
above the dataset representing buildings in the campus (Figure 17). The colormap of the
clearance is as in the previous examples. This approach helps the user in identifying the
obstacles and analysing the clearance with the use of other data.
Figure 17: The transparent clearance map exported to QuantumGIS and placed above
the dataset of the buildings of the TU Delft campus. The transmitter is located 1200 m
west of the centre of the clearance map.
Another example (Fig. 18) shows a subset of the clearance map overlayed on the
satellite image (obtained from Google). This approach also gives a good overview of the
obstructions in the path and the spatial extent of which the clearance is estimated.
4.6
Import of the data in Google Earth
Although Google Earth is not a full featured gis software, it has a high number of users,
it is free, it is well supported and it has powerful visualisation features. Google Earth
does not support GeoTiff files natively, and since it would be useful to have the Google
Earth support in the prototype, the clearance map was exported to the Google Earth’s
native format (kmz). Google Earth can overlay the clearance map on a variety of geo11 http://www.qgis.org/
(Last access: 24 October 2009)
22
Figure 18: A part of the clearance map exported to QuantumGIS and placed above a
satellite image (obtained from Google).
data: aerial (or satellite) photos, 3d perspective view of the terrain and community or
industry created 3d models. One such application is shown in the Figure 19. The GeoTiff
of the clearance map obtained in the previous section was converted to kmz and shown
with 80 of transparency over the aerial photo, with the enabled 3d models of the buildings. The obscured points are shown in black colour, while the points with the clear first
Fresnel zone are shown in white (the intermediate values are shown in grey tones). The
perspective view clearly shows the points which are obscured by the building of the ewi
faculty. Since not all buildings in the TU Delft campus have the 3d model some of the
obstructions can be identified from the aerial photo.
Figure 19: The clearance map exported to Google Earth. The 3d models of the ewi faculty
and other buildings in the TU Delft campus are shown on a satellite image. With the
use of Google Earth it is possible to easily identify obstacles in the radio path.
23
5
Optimisation of the prototype
The prototype returns the computations in a satisfactory time considering the algorithms or amount of processed data. The point-to-point assessments presented in this
report12 are generated in less than half of a second. The computations for the multiple
point assessment examples are derived in between two and fifteen minutes, which is
a good result considering the vast amount13 of calculations. However, it is possible to
further optimise the prototype for a faster execution with the following points:
• Minimise the number of segments n in the point-to-point estimation
• Lower the resolution in the point-to-multipoint clearance computation
• Lower the size of the spatial extent of the point-to-multipoint clearance computation
5.1
Minimisation of the number of segments
It is possible to speed-up the algorithm with lowering the number of height interpolations between the transmitter and receiver.
5.1.1
Point-to-point analysis
In the p2p computation the number of interpolated points plays an important role. The
computational complexity of the algorithm is O(n). By decreasing the number the segments, the computational time would be linearly decreased. However, changing the
number of segments can produce problems caused by the inaccuracy.
As an example we can observe the plot in Figure 11 on the p. 18. The plot was made
by interpolating 100 height values along the path from Tx to Rx. The prototype estimated the clearance of the first Fresnel zone of 39.4 due to a critical obstruction approx. 5200 m from the transmitter. By lowering the number of interpolated points to
70 and 50, the result has changed. The output for the computation for 70 interpolations
was
The 1st Fresnel zone is partially obstructed. Its clearance is 68.8 %.
while for n = 50 it was
The 1st Fresnel zone is clear of obstacles.
By using half of the points (50 instead of 100), the result changed from a non-satisfactory link (39.4) to a optimal prediction with a completely clear ffz (100). We
can see this innacuracy further in the generated profile plot. The Figure 20 shows the
enlarged parts of the critical obstruction 5200 m from Tx for all three cases described
above (100, 70 and 50 observations).
This example shows that by slightly changing the number of interpolations the results can dramatically change, and for more accurate predictions it is important to use a
higher number of interpolations. The number of observed points should depend on the
12 In
case of the ahn p2p example, there were 500 interpolations in the radio path.
the ahn example of the clearance map, there were 40 000 p2p computations with 200 interpolations
each, i. e. in total 8 000 000 interpolations.
13 In
24
(a) 100 interpolations
(b) 70 interpolations
(c) 50 interpolations
Figure 20: Decreasing the number of interpolations along the path significantly decreases the accuracy of the prediction. The clearance of the first Fresnel zone is 39.4,
68.8 and 100, respectively.
resolution of the data, the distance between Tx and Rx and distribution of the terrain.
This value can be defined by the user.
However, increasing the number of points is not an issue since the profile plot with
100 points was generated in less than 0.1 s and another one with 10000 points was generated in two seconds which is still a very reasonable time for all applications.
5.1.2
Point to multipoint analysis
The change of the number n of interpolations is a more important topic in point-tomultipoint analysis since the p2p analysis is now made for a several number of points
(as seen in this report – often for tens of thousands of points). Changing the number of
interpolations along the radio path gives the same concerns presented in the previous
section. Now the problems are manifested in the clearance map and the output giving
the suggested and optimal coordinates for the receiver.
As an example, the clearance map of TU Delft campus, already presented in this
section (Fig. 16, p. 21), is used. The Figure 21 shows different clearance values east of
the building of the ewi faculty for cases of 200, 100 and 50 interpolations between the
transmitter location and each analysed point.
(a) 200 interpolations
(b) 100 interpolations
(c) 50 interpolations
Figure 21: Decreasing the number of interpolations along the path significantly decreases the accuracy of the predicted clearance map. The differences in the prediction
of the clearance east of the ewi building are noticeable.
As noted in the previous section, the number of interpolations is proportional to
the quality and reliability of the prediction. However, in this algorithm increasing the
25
number of interpolations significantly increases the processing time. The user should
define the value of n, based on the application, dtm and the computational aspects.
5.2
Lower the resolution in the multipoint clearance computation
The default resolution for generating the grid in the clearance map is the same as the
resolution of the analysed dataset. The complexity of the algorithm is O(n 2 ), and by
lowering the resolution of the grid, i. e. changing the distance between analysed points
in calculating the clearance in a spatial extent, the number of the sightlines would be
reduced, and the efficiency could be significantly improved.
In the example shown in the Figure 16, the clearance was calculated for points separated by 5 m. There were 40 401 points (201 × 201). If the spacing was increased to 25 m
and the computations were executed with the same parameters (n = 200 for a spatial
extent of 1000 m × 1000 m), the number of points would be significantly decreased, to
1681 (41 × 41), making the computations significantly faster. In the 5 m case, the computational time was 14 min, while in the 25 m case it was 33 s, which is a noticeable improvement.
The results are shown in the Figure 22. Although the grid spacing is increased by
400 and the generated map is of a lower quality, the results are still comparable (compare with Figure 16 on p. 21). The clearance values between the cells were not interpolated to preserve the original values of the assessment.
446600
1.0
First Fresnel zone clearance
0.9
0.8
446400
0.7
0.6
446200
Y
0.5
446000
0.4
0.3
445800
445600
84800
0.2
85000
85200
85400
X
85600
85800
86000
0.1
0.0
Figure 22: The first Fresnel zone clearance map with the grid spacing of 25 m.
The recommendation for the use of this approach depends on the resolution of the
dtm, the size of the observed spatial extent, and the area and configuration of the terrain
and buildings.
5.3
Lower the spatial extent of the multipoint clearance computation
The size of the spatial extent also affects the algorithm O(n 2 ). In some cases there is
no need for a large spatial extent, hence by changing the size of the extent, the computational time of the prototype can be noticeably reduced. The usage of this solution
depends on the user’s needs.
26
6
Conclusion
The developed prototype gives results comparable to existing commercial software. It
introduces new features as ffz clearance maps, tin support, gis and Google Earth export, automatic optimal antenna placement and multi platform support, and it can be
used as a complement to another existing software.
It is tested with various digital terrain models to ensure it can be used for any GeoTiff data. The speed of execution for raster data is considering the amount of data and
computational aspects satisfactory, and can be further decreased by the presented optimisations (§5). The use of implemented tin data structures may be useful for some
data and applications, since it might contain additional data such as vegetation, which
is often filtered in the raster representation. However, the performance is poor due to
the slower interpolations of the heights in the radio path. The performance of tin interpolations can be improved with the use of faster algorithms, and the viewsheds can be
generated faster with the use of efficient algorithms introduced by Floriani and Magillo
[6], Wang et. al. [18], and Rana and Morley [16].
Although the isolines are a standard representation of values in a bivariate field, it
was not possible to use them due to the high variation of the values. Plots with clearance
representation with contours had been generated, however the results are not usable.
The data with a low resolution can give data smoothness problems, which can be
seen in north part of the spatial extent shown in the figures 13 and 15(b). This can be
partially solved by optimising the grid spacing of the clearance computations (§5.2).
The speed of the computations can be improved with the listed optimisations, but
the results might be degraded. For precise estimation it is not recommended to follow
the optimisation techniques. However, that does not apply for less crucial applications.
In assessing the feasibility of a link it is very important to distinguish between different areas (i. e. country and urban), since in the cities there is a higher probability of
obstructions caused by buildings and other man-made objects. Hence, the dtm used for
the cities should not be filtered for buildings and other potential obstructions. Filtered
data for the urban area is practically worthless for this application. This can be seen in
the Figure 12 (p. 19) where most of the obstructions are caused by the buildings, and not
by the relief. Moreover, the number of height interpolations in urban areas should be as
high as possible.
In the future work, the earth curvature can be taken into account, radio propagation models can be integrated for returning various information such as the estimated
power loss, and an application with a graphic user-friendly interface can be developed.
A new algorithm could be introduced for mobile applications, for finding an optimal
arrangement for placing multiple transmitters in order to maximise the signal coverage
in a spatial extent.
27
References
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Fresnel zone calculator.
url: http://www.afar.net/
fresnel-zone-calculator/ (Last access: 22 October 2009).
[2] H. Buhler, E. Bonek, and B. Nemsic. Estimation of heavy time dispersion for mobile radio
channels using a path tracing concept. In Vehicular Technology Conference, 1993 IEEE 43rd,
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