Eindhoven University of Technology MASTER Radar signal simulation van de Pol, C.D.P. Award date: 2010 Disclaimer This document contains a student thesis (bachelor's or master's), as authored by a student at Eindhoven University of Technology. Student theses are made available in the TU/e repository upon obtaining the required degree. The grade received is not published on the document as presented in the repository. The required complexity or quality of research of student theses may vary by program, and the required minimum study period may vary in duration. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 15. Jun. 2018
Transcript
Eindhoven University of Technology
MASTER
Radar signal simulation
van de Pol, C.D.P.
Award date:2010
DisclaimerThis document contains a student thesis (bachelor's or master's), as authored by a student at Eindhoven University of Technology. Studenttheses are made available in the TU/e repository upon obtaining the required degree. The grade received is not published on the documentas presented in the repository. The required complexity or quality of research of student theses may vary by program, and the requiredminimum study period may vary in duration.
General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.
• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain
Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.
Download date: 15. Jun. 2018
Radar Signal Simulation
Corne van de Pol
June 2010
Abstract
This thesis is part of the graduation project for the Masters’ degree in Computer Science at theEindhoven University of Technology. The purpose of this project was to design a realistic realtimemaritime radar signal simulation that would be a part of VSTEP’s full mission bridge simulator.The simulation should be used for training, therefore, it should meet the requirements set by theInternational Maritime Organization before it is allowed to be used as a professional training tool.
The goals set by this project were the creation of a simulation where all kinds of spuriouseffects on the radar screen are realistically simulated, instead of manually inserting them duringtraining. From our perspective, it is important that trainees learn to recognize certain situationswhere the radar screen differs from what is expected.
Our radar model - as presented in this document - is based on radiosity, which is normallyused for creating realistic illumination in an environment containing ideal diffuse reflectors. Ourmodel is able to create highly realistic radar images, however, it cannot do this realtime in mostsituations. Still, we believe that with some improvements and further development of hardware,this model could be used to create more realistic radar simulations in the future.
iii
Acknowledgements
First of all I would like to express my gratitude towards my colleagues of VSTEP (the companywhich facilitated this graduation project) and my company supervisor ir. Pjotr van Schothorstwho provided me with valuable support and being responsable for having spent a very pleasanttime with them. I would also like to express my thanks to ir Pjotr van Schothorst, my companysupervisor.
Furthermore, I would like to thank my supervisors of the Eindhoven University of Technologydr. Andrei Jalba and dr. ir. Huub van de Wetering for spending so much time on my project.Throughout the entire project they always found and effort to provide me with valuable support.
During my graduation project I faced many issues that concerned a field of expertise other thancomputer science. Ir. Pierre Wolters provided a lot of valuable help concerning electromagneticradiation and whether my underlying ideas for my model were correct. Thank you very much foryour time!
Thanks to the help of Dick van de Pol and Kevin Gerling, I had to opportunity to step onboard of a ship equipped with radar to see how an actual radar screen behaves in certain real lifesituations, which was important in order to have an idea what is required for the simulation.
Finally, I would like to thank my family, girlfriend and friends for their neverending support.
4.1 Subdivision of surface into patches . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.2 Effective area (A′) of a patch with area A for an incoming wave . . . . . . . . . . . 224.3 Projection of patch on sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.4 Spherical coordinates (θ, φ) for a direction (~d) from the antenna (A) to a target,
where ~d′ is the projection of ~d on the horizontal plane . . . . . . . . . . . . . . . . 234.5 Set of cosines functions approximating the gain of a radiation pattern in all direc-
5.1 Drawing of echo on the radar screen with d = γ t·c2 pixels and s = γ PL·c2 . . . . . . 32
viii LIST OF FIGURES
6.1 Creation of sphere of patches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356.2 Sphere of patches deformed for the side view visualization of an arbitrary gain
function of antenna (A) in the pointing direction ~p . . . . . . . . . . . . . . . . . . 366.3 Top view overview of the setup for the radiation pattern test of antenna (A) with
pointing direction ~p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376.4 Visualization of the radiation pattern of antenna (A) with semi-isotropic radiation 376.5 Visualization of the radiation pattern of antenna (A) with single beam has an equal
horizontal and vertical beamwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . 376.6 Visualization of the radiation pattern of antenna (A) with single beam where the
horizontal and vertical beamwidth are not equal . . . . . . . . . . . . . . . . . . . 386.7 Visualization of the radiation pattern of antenna (A) with main beam that has two
sidelobes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386.8 Top view overview of two different setups for the reflection pattern and absorption
test with antenna (A) with pointing vector ~p and patch (P ) with normal vector ~n . 396.9 Visualization of the reflection pattern of patch (P ) with diffuse reflection . . . . . 406.10 Visualization of the reflection pattern of patch (P ) with specular reflection . . . . 406.11 Visualization of the top view reflection pattern of rotated patch (P ) with specular
bination with diffuse reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406.13 Top view overview of the setup for the radar equation and RCS test for antenna
(A) with pointing vector ~p and patch (P ) with normal vector ~n . . . . . . . . . . . 416.14 Visualization of diffuse reflection caused by multiple patches on plate (P ) after
applying superposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436.15 Test environment containing two ships and an antenna . . . . . . . . . . . . . . . . 446.16 Original model and expected echo, the two marked areas indicate areas where radio
waves can travel a longer distance . . . . . . . . . . . . . . . . . . . . . . . . . . . 456.17 Radar screen for the environment depicted in figure 6.15 . . . . . . . . . . . . . . . 456.18 Part of radar screen showing the echo of ship 1 . . . . . . . . . . . . . . . . . . . . 456.19 Results of varying maximum edge lengths for the patches . . . . . . . . . . . . . . 456.20 Results of varying rotation steps of the antenna . . . . . . . . . . . . . . . . . . . . 466.21 Part of the resulting radar screen for the echo scaling tests . . . . . . . . . . . . . . 466.22 Part of radar screen showing the results of the false echoes tests . . . . . . . . . . . 476.23 Overview of the semi-realistic environment . . . . . . . . . . . . . . . . . . . . . . . 486.24 Radar screen of the environment depicted in figure 6.23 . . . . . . . . . . . . . . . 496.25 Radar screen where the entire environment is covered with an ideal diffuse reflecting
STCW: International Convention on Standards of Training, Certification and Watchkeeping forSeafarers
VSTEP: Virtual Safety Training and Education Platform
Symbols:
λ: Wavelength (m)
ω0: Angular frequency (rad/s)
σ: Radar Cross Section (m2)
Ae: Effective area of antenna (m2)
c: Speed of light ≈ 3 · 108m/s
f : Frequency of the electromagnetic waves (Hz)
G: Gain
HBW : Horizontal Beam Width (rad)
I: Intensity: power density per unit solid angle for a given direction (W/(m2sr))
Pa: Antenna power (W )
Pd: Power density (W/m2)
Pi: Power density of the incident wave (W/m2)
Pr: Received signal (W )
Ps: Power density of the backscattered wave (W/m2)
PL: Pulse length (s)
r: Distance or range to a target (m)
t: Travel time of the signal (s)
V BW : Vertical Beam Width (rad)
1
Chapter 1
Introduction
Since the introduction of computers, simulations that replace real life training have become com-monplace. Depending on their purpose, simulators are often safer, cheaper, better for the envi-ronment and it is easier to create specific situations. These advantages apply to simulated radartraining as well, which made the radar simulator the standard device used for this purpose.
This chapter starts with discussing what radar is, why it useful and why training is necessary.Then the goals of this project are defined, the environment in which the project took place andthe related work that has been done in this field.
1.1 What is Radar?
Many radar workers say that the atomic bomb may have ended the Second World War, but radarwon it[4, preface]. After the success of radar in World War II, it was introduced on merchantvessels where it became an indispensable system 1.
Radar added a new technique to navigation: a system being capable of detecting objects[11].A radar device is a navigation aid that helps to safely navigate a ship to its destination.
It was Marconi, who introduced ideas for a radar system in 1922, which is usually referred toas the beginning of radar[4, chp.2]. The name is an abbreviation of Radio Detection And Ranging,which already indicates its most important properties: detecting objects with radio waves anddetermining the distance from the radar antenna to each detected object. To obtain this data,this project distinguishes two devices2: the radar antenna that sends and receives the radio wavesand the radar screen that visualizes the returning signals on a screen.
(a) Original Signal (b) Reflected Signal
Figure 1.1: Detecting a target
In radar terminology, the object that is being detected by the radar is referred to as the target.1Radar also made its appearance in many other applications but this project is specific about maritime radar.2Real radar systems consist out of more components, but they are not relevant for this project.
2 CHAPTER 1: Introduction
To detect a target, the antenna sends a signal that is reflected by the object and finally received bythe antenna (see figure 1.1). The signal itself is a radio wave, which belongs to the electromagneticspectrum just like light waves. Note that the target does not need a radar system to reflect thesignal. Instead, the signal is reflected by the surface of the target. The reflected signal that isreceived by the antenna is also known as an echo.
All the signals that are received by the antenna are visualized on the radar screen. The resultis a picture that shows the objects around the radar antenna within a specified maximum range.The maximum range of the radar screen can be selected by the radar operator. The position ofan arbitrary target (T ) on the screen, as shown in figure 1.2, depends on:
• The angle (α) between the bearing3 (~b) of the target and the heading4 (~h) of the vessel (S)carrying the radar antenna;
• The radar screen scale factor (γ), which is a distance on the screen divided by the corre-sponding real distance.
The radar screen scale factor depends on the size of the screen and the selected maximum range.
α
hb
S
T
(a) Environment
αT
S
h
γ⋅bγ⋅rs
(b) Radar screen
Figure 1.2: Mapping of the environment onto the radar screen
In situations of reduced visibility, radar can really prove its value. When two ships are oncollision course and they cannot see each other, a collision can be avoided by using radar. Figure1.3 depicts such a situation where two ships are on collision course in dense fog and the shipcarrying the radar antenna does not see the other ship until it is very close. But even in goodweather conditions radar can help by providing a clear overview of the area.
(a) Ship heading towards the radar antenna (b) Ship very close to the radar antenna
Figure 1.3: Use of radar in fog
The main purpose of radar is to avoid collisions but initially the use of it actually causedcollisions. These collisions are also known as radar assisted collisions[11, p.145]. The reason for
3The bearing of a target from a certain location is the direction from that location to the target.4Heading is the direction in which the bow (front) of the ship is pointing.
1.2. VSTEP 3
these collisions is that it requires some skills to interpret the screen correctly. Echoes may haveweird and possibly enlarged shapes compared to the object that caused them. Furthermore, echoescan be caused by unimportant objects such as rain and waves, can be false or an object mightnot return an echo at all. The reasons for this behavior can be found in more detail in chapters 2and 3. The experience required for the correct interpretation of the radar screen finally led to thesituation where radar training was made mandatory before one is allowed to use it.
1.2 VSTEP
This graduation project took place in a commercial company called VSTEP. VSTEP specializesin virtual training and one of its products is called Nautis, which is used for maritime training.Nautis can be used as a full mission bridge simulator, as depicted in figure 1.4. A full missionbridge simulator is a physical bridge5, built in a room where the outside view is created by thesimulator and the equipment of the bridge is connected to a simulator.
Figure 1.4: Full bridge simulator
Although VSTEP already developed a radar simulator, it did not meet the level of realismand functionality necessary for certification. The design of this simulator was originally based onpictures of radar screens. It used a simplistic approach that has a good computational complexity,but lacks the ability to create realistic pictures. This simulator was originally not meant fortraining purposes and hardly possessed any functionality. See appendix B for more informationconcerning this simulator.
Eventually, the new radar simulator has to interface with Nautis, for example the ship dynamicswill be handled by the Nautis. However, because of limited time, the project abstracts fromplatform dependencies.
1.3 Radar Simulators
When a simulator is used for maritime training it needs certification to guarantee a certain levelof realism. The International Maritime Organization (IMO)6 set up a collection of rules to whicha maritime simulator, including a radar simulator, should comply in order to get the certification.These rules can be found in the STCW document[14].
Due to time constraints, this graduation project is restricted to the generation of the radarsignals that are received by the antenna. Furthermore, all radio signals created by other radiating
5The bridge of a vessel is the area from which the ship is commanded.6The task of the IMO is to make international regulations concerning shipping like safety, legal matters etc.
4 CHAPTER 1: Introduction
sources than the receiving antenna itself are neglected. For certification, the additional presenceof image enhancing filters, graphical user interface and the effects of other radiating sources arenecessary as well. The required facilities regarding signal generation, including the requirementsset by the IMO, are the following:
• Unwanted echoes and echo scaling should be included, discussed in section 2.7;
• The returning energy from each object should be related to visibility and material propertiesof the surface, discussed in sections 2.3 and 2.4;
• Propagation effects of the radar signal, discussed in chapter 3.
A simulator that will be used for training must respond to actions of the operator and themovement of the ship. Therefore, the simulator should operate realtime and it should be able tocope with up to 20 other moving vessels on a dedicated computer as defined in [14]. It should bepossible though, to increase the number of moving vessels in the future. Furthermore, the simulatorshould work for any given environment and object. Although, it can be assumed that the geometryof the environment and all possible objects are known before the start of the simulation.
1.4 Related Work
All related work that has been found concerning the radar simulations is about making realisticradar pictures, see for example [1, 18, 20]. Paper [20] and the master thesis [18] are both aboutSAR simulation, which is another type of radar, mostly seen on airplanes. The goal of this SARsimulator is to simulate input data that can be analyzed in order to improve the radar systemitself. Something similar is done in [1], however, for the maritime radar in this case. Still the datacan be generated offline since it is only to compare radar antenna configurations.
No work was found that was about realtime maritime radar simulation for training purposes.Realtime radar simulators do exist, however, they are made by other commercial companies thatdo not share their knowledge. Most of those simulators do not look very realistic compared to realradar screens and fake unwanted echoes on command rather than create them realistically. Thisproject aimed at achieving a higher level realism than the current standards.
In chapter 4 some models are discussed for the computation of the propagation of the radiowaves used by radar. That chapter also covers some illumination models used in the gamingindustry for instance.
1.5 Outline of the Document
This document starts with the explanation of the basic working of radar in chapter 2. This includesthe drawbacks of the radar system, how the radar screen is drawn and what causes false echoesand echo scaling. Chapter 3 explains the basic properties of radio waves, which are used by theradar antenna to detect objects.
In chapter 4 our signal propagation model is introduced, which is based on radiosity. Thischapter starts with a discussion on existing models and why radiosity was chosen for the generationof realistic radar signals. This is followed by the additional functionality that is required for radarsimulation. In chapter 5, the radar simulation algorithm can be found, which includes our methodused for drawing the radar screen as well.
The test results of our model can be found in chapter 6. Based on the results, the conclusionsconcerning our model are drawn in chapter 7. Then, some ideas that could be applied in the futureare discussed in chapter 8.
5
Chapter 2
The Basics of Radar
This chapter briefly introduces some radar concepts necessary to obtain a general understandingof the involved problems. These concepts cover the technology behind the radar system, itscapabilities, how objects are detected and the consequences of certain approaches.
2.1 Radar Antenna
The maritime radar antenna usually sends a signal, which is an electromagnetic pulse. Thereforethis type of antenna is also known as pulse radar1[26, pp.5-6]. After the signal has been sent, theantenna waits for incoming reflected signals. Ships are generally equipped with one antenna, actingboth as transmitter and receiver. This type of antenna is also called a monostatic antenna[27, pp.1-3]. When the word “radar” is used throughout this document, it will always imply a monostaticpulse antenna, unless stated otherwise.
The primary task of radar is determining the distance (r) to each detected target. The radarantenna can measure the difference between the time the signal was sent and the time it cameback. The travel time (t) of a signal is the time that elapsed between sending and receiving thesignal. When a signal travels directly to a target and back, the distance r from the antenna tothe object can be calculated as follows[27]:
r =c · t2
[m], (2.1)
where constant c represents the speed of light.The pulse sent by the antenna has a certain pulse length (see figure 2.1). The pulse length
corresponds to the time in seconds that the antenna is emitting energy for one pulse[3, pp.33-34].For this project it is assumed that the power emitted by the antenna is constant for as long as itemits a signal. In practice, this is impossible to achieve, however, the differences are negligible[3,p.35].
When a signal is received by the antenna, the antenna cannot determine from which directionthe signal arrived. In maritime terminology this means that the antenna cannot determine thebearing2 of a target. Therefore the energy of the antenna has to be focussed into a small beam.Targets that are located outside this beam do not receive a signal directly from the antenna,therefore it is assumed that these targets will not return a signal. The direction in which theenergy is focussed will be referred to as the pointing direction of the antenna throughout thisdocument.
When the energy is focussed in a small beam, the antenna covers only a small area. To coverthe entire area around the antenna, the antenna rotates. During a full revolution the antenna
1An example of another radar type is the Frequency Modulated Continuous Wave radar which sends continuouslyand uses frequency modulation for range measurements.
2The bearing of a target is the direction of the target relative to the location from which the bearing is determined
6 CHAPTER 2: The Basics of Radar
Figure 2.1: Radar pulse length (PL)
sends multiple signals. The interval between the start of two subsequent signals is called the PulseRepetition Interval (PRI). The frequency, the Pulse Repetition Frequency (PRF ), can then becalculated by PRF = 1/PRI[27, pp.4-5]. It is assumed that all returning signals belong to currentpointing direction of the antenna.
2.2 Radiation Pattern
The most basic antenna is the one radiating isotropically in space. An isotropic antenna spreadsthe power (Pa) in Watts of the antenna evenly over all directions[3, p.42]. As time goes by, thesignal propagates away from the antenna with equal speed c in all directions. As a consequence,the initial power Pa is spread over an increasing area as the signal propagates. The power density(Pd) is defined as the power per area at some distance r from the antenna. The power density foran isotropic antenna can be calculated as follows[3]:
Pd =Pa
4πr2[W/m2], (2.2)
where r is the distance that the waves travelled. The distance can be seen as the radius of thesphere over which the energy is spread. From this equation it can be concluded that the powerper unit area falls off quadratically with distance.
To create a beam that focusses its energy into a certain direction, the intensity (I) of theradiation should differ per direction. Where the intensity is the power density per unit solid angle(see appendix A.4) for a given direction[3, pp.42-43]. Figure 2.2 shows the intensity of isotropicradiation (is) and focussed radiation (f) for each direction, which is called radiation pattern[25,pp.542-543]. By definition of the isotropic radiation, the intensity is the same for every direction.For example the intensity in direction ~B, denoted by Iis( ~B), is equal to Iis(~C). This is not thecase for the beam that is focussed in direction ~C.
The gain (G) of an antenna in a certain direction (~v) is a measure of how much the energyis focussed in that direction by the antenna relative to an isotropic antenna with the same power(Pa)[27, p.15]:
G(~v) =If (~v)Iis
. (2.3)
Note that the isotropic intensity is the same in all directions.Another useful value is the aerial gain (GD), which is a measure of the maximum intensity
relative to the isotropic antenna[25, 3]:
GD =max{If (~v) |~v}
Iis. (2.4)
This is also referred to as the effectiveness of the antenna[3, pp.42-43]. Note that the vector~v is usually denoted by spherical coordinates in terms of angles θ and φ (for more information
2.2. Radiation Pattern 7
I (B)
A
Isotropic radiation
Focussed radiation
B
I (B)
(is)
(f)
is
f
I (C)is I (C)fC
Figure 2.2: Two-dimensional polar graph with origin A of the intensity in each direction forboth isotropic radiation (Iis) and focussed radiation (If ) and two direction vectors ~B and ~C.
regarding this coordinate system see appendix A.3). Since the same antenna is used for sendingand receiving, the gain of the antenna in a certain direction applies to both sending and receiving[3,p.44].
The angular width of the beam is called beamwidth (BW ). When the aerial gain increases thebeamwidth becomes smaller. The beamwidth can be measured in two different ways[27, pp.21-25](see figure 2.3):
• the half-power beamwidth, which is the angle between the directions in the two-dimensionalplane for which the intensity is half the maximum intensity;
• the null-to-null beamwidth, which is defined as the (smallest) angle between the directionsin the two-dimensional plane for which the intensity is zero.
Intensity
Half-Power BW
Null-to-Null BW
Angle (rad)
- π - ½ π ½ π π
max (I )f
max (I ) / 2f
Figure 2.3: Two-dimensional cartesian graph of a radiation pattern explaining the beamwidth
The beamwidth is measured separately in the horizontal plane and the vertical plane, thehorizontal beamwidth (HBW ) and the vertical beamwidth (V BW ) respectively, see figure 2.4.The smaller the HBW the better the antenna is able to determine the bearing of targets, howeverthis is not the case for the V BW as shown by figure 2.5. The antenna does not correct rotationsof the vessel carrying the antenna, for example rotations caused by waves, therefore the V BWmust be larger.
8 CHAPTER 2: The Basics of Radar
HBW
(a) Horizontal beamwidth
VBW
(b) Vertical beamwidth
Figure 2.4: Half-power beamwidth
VBW
Figure 2.5: Missing object due to a VBW being too small to compensate the tilting of theantenna
As a side effect of increasing the aerial gain, more beams start to appear next to the mainbeam, shown in figure 2.6. These other beams are usually referred to as sidelobes and the intensityof each sidelobe is considerably less than the intensity of the main beam[3, pp.44-48]. In practicea radiation pattern can become rather complicated with lots of sidelobes in all directions.
(a) Radiation pattern from the side (b) Radiation pattern from the front
The power of an incoming signal returned by a target determines the brightness of the echo onthe screen. The greater the power the brighter the echo. The amount of power that is reflectedby an object is defined by the Radar Cross Section (RCS) and is determined by the material ofthe target, the size, shape, orientation and electromagnetic properties of the radio waves[15]. TheRCS is dependent on the orientation of the object relative to the antenna and the value equals asurface area. A plate with this surface area perpendicular to the incoming signal and reflecting allthe incoming energy isotropically returns the same energy as the object for the current directionfrom the antenna to the object. The RCS (σ) can be calculated for an object given the distance(r) from the antenna to the object, the incident power density (Pi) arriving at the object and the
2.4. Radar Equation 9
backscattered power density (Ps) from the object at the antenna[16, pp.64-68]:
σ(θ, φ) = 4πr2Ps
Pi(θ, φ)[m2]. (2.5)
It is nearly impossible to calculate the exact RCS for objects except from very simple onesand even approximations are hard to make. In cases where accurate RCS values are required, theobjects are often built and tested on test ranges[15].
2.4 Radar Equation
Given the RCS of an object, the returning signal for this object can be calculated for any distanceand angle. The incident power density can be calculated as follows (see figure 2.7a):
Pi(θ, φ) =PaG(θ, φ)
4πr2[W/m2], (2.6)
where Pa is the power in Watts of the antenna.When the incident power is known, the backscattered power density (Ps) at the antenna can
be calculated with the RCS equation (equation 2.5) as shown in figure 2.7b. To get the receivedpower (Pr) of the returning signal, this value has to be multiplied with the effective surface area(Ae) of the antenna, which gives the, so-called, radar equation[25, pp.5-7]:
Pr(θ, φ) =PaG(θ, φ)σ(θ, φ)Ae(θ, φ)
16π2r4[W ]. (2.7)
σ
P = P ⋅ G
i
a
4πr2
A
r
(a) Power density (Pi) arrivingat an object
P = P ⋅ σ
s
i
4πr2
Ae
(b) Power density (Ps) arriving atthe antenna
Figure 2.7: Calculating the returning energy with the radar equation
2.5 Radar Screen
When an echo arrives at the antenna with sufficient power to be detected, the echo is drawn onthe radar screen. The location of the echo depends on (see figure 2.8):
• the current pointing direction (~p) of the antenna;
• the travel time (t) of the signal, which is the arrival time minus the time when the last signalwas sent;
• the radar screen scale factor (γ);
• the speed of light (c).
10 CHAPTER 2: The Basics of Radar
Furthermore, the pulse length (PL) determines the length of the echo. The power of an echodetermines the brightness of the echo on the screen. The radar screen has several brightness levelsfor indicating the power of the echoes. The difference between two brightness levels is defined asa certain change of power in decibels (see section A.1 for the definition of decibels) [3]. All signalswith a power lower than the weakest brightness level are not shown.
p
echo
γ⋅½⋅PL⋅c
γ⋅½⋅t⋅c
Figure 2.8: Length and position of echo
Figure 2.9a shows a part of a picture taken from a real radar screen. The part that is shownis the part that visualizes the incoming signals. The location where this picture has been taken isshown in figure 2.9b. Note that it is a virtual representation and the situation (ships, containers,cranes etc) differ.
(a) Part of real radar screen (b) Virtual representation of the location
Figure 2.9: Real radar screen and an overview where the picture of the radar screen has beentaken
In order to get a better interpretation of the radar screen shown in figure 2.9a, figure 2.10presents the same radar screen with on top of it the landmass sketched in grey. There are quitesome echoes in this figure that do not represent objects like ships. All echoes on the radar screenthat a radar operator would rather not like to see are called unwanted echoes. There are two typesof unwanted echoes[23, 25]:
• false echoes, which are echoes that do not represent an object at that location;
• clutter, which are echoes that are not important for a radar operator and can even hideimportant echoes in the clutter.
Unwanted echoes can make it hard for the radar operator to interpret the screen correctly,therefore the visualization of the echoes is enhanced before it is shown. The screen is enhanced
2.6. Echo Scaling 11
by a set of filters, which are controlled by the operator with the goal to remove unwanted echoes.However, these filters can also remove “correct” echoes, hence these filters must be used with careand unwanted echoes will always be seen on the screen. These enhanced radar screens are calledsynthetic displays. The radar screen shown in figure 2.9a is such a synthetic display.
Figure 2.10: Landmass on top of radar screen
2.6 Echo Scaling
Echoes on the screen are often larger than the objects they represent with respect to the radarscreen scale factor[23, chp.5]. Figure 2.11 shows the maximum possible scaling of an echo, basedon the null-to-null horizontal beamwidth (HBW ) and the pulse length (PL). Because of thebeamwidth, the antenna can also detect objects there are a bit to the left or the right of thepointing direction. Therefore, when the antenna is rotating, an object is detected earlier than themoment it is exactly in the center of the beam. As the antenna rotates further the object is alsodetected longer for the same reason. The other effect depicted by the figure is that radar screenwill draw the echo for as long as it receives a signal. However, the scaling is not always the sameas the scaling shown in figure 2.11. Sometimes the signal is not strong enough to be detected,which reduces the scaling.
Figure 2.11: Echo scaling due to horizontal beamwidth (HBW ) and pulse length (PL)
Too large HBW or pulse length can cause objects to merge together on the radar screen.However, a shorter pulse length decreases the chances of detecting objects at long range and insituations of precipitation like rain or snow[3, pp.33-34]. Making the beam width too small couldlead to situations where objects are missed. Furthermore, it is generally believed that a (point)
12 CHAPTER 2: The Basics of Radar
target should be hit 10 times in order to maximize the probability that the target is detected[3,p.53]. Note that the amount of times a target is within the main beam can be calculated with theHBW, pulse repetition frequency (PRF) and the revolution time of the antenna.
2.7 False Echoes
False echoes do not represent an object at the location where it is drawn on the radar screen.They can be caused by a single object or by interaction of multiple objects. Figure 2.12 depicts“correct” and false echoes that are caused by a single object. Although the environment in thefigure contains two objects (A and B), the echoes are the result of a single object (A or B). Thegreen ring in the environment indicates the radar range (rs).
Figure 2.12: False echoes caused by one object
Echoes indicated with A′ are caused by the sidelobes that can detect targets in other directionsthan the direction of the main beam[21, pp.4.1-4.2]. Furthermore, there is an echo B′ on the radarscreen which is an echo caused by an object farther away than the maximum range. This meansthat object B can never cause a real echo on the screen unless a larger range is selected. Reflectionsthat return after the succeeding signal is sent by the antenna, will be treated as if they were causedby the last sent signal. If the returning signal is strong enough, the echo will appear on the radarscreen, an effect known as second-trace echoes[3, pp.206-210].
There are also echoes caused by inter-reflections between objects. The signal, depicted byfigure 2.13, travels from the antenna to A and reflects back to both the antenna and to B. In thesame way, the signal reflected by A to B is reflected back to A and then back to the antenna. Theantenna receives the signal and will draw it in the current direction and the distance according tothe travel time. In this particular case the travel time for the false echo (A + B)′ is the time ittook for the signal to travel the following path: antenna→ A→ B → A→ antenna.
2.8 Clutter
Section 2.7 covered the subset of unwanted echoes called false echoes, in this section unwantedechoes are discussed which are not false. Some echoes on the radar screen represent objects thatare not relevant for the radar operator, these echoes could distract the radar operator and mighteven hide important echoes. This type of echoes is called clutter and form together with the falseechoes the set of unwanted echoes[25, pp.403-404]. Clutter can be caused by all kinds of objects,for instance sea, weather, animals etc. The most important types of clutter are sea clutter andrain clutter, which is a type of weather clutter (see figure 2.14).
2.8. Clutter 13
(a) Situation and effect
A
B
(b) Cause
Figure 2.13: False echo caused by two objects
(a) Reflections from rain drops (b) Reflections from waves
Figure 2.14: Rain and sea clutter
15
Chapter 3
Electromagnetism
The medium used by radar to detect objects are electromagnetic waves. This chapter covers themain properties of these waves. Furthermore, effects of radar waves, which are important forsimulation are introduced. For more information regarding EM waves see appendix C.
3.1 Electromagnetic Radiation
Electromagnetic (EM) radiation are changing electric (E) and magnetic (H) fields that change inphase[27, pp.3-7], see figure 3.1. When an electric field is changed, a magnetic field is induced,which at its turn, induces an electric field and so on[29, p.9]. This effect is known as wavepropagation, which travels at constant speed in all directions.
Throughout this document the word “waves” is used to indicate EM propagation. However,already in the beginning of 20th century it was discovered that light was not continuous, assuggested by the wave theory[8]. Instead, the theory Quantum ElectroDynamics (QED), which ismost successful in explaining the behavior of EM fields, states that EM are particles, which havesome wave properties. Still, wave theory approximates EM fields close enough for the purposes ofthis project and is less computational complex.
EM waves have a polarization, which indicates the orientation of the electric field (E) and themagnetic field (H) relative to the propagation direction[27, pp.3-7], depicted by figure 3.1. Theelectric field is always perpendicular to the magnetic field. The EM waves propagate with thespeed of light (c) and have a wavelength (λ) that is related to the frequency (f) by[27, p.5]:
λ =c
f. (3.1)
The propagation speed is always constant and independent of the speed of the source and targets[27].However, the frequency can change when the source and an arbitrary target move relative to eachother, an effect known as the doppler effect [26, p.10].
Figure 3.1: Polarization electromagnetic wave
When multiple EM waves are at the same location at the same time, they start interfering witheach other. The result is the sum of the waves at that location, also known as the superpositionprinciple[5]. Generally, two types of wave interactions can be distinguished: constructive and
16 CHAPTER 3: Electromagnetism
destructive waves, see figure 3.2. Constructive waves amplify each other while destructive wavesfade each other out. Waves are constructive when ∀δ [ δ ∈ [0, λ] : δ < 1
3λ ∨ δ >23λ ] holds, where
δ is the phase shift. Waves are destructive when ∀δ [ δ ∈ [0, λ] : δ > 13λ ∨ δ <
23λ ] holds. Note
that the electric and magnetic fields superposition with other electric and magnetic fields and thatthe power density of the waves is proportional to E2[13], which is important for calculating theresulting wave.
-6 -4 -2 2 4 6
-2-1.5-1
-0.5
0.51
1.52
(a) Constructive waves
-6 -4 -2 2 4 6
-2-1.5-1
-0.5
0.51
1.52
(b) Destructive waves
Figure 3.2: Superposition principle where the thick line represents the resulting wave
3.2 Antenna Gain
The radar antenna consists of multiple sources, each sending the same signal. Gain is caused by theinterference of these signals. Figure 3.3 depicts an antenna (A) with two radiating sources (S1 andS2) and the distances (d1 and d2) from respectively S1 and S2 to an arbitrary point P . Supposethat the initial signals sent by S1 and S2 start in phase then the phase difference at P is causedby a difference between d1 and d2. The phase difference between the signals determines whetherthe interference is constructive or destructive. The distances from S1 and S2 to an arbitrary pointon line L are equal, meaning that signals are always constructive.
A
S
S1
2
P
Ld
d2
1
Figure 3.3: Distances from sources S1 and S2 to arbitrary points P1 and P2
The effective area (Ae) of an antenna and the wavelength (λ) of the signal determine the gain(G) of the antenna in a certain direction[27, p.9]:
G(θ, φ) =4πAe(θ, φ)
λ2. (3.2)
From this equation it can be concluded that the gain is also applied when the antenna receives asignal. With equation 3.2, the Radar Equation (equation 2.7) can be rewritten as follows:
Pr(θ, φ) =PaG(θ, φ)2σ(θ, φ)λ2
64π3r4[W ], (3.3)
where Pr is the received power by the antenna and σ is the RCS of the reflecting object.
3.3 Basic Interaction Properties
Generally, the following main effects of EM waves can be distinguished[10, 15]:
• absorption, part of the energy is absorbed by a medium;
3.4. Environmental Effects 17
• reflection, part of it is reflected by a medium;
• transparency, part of energy passes through a medium;
• diffraction causes the EM waves to bend around edges of an object.
When EM energy is absorbed, the energy is converted in another kind of energy, usuallyheat[25, p.521]. The amount of energy of an EM wave that is absorbed by a medium depends onthe properties of that medium and the wavelength of the EM waves. Absorption increases whenthe frequency of the EM wave approaches the resonance frequency of the molecules of the medium.
A medium can counteract the incoming EM wave based on the properties of the medium[3].The medium creates an EM wave that counters the incoming wave, which is called reflection.Since the medium tries to counter the incident wave, the phase of the wave is shifted such that theincident and the reflected waves are destructive[3, p.50]. For this project, it is assumed that thereflected wave is always shifted by exactly half a wavelength. Depending on the roughness of thereflecting material the reflection can be specular or diffuse[25, pp.487-489]. The Rayleigh roughnesscriterion specifies that a material is considered smooth when the criterion is satisfied[25]:
h sinψ < λ/8, (3.4)
where h is the difference between the extremes of the surface height and ψ is the angle betweenthe surface and the incident angle, called grazing angle, see figure 3.4.
ψ
h
incident wave
surface
Figure 3.4: Surface roughness determination
When a medium is (semi) transparent, the medium lets (a part of) the incoming wave gothrough. The incident waves are bent towards the surface normal (~n) of the medium if thepropagation speed is lower than the propagation speed in the medium it came from and the otherway around if the speed increases (see figure 3.5a)[7]. The effect of bending waves by differencesof the propagation speed in different media, is known as refraction.
Diffraction is the bending of EM waves around edges as shown in figure 3.5b [25]. The amountof bending depends on the wavelength and the dimensions of the object[7]. A special case ofdiffraction is when the waves are diffracted in such a way that they follow the surface of theobject, which is called creeping waves[15].
n
Medium 1 Medium 2
(a) Refraction (b) Diffraction
Figure 3.5: Refraction and diffraction
3.4 Environmental Effects
This section describes how EM wave propagation effects manifest themselves in real-life maritimeradar applications. The first effect covered by this section is atmospheric attenuation. Atmo-spheric attenuation is the absorption of energy by the atmospheric gases that contain water vapor
18 CHAPTER 3: Electromagnetism
and oxygen[25, pp.521-524]. The amount of attenuation depends on the frequency of the signal,moisture of the atmosphere and the altitude. The atmospheric attenuation starts to be increas-ingly important at frequencies higher than the maximum frequency used by the standard maritimeradars.
Figure 3.6a shows two different paths to travel from one location to another location, in thiscase from A to B, causing superposition of both signals at location B. The reflection of the signalon surface S is called forward scattering. Especially with a flat surface forward scattering influencesthe radiation pattern, for instance calm sea. At some locations the direct signal and the forwardscattered signal are constructive, at other locations the signals are destructive, which breaks theradiation pattern into vertical lobes (depicted in figure 3.6b), called lobing1[25, pp.483-489]. Inreality, the structure will be a bit different since the earth is not flat but round[25, pp.490-493].
A B
S
(a) Forward scattering
S
A Constructive
Destructive
(b) Lobing
Figure 3.6: Forward scattering and lobing
When the atmosphere is uniform everywhere, the EM waves would travel straight lines throughit. However, usually the atmosphere is not uniform and depends on pressure, temperature, watervapor and the frequency of the waves, which causes atmospheric refraction (shown in figure 3.7)[25,pp.494-502]. The standard type of refraction is when the EM waves are bent a bit towards theearth’s surface, extending the line of sight beyond the geometrical horizon. In some cases, thewaves are bent stronger and can even be bent in such a way they follow the earth’s curvature,which is called superrefraction. In rare occasions, the waves are bent the other way around,which is potentially a very dangerous situation, an effect known as subrefraction. Sometimes,waves are bent so much towards the earth’s surface that the angle is greater than the earth’scurvature causing ducting [25, pp.502-518]. Ducting traps the EM waves close to the surface of theearth and can be caused by water evaporation. Therefore, duct is often encountered in maritimeenvironments.
Ducting
Superrefraction
Standard refraction
No refraction
Subrefraction
Earth's surface
Figure 3.7: Atmospheric refraction
Another effect that extends the line of sight beyond the geometrical horizon is diffraction[25,pp.518-521] (see figure 3.5b), which depends on the frequency.
1Not to be confused with the sidelobes of the radiation pattern itself
19
Chapter 4
Signal Propagation Model
Much research has been done in the field of modeling EM radiation[19, 28, 12, 15]. This chapterstarts with the introduction of some existing EM propagation models and discusses the advantagesand drawbacks of these models. Next, some illumination models[10, 24] are introduced that haverealtime performance as their top priority. Finally, radiosity is discussed and a signal propagationmodel based on radiosity is presented.
4.1 Existing EM Propagation and Illumination Models
For some other applications rather precise EM propagation models are required, e.g. for theestimation of the Radar Cross Section (RCS) of an object. The exact way to calculate the RCSis by using the Maxwell Equations[15]. An advantage of this approach is that a function can becomputed for an object, which can be used to calculate the RCS of that object for each position inspace[15]. The drawback of this approach is that it is computationally expensive and as a resultnot useable for complex objects.
The Method of Moments is also an exact model, although, small deviations can occur[15]. TheMethod of Moments is a numerical model, which uses an adapted version of the Maxwell Equationsas a starting point for its calculations[16, pp.110-112]. For this method, the surfaces of the objectsneed to be split into a collection of small patches (see figure 4.1). Each patch should have a sizethat is typically less than λ/5, such that the unknown currents and charges are constant or can bedescribed with simple functions. As a consequence, the Method of Moments is limited by the sizeof an object compared to the wavelength, if the object is too large, too many patches are requiredand the computation time increases dramatically.
(a) Original surface (b) Patches
Figure 4.1: Subdivision of surface into patches
Most of the energy returning to the antenna in this project are echoes from objects that arelarge compared to the wavelength of the signal, which is usually not greater than 10 cm formaritime radars (see appendix C.4). The RCS of an object that is in this so-called optics region isproportional to the area of the object[15, p.16]. Typically, objects belong to the optics region whenthe body size is greater than three times the wavelength. Models like the Method of Momentsare too computationally complex for these objects and approximating models do a better job, like
20 CHAPTER 4: Signal Propagation Model
for instance the High Frequency Asymptotic Techniques(see section C.3). The High FrequencyAsymptotic Techniques are either current-based or ray-based [12, pp.26-28]. Each model has itsown advantages and drawbacks, with some of them, the RCS can be predicted rather precise inthe optics region. However, these models are too computationally complex to be used realtimewhere the returning energies for an entire environment need to be calculated several times persecond.
Illumination models that can be found in e.g. games, need to compute the illumination of theenvironment at least 20 times per second. Therefore, these models are a better starting pointfor realtime radar simulation than EM models. The computation of the RCS of an arbitraryobject becomes less accurate when using illumination models, however, the performance gainis more important than an accurate RCS calculation. The simplest illumination model is thebasic illumination model [10, pp.563-573]. Instead of modeling the electromagnetic propagation,this model determines the brightness (and color) of each surface by taking a constant term forthe influence of ambient light plus the direct influence of each light-source. The ambient-lightconstant replaces the inter-reflections of light between the objects in the scene. However, forradar simulation inter-reflections are important and cannot be replaced by a constant. Two, moreadvanced, illumination models that include the computation of reflections are ray-tracing andradiosity.
Ray-tracing is a ray-based method just like some of the High Frequency Asymptotic Techniques,but some abstractions have been made to gain speed[10, pp.597-614]. Ray-tracing is still very goodat specular reflections and transparency, including refraction. The drawbacks of ray-tracing arethe great amount of rays that are required for detection of objects at great distances and the poorsimulation of diffuse reflections.
4.2 Radiosity
Radiosity is an illumination model based on methods used in thermal engineering[9]. When asource radiates light, the model will determine for every other surface in the environment whichfraction of the radiated energy each surface will receive, given that each surface has a finite surfacearea. Inter-reflections are created by repeating this process, but now all the surfaces that receiveda signal become a radiation source and send their energy into the environment. The result of thisrepeating process is realistic ambient light.
In radiosity, it is assumed that all surfaces in the environment are ideal diffuse reflectors, i.e.lambertian reflectors[9]. Furthermore, it is assumed that the material properties of a surface arethe same for the entire surface and the energy that arrives at the surface is uniform over the wholesurface as well. This can be achieved by subdividing a surface into smaller pieces called patches,which is also done in the Method of Moments. Radiosity is mostly used for indoor environmentsand the calculations are often done offline, however, in recent years radiosity is used in realtimeapplications as well[17].
Many objects in the environments used in this project contain bumps and little obstaclesthat are small compared to the wavelength, which causes diffuse reflections (see section 3.3).Therefore, radiosity has been chosen as the base model for our radar signal propagation, despitethe fact that the used environments are not indoor. Objects are represented by small echoes onthe screen, which usually do not comply with the exact shape of the original objects (see chapter2), therefore, objects can be simplified. Additionally, due to the same reason and the fact thatwaves travel great distances the patch size can be bigger as well. Finally, parts of the radiatedenergy might be lost in the open air, lowering the remaining energy in the system, which reducesthe computation time as explained in chapter 5.
4.3. Radiosity for Radar Signal Propagation 21
4.3 Radiosity for Radar Signal Propagation
The radiosity algorithm has to be adapted in order to fit the radar properties, table 4.1 showsthe differences. First of all, in radiosity it is assumed that during the calculation of the globalillumination the light sources radiate continuously the same energy. For radar this is not thecase, instead it sends a pulse with a certain pulse length (see section 2.1). A surface radiatingelectromagnetic energy, only radiates for the duration of the pulse. Furthermore, it is assumedthat the antenna itself is the only EM source in the environment.
Standard RadarLight sources radiate continuously 3 7Multiple light sources in the environment 3 7The received energy of all individual patches are important 3 7Varying wavelengths supported 3 7Travel time of individual signals important 7 3Radiation intensities can be defined for each direction 7 3
Table 4.1: Differences between standard radiosity and radiosity required for our radar simulation
The original signal sent by the antenna is divided into a collection of signals spread over theenvironment due to reflections. The signals that are important for the radar signal simulationmodel are only the signals that are received by the antenna. The frequency of the antenna isstatic during simulation and the Doppler effect is omitted, so that all waves in the model have thesame wavelength.
For regular radiosity applications, the travel time of an individual electromagnetic wave is notimportant, however, for radar simulation it is. Radar determines the distance to an object bymeasuring the travel time (see section 2.1). Therefore, the model is extended with a travel timefor each signal in the system.
In regular radiosity, it is assumed that all surfaces are ideal diffuse reflectors, although, for ourradar model it should be customizable. First of all the radiation pattern, where the intensity canvary a lot between different directions, but also specular reflection is part of our radar simulation.Finally, part of the energy can be absorbed.
4.4 Energy Transfer
The environment in which the antenna is placed consists of objects that are able to move relativeto each other, for instance buildings, ships etc. Each object consists of a number of flat surfaceswith a finite area, which are split into a collection of smaller patches until they satisfy a givenmaximum size requirement (see appendix D.2), such that the incident signals are uniform on theentire surface of the patch. For the sake of simplicity, all patches in our model are triangles, whichare the simplest objects that can be used to create three dimensional objects.
Each patch has material properties, which determine the basic interaction properties (as de-fined in section 3.3). However, not all basic interaction properties are covered by our radar model.Drawbacks of radiosity are the difficulties to handle diffraction and transparency (especially re-fraction), therefore, these properties are not part of our model.
When a patch has a signal with a certain power (Psp) in Watts, this signal is sent into theenvironment. For all other patches in the environment it is checked which patches are visible. Apatch is considered visible when the ray from the centroid (see section A.2 for the definition ofcentroid) of the source patch to the centroid of the target patch does not hit the surface of anotherpatch. Suppose that a certain patch is visible then the power density (Pd) arriving at that patchcan be calculated as follows (see chapter 2):
Pd(θ, φ) =PspG(θ, φ)
4πr2, (4.1)
22 CHAPTER 4: Signal Propagation Model
where G is the gain of the source patch in the direction of the ray and r is the distance betweenthe source and the target patch (or the length of the ray). The power that is received by apatch depends on the surface area of the target patch. However, as shown in figure 4.2 not theentire surface area might effectively receive the incoming signal, unless the incident wave is exactlyperpendicular to the surface of the patch. Then the power (Ptp) that is received by a target patchis the area (A′) of the target multiplied by the power density at that location:
Ptp =PspG(θ, φ)
4πr2·A′. (4.2)
AA' α
Figure 4.2: Effective area (A′) of a patch with area A for an incoming wave
When the target patch is relatively far away, the easiest way to calculate the effective area isby the following approximation:
A′ = cosα ·A, (4.3)
where α is the incident angle and A is the surface area of the receiving patch.Equation 4.3 only works when the power density is uniform at all locations on the receiving
patch. When the size of the target patch is large compared to the distance, the power density isnot uniform and the approximation of equation 4.3 deviates too much. First of all, the distancer is based on the distance between the center of the source and the center of the target. Whenthe distance is small compared to the size of the patches, distance r is likely to deviate much fordifferent points on the patches. Furthermore, the projected area is a flat triangle while it shouldhave been a spherical triangle.
The correct area, which effectively receives a signal, can be calculated by projecting the targetpatch on the unit sphere around the source patch (see figure 4.3). This projected area is the solidangle of the target and can be calculated by determining the spherical excess (E) of the targetpatch[34]:
E = 4 · arctan√
tan( 12s) tan(1
2 (s− a)) tan(12 (s− b)) tan(1
2 (s− c)), (4.4)
where a, b and c are the angles between the vectors from the source to each vertex of the targetpatch and s is the semiperimeter [35]:
s = 12 (a+ b+ c). (4.5)
With the spherical excess, the power that is received by the target patch can be calculated asfollows:
Ptp =PspG(θ, φ)E
4π. (4.6)
The gain can vary a lot for small differences in angles. The gain that is used, is based on thevector from the centroid of the source to the centroid of the target. Therefore, the received energycan still deviate from its correct value, caused by the difference in gain in the direction of theedges. However, the presented model will not cope with this error.
After the incoming signal at a target patch has been calculated, the absorption of the targetpatch is applied. Then, the new signal can be sent in the same way, unless, the receiving patchwas an antenna patch, which only receives signals and does not reflect signals.
4.5. Radiation Pattern 23
Source
Target
Projected area
Figure 4.3: Projection of patch on sphere
4.5 Radiation Pattern
This section presents a model for the gain (G) of the radiation pattern (see section 2.2 for infor-mation regarding the radiation pattern). The antenna is assumed to be at a large distance fromall other objects which enables to antenna to be treated as a point source and the intensity of theantenna in an arbitrary direction is equal for any location in that particular direction. Further-more, the energy that is radiated in directions, for which the angle between that direction andthe pointing direction of the antenna is more than 1
2π, is neglected and the presented model onlysupports sidelobes in the horizontal plane. Although sidelobes can appear in any direction, onlythe sidelobes that are shifted in the horizontal plane with respect to the pointing direction cancause false echoes (see section 2.7).
The gain is approximated by a number of sinusoidal functions, where the main beam and eachindividual sidelobe is represented by two cosine functions: one for the horizontal plane and one forthe vertical plane. The direction from the antenna to an arbitrary target is expressed in sphericalcoordinates (see appendix A.3), as shown in 4.4. It is assumed that the pointing direction (~p) ofthe antenna is always in the horizontal plane. Note that for the convenience of the gain function,the angle φ is used differently than normally, suppose the correct angle is indicated with φn thenφn = 1
2π − φ.
horizontal plane
vertical plane
p
d'
d
θ
ϕA
Figure 4.4: Spherical coordinates (θ, φ) for a direction (~d) from the antenna (A) to a target,where ~d′ is the projection of ~d on the horizontal plane
First suppose the two-dimensional case of the horizontal plane - as depicted in figure 4.5 - withn lobes where each lobe (i ∈ [0, n− 1]) is represented by a function Gi:
Gi(θ) ={ρi(cos (ωi0 θ + δi) + 1) for (− 1
2Hi ≤ θ + δi ≤ 12Hi)
0 else, (4.7)
where θ is the angle between the direction to the target and the pointing direction of the antennain the horizontal plane, ρi (where ρi > 0) is the amplitude of lobe i, δi is the phase shift and Hi
24 CHAPTER 4: Signal Propagation Model
is the null-to-null horizontal beamwidth (HBW) of lobe i. The angular frequency ωi0 in horizontalplane, is related to the HBW as follows: ωi0 = 2π/Hi. Note that the HBW equals a wavelength ofthe original cosine function and for all i ∈ [0, n− 1] and all α ∈ [− 1
2π,12π] holds that Gi(α) ≥ 0.
H
δ
G
θ
ρ
max(G )i
i
i
i
G(i-1)
G(i+1)
Gi
Figure 4.5: Set of cosines functions approximating the gain of a radiation pattern in all directionsof the horizontal plane
For the three-dimensional case, each lobe in the horizontal plane is extended with a verticalbeamwidth (VBW). Furthermore, φ is the angle between the pointing direction of the antennaand the direction in the vertical plane. Note that this model does not support sidelobes in thevertical plane and there is no phase shift (δ) in the vertical plane. The resulting gain of lobe i fora direction is the multiplication of the gain in the horizontal plane and the gain in vertical plane,which looks as follows:
Gi(θ, φ) ={ρi · (cos ( 2πθ
Hi+ δi) + 1) · (cos( 2πφ
Vi) + 1) for (θ + δi) ∈ [A,B] ∧ φ ∈ [C,D]
0 else,(4.8)
where Vi is the null-to-null VBW of lobe i, A = − 12Hi, B = 1
2Hi, C = − 12Vi and D = 1
2Vi.The total gain of all lobes in a certain direction is defined as the sum of the gain of each lobe:
G(θ, φ) =n−1∑i=0
Gi(θ, φ). (4.9)
The average gain should be equal to 1 for all directions. This means that the integral over alldirections (
∫ 12π
− 12π
∫ π−π G(θ, φ) sin(1
2π−φ) dθ dφ) must be equal to the integral over all directions forthe isotropic antenna, which is 4π. The total gain of equation 4.9 is scaled by a factor τ in orderto achieve the right amount of radiated power, where:
τ =4π∑n
i=0 ρiHi2 cos ( 12π −
12Vi)
. (4.10)
The derivation of τ can be found in appendix D.1. With this extension the final gain function forthis model is:
G(θ, φ) = τ
n−1∑i=0
Gi(θ, φ). (4.11)
4.6. Specular Reflection 25
In section 3.2 it is shown that the effective area of the antenna (Ae) is related to the gain (G)and the wavelength (λ) (equation 3.2). In our model, the antenna has a predefined finite area (A)just like all patches in the environment. Additionally, the gain function is also used for incomingsignals to calculate the effective area:
Ae(θ, φ) = G(θ, φ)A′(θ, φ), (4.12)
where A′ is the effective area of the original area A of the antenna. Therefore, the radar equationthat holds for the radar propagation model is:
Pr(θ, φ) =PaG(θ, φ)2σ(θ, φ)A′(θ, φ)
64π3r4[W ], (4.13)
where Pr is the received power by the antenna, σ is the RCS of an arbitrary object and r is thedistance to the object.
4.6 Specular Reflection
The primary reflection of the radiosity is diffuse reflection where the intensity of the reflectedsignal is the same in all directions. For this project, the model has been extended in order tohandle specular reflections as well. However, the specular reflection cannot handle perfect rayreflection, instead it reflects a beam with a certain angle (α), where α > 0.
n
Surface
s
s
i
rα
χ -
½αχ
r
(a) Surface specular reflecting in-coming signal (~si)
G
α
r
θ
(b) Reflected beam pattern
Figure 4.6: Specular reflection
Figure 4.6a depicts the specular reflected signal (sr) for an incoming signal (~si). For the perfectreflection vector ~r holds that the angle of incidence (χ) is equal to angle of reflection. The reflectedsignal (sr) is a beam with the maximum intensity in direction ~r. The reflected beam is similar toa single lobe of the radiation pattern, except that α is constant in all directions. A gain function(G) defines the gain in every direction relative to ideal diffuse reflection (see figure 4.6b). Thegain is maximal in direction ~r and is zero for all directions for which the angle (θ) between thatdirection and ~r is greater than 1
2α. Similar to the radiation pattern, a cosine function is used tomodel this behavior:
Gi(θ) ={τ(cos
(2πθα
)+ 1) for (− 1
2α ≤ θ ≤12α)
0 else,(4.14)
where
τ =4π
α cos ( 12π −
12α)
. (4.15)
26 CHAPTER 4: Signal Propagation Model
4.7 Superposition
Every signal that is sent by the antenna, is assumed to be a perfect harmonic wave with a certainfrequency (f). It is also assumed the signals that are returning to the antenna are still perfectharmonic waves with the same frequency. Suppose two signals (S1 and S2) defined by sinusoidalfunctions:
S1 = A1 sin (ω0t+ δ1), (4.16)S2 = A2 sin (ω0t+ δ2), (4.17)
where A is the amplitude or signal strength, δ the phase shift and ω0 is the angular frequency,which is equal to 2πf .
The travel time of a signal (t) determines the starts of the sinusoidal, which is required tocompute the phase shift:
δ = 2π(tf − btfc). (4.18)
Every time a signal reflects, the phase is shifted by exactly half a wavelength. Suppose that h isthe amount of hops of a particular signal then the phase becomes:
δ = 2π(tf − btfc) + (h− 1)π. (4.19)
The sum of two harmonic waves is again a harmonic wave[31]. The superposition of the twosignals gives the following resulting signal (S), considering the fact that the power density of asignal is proportional to E2 (see section D.3 for the derivation):
S = A sin (ω0t+ δ), (4.20)
where:
A = A1 +A2 + 2√A1
√A2 cos(δ2 − δ1), (4.21)
δ = arctan(√
A1 sin δ1 +√A2 sin δ2√
A1 cos δ1 +√A2 cos δ2
). (4.22)
27
Chapter 5
Radar Simulation Algorithm
Algorithm 1, given below, is the outline of the radar simulation algorithm, which calculates thereturning echoes for an entire revolution of the antenna and returns a picture of the resulting radarscreen. Although the creation of a radar screen is not part of the requirements for this project,a simple version has been included (see section 5.7), such that the realism of the signals can beverified.
The radar simulation algorithm starts with the initialization of the simulation (line 1, this iswhere all the settings are initialized and all objects in environment are loaded and converted topatches. Note that each function only shows the parameters that can change during simulationin order to keep the algorithms clear. A list of all settings used by the simulation is presented insection 5.1.
The algorithm has two important data types: signals and patches. A signal consists of a signalstrength (P ), travel time (t), the amount of hops (h) and a pulse length (pl). Every signal in thesimulation belongs to a patch, the source patch, that received - or created it in the case of theantenna - this signal and is about to reflect this signal into the environment. Therefore, each signalhas a pointer to the source patch (p). Each patch contains its geometry, location, orientation, alist of patches (vp) that are visible for this patch and since the antenna is also modelled by a setof patches as well, it can be checked whether a patch is an element of the antenna.
Algorithm 1 Radar Simulation Algorithm
1: Patches← InitializeSimulation (); {Initialize patches and settings}2: for i← 0 to RotationSteps do3: Signals[i]←SendInstance(Patches);4: UpdatePatches (Patches); {update patches of all objects and rotate antenna}5: end;6: Superposition(Signals);7: return DrawRadarScreen(Signals);
During a full revolution of the antenna, the antenna sends multiple signals. The amount ofsignals which is sent by the antenna is called RotationSteps in the algorithm. The time betweentwo succeeding signals is referred as a send instance in this project (line 3 in the algorithm).
Every send instance starts with the sending of the initial signal of the antenna followed by thecomputation of the returning signals (see section 5.2). The returning signals of a send instance arestored in a list of signals (Signals) for each direction. After the completion of a send instance, thepatches are updated, i.e. objects might have moved and the antenna is rotated to the direction ofthe next send instance. Note that during a send instance, it is assumed that the objects do notmove.
When the signals are calculated for all directions, superposition is applied to all signals receivedby the antenna (section 5.6). Finally, the signals are inserted in the function that visualizes the
28 CHAPTER 5: Radar Simulation Algorithm
radar screen (DrawRadarScreen), which is explained in more detail in section 5.7.
5.1 Initialize Simulation
Before the simulation can start, the environments needs to be defined. During the initialization,all the objects in the environments are imported and converted to individual patches (see sectionD.2). Furthermore, all the settings required for the simulation are set:
• RotationSteps, the number of send instances in a full revolution of the antenna;
• AntennaSignal, the initial power of the antenna in Watts;
• minP , the minimum power in Watts for which the simulation continues reflecting signals(explained in section 5.3).
• H, maximum allowed number of hops (explained in section 5.3);
• BF , maximum branching factor (explained in section 5.3);
• UpdateInterval, the number of send instances that the list of visible patches for an arbitrarypatch are considered to remain constant (see section 5.4);
• rs, the maximum range in meters that is visible on the radar screen;
5.2 Send Instance
Each send instance starts with one signal, the original signal of the antenna(see line 1 in algorithm2), which will be sent to all patches that are visible for the antenna. Therefore, the algorithmrequires at least one patch, the patch of the antenna. The power of this signal equals the powerof the antenna and the travel time of the signal is zero. Based on the material properties of thepatches that receive a signal, a patch can reflect a part of the incoming signal and absorb a partof it. This process can be repeated for as long as there are signals in the system.
Algorithm 2 SendInstance (Patches)
Precondition: |Patches| ≥ 11: Signals← InitialAntennaSignal; {initially only the antenna has a signal}2: Result← ∅; {Result stores the echoes received by the antenna}3: while
∑s∈Signals s.P > minP do {check if the total remaining signal strength > minP}
4: s←max(Signals); {max returns the signal with the maximal power}5: Signals′ ← SendSignal(s, Patches);6: Result← Result ∪ {s′ ∈ Signals′ | s′.p ∈ Antenna}7: Signals← Signals ∪ {s′ ∈ Signals′ | s′.p /∈ Antenna} \ {s}8: end;9: return Result;
Postcondition:∑s∈Signals s.P ≤ minP
Generally, each patch has more than one visible patch that does not absorb all the incomingenergy. The result is an increase in the number of signals for every signal that is sent. Themaximum number of new signals caused by sending a single signal is called the branching factor.In section 5.3, methods are presented to control the branching factor.
The radar can only recognize signals with a certain minimum strength and since radiosity isused for the computation of the returning signals, progressive refinement can be applied as animprovement (see line 3). Progressive refinement in radiosity lets the algorithm stop when thetotal remaining energy drops below a specified value (MinP )[6]. To reach this state faster, the
5.3. Send Signal 29
algorithm will always pick the strongest signal still in the system to be sent next (see line 4). Notethat the algorithm automatically stops when no signals are left in the system since the remainingpower then equals zero and the threshold is larger than zero.
As shown in the algorithm in line 6 and 7, the resulting signals of sending one signal (SendSignalin line 5) are split. The signals that did not arrive at the antenna are put into the set of remainingsignals and the other signals will be added to Result and cannot be sent again.
5.3 Send Signal
Algorithm 3 is the algorithm for sending a single signal. This algorithm stores the new signalsin the set Signals, which starts empty (line 1). Before new signals can be created, the visiblepatches need to be known for the patch that is sending the signal. Function GetVisiblePatches online 2 of the algorithm returns the visible patches for patch s.p (explained in more detail in thenext section).
When the visible patches are known, the signals can be created. The number of signals dependson the branching factor. When the branching factor increases, more signals will be created,resulting in longer computation times. Therefore, the algorithm uses the following methods toguarantee that the algorithm finishes and to control the branching factor:
• maximum signal travel time;
• maximum number of hops;
• Monte Carlo algorithm.
First of all, the only echoes that are eventually drawn on the radar screen are the echoes thattravelled a distance of less then the configured maximum range. Therefore, signals for which thetravel time (t) exceeds the time required to travel twice the maximum range are not added to theset of new signals (Signals) (see line 6). Note that when these signals are not included, second-trace echoes are impossible (see section 2.7). Although, this guarantees that the number of signalswill go down after a while, it could take a long time to reach this state in situations where surfacesare close to each other.
Limiting the amount of hops (h) makes sure that the signal does not reflect more than aspecified amount (H) of times (line 7 till line 9 in the algorithm). Note that a new signal will onlybe added when the target patch is not part of the antenna and the amount of hops is less than themaximum, otherwise signals will not reach the antenna within the specified amount anyway. Theminimal value of the amount of hops must be two, which represents the group of echoes that arecaused by direct reflection, from the antenna to an object and back. Much energy is lost duringa hop, still it could be the case that signals are not added which would have caused an echo onthe screen. Not adding these signals does not really degrade the quality of the radar since thesebelong to the group of false echoes.
Furthermore, the number of signals expands very fast, every single signal that is sent will causea number of new signals. A Monte Carlo algorithm is a randomized algorithm and can be usedto control the branching factor. Before creating all the new signals for a given source signal, thealgorithm will check whether the amount of new signals exceeds a certain maximum branchingfactor (BF ), if so, Monte Carlo is applied.
When Monte Carlo is applied the energy is split into BF parts with equal power. The sumof the power of all BF signals equals the sum of the power of all signals if Monte Carlo wouldnot have been applied. Each signal is sent to a random (visible) patch, where every patch has aprobability of receiving a signal that equals the power that it would have received without MonteCarlo, divided by the sum of all signal powers.
Finally, when a weak signal is split into BF new signals, it could be the case that none ofthese signals will be used again because of progressive refinement. A better job can be done byintroducing a minimum signal strength and use that value when the number of signals is smaller
30 CHAPTER 5: Radar Simulation Algorithm
than BF , where the number of signals is the power of the sum of all signals divided by theminimum power.
Algorithm 3 SendSignal (Signal, Patches)
Precondition: Signal.h < H1: Signals← ∅; {Signals stores the new signals}2: V isiblePatches←GetVisiblePatches(s.p, Patches);3: for all p ∈ V isiblePatches do4: s′ ← EnergyTransfer(s, p); {compute the signal that would arrive at p}5: s′.h← s.h+ 1;
6: if s′.t <2rsc
then {travel time t of signal s′ < time required to travel max. range rs twice}7: if p ∈ Antenna ∨ s′.h < H then {where H is the maximum allowed hops}8: Signals← Signals ∪ {s′};9: end;
10: end;11: end;12: if min(BF, Signals.P/minSP )< |Signals| then13: {where BF is the maximum branching factor and minSP is the minimal signal power}14: Signals←MonteCarlo(Signals);15: end;16: return Signals;
Postcondition: ∀s [ s ∈ Signals ∧ s.p ∈ Antenna : s.t ≤ 2rsc∧ s.h ≤ H ]
5.4 Visible Patches
During a send instance, the patches do not change and therefore the visible patches only need tobe calculated once for each patch (line 1 in algorithm 4). However, the time between successivesend intervals can be relatively short, which means that most patches probably did not move verymuch (based on their speed). Thus, the update interval is the number of send instances the visiblepatches are assumed to be static.
Algorithm 4 GetVisiblePatches (Patch, Patches)
1: if #send instances since last time visible patches were computed > update interval then2: Patch.vp← ∅; {where vp are the visible patches of a patch}3: for all p ∈ Patches do4: if Visible(Patch, p) then5: Patch.vp = Patch.vp ∪ {p};6: end;7: end;8: end;9: return Patch.vp
Determining whether a patch is visible (line 4) is done with an axis aligned Binary SpacePartitioning tree (BSP tree). A BSP tree hierarchically subdivides the environment, the completespace, into subspaces often referred to as voxels[30]. The traversal algorithm and the constructionalgorithm are relatively simple and cheap in execution[30, p.81].
Before the simulation starts a BSP is created once for each object containing all the flat surfacesof that object (not the patches). A patch is considered visible when no surface in the BSP tree ofeach object blocks the ray from the centroid of the source patch to the centroid of the currently
5.5. Worst Case Computation Complexity 31
checked patch. The BSP tree is traversed by means of the standard voxel walking method asdescribed by Jim Arvo[2].
A significant part of the performance of the BSP tree is determined by the construction of thetree. A successful way to optimize the tree is by using a cost prediction function, which predictsthe best location for placing a splitting plane that splits a space into two subspaces. The functionused for this project is called the Surface Area Heuristic (SAH)[30, p.117]. Still, the algorithm forchecking whether the ray hits a surface can be called very often, therefore an optimized version ofthe Projection Method has been used[30, section 7.1.3] 1.
5.5 Worst Case Computation Complexity
In this section the worst case computation complexity is calculated for a single send instance.The computation complexity depends on the increasing number of signals (in algorithm 2) in thesystem and the determination of the visible patches (algorithm 4).
Initially there is only one signal, the signal of the antenna. The antenna can send its signalto at most BF visible patches. For all patches that received a signal, each of the signals can atmost be sent to another BF patches. Suppose the total remaining signal does not drop below thethreshold set for progressive refinement and all signals travel the maximum amount of hops withinthe maximum allowed time. Then the number of signals in the system would become:
BFH−1. (5.1)
Although, for each signal the visible patches must be known for the patch that holds the signal,the visible patches for each patch only need to be calculated once during an update interval ofone or more send instances. Since it is the worst case computation complexity, suppose the visiblepatches need to be calculated during the current send instance. It is assumed that the numberof objects that can move relative to each other in the environment is very low compared to thenumber of surfaces. Furthermore, in the worst case situation the amount patches equals thenumber of surfaces, then the complexity for this is[30]:
O(N2 · logN). (5.2)
Equation 5.1 and equation 5.2 results in the worst case computation complexity for a singlesend instance:
O(N2 · logN +BFH−1). (5.3)
5.6 Superposition
Since the signals (Signals) that are received by the antenna are the only interesting signals,superposition can be applied as post processing. The algorithm (see algorithm 5) will pick asignal s1 from Signals that arrived first at the antenna, which is removed from the set. Then,the algorithm will again pick a signal s2 from Signals that arrived first. If both signals overlapbased on their travel time, the signals are added (see equation 4.20) and the resulting signals2 areinserted in Signals and s2 is removed, otherwise s1 is added to the result (Result). This processis repeated until there are no signals left in the system.
5.7 Draw Radar Screen
In section 2.5 the basics were explained about how a radar screen is drawn. The radar screen usedfor this project is based on six parameters:
1Chapter 7 of that document on the projection method contains an error in one of the algorithms, the errata ofthis can be found at the website of the author
2there can be more than one resulting signal since the signals might not overlap completely
32 CHAPTER 5: Radar Simulation Algorithm
Algorithm 5 Superposition (Signals)
1: Result← ∅2: while |Signals| ≥ 2 do {there must be at least two signals}3: let s1 be a signal in Signals with the least travel time;4: Signals← Signals \ {s1};5: let s2 be a signal in Signals with the least travel time;6: if [s1.t, s1.t+ s1.pl] ∩ [s2.t, s2.t+ s2.pl] 6= ∅ then {if signals overlap}7: Signals = Signals \ {s2};8: Signals = Signals ∪ Add(s1, s2);9: else
10: Result = Result ∪ {s1};11: end;12: end;13: Result = Result ∪ Signals;14: return Result;Postcondition: ∀s [ s ∈ Result : ¬∃s′ [ s′ ∈ Result∧s′ 6= s : [s1.t, s1.t+s1.pl]∩[s2.t, s2.t+s2.pl] 6=∅ ] ]
• range (rs), the range of the radar screen determines the relative distance of the echoes;
• range resolution (rp), this defines the resolution of the range in pixels, now the radar screenscale factor (γ) can be defined as γ =
rprs
;
• number of rotation steps (R), which defines the width (α) of an echo as 2π/R;
• brightness levels (BL), the amount of different brightness levels that are used for indicatingthe power of the returning echo;
• brightness ratio (BR), the difference between the strongest and the weakest brightness level;
• gain (G), which determines the threshold of the strongest brightness level.
Figure 5.1 depicts how each signal is drawn on the screen. The direction in which the echo isdrawn depends on the pointing direction (~p) of the antenna when the signal was received. Thelength (s) of the echo is proportional to the pulse length of the signal (PL).
p
rp
echo
αα
d
s
Figure 5.1: Drawing of echo on the radar screen with d = γ t·c2 pixels and s = γ PL·c2
The determination of the brightness level in this project is a rather complex procedure, whichis based on the logarithmic amplifier as found on real radar systems[3, pp.68-70]. The threshold(MaxB) of the brightest echo on the screen is defined as MaxB = log10G and the threshold(MinB) of the weakest brightness level as MinB = MaxB/BR. The logarithmic difference σ in
5.7. Draw Radar Screen 33
power between two successive brightness levels is defined as σ = MaxB−MinBBL−1 . Then the brightness
level L (0 ≤ L ≤ BL) for a signal (s) with power P can be calculated as follows:
L = min(max(b log10(s.P ·G)−MinB
σc+ 1, 0), BL). (5.4)
It could be the case that multiple echoes overlap on the screen, for overlapping areas thestrongest brightness level of the overlapping signals is drawn.
35
Chapter 6
Results
In this chapter the results are presented for the implementation of the signal propagation model.The first aspects that will be tested are the gain functions of the radiation pattern and specularreflection. Furthermore, it is investigated whether the radar screen shows objects at the correctposition and whether invisible objects are actually invisible. Also the echo scaling is analyzed andappearance of false echoes has been tested. Finally, the running time of our simulator is measured.
6.1 Test Environment
The model has been implemented in C++ and is compiled with the GNU g++ (C++) compiler,version 4.4.3. The tests in this chapter ran on an Intel Core i5 660 CPU with 4GB RAM memoryrunning Ubuntu 10.04 with kernel 2.6.32-22 64 bit. The implementation does not utilize thegraphics card, but it is multi-threaded, running on the 4 cores of the CPU. During a send instance,each thread sends the strongest signal left in the system until the total remaining energy dropsbelow a preset threshold.
6.2 Method for Testing the Gain Function
To test the gain function, a sphere is approximated by a number of patches that are placedaround the radiating source for measuring the energy a source emits and visualizing its radiationor reflection pattern. The sphere is created by splitting each triangular face of an icosahedron (seeappendix A.5) (see figure 6.4a) into a predefined number of equally sized triangles (see figure 6.4b),which are called patches. To approximate the shape of a sphere, the vertices of all triangles areplaced at the same distance from the center of the sphere (figure 6.4c). Note that the size of thepatches is not exactly equal anymore after changing the distances to each vertex. The advantageof using a sphere of patches based on an icosahedron is that the patches of an icosahedron allhave approximately the same size, such that the accuracy of the measurements of the energy isthe same in all directions.
(a) Icosahe-dron
(b) Patches (c) Scaled
Figure 6.1: Creation of sphere of patches
36 CHAPTER 6: Results
When the source in the center of the sphere radiates a signal, some patches receive a signal,which patches receive a signal depends on the gain function and the power of the original signal.The amount of radiated energy can be measured by summing up the energies received by eachindividual patch. The visualization of the pattern is done by rendering the sphere of patches withOpenGL and adapting the distance from the center of the sphere to each vertex of the sphereaccording to the average received signal per m2 in decibels (see appendix A.1) of the neighboringpatches (see figure 6.2a). Colors have been added to emphasize the intensity in a certain direction(see figure 6.2b). Directions with a high intensity are colored red, average intensities are coloredyellow and low intensities are green. Finally, as depicted in figure 6.2c the pattern is illuminatedsuch that the shadow creates a three dimensional impression of the shape.
Ap
(a) Patches of the sphere deformed in orderto show pattern
(b) Colors of sphere arechanged to indicate theamount of energy receivedby each patch
(c) The pattern is illumi-nated to create a three di-mensional effect
Figure 6.2: Sphere of patches deformed for the side view visualization of an arbitrary gainfunction of antenna (A) in the pointing direction ~p
6.3 Radiation Pattern
Each send instance starts with only one signal, the signal of the antenna. The radiation patternhas a great influence on the resulting radar screen. Therefore, it is important that the pattern iscorrect and it sends the correct amount of energy.
Four different radiation pattern setups have been tested:
1. a semi-isotropic radiation pattern, the intensity is the same in all directions of the hemispherethat are in front of the antenna and zero in backwards directions;
2. a single lobe with an equal horizontal beamwidth (HBW) and vertical beamwidth (VBW);
3. a single lobe where the HBW and VBW are not equal;
4. multiple lobes with a main lobe and a single sidelobe at each side of the main lobe.
To measure the intensity in many directions, measuring the total sent energy and visualizingthe gain function, a sphere of patches has been placed around the antenna (see figure 6.3). Theradius of the sphere was set to 100 m for all tests. Furthermore, in each of the tests the powerof the initial signal of the antenna was equal to 50 kW . Table 6.1 shows further test settings foreach setup. A visualization of the radiation pattern is given from the top view, side view and thefront view. Note that a larger amount of patches for the sphere of patches has been used in testfour to achieve a smoother result for the visualization of the gain function.
The total received power by the sphere of patches should approximately be equal to the initialenergy of the antenna in all tests. The visualization of the radiation pattern should be a hemispherein the pointing direction of the antenna for the first setup. Because the visualization draws alldirections with maximum intensity red, the entire hemisphere should be red. For the second setup,the horizontal and vertical beamwidths are equal, thus the top and side view should be the sameand the front view should be spherical. The results when the HBW and VBW are not equal should
6.3. Radiation Pattern 37
Ap
Sphere of patches
Figure 6.3: Top view overview of the setup for the radiation pattern test of antenna (A) withpointing direction ~p
Setting 1 2 3 4Number of patches on sphere 200.000 200.000 200.000 1.250.000HBW - 40◦ 20◦ 5◦
VBW - 40◦ 60◦ 50◦
Number of sidelobes 0 0 0 2Relative strength sidelobes - - - 1
10
HBW of sidelobes - - - 5◦
VBW of sidelobes - - - 50◦
Shift of sidelobes - - - ±5◦
Table 6.1: Test settings for each radiation pattern test setup
be best visible in the front view, there the shape should be changed to an ellipse. The visualizationof the last test should show sidelobes on either side of the main beam and the sidelobes should besmaller due to the fact that the intensity of the sidelobes is smaller.
Test variable 1 2 3 4Total received signal 49.899 W 50.626 W 51.429 W 50.984 W#Patches that received a signal 99.800 7.188 4.934 19.520
Table 6.2: Results for each setup
A
(a) Topview
A
(b) Sideview
(c) Front view
Figure 6.4: Visualization of the radiation pattern of antenna (A) with semi-isotropic radiation
A
(a) Top view
A
(b) Side view (c) Frontview
Figure 6.5: Visualization of the radiation pattern of antenna (A) with single beam has an equalhorizontal and vertical beamwidth
38 CHAPTER 6: Results
A
(a) Top view
A
(b) Side view (c)Frontview
Figure 6.6: Visualization of the radiation pattern of antenna (A) with single beam where thehorizontal and vertical beamwidth are not equal
A
(a) Top view
A
(b) Side view (c)Frontview
Figure 6.7: Visualization of the radiation pattern of antenna (A) with main beam that has twosidelobes
The results of each test can be found in table 6.2 and the visualization of each radiation patternis depicted in figure 6.4, 6.5, 6.6 and 6.7. The total received energy by the sphere of patches isapproximately equal to the initial energy of the antenna for all tested situations. Minor differencescan (partly) be explained by the fact that the centroid of each patch is used for the determinationof the gain on the entire surface of the patch. The amount of received energy varied most in thesituation where the HBW and VBW (test 3) were not equal. There is no clear indication why thisis the case. The visualization of each radiation pattern is as expected.
It can be concluded from the tested situations that the received energy can vary slightly.Generally, small variations are no problem since the brightness levels on the radar screen are on alogarithmic scale and they cannot be verified by the operator. Finally, the radiation pattern shouldbe able to handle any number of sidelobes with different relative strengths without necessarilylosing precision meaning, based on the tested situations. Therefore, it should be possible to createa rather realistic radiation pattern in the simulator without using multiple radiating sources.
6.4 Reflection and Absorption
As described in section 4.4, only absorption and (specular) reflection were implemented of thebasic interaction properties (see section 3.3). The echoes on the screen are the result of reflections,therefore it is important that these reflections are correct as well.
The following setups have been tested:
1. diffuse reflection;
2. diffuse reflection with absorption;
3. specular reflection;
4. specular reflection where the patch is not perpendicular to the incoming signal;
5. diffuse and specular reflection.
6.4. Reflection and Absorption 39
To test these setups, an environment has been set up with a simple antenna and a single patchexactly in the pointing direction of the antenna with a distance of 100 meters between the two(see figure 6.8a). For test 4, the patch has been rotated with 1
4π rad in clockwise direction to testwhether the reflected direction is computed correctly (see figure 6.8b). Similar to the test of theradiation pattern, a sphere of patches is used to measure the total radiated energy and visualizethe pattern, but this time from the patch instead of from the antenna. The sphere of patchesonly receives signals from the patch, had a radius of 100 meters and counted 288000 patches. Theantenna used in this test has a single lobe with a HBW of 5 degrees and and a VBW of 60 degrees.The amount of energy that was received by the patch was 24,623 W . The values for each testsetup are listed in table 6.3.
Ap
Sphere of patches
Pn
100 m
(a) Patch perpendicular to in-coming signal of antenna
¼πA
p
Sphere of patches
P
n
100 m
(b) Patch rotated with 14π rad
Figure 6.8: Top view overview of two different setups for the reflection pattern and absorptiontest with antenna (A) with pointing vector ~p and patch (P ) with normal vector ~n
Table 6.3: Test settings reflection and absorption for each test setup
It is expected that the total amount of energy received by the sphere of patches equals thepower that was received by the patch, except for test 2, where it should be reduced to 60 % due toabsorption. The visualization of the reflection patterns should be hemispheres in direction ~n fortests 1 and 2 since the intensity of diffuse reflection is equal in all directions. Test 3 and 4 shouldbe single beams. For test 3, the beam should be in direction ~n and for test 4, the direction ofreflection should be rotated by 1
2π rad. Finally test 5 should show a combination of the outcomeof test 1 and 3, however, the intensity of the specular part should be higher in direction ~n thanthe intensity of the diffuse part.
Test variable 1 2 3 4 5Total received signal 24,582 W 14,749 W 23,574 W 23,574 W 24,078 W#Patches that received a signal 143.760 143.760 12.932 12.932 143.760
Table 6.4: Results of reflection and absorption tests for each setup
The visualization of the patterns (see figure 6.9, 6.10, 6.11 and 6.12) look as expected. Alsothe pattern with the rotated patch (depicted in figure 6.11) reflects in the right direction. Thevisualization for test 2 had not be included since it was exactly the same as the result of test 1.
40 CHAPTER 6: Results
P
(a) Topview
P
(b) Sideview
(c) Front view
Figure 6.9: Visualization of the reflection pattern of patch (P ) with diffuse reflection
P
(a) Top view
P
(b) Side view (c) Front view
Figure 6.10: Visualization of the reflection pattern of patch (P ) with specular reflection
P
Figure 6.11: Visualization of the top view reflection pattern of rotated patch (P ) with specularreflection
P
(a) Top view
P
(b) Side view (c) Front view
Figure 6.12: Visualization of the reflection pattern of patch (P ) with specular reflection incombination with diffuse reflection
The total received energy of the sphere of patches is approximately equal to the original powerof the patch (see table 6.4), except for test 2 where absorption was applied. In the case whereabsorption was applied, the total received energy dropped to exactly 60% of the energy that wasreceived in test 1. Note that the total power received by the sphere of patches in test 5 was exactlythe average of the power received in test 1 and 3. The cause of difference between the originalsignal strength and the total received signal is probably due to the same reasons as the differencein power that was measured when testing the radiation patterns.
With this information it can be concluded that the reflection pattern behaved as expected inall the tested situations, therefore the reflection pattern is considered to be realistic.
6.5. Radar Equation and Radar Cross Section 41
6.5 Radar Equation and Radar Cross Section
The radar equation and the radar cross section (RCS) are responsible for the transmission ofenergy and determine the power of the received signals.
To test the radar equation and RCS, a plate has been placed in the pointing direction of theantenna, at a distance of 1000 m (see figure 6.13). The plate has an area of 1 m2 and reflectsall incoming energy isotropically (see settings in table 6.5). To improve the approximation of thepower received by the plate, the plate has been split into smaller patches with a maximum edgelength of 10 cm. In order to keep the gain at different locations on the plate almost constant, theantenna has a HBW and VBW of 60 degrees.
Ap
Pn
1000 m
Figure 6.13: Top view overview of the setup for the radar equation and RCS test for antenna(A) with pointing vector ~p and patch (P ) with normal vector ~n
Setting ValueInitial energy antenna 50 kWHBW & VBW 60◦
Surface area antenna 0.1 m2
Surface area plate 1 m2
Maximum edge length patch 0.1 mNumber of patches 512
Table 6.5: Test settings for testing the radar equation and RCS
The scaling factor (τ) for the current beam can be calculated by using equation 4.10 andequals 12. Suppose the maximum gain is received at every location on the plate, then the gain forthe current plate is 48 (see equation 4.8). The incoming power density (Pi) at the plate can becalculated by using equation 2.7, which is 0,19098593 W/m2. Since the area of the plate is 1 m2,the expected power received by the plate should be 0,19098593 W (see second column in table6.6).
When the power received by the patch is known, the backscattered power density (Ps) at theantenna can be calculated in the same way, which is 3, 0396355 · 10−8 W/m2. Note that the patchonly reflects isotropical in directions for which the angle between that direction and the normalof the patch is at most 1
2π rad. Normally, the wavelength, gain and effective area of the antennaare related, however, this is not the case in the current model where each of these parameters canbe defined independently, which means that the received signal by the antenna should be equal to1, 4590250 · 107 W .
Test variable Expected ResultAntenna gain 48 48Power received by plate 0,19098593 W 0,19098545 WPower received by antenna 1, 4590250 · 107 W 1, 4590177 · 10−7 W
Table 6.6: Expected values and results for radar equation and RCS test
In table 6.6 it can be observed that the differences between the expected values (second column)and the values that are returned by the simulator are very small. The expected value is a bit moredue to the fact that the maximum gain is used for the entire area of the plate, however, this is
42 CHAPTER 6: Results
only the case for the center of the plate. Still, because the plate is very far away compared to thesize of the plate, the incoming energy is almost uniform at all locations on the plate. So in factthe value returned by the simulator seems more realistic then the value that was expected.
The returning energy is rather realistic in the tested situation where the interference of wavesis of no importance and the RCS is only determined by the size, position and orientation of thepatch. In the next section superposition is activated in order to achieve a more realistic RCS valueof an object.
6.6 Superposition
Although the power transfer is rather realistic, as shown in the previous section, the RCS of anobject is not. Normally, the shape of the object also has a strong influence on the RCS of anobject. However, exact approximations are hard to get, even with more complex models (seesection 4.1). Still, the RCS can be improved by subdividing each patch into smaller patches andapplying superposition on the received signals.
To test the superposition, the same environment has been used as the environment which wasused to test the radar equation and RCS (see figure 6.13). The plate is assumed to be an idealdiffuse reflector. Table 6.7 shows the test settings for testing the superposition of signals, whichare almost the same as the settings used for testing the radar equation and RCS. However, forsuperposition, the wavelength of the signal becomes important.
A sphere of patches was used to measure the total received energy radiated by the plate aftersuperposition is applied. Furthermore, the sphere of patches is used for the visualization of thereceived energy after superposition is applied. The minimum edge length in this test has increasedto 20 cm, which is the lowest possible length with respect to the memory of the computer thatcould be used in combination with the sphere of patches. As can be seen in the test settings intable 6.7, the radius of the sphere is 100 meters. The center of the sphere of patches is located atthe center of the plate and only energy reflected by the plate is measured.
Setting ValueInitial energy antenna 50 kWHBW & VBW 60◦
Wavelength of signal 10 cmSurface area antenna 0.1 m2
Surface area plate 1 m2
Maximum edge length patch 0.2 mNumber of patches on plate 128Distance between antenna and the plate 1000 mRadius sphere 100 mNumber of patches on sphere 50.000
Table 6.7: Superposition test settings
Due to the superposition effect, it is expected that gain is created in the direction of theantenna. Since the difference in distance each waves travelled is very small compared to thewavelength, the waves should be constructive. In section 2.2 it was stated that gain goes alongwith sidelobes, so when the superposition effect is very realistic, sidelobes will appear. Finally,the received energy of the sphere of patches should be equal to the energy reflected by the plateafter the superposition is applied.
Table 6.8 represents the test results, which indicates that gain is indeed created in the directionof the antenna as expected. Also the received power is almost equal to the power that was receivedby the plate, both before and after applying superposition. And as expected the reflection patternin figure 6.14 indeed shows sidelobes.
6.7. Realism of Radar Screen 43
Test variable ResultAntenna gain 48Power received by plate 0,19098544 WPower received by antenna 1, 83839 · 10−5 W#Patches on the sphere that received a signal 24.900Power received by sphere without superposition 0, 19022068 WPower received by sphere with superposition 0, 20895763 W
Table 6.8: Superposition results
(a) Top view (b) Side view (c) Front view
Figure 6.14: Visualization of diffuse reflection caused by multiple patches on plate (P ) afterapplying superposition
It can be concluded that the superposition performs well, signals are realistically superposi-tioned, which can create realistic interference patterns and gain. To achieve realistic RCS valuesthe maximum patch edge length should small compared to the wavelength. However, as will beshown in section 6.11, the amount of patches that would be necessary for this edge length restric-tion is way more that simulation can handle with the current hardware. Therefore, for modelingsemi realistic reflection gain patterns, it is better to use specular reflection. For all other interferingwaves, the superposition function is very useful.
6.7 Realism of Radar Screen
The best way to verify the realism of the radar simulator is by checking how echoes are representedon the screen. One possibility for testing the realism of the radar screen is by comparing it toa real radar screen by taking a photograph of a real radar screen during sailing through someenvironment, reproduce the environment and circumstances and check whether they look thesame. However, this is nearly impossible to achieve within the given time. First of all is it veryhard to reproduce an environment accurately and secondly it is very time consuming to reproducethe correct circumstances, even with plenty of time. Another possibility to test the realism of thescreen would be showing the radar screen to a number of people with radar experience, but thiscould not be arranged either. The realism of the radar screen could also be verified by showing itto a group of people with radar experience, but this could not be arranged either.
In this section it is checked whether the radar screens produced by the simulator meet theexpectations. The following things are tested:
1. position and shape of echo;
2. hiding of objects;
3. effect of varying the number of patches and/or maximum patch edge length;
4. effect of varying the number of rotation steps.
44 CHAPTER 6: Results
The testing environment contains two vessels, as depicted in figure 6.15. Vessel 1 represents abig container vessel and vessel 2 represents an inland cargo vessel, the specification of both shipscan be found in table 6.9. The other settings concerning the radar simulation can be found intable 6.12. The algorithm for generating radar screen images (as described in section 5.7) is usedto visualize the signals that were received by the antenna. Furthermore, for some of the generatedimages, the locations of the patches are indicated with red lines in the images. Note that in somecases only part of the radar screen is shown.
Antenna
Ship 1
Ship 2
1000 m 130 m
(a) Top view
Antenna
Ship 1
Ship 2
(b) 3d view
Figure 6.15: Test environment containing two ships and an antenna
Ship Type Length Width Height #Triangles1 Container vessel 360 m 40 m 50 m 922 Inland cargo vessel 100 m 20 m 8 m 42
Table 6.9: Specifications of ships
Setting ValueInitial energy antenna 50 kWHBW 5◦
VBW 60◦
Wavelength of signal 10 cmPulse length 0,1 µsSurface area antenna 0,1 m2
Radar range 2000 mMaximum number of hops 2
Table 6.10: Test settings for the radar screen tests
It is expected that ship 2 will not be visible on the radar screen since it is located behind ship1. The expected shape of the echo is depicted in figure 6.16. The areas indicated by the red circlesare the areas where radio waves (can) travel greater distances, which causes the weird shapes atthe top of the echo. Figure 6.18a depicts the entire expected radar screen. For test 2 and 3 it isexpected that the quality gets better when the maximum edge length decreases and the numberof rotations increases.
Figure 6.17b, 6.18, 6.19 and 6.20 show the results of each test. As expected, ship 2 disappearsfrom the radar screen (see figure 6.17b). The location of the echo can be verified with the help ofthe patches and meets the expectations (figure 6.18b).
As shown in figure 6.18a, the shape is not exactly as expected, the echo is broken into twoparts. Suppose the pointing direction of the antenna points exactly towards the gap between thetwo parts, then the centroids of all patches are outside the beam of the antenna. This is causedby a too large maximum patch edge length and thus the distance between the centroids of thepatches is too large. This problem is solved when the patches become smaller, as shown in figure6.19. For a distance of one kilometer, an edge length of 150 m seems to be sufficient. However,
6.7. Realism of Radar Screen 45
Figure 6.16: Original model and expected echo, the two marked areas indicate areas where radiowaves can travel a longer distance
(a) Expected (b) Generated by the simulator
Figure 6.17: Radar screen for the environment depicted in figure 6.15
(a) Echo ship 1 (b) Echo including the patches inred
Figure 6.18: Part of radar screen showing the echo of ship 1
(a) No restriction - 92patches for ship 1
(b) 150 m - 134 patchesfor ship 1
(c) 100 m - 200 patchesfor ship 1
(d) 50 m - 440 patchesfor ship 1
Figure 6.19: Results of varying maximum edge lengths for the patches
if the object comes closer to the antenna, the angle between the centroids of neighboring patcheswould increase and gaps might appear again.
In figure 6.20, the result of four different settings for the number of rotation steps are depicted.To avoid gaps, the maximum edge length was set to 100 m. Figure 6.20a indicates that using 36rotation steps was not enough, using 180 rotation steps gives a much better result. The differences
Figure 6.20: Results of varying rotation steps of the antenna
between figure 6.20c and figure 6.20d are only marginal compared to the increase in the numberof rotation steps.
It can be concluded from the results that the position of the echo and the shape are correctin the tested situations. For the current environment, an edge length of 150 m and 360 rotationsteps were sufficient for the correct results. However, the edge length depends very much on thedistance to an object.
6.8 Echo Scaling
In section 2.6 the maximum echo scaling was defined. Echo scaling is important because echoesof different objects might overlap each other. This effect can make it hard for the radar operatorto recognize objects.
In order to test it, three tests were performed with three different setups as defined in table6.11. The simulation generated radar pictures to show the results of each test. The location andsize of the patch is indicated with the red bar.
Setting Test 1 Test 2 Test 3Initial energy antenna 50 kW 50 kW 50 kWHBW & VBW 5◦ 10◦ 10◦
Pulse length (PL) 0,05 µs 0,05 µs 0,1 µsDistance between antenna and the plate 1000 m 1000 m 1000 mSurface area of the plate 1 m2 1 m2 1 m2
Maximum configured range radar screen 2000 m 2000 m 2000 m
Table 6.11: Test settings for the echo scaling test with a single ideal diffuse reflecting plate
It is expected that an increase in the beamwidth leads to a wider echo and an increase in thepulse length should increase the thickness of the echo.
(a) HBW=5◦ & PL=0,05 µs (b) HBW=10◦ & PL=0,05µs
(c) HBW=10◦ & PL=0,1 µs
Figure 6.21: Part of the resulting radar screen for the echo scaling tests
The result of the echo scaling tests are shown in figure 6.21. Note that the echo seems verybig compared to the plate, but this is caused by the fact that the plate is only 1m2. The resultsshow that echo scaling is working as anticipated in the tested situation.
6.9 False Echoes
False echoes are very important because they have a great influence on the readability of theradar screen. In section 2.7, three different types of false echoes were distinguished. However,false echoes caused by second trace are not supported by the current model.
6.10. Semi-Realistic Environment 47
The following false echoes are tested:
1. False echoes due to sidelobes;
2. False echoes due to reflections.
For the sidelobes test, the same antenna was used as the antenna that was used for test 4 ofthe radiation pattern (see table 6.1). Furthermore, the plate that had been used for testing theecho scaling is used for the sidelobes test as well (section 6.8). For the reflections test, one platewas not enough, therefore another plate with the same dimensions was added (as shown in figure6.22b with the red lines). The antenna used for test was the same as the antenna used in test 3 ofthe echo scaling except that the initial power had been increased to 5.000.000 W . Furthermore,the amount of hops was increased to 4, otherwise the false echoes caused by the reflections wouldnot be visible. A radar screen image has been generated for each test by the simulator to showthe false echoes.
For the sidelobes test, it is expected that there is a copy of the echo on either side of the echo.However, the brightness of the echo should be reduced because the power of the mainbeam isten times as strong as the power of the sidelobes. For the reflections test, two regular echoes areexpected caused by the plates and a third echo that is caused by an inter-reflection between theplates. The distance to the false echo should be larger than the other echoes since the false echohad to travel a greater distance.
(a) False echoesdue to sidelobes
(b) False echoesdue to reflections
Figure 6.22: Part of radar screen showing the results of the false echoes tests
Figure 6.22 shows the results of both tests. The radar screen in figure 6.22a is as expected.The reason why the antenna needed so much power for the reflections test is because the platesare very small and located at a rather large distance (1000 m). Normally, only big objects causevisible reflection echoes and most of the times they should also be located close to the antenna.
From the results, the conclusion can be drawn that it is possible to create false echoes. Thisimplies that forward scattering should be working as well, however, this could not be tested becauseof very high computation times and lack of memory.
6.10 Semi-Realistic Environment
In the end the simulator should be used for more realistic environments, i.e. environments con-taining more objects and that are not restricted to ships.
For this test two environments were used, one semi-realistic environment (shown in figure6.23) without large horizontal planes, e.g. the water. The other environment consists only of alarge horizontal plane, which will be used for the motivation why large horizontal planes are notconvenient. Other test settings can be found in table 6.12.
Figure 6.24a depicts the expected radar screen. Note that one skyscraper is missing due to thefact that is hidden by another skyscraper. Furthermore, there is gap in the left quay, this partis hidden by the vessel that is located between the antenna and that part of the quay. The echoof the skyscraper should have a weird shape because of the reflections caused by the side of theskyscraper. The horizontal plane should be hardly visible, but because it is an ideal reflectingplate it is supposed to fill the entire screen green with exception of the area around the antennawhere the beam does not hit the plane yet.
48 CHAPTER 6: Results
Antenna 2000 m
(a) Top view of the envi-ronment
Antenna
(b) 3d view of the environment
Figure 6.23: Overview of the semi-realistic environment
Setting ValueHeight of antenna 5 mRange 1000 mRotation steps 3600Maximum number of hops 2Maximum edge length 35 mNumber of patches 3558
Table 6.12: Test settings radar screen
The results of the semi-realistic environment look rather realistic (figure 6.24b), in our opinioneven more realistic than the expected radar screen. However, as can be seen in figure 6.24b, amaximum edge length of 35 m is too large large for the quay in the neighborhood of the antenna,the result is that separate lines can be seen. Figure 6.25 shows the problem of the horizontalplane. There are three problems with (large) horizontal planes (see figure 6.25):
• simple ideal diffuse reflection, which works perfect for other surfaces, returns too much energyfor horizontal planes, turning the whole screen green;
• the entire environment is covered with some kind of horizontal plane, causing lots of patchesand consequently lots of signals and even more reflections;
• the patches should be small otherwise the echoes of the individual patches can be seen onthe screen.
Although specular reflection could be used, this only solves the first problem.It can be concluded the overall realism of the simulator is pretty good in the tested situation.
A drawback is that many patches are required, especially in the neighborhood of the antenna,which results in long computation times (discussed in section 6.11) and possibly even memoryproblems. Furthermore, it is usually better to leave out big horizontal plates, especially for thecomputation time.
6.11 Computation Time
Next to the requirements regarding realism, was realtime performance with up to 20 vessels alsoan important requirement. Therefore, the computation time of the simulation is tested.
In order to test the computation speed, 4 environments have been created and tested (seetable 6.13). Three of the environments only contain ships and one environment contains quays
Figure 6.24: Radar screen of the environment depicted in figure 6.23
Figure 6.25: Radar screen where the entire environment is covered with an ideal diffuse reflectinghorizontal plane containing 2048 patches
and buildings as well. Note that environment 4 is an environment with 20 ships and should runrealtime, which means that it has to finish a full revolution of the antenna within the time a realantenna would finish a full revolution, for instance 4 seconds (see section C.4).
For each environment, the computation time for a full revolution of the antenna is measuredfor an increasing number of patches with three different settings for the maximum number of hops.The computation times for each environment are presented in a graph with a logarithmic scalefor the time, which will be compared with the worst case computation complexity (see equation5.3). Table 6.14 shows the other values of the settings for the simulation. A few new settingsappear in the table, the maximum branching factor, which is used for the Monte Carlo algorithm,the progressive refinement threshold and the update interval, which indicates the number of sendinstances the visible patches remain static (definition of all section can be found in chapter 5).
It is hard to estimate the exact computation time (ct) because it depends on many factors, e.g.the speed of the hardware. However, it can be estimated what the graph will look like when thenumber of patches increases based on the worst case computation complexity, which is defined by(equation 5.3):
O(N2 · logN +BFH−1). (6.1)
Suppose a certain amount of hops (H), then the line of the graph with log ct for an increasing
number of patches is expected to have a decreasing slope because BFH−1 is constant and doesnot influence the computation time:
log(N2 · logN) = (6.2)2 log(N) + log (log (N)).
From the worst case computation complexity equation it is expected that increasing the numberhops has the greatest effect on the computation time. For a constant number of patches, N2 · logNdoes not play a role in the worst case computation time and it is expected that log ct increaseswith a constant factor when the maximum number of hops is increased:
log(BFH−1) = (6.3)(H − 1) · logBF.
The graphs of the results are shown in figure 6.26. As expected, increasing the number of hopshas the greatest impact on the computation time, which seems to increase with a constant factorwhen increasing the number of hops as well. In figure 6.26a and 6.26b, it can be seen that the linesare steeper, which could have to do with the fact that the relative increase in patches is largercompared to the other two. Note that 5 hops could not be performed for environment 4 due tofact that the required memory exceeded the available memory.
Due to the great impact on the simulation time when the amount of hops increases, it can beconcluded that the simulation can only run 20 ships realtime with a maximum of two hops. Asa consequence no false echoes due to reflections are generated and the entire radiosity algorithmdoes not make much sense anymore. However, when the simulator would become a constant timesfaster, very realistic simulations could be made realtime.
6.12 Multithreading
The implementation of the model had Multithreading in order to run better on computers withmultiple processor cores. This multithreading has been implemented in such a way that each coretakes the strongest remaining signal. In this section the efficiency of multithreading in the currentalgorithm is checked.
6.12. Multithreading 51
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Figure 6.26: Results for variable amount of hops limit for each environment
For this test it should not be relevant which environment is taken and what the settings arefor the simulation. Therefore, arbitrary settings has been taken with an arbitrary environment.
When the multithreading would perform perfectly the simulation would run a factor 4 fasterusing 4 cores compared to 1 core. However, since a thread gets blocked when its trying to accessthe remaining signals during the time that another thread is using it, it is expected the simulationwill not reach a factor 4.
#threads Time1 9.7 s2 6.2 s3 5.9 s4 5.6 s
Table 6.15: Computation times with different amount of threads for arbitrary environment andsettings
Table 6.15 shows the results of the multithreading test. It can be seen that the performanceof the multithreading does not improve very much when the number of threads increases. Thecomputation time with 4 threads is not even half of the computation time with only 1 thread. Weassume that is caused due to the blocking on the remaining signals list.
It can be concluded that the current implementation of multithreading does improve the per-formance, however, it does not approach the full efficiency.
53
Chapter 7
Conclusion
The purpose of this project was to create a radar signal simulator that can be used for training andthat meets the requirements set by the International Maritime Organization (IMO). This projecttook place in the company VSTEP, which wanted to expand their training simulations with anIMO approved radar simulator. Although a radar simulator was already in use within VSTEP,that simulator did not meet the requirements set by the IMO. Due to time restriction, the projectscope was limited to the simulation of realistic radar signals which would be the input for theradar screen.
The first main goal of this project was realism, the simulator should be capable of simulatingfalse echoes, instead of doing it the conventional way by faking them on demand. Our radar signalsimulation model is based on radiosity, which possesses most of the important aspects neededfor our goals. Radiosity is a realistic illumination model for ideal diffuse reflecting surfaces. Inmaritime environments many objects have rough surfaces compared to the wavelength, causingdiffuse reflection. Radiosity has been adapted in order to fit the purposes required for radarsimulation.
The second important requirement was that the simulation has to run realtime with up to 20vessels. Although, radiosity is often used in offline rendering, it advances in realtime applicationsas well due to the increasing speed of computer hardware. The worst case computation complexityfor a single send instance of our radar model equals O(N2 ·logN+BFH−1), where N is the numberof patches, BF is the maximum branching factor and H is the maximum allowed hops of a singlesignal. Still realtime computation can be achieved by keeping the number of objects that canmove relative to each other, as low as possible, e.g. 21 objects for 20 ships and 1 for the quays,buildings etc. Because the distances the electromagnetic (EM) waves have to travel, are very largecompared to the resolution of the radar screen, the number of triangles for the objects can belowered.
The realism and computation time of the radar simulation were submitted to extensive tests(see chapter 6). Concerning realism, the implementation successfully simulated false echoes, echoscaling and visibility of objects. It turned out that the model is capable of creating realisticradiation and reflection patterns.
Although the simulator is capable of generating a realistic radar screen, not all interactioneffects of EM waves were included. Transparency (refraction) and diffraction are not in the modelbecause they are not supported by the radiosity model. Especially transparency could be usefulfor the simulation of for example yachts that let EM waves through. Although these objects couldbe made invisible by increasing the absorption level, more energy gets lost than would be thecase in real world situations. Furthermore, none of the environmental effects can be simulated,although forward scattering should be working, this could not be tested due to lack of memory.
From the results it can be concluded that the computation time of the simulator is the mostimportant drawback. The required amount of 20 vessels can only be rendered realtime when nointer-reflection are taken into account and when there are no other objects in the environmentsbesides the ships. Without inter-reflections there is, however, no point of using radiosity anymore.
54 CHAPTER 7: Conclusion
Still, realtime computation time with multiple hops is within sight and could be achieved byimproving the algorithm or by utilizing the graphics card (see chapter 8).
Overall, the radar screen meets the requirements concerning the realism, the level of realismeven exceeds the required level set by the IMO in several aspects. However, the simulation is notready to be deployed due to mainly performance issues but also due to memory problems, whichstarted appearing in the end of the project. Nevertheless, realtime simulation could be achievedwith further research, improved implementations and the increasing capabilities of hardware. Ifthe simulation achieves its realtime requirement, the simulation would be cutting edge and aheadof simulations created by most competitors. Finally, we believe our simulation is a good examplefor the level of realism, realtime radar simulations will achieve within a few years.
7.1 Evaluation
This project started with a thorough research in radar systems and electromagnetism in order toset up the right requirements. This research went much deeper into the material than might seemin this document, such that the important properties required for realistic simulation could beidentified. During this period it was also defined what the exact goals of this project would be,considering what could be achieved within the time limits.
The algorithm and implementation are carefully designed such that it would be realistic andfast at the same time. Quite some time has been invested to keep to implementation code clean,dynamic, efficient and scalable. Furthermore, a lot of effort has been done to achieve its currentspeed, although it is still not realtime in most situations. At the last moment it was even decidedto include multithreading as well to get the full potential out of processors with multiple cores.
The level of realism, however, meets all expectations. Extensive test facilities have been created,e.g. a radar screen to visualize the received signals and a sphere of patches to measure the intensityof a source in many directions. In all the tests that where performed the simulation has shown itsversatility and realism.
Finally, I would like to add that this project brought me great joy and I believe it marks animportant phase in my educational career. It gave me significant insight in how theory is putinto practise and I am looking forward to be able to use and extend this experience during myprofessional career.
55
Chapter 8
Future Work
The main problem with our current model and algorithm is that it is slow. Therefore, most ideaspresented in this chapter concern the speed. Because the implementation also has an importantinfluence on the computation time, some suggestions in that area are included as well in thischapter.
8.1 Global Monte Carlo
The Monte Carlo algorithm in our simulation controls the branching factor. However, it could bean idea to create a global Monte Carlo which controls the maximum number (S) of signals duringa sent instance. It would work as follows, the initial signal of the antenna is split into S signalswith equal strength. Then the algorithm picks an arbitrary signal and sends it to a random patch.The probability that a certain patch receives the signal equals the power that this particular patchwould have received without Monte Carlo divided by the total of signals that would have createdfor the current signal without Monte Carlo. This process can be repeated for each signal until:
• the signal arrives at the antenna;
• the hops of the signal exceeds the maximum allowed hops;
• the maximum travel time of the signal is passed.
When all S signals have been sent, the send instance is completed.Currently, the algorithm does not take into account the probability that the signal might not
hit an object. If this would be incorporated during the determination of the next patch, signalshave a probability that they do not hit an object and traversal of the signal stops. However, thiswould lead to a high number of signal losses, lowering the probability that a signal will be receivedby the antenna and more initial signals would be required to achieve the same approximation of thereceived signals. Therefore, it would be better to reduce the signal strength with the probabilitythat the signal is lost in free space when the signal is sent to the next patch.
Benefits of using global Monte Carlo instead of our current algorithm presented in chapter 5are:
• the number of signals in the algorithm only goes down during computation, while they goup most of the time in our current algorithm;
• the computation time of a single send instance is more predictable compared to our currentmodel since the number of signals that will be sent is constant, which is better for realtimesimulation;
• with global Monte Carlo the risk that weak signals are created is lower due to the fact thatcertain patches have a very low probability of receiving a signal.
56 CHAPTER 8: Future Work
A disadvantage is that progressive refinement, which is used as an optimization in our currentalgorithm would not work anymore, however, this should matter much since very weak signals areless likely to be created. Also it could be the case that the number of signals in this approachis higher in some situations compared to our model, but as long as the simulation finishes a fullrevolution of the antenna within the required time this is no problem.
Global Monte Carlo would also provide a few advantages for the implementation of the algo-rithm:
• in our current model, every time the Monte Carlo algorithm is used, the set of new signalsfor a single signal is calculated twice (see algorithm 3);
• in our current model, new signals have to be inserted into the sorted remaining signals list,required for progressive refinement in order get the signal with the most signal strength fast;
It could also help in area of multithreading. Only once thread can access the remaining signalslist at a time, causing blocking of threads. Because there is no need anymore for such a list, theprobability that a threads gets blocked goes down, improving the performance of multithreading.Finally, in our algorithm there is only one signal and only one thread can work until more signalsare created. This is not the case for global Monte Carlo where each thread can start workingimmediately after the visible patches are determined.
8.2 Improvements for the Algorithm
Other ideas to improve the speed of the algorithm:
• instead of checking whether the travel time exceeded the maximum travel time it is betterto check whether the current travel time plus the minimum required to travel back to theantenna would exceed the maximum time;
• use a hierarchy in triangulation, which patch size should be picked for a signal depends onthe distance between the source and the target;
• improve progressive refinement by replacing the power of the signal with the power of thesignal that would remain if the signal would travel directly to the antenna;
• possibility of including objects that do not reflect signals from the antenna and do not reflectsignals to the antenna, for instance own ship that should appear own radar screen but isuseful for false echoes caused by the inter-reflections;
• include objects that are only inserted in the BSP tree and are rendered with a more simpleapproach, e.g. buildings.
8.3 Improvements for the Implementation
Some suggestions for improvements of the implementation:
• use the graphics card, it is very fast and can increase the speed of the algorithm a lot;
• mailboxing[30, sec.3.3.2.2], avoids checking the same triangle multiple times when traversingthe BSP tree for a certain ray;
• investigate cash misses and update data layout;
• use SIMD instructions for faster float calculations;
• replace time with distance, calculate the travel time only once at the end of send instance,this spares an operation every time the time to the next patch is calculated;
8.4. Quality Improvements 57
• vertices are currently saved per patch causing redundancy;
• lots of improvements can be applied concerning memory, e.g. changing doubles to floats andremoving variables during signal calculating that are only used for post processing.
8.4 Quality Improvements
Some ideas concerning quality improvements, which can be done as post processing:
• generate random noise;
• generate (fake) sea clutter based on current sea state and wind direction;
• generate (fake) weather clutter based on current weather[25, pp.33-35];
Possible improvements that would effect our current model:
• second-trace echoes;
• atmospheric attenuation;
• transparency;
• polarization[25, pp.383-384];
• support multiple EM sources.
Some of these improvements will have a negative effect on the computation time.
59
Appendix A
Mathematics for Radar SignalSimulation
A.1 Decibels
Because hugh differences can exist between 2 power values in Radar engineering decibels are oftenused. Decibels indicate a logarithmic relationship as follows[27][25]:
dB = 10 · log10 P (A.1)
Where ”dB” indicates that the value is decibels and P is some power.A multiplication of the power by 2 relates to +3 dB and a division of 2 relates to -3 dB[27].
Sometimes there is confusion whether to use the constant 10 or 20 but it will always be 10 in thecase of powers. Naturally when decibels are used in equations they first have to be converted toits numerical equivalent[25].
A.2 Centroid of Surface
The centroid (~p) of a surface with a set of n vertices (V ) is defined as:
~p =∑ni=1 Vin
. (A.2)
A.3 Spherical Coordinates
Spherical coordinates is curvilinear-coordinate system, which is a non-Cartesian reference frame[10,appendix A]. Spherical coordinates are for describing positions in a sphere and can be seen as anextension to the polar coordinates[33]. Figure A.1 depicts how the spherical coordinates are usedto describe an arbitrary point P . The spherical coordinates uses the following variables to describea given point:
1. θ defines the azimuthal angle;
2. φ defines the polar angle;
3. r describes the distance.
The spherical coordinates can be transformed into Cartesian coordinates as follows[10]:
x = r cos θ sinφy = r sin θ cosφ (A.3)z = r cosφ
60 CHAPTER A: Mathematics for Radar Signal Simulation
x
y
z
θ
ϕ
r
P
Figure A.1: Describing P with spherical coordinates
Sometimes the spherical coordinates are used without the distance to indicate a direction. Inthose cases the z-axis is equal to the normal of the surface from which the direction is measured.
A.4 Solid Angle
A solid angle ω is a three-dimensional angle, it gives a measure of how large a surface appearswith respect to some point P [10]. The solid angle equals the area of the projection of a surface Son the unit sphere centered at P , see figure A.2.
Pω
S
Figure A.2: Solid angle of surface S
The solid angle is dimensionless, the dimensionless unit for solid angle is steradians (sr). Thevalue of a solid angle is between zero and the surface area of the unit sphere: 4π.
A.5 Icosahedron
Figure A.3 depicts an icosahedron, which is 20-faced polyhedron[32]. All faces are identical equi-lateral triangles. In total the icoshedron consists of 20 faces, 30 edges and 12 vertices.
Figure A.3: Icosahedron
The icosahedron has been used in this project because each of the faces has the same size.Regular three dimensional spheres do not have this property.
61
Appendix B
Radar in Ship SimulatorProfessional
The professional maritime simulator by VSTEP already possessed an radar simulator. This sim-ulator was, however, very basic. The radar screen in Ship Simulator Professional was initiallydeveloped to give an impression of a radar screen. It was not meant to be used as professionaltraining tool. As a result of this, it did not meet the required level of realism and functionality -with respect to the STCW - to be approved as an official training tool.
The pictures and most of the explanations in this chapter are based on a research that has beendone in the beginning of this graduation project. The radar screen in general and functionalityin specific improved considerably since then. The visualization of the incoming sigals in the newversion still uses the same approach and still exhibits some of the same flaws, and it even introducedsome new. Hence, most of the improvements described in section B.2 can still be applied.
B.1 Approach
Since the radar screen represents the area around the ship in a kind of two dimensional top downview, this has been taken as the main approach for the radar screen. To create a radar screen, anorthographic camera is placed high in the sky in the virtual environment, right above the locationof the vessel and is pointing straight down. For each radar screen update, the camera takes apicture which is taken as the basis for the radar screen. Finally, several filters are applied, whichgenerate the final radar screen from the intial picture.
Figure B.1 depicts the procedure of radar screen creation for ship S (shown in figure B.1a).The first change to the picture is the addition of a picture with some random noise which distortsthe picture a bit1. Then the most important step is executed, edge detection, which draws lines atthe location of color transitions. Next, the colors are changed to a black background with greenlines. Finally, the echoes represented by the lines are enlarged and blurred and the ships are addedas dots.
B.2 Possible Improvements
The echoes in the current radar are created based color transitions, in reality echoes are caused byreflecting surfaces. Because color transitions are used, an transition from grass to paving stoneswill cause a strong echo, even if there is no height difference. A better approach would be creatinga height map from the camera where different colors indicate different heights. And then performedge detection on the height map.
1This way of distortion creates unrealistic false echoes and is therefore removed in the current version
62 CHAPTER B: Radar in Ship Simulator Professional
(a) Area
(b) Orthographic picture (c) Radar screen
Figure B.1: Ship Simulator Professional radar
Depending on the direction of the height difference the edge detection can be done a bit moreintelligent. Radar will not detect the backside of a building as well as height increasements thatare blocked by other objects closer to the antenna. Figure B.2 shows a situation where buildingsB, C and D are invisible because they are blocked by building A. Note that building D is evenhigher than building A, still D lies in the shadow of A.
A B C D
Antenna
Line of sight
Figure B.2: Line of sight of radar antenna
Suppose a height difference at position P as indicted in figure B.3. The figure shows twovectors, vector ~b, which is the vector from the antenna (A) to the position of the height increase(P ) and vector ~h, which is the direction of the height increase itself. The length of ~h is proportionalto the slope of the height difference. With this information a rule can be applied regarding thevisibility of the height increase at location P : P is visible when the angle between ~b and ~h issmaller than a specified angle α and P is not blocked by another point somewhere on ~b. Angleα can maximally be 1
2π and the brightness of the echo must depend on the height difference of
B.2. Possible Improvements 63
the point on ~b which approximates the line of sight to P the closest and the heighest point Pitself. Furthermore, the brightness can be influenced by α depending on roughness of the materialand even absorption can be included. Note that this approach is still not perfect, for examplea decrease in height can also be visible to the radar. Finally, the approach fails for open andtransparent objects, like for instance a bridge where EM waves can travel underneath the bridge.
A Pb
h
Figure B.3: Direction (~b) of the antenna (A) to the location (P ) of the increase in height andthe direction (~h) of the increase in height
The current edge detection fails at two other things as well. First, large transitions yield in athick line, while it should only effect the brightness of the line. Furthermore, the line is placedat the wrong location at the moment, for example the transition line from the water to quay isdrawn in the water, while it should be located on the quay.
As stated in section B.1, the ships are added as dots, which is not very realistically comparedto actual radar images. The cause for this approach were complaints from maritime experts onthe actual ship shapes, which was used before. If such an approach is chosen, the best way wouldprobably be a combination of the two, for example taking a square box with ships dimensions andround edges.
Echo scaling can be implemented fairly easy. The pulse length can be mimiced by stretchingeach echo straight away from the antenna, or with some random value between zero and the lengththat corresponds to the pulse length. The horizontal beamwidth effect can be achieved by rotatingthe image half a beamwidth right and left.
False echoes are hard to generate with this model, the least complex way would probably befaking them on command. Rain and sea clutter should also be included, however, they can befaked as well.
65
Appendix C
Research
C.1 Electromagnetic Waves
This section starts with electric fields of which the effects where probably already discoveredsomewhere in the prehistory[4, chp.1]. Already back in those days people where aware of theforces caused by electric fields. To explain electric field we start zooming in on atom, the buildingblocks of molecules. Figure gives an example of such an atom, it consists out of protons, neutronsand electrons. The nucleus is the core of the atom and this is where the neutrons and protons arelocated. The electrons fly around the neucleus.
Electron
Proton
Neutron
Figure C.1: Atom
The protons and electrons have an electric charge. Charge Q is measured in Coulomb (C) andthe charge of a proton is equal to the elementary charge 1.60217733 · 10−19C, often denoted bye[22, p.6]. The charge is of the electron is exactly equal to the charge of a proton, only opposite:−e.
Q1 Q2
r
Figure C.2: Electric force
Suppose there are two charges, Q1 and Q2, then the force between them in direction ~r (seefigure C.2) is given by the relation[5, p.11]:
F =Q1Q2
4πε0r2~r [N ], (C.1)
where ε0 is a positive electric constant called permittivity of vacuum. From the equation it canbe derived that charges with the same sign repel each other while opposite charges attract eachother. The electric forces caused by this charge keep the electrons bound to the nucleus[5].
66 CHAPTER C: Research
In practise, it is usually more convenient to know how strong an electric field is instead ofknowing the forces between charges. Therefore, when the strength of an electric field E is calcu-lated, it abstracts the charge that is brought into this field. In other words, the electric force isdefined as F = Q2E. With the definition of electric field, it is possible to calculate the electricforce at any position in space given a charge Q1.
+
(a) Positivecharge
-
(b) Negativecharge
Figure C.3: Electric field lines
The electric field can be visualized as shown in figure C.3. The field lines describe the electricfield, the more dense the field lines become, the stronger the field. By convention, the field linespoint outward from a positive charge and towards the charge when the charge is negative.
Magnetic fields are very similar to electric fields, although, the discovery of magnetic forces isprobably not so long ago as the discovery of electric fields[4, chp.1]. The first records of magnetismdate from the 12th century. The main difference in definition between magnetic field and electricfields is that magnetic fields are not about positive and negative charges, but about so-called northand south poles. The magnetic field lines point away from the north pole and points towards thesouth pole. Unlike for instance an electron in electric fields there is no magnetic monopole.
The discovery of magnetism started the era of confusion why magnetic and electric forces areso similar and at the same time so different. It took till 1819 before Cristian Oersted discoveredthat a current through a wire could deflect a compass needle. This discovery, finally made anend to the question whether electricity and magnetism are related[4, chp.1]. Still in that sameyear, Andre-Marie Ampere assumed correctly that the deflection was caused by the induction ofan magnetic field by the current through the wire[29, p.2].
B
I
(a) Wire
IB
N
S
(b) Coil
Figure C.4: Induced magnetic field
Figure C.4 depicts the magnetic field induced by a wire and a coil. Note that the direction ofthe current I and the direction of the magnetic field B are not really important here. In figure C.4a,the magnetic north and south are also visualized, which means that the coil acts as an magnet.Michael Faraday showed in 1831 that the opposite of magnetic induction is also true: a changingmagnetic field induces an electric current[29, pp.4-8]. This was the discovery of “electromagneticinduction”.
Figure C.5 shows a circular wire and a magnet that moves towards the wire loop. When themagnet moves with respect to the wire loop, the magnetic field around the wire changes, whichinduces a current in the wire. The current is directed in such a way that the magnetic field inducedby this current exactly opposes the change of the magnetic field caused by the movement of themagnet.
Figure C.4b already showed that a coil with an electric current can function as a magnet. Infigure C.6a there is a new situation depicted, two coils above each other. When a current starts
C.1. Electromagnetic Waves 67
NS
I
Figure C.5: Electric induction
flowing through the bottom coil, an magnetic field is induced, as seen in figure C.6b. Since themagnetic field is created, the magnetic field around the top coil changes. In the top coil, anelectric current will be induced that opposes the changing magnetic field, see figure C.6c. Whenthe current I in the bottom coil will remain the same the magnetic field will not change anymoreand thus current stops flowing in the top coil. If the current I would change or stop then themagnetic field would change and current starts flowing through the top coil again.
N
S
(a)
I
N
S
B
(b)
I
N
S
I
B
(c)
Figure C.6: Electromagnetic induction
The electromagnetic induction depicted in figure C.6 is still not electromagnetic radiation sincethe top coil is required to create electric current[29, p.5]. For EM radiation to exists, an electricfield should be created indepedent of the precense of the top coil. Quite some years later JamesMaxwell discovered that something was missing in the currently available equations governingelectricity and magnetism.
In figure C.7 a capacitor is visualized with a charge Q at the right plate and a charge −Qat the left side. When the wire at the right side is connected with the wire at the left side acurrent will start flowing. Ampere discovered that a current through a wire creates an magneticfield around it, see figure C.4a. However, the magnetic field between the plates of the capacitoris exactly the same, although no current is flowing here. Maxwell pointed out the missing part:displacement current [29, p.8]. Since the capacitor decharges, the electric field between the plateschanges, which has the same effect as moving current through a wire.
Q-Q
E II
Figure C.7: Capacitor problem
Maxwell extended the existing equation for electricity and magnetism with displacement cur-rent. With this extension the field of electricity and magnetism finally became united. In 1864Maxwell published his unified laws of electromagnetic fields that became known as the Maxwell
68 CHAPTER C: Research
Equations, although he did not derive all of them[4, chp.1]. The laws are the second great fun-damental laws in physics after the Newton’s laws of mechanics and probably the most importantdiscovery of the 19th century.
With the Maxwell Equations, the fact that a changing electric field creates a changing magneticfield can be explained[29, p.9]. The other way around is also possible, which makes existance ofelectromagnetic waves possible. When a electric field is changed in the right way, an magneticfield is induced, which at its turn, induces a electric field and so on. This effect is known as wavepropagation that expands spherically in space.
The equations by Maxwell revealed as well that the right way to create EM wave propagation isto accelerate charge[29, pp.10-13]. The field lines of an electric charge are always straight lines asindicated by figure C.3. Although, in reality the field lines compress in the direction perpendicularto the movement of the charge as it approaches light speed (see figure C.8).
Figure C.8: Electric field lines of moving charge
Suppose a charge Q at rest is accelerated for a brief moment (t0). During this acceleration, thecharge moved from position P0 to position P1. After the acceleration the charge moves on withconstant speed. Moving with constant speed for time t1, the charge arrives at position P2.
Q
t0 t1P0 P1 P2
Figure C.9: Accelerate charge
The information of the electric field propagates at the speed of light (c). This means that aftertime t0 + t1, all locations outside the sphere P0 + (t0 + t1) · c have no knowledge about the factthat the charge has been accelerated. After t0, the charge continues with a constant speed, whichmeans that for all locations within the sphere P1 + t1 · c the electric field lines are known. Partsof these spheres are visualized in figure C.10a. Figure C.10b depicts a random field line A. Alllocations outside sphere P0 + (t0 + t1) · c think the field line is represented by A. But since thecharge has been accelerated, the real field line A′ is located somewhere else. Since field lines mustbe continuous[29], there must be a kink in the field line. When multiple field lines are drawn thepicture looks like figure C.10c.
When there is a kink in the electric field line, the field changes. Moreover, when a chargeaccelerates, the magnetic field changes, which means that the magnetic field changes exactlybetween the two spheres as well. The change of the electric and magnetic fields are exactly inphase and that is what produces the electromagnetic waves. Note that a deceleration is also anacceleration and therefore also produces EM waves.
Light is also an EM wave, it has a certain wavelength or frequency and a propagation speed.The human ability to distinguish different colors is caused by the fact that light with differentwavelengths is perceived as different colors. The spectrum of different wavelengths humans aregenerally capable of detecting is relatively small and all “light” with wavelengths outside of thatspectrum is invisible for our eyes. To be more precise, light is in fact an electromagnetic (EM)wave and the spectrum of wavelengths/frequencies visible to the human eye is usually referred toas “light”. The radio waves are also EM waves[27, p.1] but cover a different spectrum which are
C.2. RCS 69
PP P P0 1 2
P + (t + t ) ∙ c0 0 1
P + t ∙ c1 1
(a)
Kink
A
A'
E
(b) (c)
Figure C.10: Kink in electric field lines
invisible for the human eye. So theoretically radio waves have the same properties as light exceptthat they have a different wavelength.
C.2 RCS
When EM energy hits a target, energy is scattered in every direction, the RCS σ only gives avalue for the amount of energy that is backscattered at the antenna, that is in case of a monostaticantenna. The formal definition of the RCS is given by[15]:
σ = limr→∞
4πr2|Es|2
|E0|2(C.2)
Where Es is the backscattered electric field strength and E0 the electric field strength of theincident wave.
It is generally assumed that the antenna is far away from the object, also called the far field orFraunhofer region. This way the source can be considered a point source and the radiation a planewave. Let D be the dimension of the radiating source then the far field is given by[25, p.545][27,p.97]:
r >D2
λ(C.3)
In this field the RCS is no longer depended of r and so the limit can be removed from the RCSequation.
C.3 High Frequency Asymptotic Techniques
The models that fit the needs for the problems encountered in this project more are the approximat-ing methods, especially the high frequency asymptotic techniques[28]. High frequency asymptotictechniques aim at determining the RCS for objects in the optical region. They perform better thanthe numerical approaches for objects with a large size. Examples of high frequency asymptoticmethods are geometric optics, physical optics, geometric theory of diffraction and physical theoryof diffraction.
The most basic method is geometric optics which is a ray based method[12]. This methodhandles transparency, or in other words the transmission of rays through the the boundary, whererefraction is taken into account[15]. The size of the resulting RCS depends on the convergenceof the waves towards each other after reflection or the divergence. However, the curvature of the
70 CHAPTER C: Research
surface determines this convergence or divergence factor which goes wrong for flat or singly curvedsurfaces1. With a flat or singly curved surface the RCS becomes infinitely large.
Another method for approximating the RCS in the optics region is physical optics.So thereis always a tradeoff between realism and performance. The solution with physical optics is ob-tained by approximating the induced current density on the surface. This method can handleflat and singly curved surfaces but cannot cope with dielectric surfaces[12, 15]. Furthermore doesthis method not have a dependence on polarization and the error grows when the direction ofobservation moves further away from the specular direction.
The next method, geometric theory of diffraction, introduces the assignment of diffracted raysat smooth shadow boundaries in order to overcome the problems of the former method[12, 15].Geometric theory of diffraction is a ray-tracing method, it is in fact an extension to geometricoptics, that creates a cone2 of reflected rays when a ray strikes an edge. This method still fails inspecial situations with respect to the shadow boundary and that why another methods has beeninvented, physical theory of diffraction. But the last method starts to get very computationalcomplex again.
C.4 Representative Radar Values
The electromagnetic spectrum has been divided in many standardized subregions called bands[25,pp.11-13]. The two bands allocated for civil marine radar are the X-band and the S-band. TheX-band has frequency between 9320 Mhz and 9500 MHz which corresponds with approximatelya wavelength of 3 cm. The S-band is between 2900 Mhz and 3100 MHz which is approximatelya wavelength of 10 cm. Each of them have their own properties and advantages over the otherthat lead to small differences on the screen. The downside is that an antenna is either X-bandor S-band, it is not possible to switch between both modes[3, pp.37-39]. That is why many shipshave both antennas at their disposal.
Some facts concerning the radar antenna:
• the initial power of the antenna is usually between 10 kW and 60 kW for merchant ships[3,p.35];
• the antenna rotates in clockwise direction if seen from above;
• the IMO prescribes a maximum HBW of 2.5 degrees while the vertical beam width shouldbe at least 20 degrees for regular vessels[3];
• the IMO demands a maximum revolution time of 5 seconds[3, p.9].
The PRI should be carefully chosen in combination with the signal length and power of thesignal. When the antenna receives a signal, it has no knowledge of when the signal was sent.Therefore it assumes that it has been sent during the last send instance. If the PRI is too short, itis possible that a relative strong echo still returns from the previous send instance. On the otherhand the PRI should not be too large either, since not every target in the beam will lead to anoticeable echo. Therefore, every target should be hit multiple times. It is generally believed thatthe beam should hit a target at least 10 times to make sure that a target shows up at the screen[27,p.53]. This means the PRI, HBW, pulse length and power have to be carefully adjusted for properresults. Table C.1 gives some representative example values for such settings[21, p.2.2]3.
There are several kinds of antennas in the maritime world, the most basic one is the parabolicreflector, shown in figure C.11a. The antenna usually encountered on merchant vessels is theso-called “Slotted waveguide aerial”, depicted in figure C.11b. The slotted waveguide producesdirect emission and offers a higher aerial gain compared to the parabolic reflector. A new techniquerising in popularity on navy vessels is the “phased array antenna”. This antenna consists out of a
1A singly curved surface is a surface that is not curved in both axis, i.e. the outside surface of a cylinder.2This cone is also called the Keller cone, named after the inventor of geometric theory of diffraction method.3NM is a nautical mile (1NM = 1, 852km)
number of controllable elements for a dynamic beam. During this project, the radiation pattern isalways constant during simulation and targeted at the slotted waveguide although it is no problemto use it for a parabolic reflector as well.
(a) Parabolic reflector (b) Slotted waveguide
Figure C.11: Radar antennas
73
Appendix D
Algorithmic Details
D.1 Derivation of the Scaling Factor
The radiation pattern function presented in section 4.5 contains a scaling factor (τ) to ensure thatexactly Pa is radiated:
G(θ, φ) = τ
n−1∑i=0
Gi(θ, φ). (D.1)
The integral over all directions must be equal to the integral over all directions for the isotropicantenna, which is 4π: ∫ 1
2π
− 12π
∫ π
−πG(θ, φ) sin(1
2π − φ) dθ dφ = 4π(D.2)
∫ 12π
− 12π
∫ π
−πτ
n−1∑i=0
Gi(θ, φ) sin(12π − φ) dθ dφ = 4π
τ
(∫ 12π
− 12π
∫ π
−πG0(θ, φ) sin( 1
2π − φ) dθ dφ+ . . .+∫ 1
2π
− 12π
∫ π
−πGn−1(θ, φ) sin( 1
2π − φ) dθ dφ
)= 4π,
where sin( 12π− φ) is caused by the fact that the integral is defined as a range of spherical coordi-
nates. Each individual gain function (Gi) only has a value different from zero between a certaininterval, which means the integral only has to cover that interval:
τ
(∫ 12V0
− 12V0
∫ 12H0−δ0
− 12H0−δ0
G0(θ, φ) sin( 12π − φ) dθ dφ+ . . .+
∫ 12π
− 12π
∫ π
−πGn−1(θ, φ) sin( 1
2π − φ) dθ dφ
)= 4π,(D.3)
τ
(ρ0H0 V0 + . . .+
∫ 12π
− 12π
∫ π
−πGn−1(θ, φ) sin(1
2π − φ) dθ dφ
)= 4π,
where Hi represents the horizontal beamwidth of lobe i and Vi the vertical beamwidth of lobe i.When this is done for the gain function of each lobe, τ can be derived:
τ =4π∑n−1
i=0 ρiHi 2 cos( 12π −
12Vi)
(D.4)
D.2 Patch Generation
Before the simulation starts, triangles that do not satisfy the maximum edge length are automat-ically split into smaller triangles until they do satisfy the requirement. The simulation will pickthe edge with the maximum length and create an new vertex at the center of the edge, which willbe used to create two new triangles (see figure D.1.
74 CHAPTER D: Algorithmic Details
a
b
c
d
Figure D.1: Splitting triangle abc into two triangles (adc and abd)
D.3 Derivation Superposition
Suppose two harmonic waves:
S1 = E1 sin (ω0t+ δ1), (D.5)S2 = E2 sin (ω0t+ δ2), (D.6)
where E is the electric field strength of the wave.Then the addition of these two is defined as[31]:
S′ = E sin (ω0t+ δ), (D.7)
where:
E =√E2
1 + E22 + 2E1E2 cos(δ2 − δ1), (D.8)
δ = arctan(E1 sin δ1 + E2 sin δ2E1 cos δ1 + E2 cos δ2
). (D.9)
However, the simulation works with the power in Watts instead of the electric field. The power(A) of an electromagnetic wave equals C ·E2[13], where C is a constant which value is not relevantfor the derivation.
The function required for the simulator is:
S = A sin (ω0t+ δ), (D.10)
where
A = C · E2, (D.11)
= C · (A1C + A2
C + 2C
√A1
√A2 cos(δ2 − δ1)),
= A1 +A2 + 2√A1
√A2 cos(δ2 − δ1),
and
δ = arctan
√
1C
√A1 sin δ1 +
√1C
√A2 sin δ2√
1C
√A1 cos δ1 +
√1C
√A2 cos δ2
, (D.12)
= arctan(√
A1 sin δ1 +√A2 sin δ2√
A1 cos δ1 +√A2 cos δ2
).
D.4 Model / World Coordinates
The vertices of each patch are defined in local coordinates relative to the position and orientationof the parent object. In order to apply operations between different objects world coordinates arerequired. Therefore, model coordinates are transformed to world coordinates using the algorithmdescribed in [10, section 5-15].
75
Bibliography
[1] A. Arnold-Bos, A. Khenchaf, and A. Martin. Bistatic radar imaging of the marine environment- part i: Theoretical background. IEEE transactions on geoscience and remote sensing, 2007.
[2] J. Arvo. Linear-time voxel walking for octrees. ray tracing news 1(12). 1988.
[3] A. Bole, B. Dineley, and A. Wall. Radar and Arpa Manual. Elsevier, Great Britain, 2ndedition, 2005.
[4] L. Brown. A radar history of World War II : technical and military imperatives. Institute ofPhysics Publishing, Bristol, 1999.
[5] R. G. Carter. Electromagnetism for Electronic Engineers. Ventus Publishing ApS, 2009.
[6] G. Coombe and M. Harris. GPU Gems 2 - Programming Techniques for High-PerformanceGraphics and General-Purpose Computation. Addison Wesley, 2005.
[7] B. Crowell. Simple Nature. Fullerton, California, 2009.
[8] R. P. Feynman. QED. Princeton University Press, USA, 4th edition, 2002.
[9] C. M. Goral, K. E. Torrance, D. P. Greenberg, and B. Battaile. Modeling the interaction oflight between diffuse surfaces. SIGGRAPH Comput. Graph., 18(3):213–222, 1984.
[10] D. Hearn and M. P. Baker. Computer Graphics. Pearson Prentice Hall, Upper Saddle River,NJ, USA, 3rd edition, 2004.
[11] W. Heijveld. Navigeren tussen ambacht en automaat. In L. Akveld, editor, Koersvast. Aprilis,Zaltbommel, 2005.
[12] T. Hubing, C. Su, H. Zeng, and H. Ke. Survey of current computational electromagneticstechniques and software. 2008.
[13] N. Ida. Engineering Electromagnetics. Springer-Verlag, New York, United States of America,2003.
[14] IMO. STCW. England, 2005.
[15] E. F. Knott. Radar cross section. In M. Skolnik, editor, Radar Handbook. McGraw-HillCompanies, USA, 3rd edition, 2008.
[16] E. F. Knott, J. F. Shaeffer, and M. T. Tuley. Radar Cross Section. SciTech Publishing, Inc.,USA, 2nd edition, 2004.
[17] S. Laine, H. Saransaari, J. Kontkanen, J. Lehtinen, and T. Aila. Incremental instant radiosityfor real-time indirect illumination. Eurographics Symposium on Rendering, 2007.
[18] R. Lengenfelder. The design and implementation of a radar simulator. Master thesis, CapeTown, 1998.
76 BIBLIOGRAPHY
[19] F. Molinet, H. Steve, and J.-P. Adam. State of the art in computational methods for theprediction of radar cross-sections and antenna-platform interactions. 2005.
[20] J. Nasr and D. Vidal-Madjar. Image simulation of geometric targets for spaceborn syntheticaperture radar. IEEE transactions on geoscience and remote sensing, 1991.
[21] Nova Contract. Radar Zeevaart. GDS Printing BV, The Netherlands, 4th edition, 2009.
[22] E. J. Rothwell and M. J. Cloud. Electromagnetics. CRC Press, 2001.
[23] Royal Navy. The Principles of Navigation. The Nautical Institute, United Kingdom, 10thedition, 2008.
[24] P. Shirley. Fundamentals of Computer Graphics. 2nd edition, 2005.
[25] M. Skolnik. Introduction to Radar Systems. McGraw-Hill Companies, USA, 3rd edition, 2001.
[26] M. Skolnik. An introduction and overview of radar. In M. Skolnik, editor, Radar Handbook.McGraw-Hill Companies, USA, 3rd edition, 2008.
[27] J. Toomay and P. J. Hannen. Radar Principles for the Non-specialist. SciTech Publishing,Inc., Norwich, NY, USA, 3rd edition, 2004.
[28] C. Uluisik and L. Sevgi. Radar cross section (rcs) prediction techniques: From high-frequencyasymptotics to numerical simulations. 2004.
[29] H. J. Visser. Array and Phased Array Antenna Basics. John Wiley & Sons Ltd, England,2005.
[30] I. Wald. Realtime ray tracing and interactive global illumination. PhD thesis, SaarlandUniversity, 2004.
[31] E. W. Weisstein. Harmonic addition theory. Mathworld - A Wolfram Web Resource.http://mathworld.wolfram.com/HarmonicAdditionTheorem.html.
[32] E. W. Weisstein. Icosahedron. Mathworld - A Wolfram Web Resource.http://mathworld.wolfram.com/icosahedron.html.
[33] E. W. Weisstein. Spherical coordinates. Mathworld - A Wolfram Web Resource.http://mathworld.wolfram.com/SphericalCoordinates.html.
[34] E. W. Weisstein. Spherical excess. Mathworld - A Wolfram Web Resource.http://mathworld.wolfram.com/SphericalExcess.html.
[35] E. W. Weisstein. Spherical trigonometry. Mathworld - A Wolfram Web Resource.http://mathworld.wolfram.com/Spherical Trigonometry.html.
