Evaluation of CST Studio Suite for simulation of radar ...

Evaluation of CST Studio Suite for simulation of radar cross-section

Jonas Lindgren

Department of Physics

Umeå University

A thesis submitted for the degree of

Master of Science in Engineering Physics

Autumn 2021

Master’s Thesis in Engineering Physics, 30 ECTS

Jonas Lindgren, [email protected]

Supervisors: Jörgen Vedin BAE Systems Hägglunds AB

Clayton Forssén Department of Physics

Examiner: Magnus Andersson Department of Physics

Copyright © 2021. All Rights Reserved.

mailto:[email protected]

Abstract

When designing military vehicles, it is of interest to make the vehicles difficult to detect using radar.

The radar cross-section (RCS) property indicates how easily a vehicle is detected by radar and

should thus be minimized. However, the RCS of a vehicle represents the cross-sectional area of a

perfectly reflecting sphere that would produce the same reflection strength as the vehicle in

question. Since this is extremely complicated to calculate as military vehicles are quite complex,

these calculations are performed using computational simulations. BAE Systems Hägglunds is

looking into changing from their current simulation software OPTISCAT to CST Studio Suite and

thus want to know how CST performs and compares against OPTISCAT. In this work, we show

that CST obtains results within 2% of theoretical data when simulating a sphere and a slab. When

simulating vehicles, the RCS difference between the two software is from 3% to 55% while showing

similar general behavior. Results indicate that CST performs well when simulating simple objects

but deviates from OPTISCAT when simulating the vehicle. It is not surprising that the software

does not match up perfectly since they use different theoretical approaches, OPTISCAT uses

physical optics while CST an extension to physical optics called the Shooting Bouncing Ray

method. Even though the software differs to this extent it is most likely possible that CST can be

a suitable replacement for OPTISCAT. When looking at RCS the important part is the location of

spikes and since they have similar general behavior, those spikes may still be possible to identify.

This thesis will hopefully act as a starting point for further examination of CST as a software for

simulating RCS, for example by comparing results from CST to experimentally measured data.

Hopefully it will also be used to improve the design process of making military vehicles harder to

detect.

Table of contents

1 Introduction .......................................................................................................................................... 1

1.1 Background ................................................................................................................................... 1

1.2 Purpose and goals ........................................................................................................................ 1

1.3 Limitations .................................................................................................................................... 1

2 Theory .................................................................................................................................................... 2

2.1 RCS ................................................................................................................................................ 2

2.2 OPTISCAT ................................................................................................................................... 3

2.3 CST ................................................................................................................................................ 3

2.3.1 I-solver .................................................................................................................................. 3

2.3.2 A-solver ................................................................................................................................. 4

3 Validating CST and choosing solver ................................................................................................. 4

3.1 Performance ................................................................................................................................. 4

3.2 Sphere ............................................................................................................................................ 5

3.3 Slab ................................................................................................................................................. 7

3.4 Conclusions .................................................................................................................................. 8

4 Performance .......................................................................................................................................... 8

4.1 Simulation model ......................................................................................................................... 8

4.2 Software inputs ............................................................................................................................ 9

5 Results .................................................................................................................................................. 10

5.1 0° elevation angle ....................................................................................................................... 10

5.2 20° elevation angle ..................................................................................................................... 12

5.3 60° elevation angle ..................................................................................................................... 14

6 Discussion ........................................................................................................................................... 17

6.1 Validating CST and choosing solver ....................................................................................... 17

6.2 Simulations of the CV90 ........................................................................................................... 17

7 References ........................................................................................................................................... 18

1

1 Introduction

The ability to remain undetected by the enemy is an important feature of modern military vehicles.

Of special interest is stealth technology which makes the vehicle invisible by radar. To minimize

the risk of a vehicle being detected by radar the property called radar cross-section (RCS) needs to

be minimized. An important part of the process of creating vehicles with low RCS is the use of

simulation [1]. BAE Systems Hägglunds is currently looking to use a new software for these

simulations which created the focus of this project. Before switching software it is preferable to

know how the new software performs and also how the different software compares against each

other.

1.1 Background

BAE Systems Hägglunds stationed in Örnsköldsvik, Sweden is a limited company in the defense

industry owned by BAE Systems AB. It has its origins in Hägglund & Söners division for military

vehicles but was sold to Alvis in 1997, which in turn was bought by BAE Systems in 2004. As the

technology in the world improves and becomes more available, the production of military vehicles

also has to evolve to ensure that the vehicles can maintain the ability to stay undetected by radar.

This is done by, as already mentioned, simulating vehicles RCS.

The definition of RCS is the hypothetical cross sectional area required to intercept the transmitted

power density at the target such that if the total intercepted power were re-radiated isotopically,

the power density observed at the receiver is produced [2]. The property of RCS rarely has anything

to do with the physical size of an object but rather the reflectivity of the object.

The software Hägglunds historically has been using for this is OPTISCAT, however it is no longer

maintained and its GUI only works with Windows 95. The alternative Hägglunds are looking at is

CST Studio Suite. The two software simulates RCS using different theoretical approaches,

OPTISCAT is based on physical optics with a number of add-ons [3], where CST contains a

number of different solvers to choose from depending on the specific needs of a simulation (e.g.

ray tracing and electromagnetic full-wave simulation) [4].

1.2 Purpose and goals

The purpose of this project is to develop a simulation technique for RCS in CST along with

deciding which solver and resolution is required to obtain comparable results to earlier

simulations from OPTISCAT. The results from OPTISCAT that will be used for comparisons

with CST are from a restricted technical report regarding the RCS of a CV90 done at Hägglunds,

then Alvis, in 2003. It is also of interest to find any possible limitations in CST.

1.3 Limitations

When talking about radar it is possible to create an infinite combination of settings for the radar

to operate at that would result in different results. Since the main purpose of this project is the

comparison between two different software with the help of an earlier technical report which

used OPTISCAT, this project will be limited by what was done in said report. The project will

follow the same or corresponding simulation settings that was used in the technical report, this

will include frequencies, materials, incident angles etc.

2

2 Theory

2.1 RCS

The definition of RCS is quite a handful but can be made easier to understand by taking a look at

the ideal monostatic radar equation term by term [5]:

𝑃𝑟 = 𝑃𝑡𝐺𝑡

4𝜋𝑟2𝜎

1

4𝜋𝑟2𝐴𝑒𝑓𝑓 , (1)

where Pt is the transmitter’s input power (W); Gt is the gain of the radar transmit antenna

(dimensionless); r is the distance from the radar to the target (m); 𝜎 is the radar cross-section of

the target (m2); Aeff is the effective area of the radar receiving antenna (m2); Pr is the power received

back from the target by the antenna (W).

The first term in equation 1, 𝑃𝑡𝐺𝑡

4𝜋𝑟2, represents the surface power density (W/m2) produced by the

radar transmitter at the target. This power density is then intercepted by the radar cross-section 𝜎

(m2) of the target. The product 𝑃𝑡𝐺𝑡

4𝜋𝑟2 𝜎 thus has the dimension of power (W) and is a representation

of the hypothetical total power intercepted by the target. The term 1

4𝜋𝑟2 represents the isotropic

scattering of the intercepted power from the target back to the radar receiver. Thus the product 𝑃𝑡𝐺𝑡

4𝜋𝑟2 𝜎1

4𝜋𝑟2 represents the reflected surface power density at the radar receiver (𝑊

𝑚2). Finally, the

receiver antenna collects the power density with effective area 𝐴𝑒𝑓𝑓 and thus yields the power

received by the radar as the full radar equation above [6].

It is important to note that the scattering of incident radar power by a target is never isotropic, even for spherical targets, and the RCS is a hypothetical area that can be viewed as a correction

term that makes the radar equation “work out” for experimentally observed ratios 𝑃𝑟

𝑃𝑡. However,

since RCS is a property of the target alone it is an extremely valuable concept that allows the performance of a radar system to be analyzed independent of the radar and engagement parameters.

Now, to obtain the commonly used formula for calculation of RCS we simply make use of the

incident and scattered surface power densities.

𝑆𝑖 = 𝑃𝑡𝐺𝑡

4𝜋𝑟2 , (2)

𝑆𝑠 = 𝑃𝑡𝐺𝑡

4𝜋𝑟2𝜎

1

4𝜋𝑟2=

𝑃𝑟

𝐴𝑒𝑓𝑓 . (3)

It is easy to see that both of these approach a limit as r -> ∞.

If we now rearrange equation 2 and 3, insert them into equation 1 and solve for 𝜎 we get:

𝜎 = lim𝑟→∞

4𝜋𝑟2𝑆𝑠

𝑆𝑖 . (4)

One thing to note is that RCS is independent of the magnitude of the signal and the distance

between the object and radar. Although these factors are important in detecting targets they do not

affect the RCS since RCS is a property of an object’s reflectivity.

3

Now, equation 4 does seem to depend on the distance between radar and target thus contradicting

the earlier statement that RCS is independent of distance. However, by analyzing Si and Ss again

we can see that the distance does cancel out with the term 4𝜋𝑟2 that simply describes the isotropic

scattering by the following in equation 5 below:

𝑆𝑖 ∝ 1

𝑟2, 𝑆𝑠 ∝

1

𝑟4, 𝜎 ∝ 𝑟2

𝑆𝑠

𝑆𝑖 ∝ 𝑟2

1𝑟4

1𝑟2

∝ 𝑟4

𝑟4 ∝ 1 . (5)

This is also where the informal and most used definition of RCS comes from: the RCS of an object

is the cross-sectional area of a perfectly reflecting sphere that would produce the same strength

reflection as the object in question.

In electromagnetic analysis, equation 4 can also be re-written as:

𝜎 = lim𝑟→∞

4𝜋𝑟2|𝐸𝑠|2

|𝐸𝑖|2 . (6)

Es and Ei in equation 6 are the scattered and incident electric field intensities, respectively [7].

The final thing to add to the theory about RCS in general is the fact that it is dependent on

polarization. In other words, it depends on the polarization of the output signal as well as what

polarization the receiver is set to measure. This is often clarified with a combination of the letters

H (horizontal polarization) and V (vertical polarization) in the form of HH, HV, VH and VV. The

first letter clarifies what polarization has been measured while the second letter is the polarization

that has been emitted [8]. Out of these, the HH and VV are the most valuable since they measure

the part of the signal that simply has been reflected while the HV and VH measures the part of the

signal that is reflected and has had its polarization converted. In comparison HH and VV are

generally larger than HV and VH, especially at the points where RCS peaks since those peaks are

mostly pure reflections and thus the polarization is not converted [9].

2.2 OPTISCAT

OPTISCAT utilizes an implementation of physical optics (PO) with correction for edge diffraction

and provides both pre- and post-processing in addition to the solution solver. The simulation

software is essentially a PO model of the surface integral representation of Maxwell’s equations

[10].

2.3 CST

CST Studio Suite is a high-performance 3D electromagnetic analysis software package. CST has a

number of different solvers for different scenarios, where two of them are suited for calculations

of RCS: the integral equation solver (I-solver) and the asymptotic solver (A-solver).

2.3.1 I-solver

The I-solver is based on the method of moments technique and uses the multilevel fast multipole

method. It is a 3D full-wave solver that uses a surface integral technique, thus when simulating

larger models with a lot of empty space this makes the I-solver more efficient than full volume

methods. It can also calculate the modes supported by a structure with a characteristic mode

analysis feature [4].

4

2.3.2 A-solver

The A-solver is a ray tracing solver that is based on an extension to physical optics, namely the

Shooting Bouncing Ray method. It is very viable for simulations that include structures of very

large electrical sizes where a full-wave solver is unnecessary [4].

3 Validating CST and choosing solver

Since CST is a completely new software for Hägglunds, it is fitting to begin with validating the

software to see how the different solvers match up against theory. For this, two objects were

chosen: a sphere and a slab. The sphere is suitable to do this validation with since the informal

definition of RCS is the cross sectional area of a perfectly reflecting sphere that would produce the

same strength reflection as the object in question. So, by simulating a sphere the RCS should simply

be the cross-sectional area of the sphere, namely 𝜎 = 𝜋𝑟2. The slab will then act as a

complementary shape to the sphere, so both flat and rounded shapes have been tested in this

validation.

3.1 Performance

The objects will be considered as metallic and thus have the properties of a perfect electrical

conductor (PEC).

The standard settings used in these simulations were the preset accuracy of “high” for both the I-

and A-solver and for the second simulation with each solver the accuracy was manually increased.

For the I-solver, the maximum cell mesh settings were used can be seen in Table 1 below:

Table 1 Solver settings used for the I-solver.

Standard mesh Finer mesh

Cells per wavelength, model: 5 10

Cells per max model box edge, model:

2 2

While for the A-solver the ray sampling settings used can be seen in Table 2 below:

Table 2 Solver settings used for the A-solver

Setting: Standard rays Denser rays

Ray spacing in wavelengths: 0.7 0.4

Minimum number of rays: 1000 1000

Adaptive ray sampling: Yes Yes

Maximum ray distance in wavelengths: 1.5 1

Minimum ray distance in wavelengths: 0.015 0.015

The sign conventions for the sphere and slab can be seen in Figure 1 below:

5

Figure 1 Sign conventions in simulation models for azimuth (theta) and elevation (phi) angles.

The input parameters for these simulations can be seen in Table 3 below:

Table 3 Input parameters for the simulations of the sphere and the slab.

Frequency [GHz] Elevation, phi Azimuth angle, theta Azimuth sweep, Δtheta

10 0° 0° − 360° 0.2°

3.2 Sphere

The specific size of the sphere in these simulations is set to a radius of 564.1895835 mm which corresponds to a sphere with a cross-sectional area of very close to 1m2. One thing to note is the fact that the RCS of a sphere is independent of frequency according to the informal definition.

However, this is only acceptable as long as 𝜆 ≪ 𝑟 because otherwise creeping waves will be

interfering with the result. The cut-off for creeping waves can be determined by the equation 2𝜋𝑟

𝜆>

10 [11]. By inserting the values in the simulations we get

2𝜋𝑟

𝜆=

2𝜋𝑟𝑓

𝑐=

2𝜋 ⋅ 0.5641895835𝑚 ⋅ 10 ⋅ 109𝐻𝑧

299792458𝑚𝑠

≈ 118 > 10 .

In other words, the size of the sphere along with the used frequency is sufficient to not be affected

by creeping waves.

The resulting HH-polarization results for the I- and A-Solver with standard and fine mesh can be

seen in Figure 2 below:

6

Figure 2 A) Plot of the HH polarization of the simulated sphere using the I-solver along with mean, max and expected value. B) Plot of the HH polarization of the simulated sphere using the A-solver along with mean, max and expected value. C) Plot of the HH polarization of the simulated sphere using the I-solver with a finer mesh along with mean, max and expected value. D) Plot of the HH polarization of the simulated sphere using the A-solver with denser rays along with mean, max and expected value.

A summary of Figure 2 can be seen below in Table 4:

Table 4 Table containing the mean and max values along with the simulation time for the different solvers used to simulate the sphere.

Mean Max Simulation time

I-solver 1.0766 1.2020 2h

A-solver 0.9926 1.0210 2min

I-solver with finer mesh

1.0128 1.0360 40h (only 45° simulated in that

time)

A-solver with denser rays

0.9816 1.0070 3 min

A B

C D

7

3.3 Slab

The RCS of a slab can be calculated by the formula 𝜎 = 4𝜋𝐴2

𝜆2 [11] when the incident signal is

perpendicular to the face of the slab which occurs at azimuth angles 180° and 0°. These angles of course produce maximum values of RCS in the simulations. Unlike the sphere, the RCS of a slab is dependent on the frequency. The specific size of the slab in these simulations is set to a side length of 91.9618894 mm which corresponds to a RCS very close to 1m2. The resulting HH-polarization results for the I- and A-solver with standard and fine mesh can be seen in Figure 3 below:

Figure 3 A) Plot of the HH polarization of the simulated slab using the I-solver along with mean, max and expected value. B) Plot of the HH polarization of the simulated slab using the A-solver along with mean, max and expected value. C) Plot of the HH polarization of the simulated slab using the I-solver with a finer mesh along with mean, max and expected value. D) Plot of the HH polarization of the simulated slab using the A-solver with denser rays along with mean, max and expected value.

A summary of Figure 3 can be seen below in Table 5:

A B

C D

8

Table 5 Table containing the mean and max values along with the simulation time for the different solvers used to simulate the slab.

Mean Max Simulation time

I-solver 0.0589 1.0680 1.5h

A-solver 0.0482 0.9934 20 sec

I-solver with finer mesh

0.0534 0.9848 6h

A-solver with denser rays

0.0482 0.9934 3 min

3.4 Conclusions

By taking a look at Figure 2 and Table 4 it is possible to see that the mean value of the simulations

of the sphere is closest to the expected value for the A-solver with standard rays. By looking at the

solvers disregarding the simulation resolution the A-solver is also closer than the I-solver. In the

figures it is also possible to see that the A-solver varies less than the I-solver. Finally, in the table it

is very clear that the A-solver is a lot faster than the I-solver when it comes to simulation time.

If we then take a look at Figure 3 and Table 5 we can see that the A-solver obtains the same values

no matter what simulation settings are being used and these are also closer to the expected than

any of the I-solver simulations. Once again, the A-solver is also a lot faster than the I-solver.

Taking all this into account, the A-solver in general seems to give a little bit better results than the

I-solver but the biggest perk with the A-solver is the simulation time. Because of this the A-solver

will be used when simulating the CV90.

4 Performance

4.1 Simulation model

In Figure 4 below, the simulation model that was built in AUTOCAD for the CV90 is shown.

Tools and components stowed externally with length significantly smaller than five wavelengths

(5λ) were either not modelled or represented as simplified geometry. The model resolution is based

on the highest frequency used in the original simulations in OPTISCAT, i.e. 35 GHz which

corresponds to a wavelength of about 8.6 mm. In other words, tools and components stowed

externally which are smaller than 4.3 cm were either not modelled or represented as simplified

geometry. In the simulation software, all modelled surfaces are considered as metallic and

consequently perfect electric conductors.

9

Figure 4 Surface model of the CV90; geometry data for the RCS simulation software OPTISCAT and CST.

As shown in Figure 5 below, the azimuth and elevation angles do not match up between the

software. The main reason for this is that the model created was created almost 20 years ago which

created problems with manipulating it in CST and thus the sign conventions are far from

conventional. Because of this, the data from CST was rearranged to match up with the data from

OPTISCAT and thus the conventions from OPTISCAT will be used.

Figure 5 A) Sign conventions in simulation model for azimuth (α) and elevation (γ) angles in OPTISCAT. B) Sign conventions in simulation model for azimuth (phi) and elevation (theta) angles in CST.

4.2 Software inputs

In the OPTISCAT report the angular step length was chosen by the formula:

∆𝛼 < 2

𝐹 ⋅ 𝐿 [°] (7)

Where F and L describe the radar frequency [GHz] and the length parameter [m]. The length

parameter is the largest flat length in the direction of the sweep. For the model of the CV90, the

A B

10

length parameter was about one meter. Equation 7 gave the required angular increment Δα < 0.2°

and thus the same will apply for CST to make comparisons of data easier.

Table 6 below summarizes the input parameters for the simulations:

Table 6 Input parameters for the simulations of the CV90

Frequency [GHz] Elevation, γ Azimuth angle, α Azimuth sweep, Δα

10 0 -180° − 180° 0.15° 10 20 -180° − 180° 0.15° 10 60 -180° − 180° 0.15°

The simulations were conducted at three different settings for the A-solver in CST. The different

settings can be viewed in Table 7 below:

Table 7 Solver settings used for the simulations of the CV90

Setting: Sparser rays Standard rays Denser rays

Ray spacing in wavelengths: 1 0.7 0.4

Minimum number of rays: 1000 1000 1000

Adaptive ray sampling: Yes Yes Yes

Maximum ray distance in wavelengths: 2 1.5 1

Minimum ray distance in wavelengths: 0.03 0.015 0.015

Since the geometrical data of the CV90 is classified, it cannot be shown in this report. However, it

is still possible to do comparisons between the different software in the form of simple quotas and

relative cumulative frequency. The quotas are as simple as the CST data divided by the OPTISCAT

data to see how much they differ. The cumulative frequency is the sum of the data points of a

specific RCS value and all the RCS values below it. What then makes it a relative cumulative

frequency is that it is divided by the total number of data points making it a fraction.

5 Results

All plots and data shown below are using the HH-polarization of the simulations. When calculating

the differences between CST and OPTISCAT the data is handled in linear form and if needed

transformed into decibel to make plots or data more clear. This is done by the formula in equation

8 below:

𝑅𝐶𝑆 = 10 ⋅ 𝑙𝑜𝑔10 (𝜎

𝐴𝑟𝑒𝑓) [𝑑𝐵𝑠𝑚] (8)

where σ and Aref represent the RCS and reference area respectively. The reference area is usually set

to 1 m2.

5.1 0° elevation angle

Panel A) in Figure 6, Figure 7 and Figure 8 below shows the quota of the CST data divided by the

OPTISCAT data for the three different simulation settings. The data has been converted to dB for

clarity. The simulation contains an azimuth angle sweep from -180° to 180°.

11

Panel B) in Figure 6, Figure 7 and Figure 8 show the relative cumulative frequency from CST and

OPTISCAT for the three different simulation settings.

Figure 6 A) The quota of the CST data divided by the OPTISCAT data converted to dB for the simulation using sparser rays at an elevation of 0° (blue markers). The mean is represented by the orange line and the Gaussian distribution is shown by the black, full and dashed, lines in the form of ± 1 and 2 sigma respectively. B) Relative cumulative frequency for the CST (blue line) and OPTISCAT (orange line) data using sparser rays at an elevation angle of 0°.

Figure 7 A) The quota of the CST data divided by the OPTISCAT data converted to dB for the simulation using standard rays at an elevation of 0° (blue markers). The mean is represented by the orange line and the Gaussian distribution is shown by the black, full and dashed, lines in the form of ± 1 and 2 sigma respectively. B) Relative cumulative frequency for the CST (blue line) and OPTISCAT (orange line) data using standard rays at an elevation angle of 0°.

A B

A B

12

Figure 8 A) The quota of the CST data divided by the OPTISCAT data converted to dB for the simulation using denser rays at an elevation of 0° (blue markers). The mean is represented by the orange line and the Gaussian distribution is shown by the black, full and dashed, lines in the form of ± 1 and 2 sigma respectively. B) Relative cumulative frequency for the CST (blue line) and OPTISCAT (orange line) data using denser rays at an elevation angle of 0°.

When looking at panel A) in Figure 6, Figure 7 and Figure 8 we see that all of their mean values

are above 0 dB, which corresponds to the CST data being bigger than the OPTISCAT data when

comparing for each azimuth angle. We also see that the data is quite spread and thus the standard

deviation is quite big. To cover 95% of all the data points in the quota the interval has to be

somewhere around [15 -15] dB which corresponds to the CST data being 32 times bigger/smaller

than the OPTISCAT data.

Panel B) in Figure 6, Figure 7 and Figure 8 show that the CST data tends to be a bit bigger than

the OPTISCAT data but the software seems to behave very similarly. The RCS value for the CST

data is generally a bit larger than for the OPTISCAT data when looking at the same relative

cumulative frequency.

Table 8 below summarizes the max and mean values from Figure 6, Figure 7 and Figure 8 along

with their respective simulation time:

Table 8 Table showing the percentage difference between CST data and the OPTISCAT data for the elevation angle 0°.

Simulation setting: Simulation time: Max value: Mean value:

Sparser rays 39 min -50,9 % -34,9 %

Standard rays 1h 12 min -51,1 % -34,9 %

Denser rays 1h 44 min -51,4 % -35,2 %

In Table 8 it is clear that the max value and the mean value of the CST data are significantly smaller

than that of the OPTISCAT data. It is also notable that as the simulation settings are turned up,

the results stray further away from that of OPTISCAT.


Panel A) in Figure 9, Figure 10 and Figure 11 below shows the quota of the CST data divided by

the OPTISCAT data for the three different simulation settings. The data has been converted to dB

for clarity. The simulation contains an azimuth angle sweep from -180° to 180°.

A B

13

Panel B) in Figure 9, Figure 10 and Figure 11 shows the relative cumulative frequency from CST

and OPTISCAT for the three different simulation settings.



A B

A B

14


Similarly as for the 0° elevation angle, when looking at panel A) in Figure 9, Figure 10 and Figure

11 we see that all of their mean values are above 0 dB, which corresponds to the CST data being

bigger than the OPTISCAT data when comparing for each azimuth angle. We also see that the

spread in the data is quite big and thus the standard deviation is quite big. To cover 95% of all the

data points in the quota the interval has to be somewhere around [15 -15] dB which corresponds

to the CST data being 32 times bigger/smaller than the OPTISCAT data.

Also like the 0° elevation angle, panel B) in Figure 9, Figure 10 and Figure 11 show that the CST

data tends to be a bit bigger than the OPTISCAT data but the software seems to behave very

similarly. The RCS value for the CST data is generally a bit larger than for the OPTISCAT data

when looking at the same relative cumulative frequency.

Table 9 below summarizes the max and mean values from Figure 9, Figure 10 and Figure 11 along

with their respective simulation time.


Simulation setting: Simulation time: Max Mean



Denser rays 1h 45 min -42,3 % -2,9 %

In Table 9 we see that the max values for the CST data is significantly bigger than for the

OPTISCAT data, but when it comes to mean value the software generates quite similar results. On

the contrary to the 0° elevation angle, when the simulation settings are turned up the results start

to close in on that of the OPTISCAT data.


Panel A) in Figure 12, Figure 13 and Figure 14 below shows the quota of the CST data divided by

the OPTISCAT data for the three different simulation settings. The data has been converted to dB

for clarity. The simulation contains an azimuth angle sweep from -180° to 180°.

A B

15

Panel B) in Figure 12, Figure 13 and Figure 14 shows the relative cumulative frequency from CST

and OPTISCAT for the three different simulation settings.



A B

A B

16


When looking at panel A) in Figure 12, Figure 13 and Figure 14 we once again see that all of their

mean values are above 0 dB, which corresponds to the CST data being bigger than the OPTISCAT

data when comparing for each azimuth angle. We also see that the data is quite spread and thus the

standard deviation is quite big. To cover 95% of all the data points in the quota the interval has to

be somewhere around [15 -15] dB which corresponds to the CST data being 32 times

bigger/smaller than the OPTISCAT data.

Panel B) in Figure 12, Figure 13 and Figure 14 show that the CST data tends to be a bit bigger

than the OPTISCAT data but the software seems to behave very similarly. The RCS value for the

CST data is generally a bit larger than for the OPTISCAT data when looking at the same relative

cumulative frequency.

Table 10 below summarizes the max and mean values from Figure 12, Figure 13 and Figure 14

along with their respective simulation time.


Simulation setting: Simulation time: Max Mean



Denser rays 1h 55 min -86,1 % -54,2 %

In Table 10 it is once again clear that the max value and the mean value of the CST data are

significantly smaller than that of the OPTISCAT data. For this elevation angle we neither have the

results close in nor stray away from the OPTISCAT data as the simulation settings change.

A B

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6 Discussion

6.1 Validating CST and choosing solver

When it comes to validating CST and choosing a solver the results indicated that the A-solver was

at its worst 2% off the expected value while the I-solver was 8% off. This in itself is not the main

reason for why the A-solver was chosen, but when paired with the simulation time it was quite

clear which solver was the best fit for this project. The I-solver is the solver aimed towards

structures that are electrically smaller than what the A-solver is aimed at, which is why it took so

much longer time to simulate the sphere and slab. For example, with the sphere for the finer

simulation settings, the A-solver only took 3 minutes to simulate and was 1.8% off the expected

value while the I-solver took 40h and was 1.2% off. However, the I-solver only simulated 45° of

the sphere and would thus have taken almost two full weeks to simulate. Since the differences on

a simple sphere were only 0.6 percentage points with a time difference of 2 weeks it was quite clear

what solver was a better fit for the time frame of this project. If the time aspect could be disregarded

or the computing power available was greater it would absolutely be interesting to test the I-solver

as well, but unfortunately this was not the case. More simulation settings and more objects could

perhaps have been tested at this phase where the I-solver might have outperformed the A-solver,

but the results are still quite concise and probably still would result in the same conclusion that the

A-solvers speed is a better choice than the I-solvers possible edge in precision.

6.2 Simulations of the CV90

Regarding the simulations of the CV90, there was not a specific simulation setting that clearly

managed to obtain step-for-step similar results as OPTISCAT. The closest simulations were those

for 20° elevation angle, for those all of the simulation settings yielded pretty decent results while

for any other angle they all yielded results quite far from what OPTISCAT produced. Something

that was quite obvious from the plots of the quotas in 0° elevation angle, 20° elevation angle and

60° elevation angle was that the software did not match up good at all when looking at single

azimuth steps, but according to the plots of relative cumulative frequency they did appear to behave

similarly. Finally, the tables of max and mean values all said that CST generated max values that

were a lot smaller than those from OPTISCAT while the mean values still were quite a bit off (with

the exception of 20° elevation angle) they were not as bad as the max values. In other words, it is

possible to draw the conclusion that even though the software does not match up for each angular

step they still have similar general behavior while OPTISCAT seems to have more exaggerated

extreme points.

One quite obvious thing that could have been done differently with these simulations is the same

thing as for the sphere and slab; more simulation settings could have been tested. However, since

there was not one setting that clearly outperformed the others and there was no clear correlation

between higher simulation settings and better results this might not be the case at all. It seems

much more likely that the simple fact that two different software uses different ways to simulate

yields different results. Even though both CSTs A-solver and OPTISCAT uses physical optics, the

A-solver also uses the extension shooting bouncing ray method which is an extension of physical

optics that was specifically developed for computation of RCS. This might be one reason for the

big difference in results between the different software. Another very simple explanation is that in

the report that has been used for the OPTISCAT results does not present any form of setting used

beyond the input parameters nor any simulation times thus the settings used for the simulations in

CST might be completely off.

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It is also noteworthy to mention that as of this time, there have not been any actual measurements

of RCS on the CV90 model used in these simulations, so there is actually not known what results

should be expected from these simulations. It might be that OPTISCAT has been completely

wrong and CST is producing much more realistic results, the other way or that neither software is

even close. This was an addition that might have been included in this project, but because of time

and logistical reasons it was not touched upon. Thus an actual measurement of the CV90s RCS is

something that is needed to verify what results should be expected from simulations.

7 References

[1] Y. Ling Lim, "The Modelling and Simulation of Passive Bistatic Radar," Adelaide: School of

Electrical and Electronic Engineering, 2013.

[2] M. Skolnick, Introduction to Radar Systems, 1980.

[3] S. Nilsson, J. Rahm, M. Gustafsson, N. Gustafsson, J. Rasmusson and E. Zdansky,

"Slutrapport Radarsignaturprojektet," Totalförsvarets Forskningsintitut, Sensorteknik,

Linköping, 2003.

[4] Dassault Systèmes, "Electromagnetic Simulation Solvers - CST Studio Suite," [Online].

Available: https://www.3ds.com/products-services/simulia/products/cst-studio-

suite/solvers/. [Accessed 16 07 2021].

[5] C. Wolff, "radartutorial," [Online]. Available:

https://www.radartutorial.eu/01.basics/The%20Radar%20Range%20Equation.en.html.

[Accessed 16 07 2021].

[6] A. E. Fuhs, Radar Cross Section Lectures, Naval Postgraduate School Monterey California,

1982.

[7] Y.-W. K. Hsueh-Jyh Li, The Electrical Engineering Handbook, 2005.

[8] P.-L. Frison, Radar Fundamentals [PowerPoint slides]

https://earth.esa.int/documents/10174/3166029/Vilnius_radar_general.pdf, Université

Paris-Est Marne-la-Vallée.

[9] N. Asada, "A study of the effects on Radar Cross Section (RCS) due to "Starved horse

patterns"," 2003.

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[10] M. Sjöberg, "Simulation of Radar Cross Section, CV90 [Restricted]," Alvis, 2003.

[11] N. A. W. C. W. Division, Electronic Warfare & Radar Systems, 2013.

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