=Paper=
{{Paper
|id=Vol-2076/paper-04
|storemode=property
|title=Digital Model of Reflected Signals for a Radar Scene Simulation
|pdfUrl=https://ceur-ws.org/Vol-2076/paper-04.pdf
|volume=Vol-2076
|authors=Alexander S. Bokov,Artem K. Sorokin,Andrey E. Smertin,Evgeniy F. Zapolskikh,Vladimir G. Vazhenin
}}
==Digital Model of Reflected Signals for a Radar Scene Simulation==
https://ceur-ws.org/Vol-2076/paper-04.pdf
Digital Model of Reflected Signals for a Radar
Scene Simulation
Alexander S. Bokov, Artem K. Sorokin, Andrey E. Smertin,
Evgeniy F. Zapolskikh, and Vladimir G. Vazhenin
Ural Federal University, Yekaterinburg, Russia
a.s.bokov@urfu.ru
Abstract. This paper is devoted to reveal the best way for the reflected
signal model implementation for airborne radar systems. The main at-
tention in the paper is paid to the method of the combination of various
well-known and enhanced mathematical models of radar signals, terrains,
different lengthened objects, etc. for the effective radar scene creation.
Also, the key peculiarities of proposed models are discussed in brief.
Moreover, questions of the radar echoes computation algorithm of the
radar scene are explored. In conclusion, the requirements to the models
and suggestions are presented.
Keywords: mathematical model, terrain, reflected signal, airborne radar
system, digital signal processing, radar scene simulator
1 Introduction
Technique progress in digital signal processing and computer simulation tech-
nologies goes with the rapidly increasing requirements to complex various on-
board radar systems and reflected(backscattered) signal simulators for them [1].
This paper concentrated on the radar scene modeling, which is useful for
creating multipurpose simulators of radar echoes. It allows researchers to test an
influence of the following main parameters: flight parameters (altitude, trajec-
tory, evolutions of the airborne vehicle, etc.), terrain types (forest, ice or water
with different salty and wavy), signal distortions (fading, multi-path), type of
emitted signal, and radar parameters (antenna pattern, carrier frequency, band-
width, duration, repetition frequency, etc.).
The proposed digital model is useful in cases of creating the algorithms of
analog and digital signal processing and hardware design of radar scene simula-
tors, which are broadly used to check a radar system operation in real-time [6].
The quality of hardware-in-the-loop (HIL) simulators depends on their signal
processing capabilities and possibilities to represent all essential aspects of the
real flight [6], [13]. So, the develop of models of reflected signals for variety of
different flight circumstances is worthwhile.
The first question is what programming environment is best for mathematical
model design. It is obvious, that every well-known universal program, which is de-
voted to a signal computation, can be used for creation of radar signal processing
models. It is necessary to decide, which is the best one for the radar scene model.
30
2 Mathematical Model of Reflected Signals
2.1 Programming Environment
At this point, a brief characteristic of different numerical computing environ-
ments will be presented.
The first package is application pure C/C++ environment, but despite the
universality of this package and ability of using various libraries freely available
through the Internet, it is a very long process to create and debug the model.
So, we turned to the more specialized packages. One of them is the SimInTech
environment [2]. This program package contains a lot of libraries for creating
various systems from power supply stations to airborne vehicles. This system
supplies the visual mode for blocks combinations and signals plotting in the
scheme, which is similar to Simulink and Vissim. Moreover, libraries are written
in many languages and could be imported in the dll-mode. Other advantage is
that many blocks have open-source code and can be modified during the model
experiment. So, the producers of this program provide customers support in
design and evaluating models for any purposes. On the other hand this program
product is the proprietary software.
Another candidate is the GNU Radio [3]. This package is provided only for
the Linux OS. So, typical Windows user would feel uncomfortable to use this
product. This product provides also the visual mode of design and a lot of
libraries for various radar blocks, all libraries are provided with source code and
could be modified. But compatibility of libraries causes many questions, because
of the conception “as is”. Only enthusiasts use and improve this project.
The next candidate is the SystemVue program [4]. This product contains
libraries for radar’s signal multi-path propagation, multiple channels, jammer,
interference, etc. It is also compatible with the MATLAB system. The price of
this product is equally high.
The next product is the SciLAB, it is an analog of the MATLAB system with
free-ware license and open-source code. Most of packages have similar function-
ality, for example, the Signal Processing and Communication toolbox, Simulink,
SAR simulator, import from MATLAB libraries, etc. So, it can be used as the
cheap and effective model system for creating the radar scene. This program has
a problem with compatibility of different libraries, some of them are unstable
and could crash the system. But it is improved every year by European airspace
industry.
The last and the most popular program product is the MATLAB, it contains
a huge number of libraries, but most of them are unavailable for modification.
But the MATLAB has many advantages, some of them are technical support,
very effective improvements with each release, ability to build own libraries and
import of the third-party modules, and well-designed user interface. Also, it is
available in some universities for stuff and students. So, we have chosen the last
one.
31
2.2 Model Structure
It is necessary to divide model in some blocks and describe them separately.
Analysis of known sources showed that the most common way is to use the
following blocks: underlying surface (terrain) properties, channel of propagation,
reflected signal, and evolutions of the airborne vehicle. As it was shown in [1,
5, 6, 7], for radar signals the phenomenological model provides ideas that the
superposition of partial signals can be used for radar echoes, the reflection could
be presented in terms of geometrical optics, and underlying surface could be split
into facets, i.e., tiny pieces of terrain. Because of difficulty and impossibility of
implementing other electromagnetic methods for description of big areas of real
relief terrain we, have chosen the phenomenological facet model.
So, representation of terrain could be implemented by square or triangle
facets, each of them has its own parameters: a square, orientation, backscatter-
ing diagram, radar cross section (RCS), and position. All these parameters are
sufficient to compute an amplitude and phase of partial signals. This way allows
us to model various types of terrains, such as “meadow”, “ground”, “asphalt”,
“concrete” and so on.
The rough terrains usually could be presented in the two-scale model, which
combines low roughnesses and relief (terrain, such as rocks and hills). The rough-
nesses could be presented by their mean statistical characteristics. We chose an
effective backscattering diagram, which (as it was shown in number of sources
[1, 5, 10, 11]) is the most useful statistical characteristic for radar echo signals.
The relief could be modeled by position and orientation of the tiny facets [6, 12].
Also, it is possible to model a wavy water surface and forest by this way. But in
this paper, other more complicated way is suggested to evaluate reflected signals
from these complicated types of terrains.
Forest Modeling. Nowadays it is possible to model a reflected signal from each
tree and, also, we can change its geometry and its reflection characteristics [1,
7]. For example, we can create the model of pine, aspen, or a birch. For obvi-
ous simplification, we have divided the reflected signal in three parts or layers:
Canopy, Trunks and Ground. The forest model in Fig. 1 depicts additional (for
the Direct beam backscattering) the multi-path signal reflections [7].
Fig. 1. The multi-path signal reflection from forest layers
32
For different incidence angles and wavelengths of an emitted signal, the
weight of each part would be different. For example, if we talk about the 3
cm-wavelength with about vertical illumination the most weighty component of
the reflected signal will be from the crown (if it about leafy trees), a bit less sig-
nal will come from a ground, and very few reflected signal returns from trunks.
For the millimeters-wavelength, the most strong component is the signal from
the canopy, otherwise the meters-wavelength signal is reflected mostly from the
ground. So, the reflection depends on wavelength, and we have to get information
from real flight experiments to reveal the reflection dependencies.
So it is necessary to design a geometric model for each tree, which will be
the base for computing the multi-path signal reflections with precious values of
amplitudes and phases of all facets partial addends [6].
After this, it is preferable to model the signal from forest, which can be
presented by a number of trees. As soon as we have the geometric model for one
tree, we can apply it to many similar trees (clones, which orientation is random)
and obtain signal from all the forest. So, we do not need to evaluate signal all the
time from each tree, but we can compute it from the geometric model according
to proper angles.
There we face to other problem how to evaluate the signal, which is weak-
ened by the leaves of other trees or re-reflected from the lower part of canopy or
trunks. There is no common decision, but in some sources [6, 7] it is mentioned
that it is possible to neglect the re-reflected signal at all for typical trees because
of the weakness their relative magnitudes.
The examples of triangular facet models of the single tree (imported from the
3Ds Max library), woods (reconstructed in the MATLAB system), and the ac-
cordingly evaluated received pulse (there about 1.2 million facets in the scene for
the radar alti-tude 50 m with the vertical illumination by a short pulse radar)
are presented in Fig. 2.
Fig. 2. Examples of models of the tree, woods and a received pulse
The signal shadowing by canopy can be resolved by implementing the back-
ward raytracing method. The ability of model simplification instead of accurate
model of trees is to implement a cloud of randomly spread reflectors. It is mostly
useful for the crown model.
33
But the question is how many reflectors is necessary to use in the model. On
the one hand, it can be revealed by the comparison of results of natural experi-
ments and model results. On the other hand, we can take into account the real
accuracy of the example of radar system and fill every distance-angle volume or
bin (resolved by the common or imaging radar, SAR, etc.) by sufficient number
of facets: up to 10–50 facets inside each interesting bin. As the result, we can
create an appropriate model for such a complicated terrain type and radar sys-
tem.
Wavy Water Modeling. The next point is the model of a wavy surface. As
soon as this topic was highlighted in many researches, we have big amount
of carefully debugged models and experimental results of water surface explo-
rations.
At first, it is necessary to mention that the agitation of water surface depends
on the wind speed; so, the reflected signal will be different for variety of wind
speeds. But not only wind causes surface agitation, it can be caused by ships,
water flows, or by the attraction of the moon; and also by a change of water
depth, especially, for small depths and steep slope of water bottom. The last one
is the most challenging process in modeling the wavy surface. Other feature is
that not all emitted signal backscatters on the water surface; it can be reflected
from the ground under water, especially, for small depths, unsalted water, and
low carrier frequencies.
So, the next thing to deal with is salty of water. The magnitude of the
reflected signal depends on salty, as it was shown in [10, 11]. Sequentially, it is
necessary to design a wavy water model, which can accurately takes into account
the foregoing effects.
Revision of existing models revealed that the most suitable models are the
Pierson-Moskowitz (PM) model, Texel, Marson and Arsole (TMA) model, and
their enhanced methods [8, 9, 12], which allow us to take into account most
of the mentioned effects including the depth dependence of water waving. One
approach on the basis of the Joint North Sea Wave Project (JONSWAP) and
TMA models can be described by calculating an energy spectrum of waves [9]
∗
ETMA (f ) = EJONSWAP (f ) · Φ f , h , (1)
f
−1
f
α · g2 4 p
f
−
− 45 fp e 2·σ2
EJONSWAP (f ) = e · γ . (2)
(2π)4 · f 5
∗
Here, f is the wave frequency, Φ f , h is the Kitaigorodoskii depth function
∗ h i ∗
q
for the depth of water h; Φ f , h = 1∗ · 1 + sinh(K) K
; f = f · hg ;
s f
∗2 ∗
∗ 2
∗
−1
K=2 f ·s f ; s f = tanh 2π · f ;
α is the scaling coefficient; g is the gravity constant; γ is the peak enhancement
factor;σ = 0.07 for f ≤ fp ; σ = 0.09 for f > fp ;[9]
34
2 −0.33
fp is the maximum spectrum frequency given by fp = 3.5 · gU ·F 3 ,
10
where F is the fetch length; U1 0 is the wind speed at a height of 10 m.
According to this spectrum, the parameters for each elementary wave of water
surface are defined (height and wavelength, direction of propagation, wave phase,
etc.). These data, together with the aircraft speed vector, current time, and the
antenna direction are inserted into the analytical formula [12]
Nf −1
X
ξ(x, y, t) = σn · sin(K0n · [(x + (Vx − Un x) · t) · cos βn + . . .
n=0
(y + (Vy − Uny ) · t) · sin βn ] − Ωn · t + αn ) (3)
where x, y is the actual facet location at time t;
n is the number of wave trains;
V, Vy is the aircraft speed projection;
Unx , Uny is the waves speed projection;
z + (VUnx )t, y + (Vy Un y)t is the offsets in the Oxy plane;
αn is the wave phase;
βn is the direction of wave propagation;
Ωn is the pulsation;
K0n is the wave number;
Nf >> 1 is the number of waves;
σ is the standard deviation of sea wave heights.
Examples of model results of wavy water surface according to the model with
the wind speed 10 m/s is presented in Fig. 3. The results of model experiments
correspond to information from open sources [1, 5, 11]. The salty of water can
be taken into account by results of salty measurements. Nowadays we can base
on researches provided by many organizations and researcher teams [12].
Fig. 3. Examples of the wavy surface and computed beat signal of the radio altimeter
Other complex terrain types and objects. Another type of terrain, which
currently has no implementation in designed model, is an urban development.
This is extremely complicated type of terrain, which can be modeled by im-
plementation of 3D models of buildings, bridges, roads, power lines, and huge
35
amount of other different objects. Some their geometric models are ready and
accessible in graphic programs, such as the AutoCAD and 3Ds Max. Their sur-
face forms can be imported, for example, in the MATLAB system, and presented
as facets. So, the next step is to accurately set the reflection characteristics for
all facet materials. Usually, just a lot of experiments can be helpful for that
challenge. Therefore, this type of terrain with some simplifications also can be
added into the designed facet model. For many special local objects, such as
vans, tanks, or cars the geometric models exist, which are freely accessible (for
examples, see [6]). So, we can implement them to fulfill a radar scene.
The next and last point is combination of terrain types in one radar scene.
It can be easily presented by brushing (specifying) facets by different reflecting
characteristics. So, if one facet presents water, it can be brushed as water-terrain;
if other presents the grass, it is brushed with the grass-terrain type. This idea
allows us to create lengthened and other usual objects of any form and size.
As the result, we discussed the conceptions for terrain modeling process that
allows us to model various terrains and their combinations.
2.3 Signal Representation
The next point is how to represent the signal. It was nothing told about it earlier.
For definiteness, we talk about the pulse radar signal, but the very similar oper-
ation (as it is written in [6]) can be done for a chirp signal with linear frequency
modulation. The emitted signal can be modeled at the carrier frequency. So, it
is necessary to have more than two points per a period of signal, but the amount
of computations becomes unacceptable. Thus, the usual way is to implement low
frequency as the source of information with addition of in-phase and quadrature
components, which include the phase information. It is especially necessary in
evolution of the evaluate Doppler phase shifts and computation of radar images.
The in-phase component could be presented by the sinusoidal signal, the same
could be told about the quadrature component, but between components there
exists the phase shift of 90 degrees.
The next point is how to sum signals reflected from partial facets. We applied
the method, where partial signals can be added to the result signal with their
delays, ac-cording to the optical geometry theory. For an illuminated spot, we
collect the partial signals from all facets in the circle (or ellipse) bounding the
half-power level of the antenna pattern. We neglect other partial signals. But
the result signal presents only one pulse or repetition interval, so, it is necessary
to present the train of pulses. It depends on parameters of pulses: a pause be-
tween pulses, duration, envelope, and magnitude. The only envelope should be
discussed in detail, others are intuitive parameters. In terms of modeling process,
the pulse form could be presented by a number of plots, each of them presents a
count of the amplitude (or the power, it is the matter of convenience). For each
count with its delay, we accumulate the result signal. Therefore, we have the
reflected power (or amplitude). After that it is obvious to evaluate in-phase and
quadrature components by multiplication of the sinusoidal signal with counts of
36
reflected amplitude. At the end, we have the train of reflected pulses, which can
be processed, for example, by methods of synthesis the radar image.
3 The Digital Model Implementation
At this moment we described the distinctions of the designed model, and now it
is the time to describe exactly the implementation of the designed model.
In Fig. 4, the scheme of the radar scene model is shown, which implements
all foregoing ideas in one scheme. Here, following sequence of computation is
implemented: constants definition and model parameters; input the track, signal
and terrain parameters; track, vehicle, and illuminated spot evaluating; cycles
for all antennas and for all points of trajectory where the reflected signal is
evaluated; displaying the model results and radar image preparation.
Fig. 4. The algorithm of the model of radar echo signal
This model allows us to change separately each part of the model without
changing others; also, it suits as well for pulse radar as chirp radar. Also, as it
was mentioned above, we can add local objects, such as trees or cars, combina-
tions of terrains, change signal, vehicle and terrain parameters. Therefore, this
model is flexible and powerful enough to build the simulator of the radar scene.
37
Therefore, it is possible to extend this model by adding more complex signal
forms, extending database of terrains and local objects or connecting this model
to the real-time services of vector maps, which are freely available through the
Internet, for example, Google-maps.
As soon as we have the model, it is necessary in brief to describe the module
structure of the radar scene model. In Fig. 5 the modules are highlighted in bold
names. For example, in the MATLAB system, modules are presented in separate
files. Also, nearby the names of modules, the brief descriptions are given.
Fig. 5. Module structure of the radar scene model
The module Get Traject is the clock module, which synchronize all mod-
eling process; so, the parameters of emitted signal and trajectory at first are
passed to this block. Also, this model has the following distinctions: the parame-
ters of the transmitter can be passed in the Set RvParam module; the receiver
parameters (if it is necessary) could be implemented afterward.
4 Conclusions
In this paper, the radar scene model is described; it can be implemented and
helpful for various explorations from radar image algorithm verification up to
simulator design [6, 13]. The designed digital model operates with facets, which
can represent difficult shapes and layers of natural surfaces. Additional facet
radar properties, such as an orientation, RCS, and backscattering diagram are
used to compute the multi-path reflections and overall reflected signal. Also, the
radar system carrier motion is taken into account.
Now the model works in the MATLAB environment; so, it allows us to change
parameters of signal processing, edit blocks and redesign the model according to
specifications of existing and prospective radar systems. Furthermore, the model
38
is sufficiently flexible, in other words, each block can be improved and trans-
formed separately by a researcher for different radar and navigation systems.
The next step is the following: weakening relations between modules, terrain
database fulfillment, and addition various algorithms for digital signal process-
ing.
Acknowledgments. This work was supported by the grant of the Ministry of
Education and Science of the Russian Federation, Project no. 8.2538.2017/4.6.
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