Análisis de desempeño de una herramienta de simulación de un radar sobre horizonte por onda de cielo

Zenon Saavedra; Adrian Llanes; Gonzalo Alderete Hero; Julian Di Venanzio; Ana Geogina Elias

Performance Analysis of a Sky-Wave Over-the

Horizon Radar Simulation Tools

Análisis de desempeño de una herramienta de simulación de un radar sobre horizonte

por onda de cielo

Zenon Saavedra

#*1

, Adrián Llanes

, Gonzalo Alderete Hero

, Julian di Venanzio

,

Ana G. Elias

Laboratorio de Telecomunicaciones, Facultad de Ciencias Exactas y Tecnología

Universidad Nacional de Tucumán

Av. Independencia 1800, San Miguel de Tucumán, Argentina

zsaavedra@herrera.unt.edu.ar

allanes@herrera.unt.edu.ar



Dirección Nacional de Investigación y Desarrollo, Fuerza Aérea Argentina

Buenos Aires, Argentina

Consejo Nacional de Investigaciones Científicas y Técnicas

Crisostomo Alvares 722, San Miguel de Tucumán, Argentina

aelias@herrera.unt.edu.ar

Abstract— This paper presents the main features of a

skywave over-the-horizon radar simulation software and

results on its ability to represent and detect different search

scenarios. Through a series of simulations of the primary

phenomena involved in the search process, the software

can estimate the behaviour of a radar system in different

scenarios. This capability allows the simulator to assist in

selecting the most suitable radar configuration to achieve

an acceptable level of successful detection probability for

a given set of scenarios. It also facilitates various studies

and analyses of different factors present in the behaviour

of these types of radars.

Keywords: OTH Radar; Radar Simulator; Radar System;

Signal Processing Radar.

Resumen— Este trabajo presenta las principales

características de un software de simulación de un sistema de

radar sobre horizonte por onda de cielo y los resultados

obtenidos de su capacidad para representar y lograr detección

en diferentes escenarios de búsqueda. Mediante una serie de

simulaciones de los principales fenómenos involucrados en

proceso de búsqueda, el software puede estimar el

comportamiento de un sistema de radar en diversos escenarios.

Esta capacidad permite al simulador ayudar a seleccionar la

configuración de radar más adecuada para alcanzar un nivel

aceptable de probabilidad de detección exitosa para un

conjunto determinado de escenarios, y su vez también facilita

diversos estudios y análisis de diferentes factores presentes en

el comportamiento de este tipo de radares.

Palabras clave: Radar OTH; Simulador de Radar; Sistemas de

Radar; Procesamiento de Señales de Radar.

I. INTRODUCTION

Skywave Over-The-Horizon (OTH) radars are

specialized radar systems capable of detecting targets

beyond the line of sight by leveraging the Earth's ionosphere

as a reflector for the radar's emitted electromagnetic waves

[1], as is schematically shown in Fig. 1.

The complexity and ionosphere usage of these radars

imply a high manufacturing cost and a large number of

components, making their preliminary study and design

crucial steps before development and deployment.

Computer-aided simulations serve as an effective

methodology for this purpose, enabling designers to define

specific radar system configurations and evaluate their

performance against various proposed search scenarios.

This process would ultimately determine the viability of the

chosen configuration.

Fig. 1. OTH-SW Radar operates by reflecting its bean from the ionosphere.

Several studies have presented partial models of an OTH

simulator, including those by Feng et al. (2022) [2], Sun et

al. (2022) [3], Cervera et al. (2018) [4] and Zhu et al. (2014)

[5]. These works focus on different aspects of the OTH

radar system, such as target tracking, wave propagation,

Revista elektron, Vol. 8, No. 2, pp. 82-93 (2024)

ISSN 2525-0159

Recibido: 13/08/24; Aceptado: 17/09/24

https://doi.org/10.37537/rev.elektron.8.2.193.2024

Original Article

interaction with the environment and target, and sea state

characterization. However, they leave out other vital aspects

for system evaluation, such as signal generation, digital

processing, coordinate conversion, and antenna arrays.

In this paper, we propose a comprehensive simulation

software that encompasses all these phenomena, providing a

more holistic representation for a thorough evaluation and

analysis of system performance. Our tool encapsulates the

entire search process chain, from the emission of the

electromagnetic wave to the visualization of the detections.

The software is intended to be included in a process to

iteratively adjust the configuration setup, evaluating the

alignment of detections with the proposed scenario (see Fig.

2). This leads to more accurate and complete assessment of

the system's viability.

This approach gives control to the user to choose which

set of parameters to keep constant and which to change. For

example, the user can choose to keep the constructive

parameters of the radar unchanged and optimize exploration

setup for different scenarios. As another example, the user

can choose specific scenarios to detect, and optimize for

radar and exploration parameters. If output detections

poorly match the proposed ones over different exploration

setups, then radar configuration is considered inviable.

Otherwise, radar config is considered viable after having

acceptable detections over a large enough pool of proposed

scenarios.

Fig. 2. Evaluation process of a radar configuration against search scenario.

The rest of paper is organized as follows: in Section II we

are describing the theoretical models adopted for the

OTHR-SW Simulator. The results of simulations and their

analyses are presented in Section III. Conclusions are drawn

in Section IV, followed by an appendix which gives further

details of the simulator's configurable parameters.

II. METHODOLOGY

The OTH-SW simulator simulates the signal interaction

with the medium as it propagates from the transmitting

array to the searching area, the searching area composed of

targets and sea, as proposed by the user and the medium as

the reflected energy propagates from the searching area to

the receiving array.

After generating the received signal in digital domain, a

digital processing module performs the “operative” stage of

the radar. Here, a series of filters are applied that

progressively de-noise the signal for range, doppler

frequency and amplitude estimation. At the final stage,

these parameters are converted to geographical coordinates

and velocity, respectively. All the simulations process is

represented in a block diagram in Fig. 3

Fig. 3. General block diagram of the Skywave Over-the-Horizon (OTH-

SW) Radar Simulation software.

To achieve this, we propose the following

implementation scheme (also shown in Fig. 4):

• User Interface: is responsible for the interaction

between the user and the simulator tool. It allows the

user to input configuration parameters and visualize

the output results.

• Core Entry point: establishes the communication

channel between the front end and the core,

synchronizing and controlling the data flow between

blocks.

• Core: is the calculation engine of the tool that

simulates the signal propagation and the radar

operation to recover that signal (see Fig. 4).

Fig. 4. Implementation scheme of (OTH-SW) Radar Simulation software.

The major blocks in the Fig. 4 are describe below with

put focus in the Core implementation.

A. Input Stage (Frontend)

The first step of the process is to setup all input

configuration parameters exposed to the user. We classified

them into a two-tier hierarchy: the top-most level has three

groups:

• Radar Setup: constructive parameters of the radar.

• Proposed scenario Setup: A searching area location

and targets setup.

• Exploration setup: parameters for shaping the

exploration signal characteristics.

Each group has subgroups as shown in Fig. 5.

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Fig. 5. Possible configuration parameters of the Over-the-Horizon Radar

Simulator (OTHR-SW). The parameters are sorted into three groups: radar

setup, proposed scenario, and exploration setup.

B. Target Model

The user can set up the targets for the proposed scenario.

These are loaded from pre-generated files that contain target

the Radar Cross Section (RCS) data.

For this work, RCS data for the following targets has

been generated (shown in Fig. 6):

• Boeing 787 Aircraft

• F-117 Aircraft

• Panamax-like Vessel

• Fishing Vessel

Fig. 6. Types of targets selectable in the Over-the-Horizon Radar

Simulator (OTHR-SW).

1) Radar Cross Section: The radar cross section is the

ability of an object to reflect a certain percentage of the

electromagnetic waves that impact it. Various sources

define this factor as a measure of what "an electromagnetic

wave can observe on its propagation path through space".

The RCS of a given target depends on aspects such as the

physical structure of the target and its external

characteristics, the direction of ray incidence, the frequency

of the radar transmitter as well as the construction materials

of the illuminated object.

In the simulator, the RCS of each target was obtained

through an electromagnetic simulator software. The RCS

data is stored in matrices as a function of the incident angle,

carrier frequency, and wave polarization. Fig. 7 presents a

graphical representation of the RCS surfaces of the large

plane target.

Fig. 7. Diagram of the Radar Cross Section of a large plane type target, at

a frequency of 10 MHz, horizontal polarization.

C. Kinematic Model

This model allows evaluating and determining how the

position and velocity of the targets evolves over time (see

Fig. 8). The possible trajectories they can describe are

rectilinear or curvilinear

Fig. 8. Kinematic Model of the Targets. Input and output parameters.

An x, y, z coordinate system is used, where the origin

matches the location of the radar (See Fig, 9). The variables

correspond to latitude, longitude, and altitude, respectively.

Fig. 9. Representation of the chosen coordinate system, along with an

example of the straight and curved trajectories followed by the targets.

For straight trajectories, the determination of the next

state of movement in the x, y plane is based on the

equations of classical kinematics for uniform rectilinear

motion.

For curved trajectories, the determination of the next

state of movement in the x-y plane is based on the equations

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of the Archimedean spiral, which in turn is based on polar

coordinates.

Finally, the conversion from polar coordinates to

rectangular coordinates must be carried out to represent the

trajectory in the selected coordinate system. For

simplification purposes, the target moves describing the

curved trajectory with constant speed.

To determine the positions that the target acquires in its

"z" axis, which represents the altitude, we used the

multipath fading effect based on Earth curvature model [6].

D. Antenna Array Model

This model simulates the behaviour of antennas arrays, as

the interaction of many individual radiators distributed on a

surface that conform either the transmitter or the receiver.

The user can setup the following parameters for each of

the arrays: number of elements, geometry type (rectangular,

circular, and star), physical separation between elements,

radiation pattern of elements (quarter-wave dipole or

isotropic radiator) and working frequency.

The array model is presented in Fig. 10.

Fig. 10. Transmitter and Receiver antenna array model.

After both the user input and the aiming direction have

been defined, the model is able to steer the main lobe of the

transmitting array through beamforming techniques. The

desired aiming direction is obtained from the Ray

Parameters model.

On the other hand, the receiving array simulates the

spatial phase shift of the signal received by each element as

it propagates through the array. This phase shift information

is later used by the Signal Generation model and the

Processing Digital Signal model for estimating angle of

arrival. Fig. 11 presents three examples of steered

transmission arrays.

Fig. 11. Transmission arrays with 150 elements with rectangular (a),

circular (b), and star distributions (c). Arrays oriented in elevation and

azimuth: φ = 60 °, θ = 20 °, with a design frequency of 5 MHz.

E. Ray Parameters Model

This model determines the characteristics that an

electromagnetic wave must have to achieve propagation in

the Earth's ionosphere, between an initial point (radar

position) and final point (target position) located on the

surface of the Earth or sea. The characteristics of the wave

are the frequency, aiming direction, delay, ranges, and

propagation attenuation.

The model is composed of two submodels: an analytical

ray tracer and an ionosphere modeler, both presented in Fig.

12.

Fig. 12. Ray Parameters Model. Input and output parameters, submodels

of Earth's Ionosphere and Ray Tracer.

1) Ionosphere Model: The ionosphere model is based

on the International Reference Ionosphere model IRI-2012

[7]. The IRI model is the result of the efforts of the

scientific community who have worked over the last 60

years to improve and update a standard model of the Earth's

ionosphere. This is a complex empirical model that

determines different values of the ionosphere state. The

most relevant for this study are electron density, critical

frequency and peak height of the layers, semithickness and

composition. These parameters are function of geographic

coordinates, date and time; which in turn define the solar

activity level on which the ionosphere strongly depends.

2) Ray Tracing Model: The ray tracer allows, based on

the frequency and direction of an electromagnetic wave, to

determine its propagation path within the medium formed

by the ionosphere and the lower layers of the troposphere,

stratosphere, and mesosphere. An example of the

propagation path of a wave determined by the tracer is

presented in Fig. 13. The model is based on a system of

equations that analytically determine parameters such as:

group and phase delay, terrestrial and oblique range reached

by the wave [8].

Fig. 13. Example of the path followed by an electromagnetic wave

between two points on the Earth's surface. The wave has a carrier

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frequency of 10 MHz and this is oriented in elevation and azimuth: θ = 5°,

φ = 98 °, on the other hand we considered an ionosphere in calm with a

date: 15-06-2010.

F. Received Signal Characterization Model

The characterization model determines parameters of the

signal received by the receiving system after the

electromagnetic wave has interacted with the medium and

the proposed scenario. This is important to later generate

signals based on the parameters obtained in this stage.

The received signal is modelled according to the

following equation.

= Echo + Noise + Clutter , (1)

Where 𝑆

𝑅

is the received signal, Echo is the signal

reflected by the targets of interest, Noise is an unwanted

random signal coming from the surroundings of the antenna

arrays and Clutter corresponds to the undesired reflection of

electromagnetic energy in the surroundings of the targets.

For this study, the sea is the Clutter source.

The parameters of interest for the received signal are

amplitude levels, frequency, and phase. The mathematical

models and equations used in the radio link model can be

found in [9],[10]. Figure 14 presents a block diagram with

the submodels that determine each of the parameters of 𝑆

𝑅

Fig. 14. Model of characterization of the received signal. Input and output

parameters, submodels for determining parameters of Noise, Clutter, and

Echo.

G. Signal Generation Model

This model is responsible for generating time series of 𝑛

samples corresponding to the signal received by an antenna

array of 𝑘 elements during a coherent integration interval of

𝑚 pulses. During this time, it is possible to constructively

combine reflected pulses without losing phase coherence.

These are treated as a three-dimensional matrix M (𝑛×𝑚×𝑘)

for subsequent processing. Figure 15 shows the block

diagram of the signal generator. The simulator is based on a

mono-static pulsed radar system, where transmission and

reception take place at different time intervals

In the model, there are three generators:

• Noise Generator: generates a time series of 𝑛 samples,

based on pulse repetition frequency (PRF) and

sampling frequency (𝑓𝑠). For the amplitude, we use

Log-Normal probability distribution function with the

average level coming from the Characterization

model. The generation of this series is repeated 𝑚

times, 𝑚 being the number of integrations.

• Echo Generator: generates a time series of 𝑛 samples

based on PRF, pulse width (T), bandwidth (AB), and

sampling frequency. A delay is added to represent the

time it takes for the wave to propagate the full round

trip (from transmitter to receiver). Additionally, the

Doppler Frequency associated with the target's state

of motion influences the carrier frequency present in

the series. For the amplitude, we use Swerling I-II-III-

IV probability distribution function with the average

level coming from the Characterization model. The

distributions I and II are useful when the target has

many small reflective surfaces and the interpulse

variations are independent or uncorrelated. On the

other hand, distributions III and IV are used when the

target has few main reflective surfaces and the

interpulse variations are slower and uncorrelated. The

generation of this series is repeated 𝑚 times, 𝑚 being

the number of integrations.

• Clutter Generator: generates a time series of 𝑛

samples based on PRF, pulse width, bandwidth, and

sampling frequency. For this study we only consider

the sea clutter, which is the result of electromagnetic

energy impacting the sea surface. This interaction is

represented with two spectral lines on each side of 0

Hz. For the amplitude, we use Rayleigh or K

probability distribution function with the average

level coming from the Characterization model. The

first makes it possible to model the sea clutter as the

result of several independent reflections (small

waves), in which state the sea is calm. A rough sea

state can be modelled by the distribution K where the

clutter is made up of large specular reflections and a

small white noise (representing the mixture between

large and small waves). The generation of this series

is repeated 𝑚 times, 𝑚 being the number of

integrations.

Fig. 15. Received Signal Generation Model. Input and output parameters.

On the other hand, after the Echo series is generated, it

enters a Spatial Phase Shifter which models the reception of

the signal by an antenna array of 𝑘 elements, where there is

a spatial phase shift between the signals received by each

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antenna element. The phase shift is based on the arrival

direction of the signal and the spatial distribution of the

receiving antenna array, which can be rectangular, star, and

circular.

Finally, the Combiner is responsible for combining the

time series of noise, clutter, and echo to obtain the M matrix

corresponding to the received signal.

H. Signal and Data Processing Module

This module is responsible for applying various methods

and digital data processing techniques to the M matrix of

received signal samples, with the aim of extracting range,

arrival direction, and Doppler frequency information of

potential targets present in the received signals. The block

diagram of the processing module is presented in Fig. 16.

Fig. 16. Digital signal and data processing module.

The tasks performed by each of the blocks are described

below:

1) Raised Root Cosine Filter: This filter helps reduce

the inter-symbol interference produced in the transmission

channel. This phenomenon occurs because the signal is

modulated with binary codes at the transmitting stage. The

filter is applied in the sample domain (along the n-axis of

the M matrix).

2) Clutter Filter: This is responsible for removing the

clutter part from the received signal. For this work, the

exploration area is always surrounded by the sea. In this

case, the energy received is mainly due to the reflections on

the sea, as it has greater cross section area than the targets

combined, if any [11].

For this purpose, we use the Empirical Mode

Decomposition (EMD) technique [12]. This method allows

decomposing the signal into its most significant components.

We can associate clutter signal to these main components

and then filter it out from the received signal. The filter is

applied in the sample domain (along the n-axis of the M

matrix).

3) Matched Filter: This simulator simulates a radar

operating under a compressed pulsed mode. This is a very

common technique in radar systems to significantly increase

SNR figure [13],[14]. It relies on (a) encoding the phase of

the transmitting signal with some code that optimizes its

detection when received, and (b) applying a correlation

mechanism on the received signal that detects the presence

of the encoded information.

This filter is used for the latter task. It implements the

correlation function between the received signal and a copy

of the transmitted signal, detecting the autocorrelation. The

purpose of this operation is to highlight the delay present

between the transmitted signal and the echo signal (signal of

interest) present in the received signal. This filter is applied

in the sample domain (along the n-axis of the M matrix).

After applying the filter to the M matrix, the axis (n)

domain is transformed from samples to range by

multiplying each sample by the vacuum speed of light value

and dividing by 2, This number is because the determined

time considers the round-trip path

4) Window and Doppler Filter: When processing the

signal to extract Doppler information (see Doppler Filter)

for velocity retrieval, the raw data is segmented into

rectangular windows. This introduces significant sidelobes

in the frequency domain. To mitigate this problem, the

Kaiser-Bessel window is applied before the Doppler

filtering. This windowing technique smooths the data and

discontinuities at its edges, effectively reducing the

sidelobes and resulting in cleaner spectrum for the Doppler

filter stage [15]. This filter is applied in the pulse domain

(along the m-axis of the M matrix).

On the other hand, the Doppler filter is designed to

estimate the relative velocities of detections. When a radar

wave bounces off a moving target, the returned signal's

frequency changes. The Doppler effect highlights this

frequency shift, which is proportional to the object's

velocity relative to the radar.

This filter is implemented using Fast Fourier Transform

in the pulse domain (along the m-axis of the M matrix). The

output is a spectrum where the Doppler frequency

components associated with the signal of interest (echo

signals) are observed [16].

Finally, we transform the pulse axis to Doppler

frequency axis. The resulting M matrix axis are range (m),

Doppler Frequency (n) and number of elements (k).

5) Range-Doppler Detector: The spectrogram obtained

from the Doppler Filter shows how much the received

signal is alike the transmitted one. This correlation

progressively decays around points of local maxima. An

adaptive detector is used to detect these points, which are

potentially due to the presence of a target.

This stage is implemented using a Cell Averaging

Constant False Alarm Rate (CA-CFAR) detector in two

dimensions with a modified refence window: over the range

(m) and Doppler Frequency (n) domains [17].

6) Angle of Arrival Estimator: Determines the arrival

direction/angle of the received signals with respect to the

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receiving antenna array. The applied method is called

Propagator Direct Data Acquisition (PDDA) [18]. This

method is applied in the sample and element domains (along

the n and k axes of the M matrix).

The method uses the positions detected (along the range

axis) by the Range-Doppler detector as input along with the

M matrix filtered by the matched filter. The information

from the previously detected positions is used to focus the

search on positions where there is already prior knowledge

of the possibility of the existence of a potential target echo.

After applying this method, the element axis (k) of the M

matrix transforms into the angle of arrival axis.

In this point the dimensions of the M matrix are n =

range, m = Doppler Frequency and k = arrival angle.

7) Angle of Arrival Detector: After applying the angle

of arrival estimator, angle spectrograms (theta and phi)

associated with the search area are obtained. The detector

allows identifying possible targets within the DIR area and

also obtaining phi (azimuth) and theta (elevation) angles

values from the spectrograms. The detector is of the

adaptive type, particularly the CA-CFAR in two dimensions.

This data processing technique is applied over the range and

arrival angle domains (along the n and k axes of the M

matrix).

Finally, after applying the entire processing chain, a set

of detections characterized by range, arrival direction, and

Doppler frequency values are obtained, which are suspected

to belong to the echoes of targets present in the search area.

I. Radar-to-Geographic Parameters Conversion Module

This module is responsible for transforming the values of

range, arrival angle, and Doppler frequency into

geographical position and radial speed of the detections (see

Fig. 17).

Fig. 17. Radar-to-Geographic Parameter conversion module. Input and

output parameters.

The Range Conversion module uses a set of equations to

convert the oblique range, which is the propagation path

followed by the electromagnetic wave in its full round trip,

into ground range, which is the projection of the oblique

range onto the earth's surface.

The Coordinate Conversion allows the transformation of

radar relative coordinates (ground range and direction) into

geographical coordinates (latitude and longitude).

On the other hand, radial speed is determined by

multiplying Doppler frequency by the vacuum speed of

light value and dividing by carrier frequency of the

transmitted signal.

J. Detection Output

The output detections are saved to both an interactive

map and a plain table (csv file). This tool specifically saves

the following files after each exploration:

• params.json: all the parameters setup by the user for

this run.

• datos_cinematica.csv: position and speed information

for every target set up in the proposed scenario.

• mapa_con_detecciones.html: interactive geographic

map for viewing proposed scenario and output

detections (see Fig. 18).

• resultados.csv: plain table of output detections.

Fig. 18. Visualization of the detections found, in the User Interface of the

simulator (OTHR-SW).

III. RESULTS

In this section, we choose a specific radar configuration

and evaluate it against two search scenarios:

• Scenario 1: A single target navigating a curved path,

with movements towards and away from the radar

and points where the radial velocity is null even while

in motion.

• Scenario 2: Features multiple targets each pursuing a

distinct linear trajectory, operating independently of

one another.

The radar system settings, antenna locations, and the

search area remain the same across scenarios. The antenna

systems have star geometry, comprises 150 elements, and

are located in Chubut, Argentina. The center of the DIR

exploration region is located about 1000 km to the east and

extends to approximately 1500 km. This represents roughly

half the range of these types of radars [1]. We varied the

targets quantity and motion and the exploration

configuration.

A. Scenario 1

In this case study, we focus on evaluating the OTHSW

simulation tool for positive, negative, and near zero radial

velocity values.

For this, we designed a scenario where a Cargo Ship,

being the only target, follows a curved path at constant

speed, as illustrated in Fig. 19. This target is scanned in this

simulation, 15 times at intervals of 16 minutes.

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Fig. 19. Representation of the radar system positions, search area, and the

target's trajectory.

Tables I, II, and III detail the parameters configured for:

proposed scenario, exploration, and radar system.

TABLE I

CONFIGURATION OF PROPOSED SCENARIO.

Proposed Scenario Setting

Search Area

Value

Radar Location

42.55 ° S 63.83 ° W

DIR Location

42.70 ° S 51.46 ° W

Target

Value

Type

Panama-like

Initial Course

20 º

Initial Speed

11,8 m/s

Path

Curl

Initial Location

42.04° S 51.49° W

Environment

Value

Ionosphere State

Calm

Sea State

Moderate (Wave height

1.25 to 2.5 m)

Zone Type

Rural

Date And Hour

2005-05-15T16.00

TABLE II

CONFIGURATION OF EXPLORATION.

Exploration Setting

Scans

Value

Period

16 min

Number of scans

Tx Signal

Value

Operation mode

Pulsed-Coded

Bandwidth

10 kHz

PRF

40 Hz

Power

40 dBW

Sample Freq.

30 kHz

Code Type

Barker 11

Digital Processing

Value

Range-Doppler Detector (Pfa)

7.0 10-3

Arrival Angle Detector (Pfa)

4.0 10-3

TABLE III

CONFIGURATION OF RADAR.

Radar System Setting

Antenna Arrays (Tx and Rx)

Value

Geometry

Star

Elements

150

Spacing

0.15 λ

Design Freq.

5.0 MHz

Base pattern

λ/4 dipole

Receiver

Value

Signal Gain

250 dB

SNR

40 dB

SCR

20 dB

Inter. Freq.

0.0 Hz

Bandwidth

30 MHz

After setting all parameters, we proceeded with the

simulation. Table IV shows the target's temporal evolution,

produced by the Kinematics module. These are the values

the tool should identify at the simulation's end. The

estimated and proposed values for (i) geographic position

and (ii) radial velocity are shown in Figures 20 and 21,

respectively.

Fig. 20. Detected (in black) and proposed (in red) target positions over the

15 scans.

Fig. 21. Detected (in blue) and proposed (in orange) target radial velocities

over the 15 scans.

It is important to emphasize that the configuration of the

CFAR detector will significantly influence the number of

positive detections recorded, due to its relationship with the

false alarm probability. Here we proposed a single target, so

we attribute all recorded detections to it. Finally, when

calculating the errors, we use the worst of the estimated

values for each exploration. The detailed results of this

approach can be observed in Table V, where the errors

found in the detections are shown.

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TABLE IV

TEMPORAL EVOLUTION OF THE POSITION AND RADIAL VELOCITY OF THE

PROPOSED TARGET OVER THE 15 SCANS.

Proposed Target’s Motion

Scan Nº

Geographical Location

(Lat, Lon)

Radial

Velocity

42.04° S, 51.49° W

11.8 m/s

41.94° S, 51.41° W

19.8 m/s

41.89° S, 51.27° W

31.3 m/s

41.87° S, 51.10° W

36.2 m/s

41.92° S, 50.92° W

34.8 m/s

42.02° S, 50.75° W

29.2 m/s

42.17° S, 50.62° W

20.9 m/s

42.36° S, 50.55° W

11.3 m/s

42.59° S, 50.56° W

1.4 m/s

42.82° S, 50.67° W

-8.2 m/s

43.04° S, 50.88° W

-16.9 m/s

43.22° S, 51.19° W

-24.3 m/s

43.35° S, 51.58° W

-30.0 m/s

43.40° S, 52.04° W

-33.8 m/s

43.36° S, 52.53° W

-35.2 m/s

TABLE V

MAXIMUM ABSOLUTE AND RELATIVE ERRORS OF POSITION AND RADIAL

VELOCITY. THE ERRORS ARE CALCULATED BETWEEN THE ESTIMATED

VALUES FROM THE DETECTIONS AND THE PROPOSED TARGET VALUES.

Max. Estimated Error

Scan Nº

Absolute error

Geographical Location

Relative error

Radial Velocity

39.77 km

0.17

40.91 km

0.10

30.44 km

0.13

No detections

28.04 km

0.12

33.01 km

0.13

6.30 km

0.12

No detections

36.98 km

0.41

50.45 km

0.18

39.31 km

0.16

61.85 km

No detections

18.73 km

0.12

55.77 km

0.13

44.45 km

0.15

In summary, in this case study, the OTH-SW simulation

tool was able to track the target adequately along its

trajectory, identifying positive, negative, and near-zero

radial velocity values.

B. Scenario 2

In this case study, we explore the interactions of three

independent targets, each following a straight trajectory. We

focus on the evaluation of simultaneous detections of all

targets, for positive, negative and near zero radial velocities.

The proposed scenario includes two fishing vessels and a

commercial airplane moving on independent trajectories

and being explored 10 times at intervals of 13 minutes. The

design is illustrated in Fig. 22.

Fig. 22. Representation of the radar system positions, search area, and the

trajectory of three targets.

Tables VI, VII, and VIII detail the parameters configured

for: proposed scenario, exploration, and radar system.

TABLE VI

CONFIGURATION OF THE PROPOSED SCENARIO.

Proposed Scenario Setting

Search Area

Value

Radar Location

42.55 ° S 63.83 ° W

DIR Location

42.70 ° S 51.46 ° W

Target 1

Value

Type

Commercial Aircraft

Initial Course

90 º

Initial Speed

200 m/s

Path

Stright

Initial Location

41.70° S 52.43° W

Target 2

Value

Type

Fishing Vessel

Initial Course

180 º

Initial Speed

20 m/s

Path

Stright

Initial Location

43.32° S 52.58° W

Target 3

Value

Type

Fishing Vessel

Initial Course

270 º

Initial Speed

40 m/s

Path

Stright

Initial Location

42.68° S 53.09° W

Environment

Value

Ionosphere State

Calm

Sea State

Moderate (Wave height

1.25 to 2.5 m)

Zone Type

Rural

Date And Hour

2005-05-15 16.00

TABLE VII

CONFIGURATION OF EXPLORATION.

Exploration Setting

Scans

Value

Period

13 min

Number of scans

Tx Signal

Value

Operation mode

Pulsed-Coded

Bandwidth

10 kHz

PRF

40 Hz

Power

40 dBW

Sample Freq.

30 kHz

Revista elektron, Vol. 8, No. 2, pp. 82-93 (2024)

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Code Type

Barker 13

Digital Processing

Value

Range-Doppler Detector (Pfa)

1.0 10-3

Arrival Angle Detector (Pfa)

4.0 10-3

TABLE VIII

CONFIGURATION OF RADAR.

Radar System Setting

Antenna Arrays (Tx and Rx)

Value

Geometry

Star

Elements

150

Spacing

0.15 λ

Design Freq.

5.0 MHz

Base pattern

λ/4 dipole

Receiver

Value

Signal Gain

250 dB

SNR

40 dB

SCR

20 dB

Inter. Freq.

0.0 Hz

Bandwidth

30 MHz

After the initialization of the parameters, we executed the

simulation. Tables XI-A, X-A and XI-A show the temporal

evolution of each target, determined by the Kinematics

module. These are the values that the tool should recognize

at the end of the simulation. Fig. 23 showcase estimated vs.

proposed values of geographic position.

Fig. 23. Detected (in black) and proposed (in red) target positions over the

10 scans.

To address the problem of mapping each detection to

each target, we used radial velocity as the main grouping

criterion, a strategy illustrated in Fig. 24. Then, in Fig. 25,

we compare the proposed radial velocities with those

derived from the detections.

Fig. 24. Proposed (in red) and detected (in blue, green and yellow)

positions of three targets over the 10 scans.

Fig. 25. Detected (in blue) and proposed (in orange) radial velocities of

three targets over the 10 scans.

Similar to Scenario 1, we took the largest difference

found in each exploration to determine the errors in latitude,

longitude, and velocity. The most significant errors are

detailed in Tables IX-B, X-B, and XI-B.

In summary, this case study demonstrated that the OTH-

SW simulation tool can successfully identifies and follows

each target along its respective trajectory, accurately

discerning the variations in radial velocities and geographic

locations, considering the maximum errors. Thus, this

scenario corroborates the tool's ability to handle complex

scenarios with multiple targets moving on independent

straight trajectories.

TABLE IX

(A) TEMPORAL EVOLUTION FOR TARGET 1 (COMMERCIAL AIRPLANE) FROM KINEMATICS MODULE. (B) ABSOLUTE AND RELATIVE MAXIMUM ERROR FOR

EACH SCAN.

Target 1

Proposed Target’s Motion

Max. Estimated Error

Scan Nº

Geographical

Location (Lat, Lon)

Radial

Velocity

Absolute error

Geographical Location

Relative error

Radial Velocity

41.70 ° S, 52.43 ° W

182.88 m/s

53.98 km

0.106

41.70 ° S, 51.35 ° W

185.69 m/s

34.50 km

0.087

41.70 ° S, 50.28 ° W

187.74 m/s

37.54 km

0.071

Revista elektron, Vol. 8, No. 2, pp. 82-93 (2024)

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41.70 ° S, 49.20 ° W

189.50 m/s

37.48 km

0.060

41.70 ° S, 48.12 ° W

190.89 m/s

92.64 km

0.049

41.70 ° S, 47.04 ° W

191.96 m/s

No detections

41.70 ° S, 45.96 ° W

192.93 m/s

No detections

41.70 ° S, 44.89 ° W

193.58 m/s

No detections

41.70 ° S, 43.81 ° W

194.17 m/s

No detections

41.70 ° S, 42.73 ° W

194.62 m/s

No detections

TABLE X

(A) TEMPORAL EVOLUTION FOR TARGET 2 (FISHING VESSEL) FROM KINEMATICS MODULE. (B) ABSOLUTE AND RELATIVE MAXIMUM ERROR FOR EACH

SCAN.

Target 2

Proposed Target’s Motion

Max. Estimated Error

Scan Nº

Geographical

Location (Lat, Lon)

Radial

Velocity

Absolute error

Geographical Location

Relative error

Radial Velocity

43.32 ° S, 52.58 ° W

2.79 m/s

132.26 km

0.445

43.43 ° S, 52.58 ° W

3.02 m/s

49.36 km

0.327

43.53 ° S, 52.58 ° W

3.24 m/s

No detections

43.64 ° S, 52.58 ° W

3.46 m/s

28.10 km

0.164

43.74 ° S, 52.58 ° W

3.67 m/s

48.97 km

0.111

43.84 ° S, 52.58 ° W

3.88 m/s

49.38 km

0.045

43.95 ° S, 52.58 ° W

4.10 m/s

127.27 km

0.019

44.05 ° S, 52.58 ° W

4.31 m/s

No detections

44.15 ° S, 52.58 ° W

4.53 m/s

No detections

44.26 ° S, 52.58 ° W

4.74 m/s

No detections

TABLE XI

(A) TEMPORAL EVOLUTION FOR TARGET 3 (FISHING VESSEL) FROM KINEMATICS MODULE. (B) ABSOLUTE AND RELATIVE MAXIMUM ERROR FOR EACH

SCAN.

Target 3

Proposed Target’s Motion

Max. Estimated Error

Scan Nº

Geographical

Location (Lat, Lon)

Radial

Velocity

Absolute error

Geographical Location

Relative error

Radial Velocity

-42.69 ° S, 50.51 ° W

-36.40 m/s

No detections

-42.69 ° S, 50.80 ° W

-36.23 m/s

46.58 km

0.076

-42.69 ° S, 51.08 ° W

-36.07 m/s

32.71 km

0.082

-42.69 ° S, 51.37 ° W

-35.89 m/s

31.44 km

0.094

-42.69 ° S, 51.66 ° W

-35.78 m/s

25.67 km

0.104

-42.69 ° S, 51.95 ° W

-35.50 m/s

39.59 km

0.129

-42.69 ° S, 52.23 ° W

-35.37 m/s

26.48 km

0.131

-42.69 ° S, 52.52 ° W

-35.07 m/s

102.74 km

0.094

-42.69 ° S, 52.81 ° W

-34.82 m/s

No detections

-42.69 ° S, 53.10 ° W

-34.59 m/s

29.57 km

0.129

IV. DISCUSSION AND CONCLUSION

Throughout this research, we have developed a

simulation tool tailored for the preliminary design and

assessment of OTH-SW radar systems. This tool excels by

consolidating, within a single platform, a range of

functionalities that were previously fragmented across

existing literature. It not only embodies capabilities

previously explored but takes a step further, modelling

additional phenomena and interactions that allow a broader

and more accurate evaluation of various radar

configurations.

The scenarios outlined in the results section showcase the

simulator's ability to reproduce real world conditions with

acceptable fidelity, and detect positive, negative and near-

zero radial velocities; even when multiple targets are

present. This translates into a powerful instrument for the

preliminary validation of radar configurations, a crucial step

towards the construction of viable radar systems. With

minimal adaptations, the PDS module then can be used an

operative radar.

Looking forward, we identify several promising routes to

further expand our tool's capabilities. Two upcoming

features we are considering are:

• Machine learning techniques for automatic

determination of configuration parameters. This

should significantly ease the number of iterations

needed to arrive at local optimal results.

• Target segmentation and tracking, to identify any

number of simultaneous targets present in an

exploration region. This should significantly reduce

redundant detections and should also allow the

prediction of subsequent positions.

In conclusion, we have presented an innovative resource

that facilitates not only theoretical evaluation but also

practical implementations in the field of OTHSW radars,

fostering a pathway for faster and more accurate

developments.

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