=Paper=
{{Paper
|id=Vol-3006/31_regular_paper
|storemode=property
|title=Investigation of principles of simulation of space-time processing of wideband signals
|pdfUrl=https://ceur-ws.org/Vol-3006/31_regular_paper.pdf
|volume=Vol-3006
|authors=Vasiliy N. Vasyukov,Daria N. Zima,Igor F. Lozovskiy,Yury V. Morozov,Aleksey A. Murasev,Ivan A. Pichkov,Mikhail A. Rajfeld,Daria O. Sokolova,Aleksandr A. Spektor
}}
==Investigation of principles of simulation of space-time processing of wideband signals==
https://ceur-ws.org/Vol-3006/31_regular_paper.pdf
Investigation of principles of simulation of space-time
processing of wideband signals
Vasiliy N. Vasyukov1 , Daria N. Zima1 , Igor F. Lozovskiy2 , Yury V. Morozov1 ,
Aleksey A. Murasev1 , Ivan A. Pichkov1 , Mikhail A. Rajfeld1 , Daria O. Sokolova1 and
Aleksandr A. Spektor1
1
Novosibirsk State Technical University, Novosibirsk, Russia
2
JSC “Scientific Research Institute of Measuring Instruments – Novosibirsky Plant Named After Komintern”, Novosibirsk,
Russia
Abstract
The paper states the principles of simulation of wideband signals applied in a surveillance radar. The
resource of the radar model is analyzed with respect to sample rate of processed signals and required
memory size as generated signals, noises, active and passive interferences demand a lot of memory.
It is proposed to simulate only active intervals of operation of a pulse radar at zero frequency in the
frequency domain.
Keywords
Radiolocation, simulation, interference, sample rate, wideband signal, space-time processing.
1. Introduction
A mathematical model of a surveillance radar system (SRS) with digital phased-array antenna
(DPAA) where wideband signals are applied should be built with respect to features of solved
problems and capabilities of modern computers. There are a lot of research works on radar
simulation in Russia and abroad. General principles of radar simulation based on the radar
equation are stated in [1, 2].
A generalized structure of a program for radar simulation is stated in [3]. The authors of [3]
say that their model exactly reflect physical processes in a medium where targets fly with
respect to all possible types of noises and interferences and correctly describe algorithms of
processing signals reflected from targets. The model operates with sampled signals, noises and
interferences that are not averaged as in previous models. The simulation program divided into
modules gives possibility to analyze different variants of algorithms of radar signal processing
in presence of various noises and interferences. Besides, it is possible to process radar signal
both at carrier frequency and at zero frequency in real time or in the post-processing mode
depending on computer characteristics.
The model is aided on investigation of future radars. The high experience of SRS simulation
is mentioned. It is noted that earlier models were oriented on definite types of SRS not on future
types.
SDM-2021: All-Russian conference, August 24–27, 2021, Novosibirsk, Russia
" yu.morozov@corp.nstu.ru (Y. V. Morozov)
© 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073 CEUR Workshop Proceedings (CEUR-WS.org)
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Vasiliy N. Vasyukov et al. CEUR Workshop Proceedings 260–271
The capabilities of SRS simulation based on numerical models are analyzed in [4]. This paper
dedicated to SRS of terahertz range contains useful general simulation principles. The numerical
model proposed in [4] includes parameters input, antenna simulation, scatters characteristics
calculation, effective scattering surface (ESS) calculation, signal analysis and results output.
The input parameters are divided into the groups: radar parameters, target parameters,
atmosphere parameters, The radar parameters include wavelength, pulse width, pulse frequency,
antenna diagram, effective antenna surface, pulse power. The target parameters include only
distance, velocity vector and azimuth. Hence, this program can operate only with surface targets.
The final result of simulation is the signal-to-noise ratio (SNR) providing target detection with
a given probability for a fixed false-alarm probability. The disadvantage of this model is the
necessity to use enormous Maxwell differential equations.
The mathematical model of a radar system directed on target classification is considered
in [5]. The model is able to calculate the maximal distance and SNR by means of the radar
equation. The Bayes approach is used for the target classification.
To reduce the required computer memory volume and calculation time it is proposed to
simulate a target and a medium with FPGA [6]. The advantages and disadvantages of target
simulators produced by the key manufacturers of radio instrumentation including Keysight,
Anritsu, National Instruments are analyzed. The main disadvantage of these simulators is a
very high price. Cheaper simulators functional capabilities are limited by a small number of
simulated targets or disability to control of some parameters.
The simulation program described in [7] is similar to the model in [3] but it can operate only
with narrowband signals with 10 MHz bandwidth.
The baseband radar model for radiolocation and telecommunications is proposed in [8]. The
simulation is implemented in time domain but it is not suitable for radars with wideband signals.
The baseband radar simulation is also considered in [9] for narrowband signals. The main
attention is focused on the mathematical description of interferences, signals transformation
from high-frequency to baseband quadrature components.
Successes and problems of a wideband radar system are analyzed in [10]. The general formulas
of a baseband signal reflected from a target are considered. The advantages of wideband radar
stations are shown for target detection, coordinates measurement and classification.
The theoretical bases of radar signals spectrums transformation in a medium with a target
are considered [11]. The simulation is limited on by DPAA size 16×16 elements.
The linear frequency modulation (LFM) signal with Additive White Gauss Noise (AWGN)
reflected from a multi-scatter target is discussed in [12]. There is a high demand on memory
size.
The radar simulation system proposed in [13] consists of three main components including
a computer with a user interface generating a simulation scenario, modules with built-in
processors for calculation of signals in a medium and FPGA for baseband signals generation.
The radar model for a student tutorial on radar bases is presented in [14]. The model has
limited capabilities. The signal bandwidth is no more than 2 MHz. Hence the model cannot
operate with wideband signals with the bandwidth 100 MHz and more. The model can operate
only with single-point targets. There are a few interferences like mountains and no active
interferences. The radar system model presented in [15] was developed in Simulink by a student
from the engineering faculty of the Moratuva University, Sri-Lanka. The model generates only
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a radio impulse with pulse amplitude modulation (PAM). It simulates AWGN and delay from
target. The simplest radar system model is stated in [16]. It is a calculator of delay time from
distance in miles. It is evident that the models [14, 15, 16] are unsuitable for the scientific
research.
All the considered models of radar stations with DPAA solve main tasks that appear when
methods and aids of radar signal processing are developed. A few models are directed on
simulation of wideband signals scattered by a multi-scatter target. Usually very expensive
models requiring multi-processor systems are proposed. Therefore, a complete radar station
model which is able to operate with wideband signals and interferences and provide demanded
features is out of free open access. The model proposed in the present paper is directed on
development and investigation of a radar station based on operating with wideband signals and
interferences.
2. Principles of simulation of a radar station with DPAA
Radar is featured by using high-frequency signals. Such signals can be sampled with very
high sample rate demanding high speed and big Random-Access Memory (RAM) volume of
a computer. To provide operation of a SRS mathematical model with DPAA at a common
computer with medium speed and not big volume of RAM, it is necessary to execute simulation
at baseband (zero frequency).
A pulse radar station is featured by long time intervals between pulses. The simulation of
processes in pauses between pulses can lead to long calculation time with almost no useful
information. It is advisable to simulate only those intervals of signals and interferences that
correspond to a pulse position. To except edge effects, the duration of a simulated interval
should be increased by additional intervals before a pulse and after it.
When an interval with no signal is deleted from a radar model it is impossible to control false-
alarm probability. If false-alarm probability is about 10−7 , it is difficult to estimate experimentally
a detection threshold. Hence, it is possible to control of the detection threshold with respect to
the theoretical calculation results [17, 18].
A radar mathematical model should take into account any number of active interference
sources placed at different space points. Interferences are simulated as noises with a spectrum
wider than a signal spectrum. It is proposed to simulate passive interferences as reflectors
clouds near a target or reflectors distributed at the ground surface.
A mathematical model of a passive interference can be described by a Gauss process with
a bandwidth depending on a useful signal spectrum. The model should simulate correlations
between signal periods for providing the capability of their attenuation and adaptation to
wind speed. Passive interference is suppressed by the first-order and second-order over-period
subtraction.
The mathematical model should help to analyze the radar operation when a target is detected
from a pulse train.
The proposed model simulated an SRS with a wideband pulse signal. If the bandwidth is
100 MHz, than the distance resolution is 1.5 m. Then a target size is more than the resolution,
and a target surface has many scattering points. Each scattering point has its cross-section,
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phase drops depending on a scattering point type. Target orientation can change its scattering
features.
The detector in the proposed model has an operating window for statistical data accumulation.
The window size is matched with a target size. If a target type is changed the window size is
adapted. If resolution is tested three windows are formed. Two of them correspond to known
targets coordinates while the third one is placed to the midpoint. If the targets are resolved they
are not detected in the middle window else they are detected in all three windows.
It is important to introduce geometry into the model for taking into account the features of
the radar and its antenna and a target with controllable coordinates and orientation. An active
interference source should have the controllable parameters including their coordinates and
power spectral density (PSD).
The main attention is focused on signal transformation when it is transmitted from an antenna
to a target, then received by the antenna with following digital processing. The sounding signal
is generated with respect to an antenna diagram.
The features caused by spectrum expansion up to 100 MHz almost do not influence on the
electromagnetic field forming in the far-field region. Thus, common methods are used for
calculating power flux of an incident way with respect to the transmitted power and distance
between the radar and the target and the angle between the antenna diagram and the normal to
the array antenna surface.
A target forming a reflected signal is described as a linear stationary filter with the gain
depending on a target type, the number and positions of scattering points and its orientation
relative to a radar station.
The received signal is found at one of DPAA elements. Then it is transferred to other DPAA
elements with respect to delays. This operation is implemented in the frequency domain to
avoid complicated interpolation calculations in the time domain. The transfer of the received
signal to all antenna elements leads to appearance of the signal as a function of time and space
coordinates defined by positions of antenna elements.
The received signal is processed by an adaptive space-time filter to reduce active interferences.
If an array is flat, a space-time signal is a function of three variables including time and to
space coordinates. The received signal at all elements is described by the 3D rectangular area
sampled with certain signal values in nodes. The 3D FFT gives a 3D spectrum depending on
two space frequencies and time frequency. The SNR is maximized by using a matched filter
with the gain found from 3D spectrum of a signal and interferences. The interference spectrum
is used for adaptation when radar transmitter is switched off for accumulating a training signal
The signal at the space-time filter output is formed in the frequency domain. Then this
signal is transformed by the Inverse Fast Fourier Transform (IFFT) to the space-time signal with
attenuated active interferences and thermal noise. Then a 1D time-domain signal is extracted
from the 3D space-time signal at fixed values of space coordinates that correspond to the
maximal SNR. The 1D time-domain signal is used by a detector and an instrument for measuring
the arrival time of the reflected signal.
The arrival time estimation for measuring distance until a target is specific because of the
wideband signal high resolution. If a target has main scattering points then it is impossible to
measure a received signal with respect to the peak position. The truth target position is the
average point between the nearest to the radar and the furthest from the radar scatters. The
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measured and truth values give possibility to find measurement errors.
When a passive interference occurs, the signal after suppression of an active interference is
processed to suppress the passive interference by an adaptive over-period subtractor of the first
or second order.
The proposed model of the radar system with DPAA is based on the following principles:
all signals are simulated by complex envelopes; only active intervals of sounding signal pulses
are simulated and long pauses between sounding pulses are not simulated; all operations on
signals are performed in the frequency domain; space processing cannot be separated from time
processing.
3. User interface of the proposed model
The proposed model is implemented as a program with the control panel for setting the ini-
tial configuration parameters including model structure, sounding signal parameters, radar
characteristics, target characteristics, noise and interference parameters. Targets and active
interferences sources are described by electronic tables with their initial coordinates, velocity
projections and etc.
The control panel consists of the list of controls groups, lists for selection of files with
descriptions of targets and active interferences, buttons for control of model run and stop and
loading initial configuration parameters (Figure 1).
Figure 1: Control panel for radar station simulation.
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4. Coordinates transformation for the radar station with DPAA
model
When an SRS is simulated it is necessary to take into account geometrical aspects because of
many flying objects in the space around the radar. The radar mathematical model requires local
coordinates systems for all objects and the global stationary coordinates system.
The radar station model geometry is based on the Global Coordinates System (GCS) where
all objects of the model are described. Figure 2 contains the Cartesian GCS. The plane 𝑥0𝑦
coincides with the ground surface. The radar station is placed at the origin. The vector 0𝑇 is
directed to the target that has the azimuth 𝛼𝑇 , the elevation 𝛽𝑇 and the angles of deviation of
the survey line from coordinate axes 𝜃𝑥 , 𝜃𝑦 , 𝜃𝑧 .
The unit vector directed on a target is defined by the direction cosines:
r ⊥ ⊥ ⊥
𝑒𝑇 = 𝑖 · cos 𝜃𝑥 + 𝑗 · cos 𝜃𝑦 + 𝑘 · cos 𝜃𝑧 , (1)
⊥ ⊥ ⊥
where 𝑖 , 𝑗 , 𝑘 are the orts of the coordinates axes 𝑥, 𝑦, 𝑧.
The target position is described the Cartesian coordinates 𝑥𝑇 , 𝑦𝑇 , 𝑧𝑇 and its motion is
described by the velocity vector projections 𝑣𝑇 , 𝑣𝑇 , 𝑣𝑇 . The target azimuth and elevation are
found from the simple expressions:
𝑥𝑇 𝑧𝑇
tg 𝛼𝑇 = , sin 𝛽𝑇 = , (2)
𝑦𝑇 𝑅𝑇
√︁
where 𝑅𝑇 = 𝑥2𝑇 + 𝑦𝑇2 + 𝑧𝑇2 is the target distance.
The antenna array orientation is shown in Figure 3. The flat antenna has its own coordinates
system formed by the axes 𝑥′ , 𝑦 ′ , 𝑧 ′ . Antenna elements are placed on the plane 𝑦 ′ 0𝑧 ′ . The axis
𝑥′ coincides with the normal to the antenna plane with the azimuth 𝛼𝑎 and the elevation 𝛽𝑎 .
The target azimuth 𝛼𝑇′ and elevation 𝛽𝑇′ in the Antenna Array Coordinates System (AACS) is
𝛼𝑇′ = 𝛼𝑇 − 𝛼𝑎 , 𝛽𝑇′ = 𝛽𝑇 − 𝛽𝑎 . (3)
Figure 2: Global coordinates system.
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Figure 3: Model global coordinates system.
The values 𝛼𝑇′ and 𝛽𝑇′ are used further for calculation of delays on different elements of an
antenna array. The delays are necessary for simulation of space-time signal processing.
5. Target signal simulation with respect to the Doppler effect
The real radar operation includes some natural processes that require special algorithms of
simulation. For example, such process takes place when a received signal is influenced by the
Doppler effect. The model gives possibility to set the target motion parameters that help to
calculate the radial velocity 𝑉𝑟 . The Doppler frequency is calculated as
2𝑉𝑟 4𝜋𝑉𝑟
𝜔𝐷 = 𝜔0 · = . (4)
𝑐 𝜆
The radial velocity is found from the current target coordinates 𝑥, 𝑦, 𝑧 and the velocity projec-
tions 𝑉𝑥 , 𝑉𝑦 , 𝑉𝑧 in the GCS:
𝑥 · 𝑉𝑥 + 𝑦 · 𝑉𝑦 + 𝑧 · 𝑉𝑧
𝑉𝑝 = √︀ . (5)
𝑥2 + 𝑦 2 + 𝑧 2
Here is the wideband radio pulse train at the input of one of the antenna elements.
𝑠𝑖 (𝑡 − (𝑖 − 1)𝑇𝑛 ) = 𝑆(𝑡 − (𝑖 − 1)𝑇𝑟 )·
(6)
· cos [𝜔0 (𝑡 − (𝑖 − 1)𝑇𝑟 ) + 𝜔𝐷 𝑡 + 𝜓(𝑡 − (𝑖 − 1)𝑇𝑟 ) + 𝜑𝑖 + 𝛾] , 𝑖 = 1, 𝐼,
where 𝐼 is the number of pulses in a pulse train, 𝑇𝑟 is the repetition period. All pulses in (6) are
supposed to have the same amplitude and angle modulation, carrier frequency 𝜔0 and Doppler
frequency 𝜔𝐷 , phase incursion 𝛾. The independent random initial phases 𝜑𝑖 are caused by a
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clock generator. With respect to coherent heterodyne properties the initial phase is compensated
at the intermediate frequency:
𝑠𝐼𝐹 𝑖 (𝑡) = 𝑆(𝑡 − (𝑖 − 1)𝑇𝑟 )·
(7)
· cos [𝜔𝐼𝐹 (𝑡 − (𝑖 − 1)𝑇𝑟 ) + 𝜔𝐷 𝑡 + 𝜓(𝑡 − (𝑖 − 1)𝑇𝑟 ) + 𝛾] , 𝑖 = 1, 𝐼.
As the SRS simulation is based on complex envelopes the signals in (7) are represented in the
following form:
{︁ }︁
𝑠𝐼𝐹 𝑖 (𝑡) = Re 𝑆(𝑡 − (𝑖 − 1)𝑇𝑟 )𝑒𝑗[𝜔𝐼𝐹 (𝑡−(𝑖−1)𝑇𝑟 )+𝜔𝐷 𝑡+𝜓(𝑡−(𝑖−1)𝑇𝑟 )+𝛾] =
{︁ }︁ (8)
= Re 𝑆 & (𝑡 − (𝑖 − 1)𝑇𝑟 )𝑒𝑗𝜔𝐷 𝑡 𝑒𝑗(𝜔𝐼𝐹 (𝑡−(𝑖−1)𝑇𝑟 )+𝛾) , 𝑖 = 1, 𝐼.
where 𝑆 & (𝑡 − (𝑖 − 1)𝑇𝑟 ) = 𝑆(𝑡 − (𝑖 − 1)𝑇𝑟 )𝑒𝑖𝜓(𝑡−(𝑖−1)𝑇𝑟 ) is the complex envelope of the 𝑖-th
pulse without the Doppler effect. The multiplier 𝑒𝑗𝜔𝐷 𝑡 describing the Doppler effect is a slow
time function. Hence it can be replaced by the complex coefficients 𝑒𝑗𝜔𝐷 (𝑖−1)𝑇𝑟 :
&
𝑆𝐼𝐹 (𝑡 − (𝑖 − 1)𝑇𝑟 ) = 𝑆 & (𝑡 − (𝑖 − 1)𝑇𝑟 )𝑒𝑗𝜔𝐷 (𝑖−1)𝑇𝑟 . (9)
The FFT of (9) gives possibility to find the spectrum of the complex envelope of a received
signal with respect to the Doppler effect as the complex envelope spectrum without Doppler
effect multiplied by the complex coefficient
𝑘𝑖 = 𝑒𝑗𝜔𝐷 (𝑖−1)𝑇𝑟 . (10)
When the Doppler effect is simulated, the Doppler frequency can be multiple of the repetition
frequency of the sounding signal when a passive interference is suppressed together with a
useful signal. This leads to the noticeable decrease of the target detection probability.
6. Simulation of DPAA direction characteris
DPAA direction characteristics for the received signal are formed adaptively to achieve maximum
suppression of active interferences. The research described in this paper is based on the methods
of the theory of multidimensional signals and their space-time processing. There is no direct
description of antenna characteristics in such approach. The space-time approach is necessary
because wideband signals are used. A complex envelop of a wideband signal is not the same on
different antenna elements.
Simulation of a sounding signal can be implemented with common characteristics of antennas.
Further there are main expressions for simulation of the primary signal in the point of a target
or of reflectors creating a passive interference.
The directional diagram of a transmitting antenna is
(︂ )︂
𝛼 − 𝛼0 𝛽 − 𝛽0
𝐺(𝛼, 𝛼0 , 𝛽, 𝛽0 ) = 𝐺0 (𝛼0 , 𝛽0 ) · 𝑔 , , (11)
𝛼0,5 (𝛼0 ) 𝛽0,5 (𝛽0 )
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where 𝛼0 , 𝛽0 are the azimuth and elevation describing antenna diagram beam deviation because
of electronic scanning relative to the normal to the antenna array surface, 𝛼0,5 (𝛼0 ), 𝛽0, 5(𝛽0 )
are the beam widths on the azimuth and elevation:
51𝜆 51𝜆
𝛼0,5 (𝛼0 ) = , 𝛽0,5 (𝛽0 ) = , (12)
𝑁𝛼 𝑑 cos 𝛼0 𝑁𝛽 𝑑 cos 𝛽0
where 𝑁𝛼 , 𝑁𝛽 are the numbers of antenna elements rows and colons in a flat antenna array, 𝜆
is the carrier wavelength, 𝑑 is the distance between antenna elements. If 𝑑 = 𝜆/2, then (12)
takes the form:
102 102
𝛼0,5 (𝛼0 ) = , 𝛽0,5 (𝛽0 ) = , (13)
𝑁𝛼 cos 𝛼0 𝑁𝛽 cos 𝛽0
The results of calculations by (12) and (13) are expressed in degrees. If 𝛼0 = 𝛽0 = 0, then the
beam width is minimum. If beam deviation is nonzero the directional diagram is expanded.
The parameter 𝐺0 (𝛼0 , 𝛽0 ) in (11) describes the antenna gain. It is evident that if the angles
𝛼0 , 𝛽0 grow the gain falls. It depends on the effective antenna surface 𝑆𝑒𝑓 𝑓
𝑆𝑒𝑓 𝑓
𝐺0 (𝛼0 , 𝛽0 ) = 4𝜋 , (14)
𝜆2
which is found from the expression:
𝑆𝑒𝑓 𝑓 = 𝑁𝛼 𝑑 cos 𝛼0 𝑁𝛽 𝑑 cos 𝛽0 = 𝑁𝛼 𝑁𝛽 𝑑2 cos 𝛼0 cos 𝛽0 . (15)
With respect to (15) and 𝑑 = 𝜆/2, the expression (14) takes the form:
𝐺0 (𝛼0 , 𝛽0 ) = 𝜋𝑁𝛼 𝑁𝛽 cos 𝛼0 cos 𝛽0 . (16)
(︂ )︂
𝛼 − 𝛼0 𝛽 − 𝛽0
The multiplier 𝑔 , of (11) is a normalized directional diagram with
𝛼0,5 (𝛼0 ) 𝛽0,5 (𝛽0 )
𝑔(0, 0) = 1. It is approximated by the function 𝑠𝑖𝑛𝛾/𝛾:
(︂ )︂ (︂ )︂ ⃒
𝛼 − 𝛼0 𝛽 − 𝛽0 ⃒
⃒
⃒
(︂ )︂ ⃒ sin 3.79 sin 3.79 ⃒
𝛼 − 𝛼0 𝛽 − 𝛽 0 𝛼0,5 (𝛼0 ) 𝛽0,5 (𝛽0 ) ⃒⃒
(17)
⃒
𝑔 , =⃒ ⃒
𝛼 − 𝛼0 · ⃒.
𝛼0,5 (𝛼0 ) 𝛽0,5 (𝛽0 ) 𝛽 − 𝛽0
⃒ 3.79 3.79 ⃒
⃒ 𝛼0,5 (𝛼0 ) 𝛽0,5 (𝛽0 ) ⃒
The normalized directional diagram is featured by the properties:
𝑔(0.5; 0) = 𝑔(0; 0.5) = 0.5.
Its level decreases on each angle coordinate until the half level.
7. Testing of the model of a radar station with DPAA
The program for simulation of an SRS has been approved by experiments. The main attention
is focused on the influence of active interferences on the target detection probability. As a
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Table 1
Target detection probability for 10 AI.
𝑁𝐴𝐼 , kW/MHz 10 10 10 1 1
𝑅𝑇 , km 300 250 200 300 250
𝑞𝐷 , dB −91.4 −88 −84.4 −81 −78.3
𝑞𝐹 , dB −8.4 −1.9 1.8 1.6 4.6
𝑃𝐷 0.01 0.1 1 0.8 1
Table 2
AI angle coordinates.
𝛼𝐴𝐼 , ∘ 10 15 20 25 30 40 50 60 70 80
𝛽𝐴𝐼 , ∘ 7 9 5 7 10 5 5 6 8 5
target signal and active interferences income from different directions their spectrums are
also different. Hence, it is possible to suppress interferences. Further there are the results of
the experiment with a simulated target and 10 active interference sources. This experiment
includes simulation of space-time filtration and target detection for the following parameters:
ESS 𝜎𝑇 = 1 m2 , distance 𝑅𝑇 = 300 km, angle coordinates (𝛼𝑇 , 𝛽𝑇 ) = (0, 0)∘ , false alarm
probability 𝐹 = 10−6 , transmitter power 𝑃𝑇 𝑅 = 80 kW, signal type is the radio pulse with
the linear frequency modulation with pulse width 𝜏𝑃 = 10 𝜇s, frequency deviation ∆𝑓 =
100 MHz, number of pulses 𝑁𝑝 = 5, noise PSD 𝑁𝑁 = 10−20 W/Hz, Active Interference
(AI) PSD 𝑁𝐴𝐼 = {0.1, 1, 10} kW/MHz, AI bandwidth ∆𝐹𝐴𝐼 = 100 MHz, distance until AI
sources 𝑅𝐴𝐼 = 350 km, the member of DPAA elements 70 × 70 = 4900, sample frequency
𝑓𝑠 = 200 MHz, the statistical experiment volume is 𝑁𝐸 = 100.
The experiment results include estimations of the detection probability 𝑃𝐷 and Signal to
Noise Plus Interference Ratio (SNPIR) values at the DPAA input 𝑞𝐴 and at the output of the
Space-Time Matching Filter (STMF) 𝑞𝐹 .
Table 1 contains the experiment results for 10 AI sources. The angle coordinates of the AI
sources are shown in Table 2. The SNPIR improvement at the STMF output is about 83 dB.
If 𝑅𝑇 = 300 km and 𝑁𝐴𝐼 = 10 kW/MHz the detection probability is about zero. The stable
detection of a target takes place if 𝑅𝑇 = 200 km. If 𝑁𝐴𝐼 = 10 kW/MHz and 𝑅𝑇 = 250 km, the
detection probability is equal to one. If 𝑅𝑇 = 250 km„ the detection probability is 0.8.
8. Conclusion
The proposed model gives possibility to analyze the algorithms for radar signal processing in SRS
with DPAA. The model speed primary depends on the computer RAM volume, sounding signal
width and interferences number. The satisfactory calculation speed is achieved by simulation of
only active intervals of transmitted and received radar signals at zero frequency. The model
capabilities are approved for many AI sources.
269
Vasiliy N. Vasyukov et al. CEUR Workshop Proceedings 260–271
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