=Paper=
{{Paper
|id=Vol-2870/paper71
|storemode=property
|title=Knowledge Representation Method for Object Recognition in Nonlinear Radar Systems
|pdfUrl=https://ceur-ws.org/Vol-2870/paper71.pdf
|volume=Vol-2870
|authors=Maksym Makaruk,Alexei Nazarov,Igor Shubin,Nadezhda Shanidze
|dblpUrl=https://dblp.org/rec/conf/colins/MakarukNSS21
}}
==Knowledge Representation Method for Object Recognition in Nonlinear Radar Systems==
https://ceur-ws.org/Vol-2870/paper71.pdf
Knowledge Representation Method for Object Recognition in
Nonlinear Radar Systems
Maksym Makaruka, Alexei Nazarova, Igor Shubina and Nadezhda Shanidzeb
a)
Kharkiv National University of Radio Electronics, 14, Nauky Ave. , 61166, Kharkiv, Ukraine
b)
National Technical University «Kharkiv Polytechnic Institute», 2, Kyrpychova str., 61002, Kharkiv,
Ukraine
Abstract
Substantiation of the technical appearance of nonlinear short-range radar system designed to
detect and measure the characteristics of objects with nonlinear electrical properties is the
main topic of this article. The general principles of constructing short-range radar system are
described in the form of their structural diagrams and algorithms for their operation, which
ensure the maximization of the signal-to-noise power ratio at the output of the receiving
device. An optimal procedure for distinguishing a noise-like signal against a background of
noise and interference was proposed on the basis of measuring the moment characteristics of
the probability distributions of signals and interference.
Keywords 1
Radiolocation, Nonlinear Radar, Correlation Filtering, Radar Information Processing.
1. Correlation filtering algorithm in nonlinear radar systems
The rapid development of methods and techniques for radar sounding of objects with electrically
nonlinear properties stimulates the search for ways to optimize the structures of detecting receivers of
nonlinear radar devices and algorithms for optimal signal processing in them. The relevance of these
problems is due to the small range of action of modern nonlinear radars even when the power levels
of the emitted signal are increased to values of the order of tens and hundreds of kilowatts when a
pulsed signal is emitted. Let us list the main reasons for the low level of the signal-to-noise power
ratio at the receiver input:
• a weak level of nonlinear responses from an object with nonlinear properties at the
frequencies of harmonics or combination components of emitted signals;
• overlap of the spectrum of the emitted signal and the spectra of nonlinear responses in the
reception band of the nonlinear locator (the reception of the useful response signal from the
nonlinear object is carried out against the background of its own interference);
• low values of the gain of the locator antenna (especially in the range of radiation of the
emitted signal);
• congestion of the radio frequency range with sources of radio emissions for various purposes
in the frequency range optimal for use in non-linear radar.
We propose a procedure for synthesizing an optimal algorithm for detecting a nonlinear object by
the method of nonlinear radar against the background of additive noise and interference caused by the
influence of the above factors.
COLINS-2021: 5th International Conference on Computational Linguistics and Intelligent Systems, April 22–23, 2021, Kharkiv, Ukraine
EMAIL: maksym.makaruk@nure.ua (M. Makaruk), oleksii.nazarov1@nure.ua. (A. Nazarov), igor.shubin@nure.ua (I. Shubin),
nashanidze@ukr.net (N. Shanidze).
ORCID: 0000-0003-0008-6548 (M. Makaruk), 0000-0001-8682-5000 (A. Nazarov), 0000-0002-1073-023X (I. Shubin), 0000-0002-9613-
186X (N. Shanidze).
©️ 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 (CEUR-WS.org)
As a criterion for optimality of detection, let us take the Neyman-Pearson criterion traditionally
used in radar. The optimal filter receiver – the detector calculates the values of the correlation integral
and compares them with a threshold to make a decision about the presence of a target.
The correlation integral in the case of receiving a signal with completely known parameters is
determined by the expression
∞
𝑍(𝑡) = ∫ 𝑋(𝑡, 𝑓𝐾 )𝑌(𝑡)𝑑𝑡 (1)
−∞
where 𝑋(𝑡, 𝑓𝑘 ) - expected response signal from a nonlinear object at the frequency of the k-th
harmonic of the emitted signal.
𝑌(𝑡) = 𝑛𝑟𝑎𝑛𝑑 (𝑡) + 𝑛𝑟𝑒𝑔 (𝑡) + 𝐴𝑋(𝑡, 𝑓𝐾𝑡𝑟𝑢𝑒 ) (2)
In expression (2), the parameter A takes the values 1 (there is a target) and 0 (there is no target).
The random noise component 𝑛𝑟𝑎𝑛𝑑 (𝑡) includes unremovable intrinsic internal and external noises of
the radar receiver, which have a probabilistic irregular nature (noises of receiver elements,
atmospheric noise, etc.) The interference component 𝑛𝑟𝑒𝑔 (𝑡) is due to the contribution to the additive
mixture (2) of the regular components of the spectrum of the emitted signal with an average frequency
(𝑓0), falling into the receiver's passband, as well as the influence of external unavoidable regular
interference.
It can be shown that the elimination of the regular interference component 𝑛𝑟𝑒𝑔 (𝑡) from the
additive mixture (2) in the process of special processing of signals and interference in the receiver
leads to an improvement in the reception quality indicators. The block diagram of such an optimal
detector, which implements the algorithm for compensating its own regular interference components
in the adopted implementation, is shown in Figure 1.
Figure 1: Block diagram of detector
The proposed scheme of the optimal filter for detecting objects with nonlinear properties differs
from the known ones by the presence of a special channel 1 for calculating the correlation integral
corresponding to the quantitative contribution to the noise + interference mixture of the regular
component 𝑛𝑟𝑒𝑔 (𝑡).
Subtraction of this component leads to an increase in the signal to noise + interference ratio at the
output of the signal processing device.
The main elements of the circuit shown in Figure 1 are multipliers, integrators, a subtractor and a
threshold (decision) device.
To the first multiplier, together with the received mixture Y (t), a reference oscillation 𝑋(𝑡, 𝑓0 ) is
supplied, corresponding to the emitted signal, which is the source of the occurrence of a regular
component of its own interference 𝑛𝑟𝑒𝑔 (𝑡).
The second multiplier of the main receiving channel 2, together with the oscillation Y (t), receives
the reference oscillation 𝑋(𝑡, 𝑓𝐾 ), which corresponds to the expected response signal from the
nonlinear object at the frequency 𝑓𝐾 .
The reference expected oscillation 𝑋(𝑡, 𝑓0 ) is formed in the nonlinear radar transceiver by
converting the signal at the emitted radiation frequency 𝑓0 at the built-in nonlinear element into the
harmonic component expected as a response at the frequency 𝑓𝐾 .
Direct integration of the products 𝑋(𝑡, 𝑓0 )𝑌(𝑡) and 𝑋(𝑡, 𝑓𝐾 )𝑌(𝑡) gives the values of the correlation
integrals in the corresponding channels of the signal receiving and processing device.
Mathematically, the algorithm of the optimal filter (Figure 2) is described as follows. The
correlation integral at the output of the first integrator of the receiving device contains three
components:
∞ ∞ ∞
𝑍1 (𝑡) = ∫ 𝑛𝑟𝑎𝑛𝑑 (𝑡)𝑋(𝑡, 𝑓0 )𝑑𝑡 + ∫ 𝑋(𝑡, 𝑓0𝑡𝑟𝑢𝑒 )𝑋(𝑡, 𝑓0 )𝑑𝑡 + 𝐴 ∫ 𝑋(𝑡, 𝑓𝐾𝑡𝑟𝑢𝑒 )𝑋(𝑡, 𝑓0 )𝑑𝑡 (3)
−∞ −∞ −∞
On the right-hand side of equation (3), in the second integral, the first factor 𝑋(𝑡, 𝑓0𝑡𝑟𝑢𝑒 )
corresponds to the regular component 𝑛𝑟𝑒𝑔 (𝑡), and the second factor 𝑋(𝑡, 𝑓0 ) corresponds to the
reference emitted oscillation.
The correlation integral of the second (main) integrator of the optimal filter has the form:
∞ ∞ ∞
𝑍2 (𝑡) = ∫ 𝑛𝑟𝑎𝑛𝑑 (𝑡)𝑋(𝑡, 𝑓𝐾 )𝑑𝑡 + 𝐴 ∫ 𝑋(𝑡, 𝑓𝐾𝑡𝑟𝑢𝑒 )𝑋(𝑡, 𝑓𝐾 )𝑑𝑡 + ∫ 𝑋(𝑡, 𝑓0 )𝑋(𝑡, 𝑓𝐾 )𝑑𝑡 (4)
−∞ −∞ −∞
The resulting correlation integral 𝑍𝑟 (𝑡) = 𝑍2 (𝑡) − 𝑍1 (𝑡) at the output of the subtractor does not
∞ ∞
contain mutually exclusive components ∫−∞ 𝑋(𝑡, 𝑓𝐾 )𝑋(𝑡, 𝑓0 )𝑑𝑡 and ∫−∞ 𝑋(𝑡, 𝑓𝐾𝑡𝑟𝑢𝑒 )𝑋(𝑡, 𝑓0 )𝑑𝑡.
The resulting correlation integral, calculated as the difference between expressions (4) and (3), is a
combination of signal and noise components (with a plus sign) and noise and interference components
eliminated by the receiving structure (Figure 1) (with a minus sign):
∞ ∞ ∞
2 (𝑡,
𝑍𝑟 (𝑡) = 𝐴 ∫ 𝑋 𝑓𝐾 )𝑑𝑡 + ∫ 𝑛𝑟𝑎𝑛𝑑 (𝑡)𝑋(𝑡, 𝑓𝐾 )𝑑𝑡 − ∫ 𝑛𝑟𝑎𝑛𝑑 (𝑡)𝑋(𝑡, 𝑓0 )𝑑𝑡
−∞ −∞ −∞ (5)
∞
− ∫ 𝑋 2 (𝑡, 𝑓0 )𝑑𝑡
−∞
∞
The signal component 𝐴 ∫−∞ 𝑋 2 (𝑡, 𝑓𝐾 )𝑑𝑡 of the correlation integral 𝑍𝑟 (𝑡) is determined by the
energy of the useful response signal from the nonlinear element received in the mixture (2) at the
frequency 𝑓𝐾 . The greater the value of 𝑍𝑟 (𝑡), the higher the probability of correct detection 𝑃𝐶𝐷 with a
fixed value of the false alarm probability 𝑃𝐹𝐴 . 𝑃𝐹𝐴 is unambiguously related to the threshold level set
for making a decision on the presence of a goal.
Figure 2: The physical interpretation of the detecting procedure
The physical interpretation of the optimal filter procedure for detecting a response signal from a
nonlinear element in accordance with algorithm (3) - (5) is as follows. The presence or absence of a
useful signal in the received additive mixture (2) results in the corresponding distribution of the
probability distribution density of the correlation integral at the output of the second integrator of the
filter circuit 𝑝(𝑍2𝑘 ) and 𝑝(𝑍20 ) (Figure 2).
In accordance with this algorithm for optimal processing of the signal-noise mixture, the features
of the target detection process characteristic of nonlinear radar, which will be discussed below, are
considered.
The false alarm probability 𝑃𝐹𝐴 corresponds to the area limited by the indicated PDF and the
threshold 𝑍𝑡 (𝑡). The presence of channel 1 and a subtracting device ensures the elimination of the
regular component from the aggregate of interference and noise, which leads to a shift of the PDF
𝑝(𝑍20 ) to the left along the z axis by a value, corresponding to the constant component of the process
𝑛𝑟𝑒𝑔 (𝑡). Figure 2 the corresponding process PDF is denoted as 𝑝′(𝑍20 ).The probability of a false
alarm in the first and second cases (with the traditional method of reception and reception according
to the considered algorithm) corresponds to the area limited by the specified PDF and the threshold
𝑍𝑡 (𝑡). The figure shows that at a fixed threshold level, the probability of a false alarm (shaded area)
decreases. In this situation, by fixing the false alarm probability level, it is possible to reduce the value
of the threshold 𝑍𝑡 (𝑡), which will lead to an increase in the signal / (noise + interference) ratio at the
output of the considered filter receiver.
In the absence of a useful signal in the adopted implementation (5), at the output of the circuit
there are only random noise components with the probability density of the amplitude distribution
𝑝′(𝑍20 ). In this case, the resulting PDF obeys the normal law, and the probability of a false alarm in
accordance with the Neyman-Pearson criterion is calculated by the formula:
∞
𝑍𝑛 (𝑡) (6)
𝑃𝐹𝐴 = ∫ 𝑝′ (𝑍20 )𝑑𝑧 = 1 − 𝐹 −
2𝐸
𝑍𝑡 (𝑡) √
( 𝑁0 )
where F(*) - tabular probability integral;
2𝐸
𝑁
– signal / noise power ratio.
0
Based on (6), it is possible to determine the quantitative effect of applying the proposed algorithm
for detecting a useful signal against the background of noise and interference.
The graphs of the dependences of the measurement of the false alarm probability on the signal-to-
𝑍 (𝑡)−𝑍𝑟𝑒𝑔 (𝑡)
noise ratio obtained based on (6) for various values of the parameter ℎ = 𝑛 100% are
𝑍𝑡 (𝑡)
shown in Figure 3.
The parameter h has the meaning of a relative threshold and characterizes the influence of the
excluded interference component during signal and interference processing.
The rapid development of the theory and technique of nonlinear radar dictates the need to develop
and improve methods for optimal detection of targets with nonlinear electrical properties. By analogy
with the methods of linear radar, the optimal detection of targets in nonlinear radar is carried out by
implementing procedures of accumulation, agreed filtering or correlation reception. In all cases, the
consequence of optimal signal processing is an increase in the energy ratio signal / background (signal
/ noise, signal / interference), which provides a given signal detection efficiency according to the
selected detection quality criterion (eg, Neumann-Pearson criterion). However, with nonlinear radar,
it is not the reflection but the conversion of the probe signal, as a result of which the signal /
background ratio is usually small. In this case, the detection of the response (signal) with a given
efficiency with the direct application of linear radar algorithms becomes problematic.
It is known from the theory of linear radar that in cases of pronounced fluctuation of signal and
background reflections and radiation, the efficiency of distinguishing the useful signal against the
background of interference of natural or artificial origin is significantly reduced due to increased
probabilities of fictitious alarms. The latter occur when the level of the established detection threshold
of accidental background fluctuations or interference is exceeded. This situation is typical, for
example, for the detection of small or masked radar targets (RLC) against the background of wind-
swaying vegetation, the disturbed water surface, etc. The most noticeable deterioration in the
detection quality of the RLC at small angles of the radar sounding of targets with a high level of
specific effective scattering area (EPR). In nonlinear radar, a similar situation is observed when
searching for targets with nonlinear electrical properties against the background of objects with
unstable oxide contacts. The analysis shows that the problem of detecting objects with nonlinear
electrical properties under interference conditions has much in common with the problem of
distinguishing between fluctuating radar targets on the background of underlying surfaces with high
levels of specific EPR.
Figure 3: Dependences of the false alarm probability on the signal-to-noise ratio
The analysis of the obtained dependences shows that a decrease in the probability of a false alarm
in accordance with the processing algorithm (3) - (5) is manifested in the region of low values of the
signal-to-noise ratio, and the greater the relative contribution of the excluded component, the more
pronounced this pattern is.
Thus, the receiver structure shown in Figure 1 and relations (3) - (5) are, respectively, an optimal
filter and an algorithm for detecting an object with electrically nonlinear properties. The practical
implementation of the principles of signal and interference processing proposed here provides the
possibility of improving the quality of detection of useful signals by eliminating the regular
components of intrinsic or external interference. The consequence of these circumstances is the
possibility of increasing the range of detection nonlinear radar devices while maintaining the
performance indicators of the used receivers within the required limits.
2. Quasi-optimal algorithm of nonlinear radar information processing
The analysis of current publications on the problems of the theory and technology of nonlinear
radiolocation shows that, despite the rapid development of the technique of radar sounding of objects
with nonlinear electrical properties, the problem of improving the main indicators of the quality of
nonlinear radars is still urgent, such as the probability of correct detection, range, etc. The most
radical way to improve these characteristics is developing optimal principles for constructing
nonlinear radar systems.
Let us give a description of the technical appearance of a multifrequency nonlinear radar, which
differs from the known ones in the implementation of the method for increasing the signal-to-noise
ratio at the output of the nonlinear radar receiver by combining the frequency of the side receiving
channels with the response frequencies.
A typical nonlinear locator contains a serially connected master pulse generator, a high-frequency
emitted signal conditioner, a transceiver antenna, as well as a receiver connected to it, tuned to the
second or third harmonic of the emitted signal.
The principle of operation of the nonlinear locator is based on the fact that when objects containing
nonlinear elements are irradiated (p-n - junction, oxide-metal transition, diode, transistor, etc.), the
energy of the emitted signal is converted into the energy of higher multiple harmonics. The response
signals converted by the nonlinear element are registered by the detecting device regardless of the
operating mode of the nonlinear object (on – off).
The power of the emitted pulse signal is limited due to the need to ensure an acceptable level of
the high-frequency radiation field affecting the operator. The conversion factor of the energy of the
emitted signal into the energy of higher harmonics is very small. Therefore, the main disadvantage of
the existing nonlinear radars is its short range. To increase the range of the nonlinear radar, multi-
frequency location is used, in which the nonlinear element converts the emitted signal into a signal
containing combined frequencies:
𝑓𝑐𝑜𝑚𝑏.𝑖 = ±𝑛𝑓1 ± 𝑚𝑓2 ± 𝑘𝑓3 ± ⋯ ± 𝑞𝑓𝑁 (7)
where 𝑛, 𝑚, 𝑘, … , 𝑞 = 0, ∞;
fcomb.i - frequency of i-th emitted signal, 𝑖 = 1, 𝑁.
The signal is received at the combined frequency 𝑓1 + 𝑓𝑁 , and the receiver bandwidth ∆𝑓𝑟𝑒𝑐 is
selected from the condition:
𝑓𝑁 − 𝑓1 ∆𝑓𝑟𝑒𝑐 (8)
∆ ≤
𝑁−1 2
The fulfillment of (2) ensures the simultaneous reception of two more response signals from the
nonlinear element (multiples of the frequencies of the emitted signal or the combinational components
of the reflected signal) through the main reception channel of the superheterodyne receiver. The
bandwidth of the receiver, as follows from (2), is very wide, which reduces its noise immunity.
With dual-frequency sounding, the signal at the combination frequency 𝑓1 + 𝑓2 and the
components 2𝑓1 and 2𝑓2 comes into the passband of the receiver, i.e., in comparison with a single-
frequency locator, multifrequency nonlinear radar provides reception of three components of the
response signal. The result is an increase in the range of the nonlinear radar.
Reception of response signals from a nonlinear element (products of nonlinear transformation of
emitted signals on a nonlinear element) is provided by transferring them to the intermediate frequency
region in the mixer of the superheterodyne receiver of the locator. In this case, frequency conversion
is included in the arbitrary transfer of a part of the spectrum of the received signals to the intermediate
frequency region to ensure the required amplification of signals and their frequency selection.
However, the presence of side channels of reception in the locator (mirror, direct, etc.) with the
appropriate frequency conversion in the receiver allows you to receive more than three components of
the response signal. This can be achieved by combining the frequency of the receiving channels of the
receiver with the frequencies of the responses from the nonlinear element by imposing additional
requirements on the choice of the intermediate frequency rating and the frequency of the local
oscillator of the receiver of the detecting device. One of the requirements is that they must be rigidly
related to the nominal frequencies of the emitted signals. In this case, the practical implementation of
the combination of the reception channels with the response frequencies from the nonlinear element
can be achieved by various hardware options. There can be many such options.
Let us consider the structures most often used in practice in receivers for radio communication,
radar, radio navigation, electronic warfare, electronic intelligence, structures for constructing
detection devices, measuring the parameters of signals and interference, and extracting information.
These mainly include spectrum analyzers and measurement receivers.
Each specific version of the detection device will be determined by the type of the emitted signal
(dual-frequency, multi-frequency), the type of frequency conversion ("up", "down", single, multiple),
the frequency of the local oscillator tuning (upper, lower), the type of conversion (linear 𝑓1 ± 𝑓2;
nonlinear 𝑛𝑓1 ± 𝑚𝑓2), etc. Therefore, for the purpose of definiteness, concretization and the
possibility of industrial application, we have to consider a particular situation of two-frequency
sounding of an object by a locator with a single linear frequency conversion with a lower local
oscillator setting and with a downward frequency shift. The interpretation of the principle of
frequency matching of the receiver channels with the response frequencies is graphically shown in
Figure 4.
Figure 4 shows that if the nominal intermediate frequency is selected from the condition
𝑓𝐼𝐹 = 𝑓2 − 𝑓1 , (𝑓2 > 𝑓1 ) (9)
the differential component of the response at the frequency 𝑓𝑝 = 𝑓2 − 𝑓1 is received via the
intermediate frequency channel (forward channel). This is achieved by combining the most sensitive
side receiving channel of the receiver at an intermediate frequency with one of the most powerful
responses from a nonlinear element at a frequency 𝑓𝑝 = 𝑓2 − 𝑓1. The combination of the main and
mirror reception channel with other of the most powerful frequency components (7) is ensured by a
special choice of the heterodyne frequency rate.
Figure 4: Principle of frequency matching
a) - radiation spectrum of responses from a nonlinear element (sensing object);
b) - frequency selectivity characteristic of a nonlinear radar receiver:
1 – reception channel on the intermediate frequency;
2 – main reception channel;
3 – image frequency reception channel.
If you select the frequency of tuning the local oscillator of the locator receiver equal to the doubled
frequency of the emitted signal 𝑓1 , 𝑓ℎ𝑒𝑡 = 2𝑓1, then the total component of the response from the
nonlinear element at frequency 𝑓1 + 𝑓2 will be received through the main receiving channel:
𝑓𝑆 = 𝑓ℎ𝑒𝑡 + 𝑓𝐼𝐹 = 2𝑓1 + 𝑓2 − 𝑓1 (10)
In this case, via the image reception channel of the receiver, a signal at the next frequency will be
received:
𝑓𝑖𝑚𝑎𝑔𝑒 = 𝑓ℎ𝑒𝑡 − 𝑓𝐼𝐹 = 2𝑓1 − 𝑓2 + 𝑓1 (11)
which is one of the intermodulation frequencies of the products of nonlinear conversion of emitted
signals by the target object.
In addition, when choosing the receiver bandwidth from the condition
2𝑓2 − 2𝑓1 ≥ ∆𝑓𝐼𝐹 (12)
reception of signals at frequencies 2𝑓1 and 2𝑓2 is provided (Figure 4). Moreover, due to the
fulfillment of condition (12), the subharmonics of emissions at frequencies 𝑓1 and 𝑓2, and more
1 1
specifically 2 𝑓1 and 2 𝑓2 are received through the passband of the receiver on the intermediate
frequency channel.
Thus, due to the fulfillment of conditions (12), (9) and 𝑓ℎ𝑒𝑡 = 2𝑓1 in the dual-frequency nonlinear
radar, the reception of seven products of nonlinear conversion by the nonlinear element of the emitted
signal is provided through the most sensitive reception channels, and the reception of the most
powerful responses at frequencies 𝑓1 + 𝑓2 and 𝑓2 − 𝑓1 is provided. In practice, when designing a
multi-frequency nonlinear radar, this can be achieved by increasing the sensitivity of the side
reception channels (excluding the filter notch tuned to 𝑓𝐼𝐹 ; excluding the preselector to improve the
sensitivity along the mirror channel), while in a traditional superheterodyne receiver, measures are
taken to weakening unwanted side channels of reception by these measures.
The combination of the passbands of the side and main channels of the nonlinear locator receiver
with the most significant spectral components formed on the nonlinear element (7) and an increase in
the sensitivity of the side reception channels lead to the fact that the locator receiver becomes largely
consistent in its amplitude-frequency characteristics with the spectrum of the received signal, i.e. filter
quasi-optimal. The consequence of this circumstance is an increase in the signal-to-noise ratio at its
output, an increase in the range of the locator, and an improvement in the probability of correct
detection of an object.
The first important condition for achieving this goal (increasing the range of nonlinear radar) is
such a choice of an intermediate frequency in a superheterodyne receiver with one linear frequency
conversion downward so that the most sensitive reception channel (at the intermediate frequency)
coincides (on the frequency axis) with the difference the combination frequency of radiation from the
nonlinear element 𝑓2 − 𝑓1.
The second important requirement for nonlinear radar is the choice of the receiver local oscillator
frequency equal to the value of 2𝑓1 .
The next important requirement for the receiver of the proposed nonlinear radar system structure is
to take measures to improve the sensitivity of the radar receiver over the intermediate frequency
channel and other side reception channels. Due to the reception of signals in the receiver through a
large number of channels, the receiver of a nonlinear radar must have a threshold device to exclude
the receiver's response to extraneous signals (detection device).
Thus, the new distinctive features of nonlinear radar include the choice of the nominal
intermediate frequency in accordance with the condition 𝑓2 − 𝑓1 , as well as the choice of the
frequency of the receiver local oscillator equal to the frequency 2𝑓2 , increasing the sensitivity of the
side receiving channels in the nonlinear radar.
The possibility of practical implementation of the proposed device is confirmed by the following.
The results of theoretical and experimental studies show that the highest intensity among the
conversion products on a nonlinear element is the combination components at frequencies | 𝑓1 , ± 𝑓𝑁 |.
On the other hand, it is known that of all possible reception channels of a superheterodyne receiver,
the most sensitive is the forward channel at the intermediate frequency. Therefore, the frequency
coincidence of this most sensitive direct channel for receiving a nonlinear radar with one of the most
significant in amplitude frequency component of re-radiation of a nonlinear element at a frequency
𝑓2 − 𝑓1, provides an increased level of the useful signal at the output of the detector's receiver and,
consequently, it’s increased range.
The appropriate choice of the local oscillator tuning frequency (𝑓ℎ𝑒𝑡 = 2𝑓1 ) also contributes to an
increase in the detection range due to the coincidence of the main and image reception channels with
the response frequencies from the object.
Thus, in the proposed locating device, when these measures are implemented, the number of
responses received through various receiving channels of a nonlinear radar increases, and the most
sensitive receiving channels correspond to high amplitude frequency responses from a nonlinear
element.
The proposed structure of the nonlinear radar provides an increase in the quality indicators of the
detection of a nonlinear element by increasing the signal-to-noise ratio at the output of the
intermediate frequency receiver's path, which is due to the optimization of the principles of the
receiver design (matching the multi-frequency characteristics of the frequency selectivity of the
receiver with the radiation spectrum of the nonlinear element).
The possibility of implementing the proposed principles of constructing the nonlinear radar was
studied experimentally. For this purpose, a setup was assembled, which included two “G4-18A”
signal generators tuned to frequencies 𝑓1 = 248 and 𝑓2 = 252 kHz, respectively. The generators were
loaded onto one directional loop antenna of the “APK-15M” aviation radio compass. The receiver
was “P-880M” with an intermediate frequency of 500 kHz. The detection of a single nonlinear
element (diode of the “GC-13A” type) by the receiving unit (P-880M with a whip antenna) was
confidently carried out at distances up to 10 m at any receiver setting (via the intermediate frequency
channel). When tuning the local oscillator frequency 𝑓ℎ𝑒𝑡 = 𝑓𝑠𝑖𝑔 − 𝑓𝐼𝐹 to values of 252 and 248 kHz
(𝑓𝑠1 = 2𝑓2 + 𝑓1 = 752 𝑘𝐻𝑧 𝑎𝑛𝑑 𝑓𝑠2 = 2𝑓1 + 𝑓2 = 748 kHz), the signal at the output of the
receiver increased, which indicated additional reception of components in the main and image
reception channels.
The block diagram of the presented dual-frequency detection device is shown in Figure 5.
Figure 5: Block diagram of a two-frequency detector
1. Modulator.
2. The first conditioner of a high-frequency signal at a frequency 𝑓1 (consists of the high-
frequency generator 𝑓1 HFG1 and a power amplifier).
3. The second conditioner of the high-frequency signal at the frequency 𝑓2 (consists of the high-
frequency generator 𝑓2 HFG2 and a power amplifier).
4. Frequency multiplier 𝑓1 by two.
5. Receiver with a detection device.
6. Broadband antenna.
7. Detectable nonlinear element.
The frequency multiplier acts as a local heterodyne in the receiver. The signal from the high-
frequency generator of the first signal conditioner is fed to the receiver mixer for use as a local
oscillator signal, providing, together with the appropriate choice of the intermediate frequency and
bandwidth, the alignment on the axis of the response frequencies from the non-linear element with the
most sensitive receiving channels of the receiver.
One of the characteristic features of the development of modern radio engineering is the increasing
use of noise-like signals (NLS) to solve problems of information transmission in telecommunications
and information retrieval of targets and sounding objects in radar. Recently, NLS is increasingly used
in nonlinear radar and communications. The use of NLS in these radio and radio equipment is due to
the possibility of improving the characteristics of energy availability of radios and objects due to the
optimal processing of signals with a large base by compressing them in time or coherent
accumulation.
The widespread use of nonlinear radar methods necessitates the improvement of means and
methods for optimal detection of targets with nonlinear electrical properties. The currently used
correlation and filter algorithms for optimal signal processing in relation to nonlinear radar have a
number of significant limitations, which are as follows. In the optimal receiving structures of linear
radars, the processing of the received "signal + noise" mixture is carried out, as is known, at the
frequency of the probing signal. In nonlinear radar, reception is carried out at the harmonics of the
sounding signal or combination frequencies. This significantly complicates filter or correlation
receiver circuits.
In addition, in nonlinear radar, the sounding signal is converted, as a result of which the signal-to-
noise ratio, as a rule, decreases significantly. In this case, the detection of a signal response from a
target with a given efficiency with the direct application of linear radar algorithms becomes
problematic.
It is known that when a noise-like signal passes through a non-linear element, the form of the
distribution law of the initial noise changes. This property can be used as the basis for the principle of
target detection with nonlinear electrical characteristics. The noise generator included in the setup
generates stationary quasi-white noise with known characteristics:
𝑈2
1 2𝜎 2
𝑃1 (𝑈) = 𝑒 𝑈
√2𝜋𝜎𝑈
where 𝑃(𝑈) is the probability distribution density of the noise voltage amplitudes, 𝜎𝑈 is the amplitude
dispersion. The noise signal amplified in the amplifier is radiated through the directional antenna in
the direction of the target. If the target is characterized by a nonlinear dependence of the level of the
scattered signal on the level of the probe, approximated by a quadratic polynomial, then the PDF of
the response signal is described by the Rayleigh distribution law
𝑈2
𝑈 2𝜎2
𝑃2 (𝑈) = 2 𝑒 𝑈
𝜎𝑈
A response signal with an average response frequency Fresponse Equal to the average frequency of
the probing signal Femitted, but having a PDF of amplitudes of the form, is received by the antenna,
amplified in the receiver and fed to the probability characteristics meter to determine the degree of
difference in the noise realizations probing signal and response signal.
A significant difference between the proposed detector of nonlinear targets, in contrast to the
known detectors, is the reception not at harmonics, but at the fundamental frequency of the probing
signal - as in linear radar. The latter circumstance makes it possible to significantly simplify the
procedure for optimal signal processing in the receiving part of the detector. It is also important that
the parameters of the distribution law of the form carry information not only about the presence of a
nonlinear radar target in the detector's field of view, but also about the properties of this target, which
can be used for target recognition.
Since the information about the presence of a nonlinear target is contained in the change in the
PDF form of the adopted implementation relative to the initial one, the optimal detection algorithm
should include a threshold device for making a decision on the presence of a target in case the
established degree of difference between the PDF forms of the form and is exceeded. In this situation,
it is advisable to use the entropy criterion as the decisive rule, which, as is known, is most sensitive to
changes in the shape of the distribution law. In this regard, as the criterion for the difference in the
PDF of amplitudes at the output of the proposed information-statistical detector, we will take the
difference in the entropy of the PDF:
𝛿𝐻(𝑈) = 𝐻1 (𝑈)/𝐻2 (𝑈)
As the analysis shows, modern digital equipment provides the measurement of PDF and their
entropy in a time scale close to the real one, with a practically acceptable error not exceeding one
percent.
The main difference of this detector from similar known ones is the presence of devices for
calculating and distinguishing noise signals. We emphasize that the proposed detector does not
contain a detector, because it distorts the shape of the voltage amplitude.
The possibility of practical implementation of the information-statistical algorithm for detecting a
nonlinear radar target by the method of sounding a noise-like signal has been confirmed
experimentally. The white noise generator G2-59 was used as a noise source with a distribution close
to normal stationary in the frequency band (H6.5 MHz). Through the ferrite antenna, the noise signal
was emitted towards a passive ferrite antenna located at a distance of 1 m, simulating the target.
An oscillographic method based on measuring the probability density by the luminosity of the
cathode ray tube screen was used to measure the type of voltage amplitudes. According to this
method, the investigated random signal was applied to the vertical plates of the oscilloscope. The
vertical deflection of the tube beam was interpreted as a value proportional to the probability p (U) ∙
∆U of the implementation of U (t) in the interval U, U + ∆U. The luminosity intensity of the
oscilloscope screen was interpreted as a value proportional to the time the beam is in the U + ∆U
region in the first approximation. Therefore, if when applying to the plates of the vertical deviation of
the randomly varying voltage U (t) horizontal unfolding is excluded, the law of change of the
intensity of the screen along the vertical axis coincides with the one-dimensional voltage probability
density.
Thus, the proposed nonlinear radar structure, due to the combination of the most sensitive
reception channels of the superheterodyne receiver of the detecting device with the most powerful
frequency components of the response of the nonlinear element to the dual-frequency emitted signal,
provides an increase in the quality indicators of the nonlinear element detection in comparison with
radars that implement reception according to the traditional superheterodyne scheme.
The obtained results confirm the types of distribution laws of the probing signal (Gaussian) and the
response signal from a nonlinear radar target (Reyleigh).
Thus, the proposed information and statistical algorithm for optimal detection of nonlinear radar
by sound-like sounding and structural diagram of the detector are practically implemented and differ
from the known not only high informativeness, but also lower technical requirements for the detector
equipment.
3. Conclusion
The specificity of nonlinear radar measurements is considered in the technological procedure for
synthesizing optimal structures and algorithms for detecting and measuring the characteristics of
objects with nonlinear electrical properties by identifying possible reserves for increasing the signal-
to-noise energy ratio at the receiver output. One of the main such reserves is the elimination of the
regular component of radio interference caused by the influence of the frequency harmonics of the
probing signal formed in the transmitter of the nonlinear locator.
It is shown that the use of noise and noise-like signals in non-linear radio engineering systems in
combination with the methods of their information-probabilistic processing makes it possible to
improve the technical characteristics of the systems.
The proposed set of new technical solutions in the field of the theory of nonlinear radar
measurements is presented in the form of structural diagrams and algorithms for optimal signal
reception in advanced technology of radar sensing and measuring the coordinates of objects with
nonlinear electrical properties.
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