No. 4 (2024)

This article is devoted to the review of known and modern approaches, methods and algorithms of
full-text search. A brief history of the solution of the problem of search in unstructured text data, its development
and relevance are described. The main task of search in text data is formulated. The definition of
the database index is given. The target function of the search information system is defined in general
terms and possible compromise variations of its parameters when solving various applied problems are
described. A generalized architecture of a modern search information system is given with the division of
the search problem into two phases: the primary extraction of relevant records and their subsequent ranking
to form the final search results. The article provides basic descriptions of the main algorithms and
methods of full-text search, such as: search by terms (logical search), search using trees and their varieties
(B-trees, UB-trees, tries), search based on n-grams (including search based on frequency representation),
use of the vector space model (VSM), search based on an inverted (reverse) index, search using the apparatus of fuzzy logic and bioinspired methods. The main advantages and disadvantages of these methods
are given, their applicability in various conditions is described, and possible methods for optimizing
the search for text data to improve the accuracy, speed of search and efficiency of resource use are considered.
Possible promising directions in the field of solving the problem of primary information extraction
are presented. Some methods for determining the similarity of text records for solving the ranking
problem based on the apparatus of fuzzy logic are given. The article touches upon the issues of increasing
the relevance of primary extraction using artificial intelligence methods, neural networks, fuzzy logic and
bioinspired methods, in particular methods for expanding the search query and/or expanding the processed
text records. The influence of the boundary conditions of the search system construction on increasing
its efficiency is described. In conclusion, the article summarizes the review and discusses the prospects
for further development of various full-text search methods.

A methodology has been developed for finding solutions to the semi-infinite strip packing problem
based on models of adaptive behavior of biological systems. To reduce the overall labor intensity of the
search procedure, an approach based on decomposition of the problem being solved is proposed.
The packaging is designed for cutting by guillotine cutting of the tape into containers and non-guillotine
cutting of containers into elements. Packaging is carried out by sequentially filling the strip with containers.
The problem of packing rectangles into strips is solved in three stages. At the first stage, the agent
solves the problem of distributing a set A of rectangular-shaped elements in a set of blocks B. The problem
of forming a set of blocks B, including sets of rectangular-shaped elements A, is solved by an algorithm for
one-dimensional packing of elements into identical blocks. At the second stage, the problem of distributing
blocks among containers is solved. All containers have the same width D, equal to the width of the strip.
Each container holds two blocks. The process of distributing blocks into containers is accompanied by a
compaction procedure for each pair of blocks assigned to one container. The purpose of compaction is to
minimize the total area of the container by densely placing the blocks. Compaction is carried out sequentially
in all containers. The problem of distributing blocks into containers is reduced to the problem of
finding the maximum matching of the minimum cost. In contrast to the canonical paradigm of the ant algorithm,
when working as an agent, a clique is built on the solution search graph, on the edges of which a
pheromone is deposited. A technique has been developed for the formation of pheromone points and data
structures of collective evolutionary memory. To conduct objective experiments, well-known test problems
presented in the literature and on the Internet were used. Compared to existing algorithms, a 3-5% improvement
in results was achieved. The time complexity of the algorithm, obtained experimentally, practically
coincides with theoretical studies and for the considered test problems is ≈ О(n2).

The article illustrates a method for finding the maximum value of a dynamic flow using periodic
graphs, presented in the form of a generalized network. The interest in networks of this type is explained
by their wide practical application in places where there is periodicity, for example, management of periodic
passenger transportation on various types of transport, freight transportation, including goods with a
short shelf life, management of road traffic flow, namely regulation traffic lights, taking into account frequency
and workload. At the same time, the values of the bandwidth of the arcs of the networks under
consideration may vary depending on the time of departure of the stream and possible cycles, so we turn
to dynamic networks. Network parameters are presented in a fuzzy form due to the influence of environmental
factors and human activity. And the choice of periodic graphs is due to the presence of cycles and
the frequency of time intervals. The considered types of networks can be implemented on real roads during
transportation. To solve the identified problem, within the framework of the presented work, a brief overview
of literary sources is provided, which allows us to assess the current level of development of systems
for such purposes. As a result of this review, it was found that the most effective methods of solving the
problem posed are the use of fuzzy periodic graph methods. In this regard, it was decided to conduct a
study of these methods. The novelty of this work is determined based on the use of periodic temporal fuzzy
graphs in solving the problem of finding the maximum flow of a dynamic network.

This study provides a comprehensive analysis of the multi-traveling salesman problem, which is an
extended version of the classical traveling salesman problem. In contrast to the latter, the multi-traveling
salesman problem involves the participation of several traveling salesmen, each of whom must visit a certain
number of cities exactly once and return to the starting point, while minimizing travel costs. The multi-traveling salesman problem is of significant interest in the field of route optimization and task distribution
among multiple agents. The main goal of the research is to develop an effective method for solving
this problem, which will reduce execution time and optimize the use of resources. As part of the study, an
innovative method was developed, which is based on reducing the dimension of the solution space. This
method allows you to more effectively distribute the load and manage resources, which ultimately helps
reduce the overall time to complete tasks. One of the key features of the proposed method is its versatility
and adaptability to various scenarios, including situations with varying numbers of tasks and traveling
salespeople. A detailed study of the proposed method was also carried out from the point of view of the
influence of its hyperparameters (pheromone evaporation coefficient, number of iterations, number of
ants) on the quality of the solution and calculation time. To evaluate the effectiveness of the new method, a
comparative study was conducted using the classical method for solving the multi-traveling salesman
problem. The results were assessed according to three main criteria: the computation time for solving the
multi-traveling salesman problem, the total length of the routes traveled, and the maximum route length
among all traveling salesmen. Analysis of experimental data showed that the developed method significantly
exceeds the classical one in all key indicators. These results confirm the high efficiency of the proposed
method and its promise for practical application in various fields that require optimizing routes and
distributing tasks among several performers. Thus, the study demonstrates that the developed method has
significant potential for improving routing and resource allocation processes. Its application can significantly
increase efficiency in various areas where coordination of the work of several agents is necessary,
such as logistics, transport systems and other areas related to route optimization.

All sorting algorithms are information-equivalent. Therefore, the choice of the most effective algorithm
usually depends on its operation velocity and the capacity of used memory. At parallel, hardware
implementation, the efficiency of sorting algorithms is also affected by the degree of utilization of
hardware resources; the latency of the resulting computing structure; the number and digit capacity of
the sorted elements. The problem of sorting or ordering data is not formalized in the form of mathema tical
transformations. Therefore, each of the known algorithms for solving it is considered an atomic,
independent unit. The transition from one algorithm for solving the problem to another is possible at
describing the problem in the form of an information graph, the vertices of which represent the elementary
performed operations, and the arcs – the information dependencies between them. Having a set of
elementary transformations, it is possible to influence the functional regularity of the information
graph connections, the latency of the computing structure, the coefficient of parallelism, etc. The information
graph of the “bubble” sorting problem is a simple sorting network, developed on the “head -
tail” principle of combining steps. In this paper, the functional redundancy of such sorting networks is
shown and justified; the methods to optimize the number of operations and change the order of their
sequence are given. The main result of the paper is the method for converting sorting networks into an
odd-even Butcher mergesort. A program has been developed that automatically performs the transformation
of sorting networks and allows to adjust the information graph topology to the most effective
form, depending on the resulting degree of parallelism of the computing structure. Summarizing the obtained results, note that the automated reduction of known algorithms to “fast” ones can ensure the
optimal parallel pipeline program under specified constraints, which will significantly accelerate the
process of their development.

The work is devoted to the problem of improving the accuracy of short-term forecasting of electricity
consumption using deep machine learning tools. The influence of the specified neural network NN
hyperparameters on the error in predicting power consumption, such as: data packet size – Bs; number of
NN layers – j; neuron activation functions – Fa; optimizers – O. The optimal hyperparameters of the NN
model for predicting electrical consumption (EC) for consumers of additive and cyclic types have been
determined. The analysis of the impact of the batch size on the accuracy of the forecast showed an increase
in the effectiveness of NN training with the growth of the input data package. The analysis of the
influence of the number of layers showed that with an increase in the number of layers of the NN, the
learning time decreases and its predictions become more accurate. A study of various optimizers for
learning speed has shown that the best results are demonstrated by the optimizers “Adam” and
“RMSProp". It is shown that the choice of the activation function determines how quickly the NN will be
trained and how accurate its forecasts will be. The use of various regularization methods allows NS to
achieve better results in practice, improving their generalization ability and increasing the accuracy of
predictions. It is shown that in order to achieve the minimum forecasting error, it is necessary to individually
configure the network parameters for each consumer, taking into account significant differences in
the nature of energy consumption. The training and testing of the created network with selected parameters
was carried out on a training and test sample containing data on electricity consumption for 2 years
(17520 hours). The analysis of input data on power consumption showed that the optimal parameters of the predictive neural network model in manual mode are: package size 250 (selected empirically), 5 layers,
activation function “ReLU", optimizer “Adam". Various ways of selecting hyperparameters (manually
and by means of genetic algorithm (GA)) are considered.

The task of building a model for assessing the performance of a technical object has many applications
in the field of controlling various hazardous situations. The need for advanced monitoring of the
technical object state to prevent and control the course of abnormal situations in order to eliminate them
with minimal consequences makes the statement and fulfillment of this task relevant and timely. To perform
the assessment of the state of the technical object it is advisable to use simple models that allow to
obtain the result in real time without significant load on the microcontroller control system. The paper
considers the construction of a model for classifying the dynamics of change in the parameter of a technical
object, which will allow you to predict the change in its state in the process of assessing the degree
of serviceability of the object. The data reflecting the change of parameters in real time and presented in
the form of time series of parameter values are used. The change of the object parameter in time is fixed
with the help of a time window, which moves along the time series, cutting out of the set of initial data a
subset with an unchanged number of time samples. To classify the dynamics of parameter variation, it is proposed to use a representation of the time window points in the form of a Poincaré plot, which is actually
a special type of repetition plot or a type of scatter plot. The ellipse compression factor (ellipticity) is
used as a criterion, which encompasses the point cloud formed during the construction of the scatter diagram,
for the time series of the technical parameter. A methodology for training and using the model,
including the formation of classes of states of the dynamics of the object parameter and the calculation of
criteria, is developed. The model has been tested. The model provides the realization of procedures for
real-time detection of the possibility of an abnormal situation at an early stage of its development with the
help of a microprocessor module located at the lower level of the object monitoring system.

In today's rapidly changing and demanding work environment, the ability to quickly and accurately
assess an employee's emotional state is crucial to protecting human lives and reducing material risks.
Emotional well-being plays an important role in workplace safety, productivity, and overall mental health.
Therefore, the development of effective tools for monitoring negative emotions and responding to them is
an urgent task of our time. The purpose of this study is to develop an algorithm capable of classifying
emotions using audio data recorded by a user's smartphone. Such a tool is especially useful if integrated
into a broader health monitoring system that allows you to evaluate human health indicators in real time
using non-invasive methods. This article presents a new solution that uses acoustic signals picked up by a
smartphone microphone to detect and classify user emotions. Using convolutional neural networks
(CNNS), a type of deep learning algorithm known for its effectiveness in processing audio and visual data,
the proposed system can determine the user's emotional state. The CNN model is trained to recognize
patterns in audio data corresponding to various emotional manifestations, focusing on detecting negative
emotions such as anger or sadness. The results of the study demonstrate the effectiveness of the system:
the error rate in determining negative emotions is 19.5% for false positive results (errors of the first kind)
and 20.1% for false negative results (errors of the second kind). These indicators indicate its potential for
practical application in real conditions. By integrating this solution into existing biomedical monitoring
systems, organizations can expand their ability to monitor the emotional well-being of employees, potentially
preventing negative consequences such as industrial accidents or mental health crises. The integration
of emotion recognition using smartphones into health monitoring systems represents significant progress
in the field of non-invasive biomedical monitoring, using the ubiquitous presence of smartphones
and machine learning capabilities.

Virtual prototyping is performed during product development to validate a design using a computer
model before making a physical prototype. For this purpose, EDA for printed circuit board (PCB) design
contain SPICE circuit simulator. Typically, modern PCB assemblies include one or more large-scale integrated
circuits (LSI). The LSI functionality is complemented by auxiliary integrated circuits (IC) and discrete
components. In most cases, the required efficiency is achieved by using LSIs that include processor
cores. Therefore circuit simulators must provide a hardware/software co-simulation. System-level LSI
models are acceptable in terms of computational resource costs. Major advances in system-level simulation,
including co-simulation, come from the development of LSIs themselves. In PCB design, LSIs are
fully fabricated components. This specificity must be taken into account when implementing tools for PCB
design verifying. System-level LSI models must be integrated into the overall assembly circuit model. LSI
models must provide the required accuracy only at the external pins. Models of digital LSIs must accurately
reproduce delays between level changes at the pins and diagnose timing violations. EDA for PCB
design users must develop LSI models tailored to the project specifics. The purpose of the research is to
find solutions for building models of LSIs, containing processor cores, for prototyping circuits using
OrCAD PCB Designer with PSpice. The article discusses the task of building a C/C++ model for the
dsPIC33 microcontroller that performs signal processing in real time. An example of building a C/C++
model using the PSpice Model Editor tools and modeling results are given.

The increasing incidence of crimes committed in cyberspace, particularly on social networks and
various messengers, necessitates the development of adequate and effective countermeasures. The rise in
cybercrime is so significant that it poses a potential threat of inflicting irreparable harm to the state and
society. However, detecting such crimes and criminal activities is challenging because offenders operate
virtually and linguistically within social networks, exploiting their features to conceal their traces. Nonetheless,
various detection and identification tools capable of automatically processing natural language,
highlighting specific semantic features of criminal activities, and recognizing and identifying them could
serve as effective countermeasures. Given the impracticality of applying neural network approaches to
these situations for several reasons, this study proposes a formal method for designing a recognizer to
identify semantic objects in text streams based on their linguistic traces. Formal concepts such as the formal
model of a semantic object, behavior function, scenario, linguistic trace, and recognition function are
introduced. The reasoning is based on set-theoretical principles of computational theory of semantic interpretation
and utilizes computational representations of the meaning of text fragments for their comparison
in terms of semantic similarity. The proposed approach is general and universal, allowing for the
formal synthesis of a recognizer for semantic objects based on their linguistic descriptions and behavior.
All discussions and constructions in the work are illustrated with specific examples.

Large consumers of electricity mainly purchase electricity on the wholesale electricity and capacity
market, for example, industrial enterprises of ferrous metallurgy. For the production of products, large
industrial enterprises daily order hourly volumes of electricity consumption for two days in advance, if
necessary, enterprises have the right to send adjusted values for the day preceding the day of consumption.
At the same time, for deviations from the planned hourly volumes, enterprises incur additional costs,
which are included in the electricity tariff. One of the most important factors that affect the forecasting of
hourly electricity consumption are: the variety of types of main and auxiliary equipment, the capacities of
electricity consumers carrying out the technological processes of the enterprise; the intensity of production
load and operating modes depending on the production of the product range; the frequent use of
hours of maximum electric power during the Days; energy-intensive production. To build forecast data for
time series, a model is built to predict hourly electricity consumption by an industrial enterprise and has a
large number of input data that have a probabilistic component. Consideration of various methods for
forecasting time series of electricity consumption of industrial enterprises seems to be an urgent scientific
and technical task. This is due to the requirements of minimization, firstly, of jumps and failures in the
operation of generating capacities of the energy system of the region in which the enterprise is located
(since the load, for example, of ferrous metallurgy enterprises can reach up to 10% of the total consumption
of the region), and secondly, additional costs associated with the purchase/sale of volumes of electricity
consumed in excess of the application/unused in case of inaccurate planning of hourly volumes of electricity
consumed, which are included in the electricity tariff.

Any time series is a combination of useful information and noise. Therefore, in the analysis of financial
time series, one of the key points is the preprocessing of data in order to reduce the noise component.
One of the promising ways to clean up the time series is threading – decomposing the signal into a wavelet
spectrum to a given level, zeroing out those wavelet decomposition coefficients whose values are less than
a certain threshold value, and subsequent wavelet reconstruction of the signal using approximating and
refined detailing coefficients at each level. Tresholding is carried out using modern software tools, among
which researchers most often prefer the Matlab environment. This paper presents a demonstration of the
capabilities of the Wolfram Mathematica computer mathematics system in the preliminary processing of
financial data. Wolfram Mathematica has powerful functionality that allows high-quality processing of
time series. The system contains a large collection of wavelet families, multiple variants of discrete and
continuous wavelet transformations. The history of Sberbank's daily stock quotes over the past 3 years was
chosen as the object of the study. An analysis of the results showed that the quality of signal purification is
influenced by the choice of a basic wavelet – in our case, the use of a 6th-order Daubechies wavelet
turned out to be preferable. The maximum signal-to-noise ratio is achieved with rigid threshold processing
with a "SURELevel" threshold. The conducted studies have shown that wavelet tresholding over
the detailing coefficients of the wavelet decomposition is an effective method of suppressing outliers and
fluctuations of the time series. The cleared signal repeats the shape of the original signal, all peaks are
well expressed. At the same time, more accurate forecast values are obtained in the short-term forecast

In today's world, where environmental problems are becoming more and more urgent, the search
for alternative energy sources is becoming a priority. One of the most promising areas is solar energy.
Solar energy is a renewable energy source, which makes it attractive for use in various areas, including
power generation, heating and cooling of buildings, and transport. The development of solar energy can
contribute to solving a number of environmental problems such as pollution and climate change. However,
solar panel equipment is subject to various types of defects and contamination. Defects can adversely
affect the performance and efficiency of solar panels, so their detection is critical to improve the reliability
and durability of photovoltaic power generation systems. Effective fault finding can minimise energy losses,
improve system reliability and equipment life, and reduce maintenance costs. In addition, improved
performance of electrical equipment contributes to the sustainable development of alternative energy, thus
reducing dependence on conventional energy sources and reducing greenhouse gas emissions. The paper
presents an overview of existing methods for detecting various solar panel faults using computer vision and deep learning techniques. Infrared thermography (IR), electroluminescence (EL) imaging, or visible
spectrum imaging can be used to find the faults. This paper includes an analysis of the advantages and
disadvantages of existing methods for finding defects and contamination in solar panels, discusses the
factors affecting their performance, and presents conclusions for possible future research in this area.

In the process of mass production of ferroelectric materials, impurities of various types and concentrations
are periodically observed in the feedstock. The aim of the study was to determine the effect of
impurity phases present in the feedstock on the dielectric and electrophysical properties of ferroelectric
ceramics. In this work, the basic raw materials components included in the lead zirconate - titanate system
for the presence of impurity components were studied by spectral analysis. The results revealed a group of
impurity phases (Sb, Na, Bi, K, Fe) of different concentrations. The model object of the study was an industrially
produced ferroelectric material with a perovskite structure and the chemical formula
Pb0,95Sr0,05(Zr0,53Ti0,47)O3 + 1% Nb2O5. The objective of the study was the dosed introduction of impurity
alloying additives into the composition of the initial ferroelectric material in order to possibly change the
final properties. The study established the relevance of the dosed introduction of K and Na impurities at a
concentration of 1-2 % into the PZT system in order to reduce the values of relative permittivity by 40-45 %. The dependences of the formed ceramic structure on the introduced impurity alloying phases have been
established by scanning electron microscopy. The regularities of the "type of impurity additive – microstructure
– properties" have been established. As a result of the study, the effectiveness of dosed administration
of impurity alloying additives K and Na in order to modify the properties of ferroelectric ceramics
of the PZT system was confirmed. Such impurity alloying leads to an increase in the values of the specific
voltage sensitivity (g33) to 34-37 mV·m/N. Ferroelectric materials of this format are of high practical
interest for the creation of acoustic transducers operating in reception mode.

The purpose of the study is to calculate and design the device that measures the phase differences of
signals, with the ability to receive control commands and transmit the results via a high-speed Ethernet
interface. Any modern measuring device of the optical or ultrahigh frequency (microwave) range has an
important element in its design, without which no measurement is possible, namely, a vector voltmeter that
measures the phase shift and the ratio of signal amplitudes. Practically no one is engaged in the implementation
of such devices and such developments are mainly the intellectual property of large companies,
therefore, the design and creation of such a device in a widely available version is necessary. We have
considered modern modulation formats and the implementation of transponders for the transmission of
optical signals using multi-level formats of quadrature phase shift manipulation with double polarization
(DP QPSK) and 16-position quadrature amplitude modulation with double polarization (DP 16QAM), as
well as the basic methods for constructing vector voltmeters using microcontrollers and field programmable
gate arrays (FPGA), optical communication channels were simulated and a phase shift measurement
device was created. As a result of our research, we obtained a vector voltmeter on an FPGA, which, in
turn, can be used to create an installation for measuring the phase shift of mixers connected via an Ethernet
interface. Also, in the Verilog HDL hardware programming language for the Altera Cyclone V FPGA,
a program code has been compiled for an electronic computing machine to measure the phase difference
of two harmonic signals. A C program has been implemented for the ARM Cortex A9 processor in the
Quartus Prime Lite environment as part of the Cyclone V ultra-large integrated circuit (VLSI), transmitting
measurement results in real time over the 1GB interface to a computer with the ability to receive control
commands.

In satellite communication complexes, it is required to ensure a given level of the gain of the space
antenna in a given serviced area. A lower level of gain beyond this area is also required. The boundary of
the coverage area may have a complex shape that does not change during the operation of the communication
system. To meet these requirements, reflector antennas with a profiled reflector are used. The law
of profiling the reflector surface is described by smooth analytical functions. However, when forming a
contour lobe with a more complex shape, the required phase distribution may have discontinuities during
the transition through the period 2π. These gaps cannot be eliminated by smooth functions without distortion.
In this case, the known approaches to profiling reflectors of reflector antennas do not allow obtaining
a radiation pattern with a given quality. The goal of the work was constructing a reflector of a reflector
antenna, which provides the formation of a radiation pattern with specified parameters. To achieve
this goal, the following tasks have been solved: 1. Development of an algorithm for profiling the reflector
of a reflector antenna, taking into account the shape of the boundary of the serviced area and taking into
account the given law of distribution of the gain; 2. Conducting numerical simulations on the construction
of the reflector profile. In the course of the research, an algorithm has been developed that allows you to
obtain the reflector profile of a reflector antenna. This reflector antenna generates a field distribution at
the aperture corresponding to the radiation pattern with the required parameters. To do this, the calculation
of the field distribution on the plane was performed, and the surface of the reflector was synthesized
based on the calculation results. Numerical simulations have confirmed the possibility of constructing a
reflector antenna that forms a radiation pattern with specified parameters.

Due to the cohabitation of multiple types of communication networks and the increasing need for
high-speed data transmission, multi-frequency and broadband communication systems have gained popularity
as study topics. Omnidirectional antennas can handle more individual frequency bands and are
useful for a variety of wireless communications devices due to their radiation pattern, which facilitates
effective transmission and reception from a mobile device. However, for mobile communication systems
supporting 2G, 3G, 4G, and future 5G applications, the use of a high-bandwidth antenna may be crucial.
Since 5G offers its vast user base higher data speed, greater dependability, and reduced power consumption,
numerous studies on 5G broadband antennas have been published. Because of its many advantages,
such as higher channel capacity, better signal transmission and reception performance, the ability to
place big antennas in tiny spaces, and more, MIMO has emerged as a crucial technology for 5G. A number
of different 5G MIMO antenna types have recently been suggested for cellphones. An indoor
GSM/3G/LTE/5G communication system using a 2 × 2 wideband MIMO antenna is suggested in this
study. The antenna uses two antenna elements evenly spaced around the centre to form an omnidirectional
radiation pattern. Simultaneously, excellent omnidirectional emission properties and a broad bandwidth
are obtained. An impedance bandwidth of (0.7-5.3) GHz can be accomplished with a return loss of up to -
23 based on the simulation results, with a gain of up to 6.5 dB. ANSYS HFSS (High Frequency Structure
Simulator) 2020 is used to simulate the antenna.

The design of a low-profile antenna array of tightly coupled circularly polarized dipoles is considered.
The main design detail is two crossed printed dipoles. Quadrature excitation is provided by arcshaped
strips connecting pairs of orthogonally located arms on the upper and lower metallization layers.
To ensure capacitive coupling between the elements, metal disks are used, galvanically connected to the
base using metal rods. To expand the operating frequency band and improve the radiation characteristics
of the antenna array, a matching layer of Eccostock HiK plastic is located directly above the dipoles. The
results of a numerical study of the characteristics of an elementary cell of an antenna array with periodic
boundary conditions on the faces in the ANSYS HFSS software are presented. The possibility of operating
in a wide frequency band at a given level of matching and ellipticity coefficient is demonstrated. The dependence
of the matching characteristics and the ellipticity coefficient on the size of the strip that provides
quadrature power to the dipole arms is shown. It was established by calculation that the choice of the strip
radius, which ensures quadrature excitation of the dipole arms, is a compromise between a wide operating
frequency band and a better ellipticity coefficient in the center of the range. It is shown that the use of a
matching layer located directly above the dipole layer in arrays of tightly coupled circularly polarized
dipoles ensured matching over a wide frequency band while maintaining an electrically low profile height.
Based on the proposed element, models of finite antenna arrays of 3×3, 4×4, 5×5 and 6×6 elements have
been developed. The influence of elements located at the edges on the characteristics of the antenna array
is shown. The possibility of improving performance by connecting the outermost elements to matched
loads was investigated.

The aim of the study is to solve the problem of the influence of the nonlinearity of phase shifts of
harmonics during frequency multiplication on the measurement results of absolute phase shifts occurring
in mixers and errors in various measurement methods of these shifts in the mixer during heterodyne frequency
conversion of the input ultrahigh frequency (microwave) signal. Since the signal at the input of the
microwave mixer and the intermediate frequency signal at its output lie in different frequency ranges, it is
impossible by traditional methods to measure the phase shift introduced by the nonlinear element of the
mixer into the intermediate frequency signal during the heterodyne frequency conversion of the input microwave
signal. The problem that we have considered in this study is to identify the measurement error of
absolute phase shifts that occur in a mixing diode during heterodyne frequency conversion due to its nonlinearity.
This error can have a significant impact on the accuracy of measurements, and therefore its
accounting and compensation are important tasks in radio engineering and communications. This scientific
article demonstrates the important inequality of the phase shifts of harmonics multiplied by the phase
shift of the multiplied signal used in the measurement methods of absolute phase shifts of mixers. We also
proposed an innovative method devoid of these measurement errors, which allows us to take into account the nonlinearity of the mixing diode and provide more accurate measurements. The results of this study
are of great importance for accurate measurements in radio engineering and communications. The proposed
method, devoid of these errors, can significantly increase the accuracy of measurements of absolute
phase shifts of mixers with heterodyne frequency conversion. This innovative solution allows you to take
into account the nonlinearity of the mixing diode and provide accurate measurements, which can be very
useful when creating devices capable of measuring the phase shift of the microwave mixer under test and
vector voltmeters based on programmable logic integrated circuits (FPGAs).