Introduction. An analytical review of literature sources reporting various methods for GNSS interference mitigation using wavelet transform and signal processing in spatial and space–time domains is conducted. In his previous publication, the author proposed an approach to classifying GNSS interference mitigation methods and carried out a review of methods based on signal processing in the time, frequency, and time–frequency domains.

Aim. To carry out an analytical review of the basic principles and approaches for GNSS interference mitigation based on wavelet transform and spatial signal processing.

Materials and methods. The analysis involved literature sources published during the period from 2000 to 2024, selected in accordance with the following criteria: application of mitigation methods specifically to GNSS interference and papers containing theoretical justification and experimental confirmation of the effectiveness of the proposed methods. The author discusses methods that employ wavelet transform, super-resolution direction finding algorithms (Capon methods, MUSIC, ESPRIT), as well as methods using a Space-Time Adaptive Processor (STAP).

Results. The results of the conducted comparative review of methods and algorithms for mitigating interference in the reception of GNSS signals based on wavelet transform and signal processing in spatial and space–time domains are presented.

Conclusion. The conducted review and comparative analysis of the most common and effective methods of GNSS interference mitigation are useful for researchers and developers in terms of optimizing their literature search for the most recent achievements in the field. The use of multi-element adaptive antenna arrays is the most effective method for suppressing GNSS interference. Such antenna systems, particularly coupled with Space-Time Adaptive Processor, are a powerful tool for those consumers interested in high noise immunity of receiving GNSS signals and ready to bear the respective costs.

Introduction. Modern communication systems are supposed to use the allocated frequency band as efficiently as possible. This can be achieved by improving the spectral efficiency of such systems. One simple approach consists in introducing index modulation, which involves transmitting additional information by selecting one of possible combinations of the mutual arrangement of active and inactive resources. However, the presence of inactive resources hinder the achievement of maximal spectral efficiency, which makes it important to develop more sophisticated modulation schemes.

Aim. To develop a combined index modulation scheme with increased spectral efficiency and a receiver with acceptable computational complexity, as well as to obtain analytical expressions to estimate the noise immunity of this modulation scheme.

Materials and methods. Computer simulation in the MATLAB environment.

Results. A scheme of combined index modulation is proposed, in which all physical resources are active but have different power. In this case, high-level and low-level resources are used to transmit two separate signals. To further enhance the spectral efficiency, differential phase shift keying is introduced between the mentioned parts of the final signal. A receiver that processes each signal component separately, enabling significant expansion of the signal constellation and consequent improvement in spectral efficiency without substantial computational overhead is developed. Formulas for the error probability are obtained, the results of which are in good agreement with the simulation outcomes.

Conclusion. The developed method allows large-volume signal ensembles to be formed based on existing codebooks with insufficient spectral efficiency. The advantage of this approach to increasing spectral efficiency consists in the possibility of implementing a simplified reception method, in which the total number of arithmetic operations is determined by the sum, rather than by the product, of computational costs for processing individual signal components. Future research should extend the proposed approach by considering a combination of signals with index modulation patterns that have more than two levels.

Introduction. Compensation for the negative impact of failed elements of digital antenna arrays on the characteristics of the antenna pattern is a key problem in the creation and operation of such systems. A large number of methods have been proposed to date to solve this problem. These are based on the search for a new amplitude–phase distribution in antenna elements, which allows the beamwidth and the side lobe level to remain unchanged. In the proposed methods, a new antenna weighting vector is searched in the weight space for the extremum of a quality function that accounts for the change of the antenna pattern due to failed elements. The search is performed by one of the known optimization methods, such as conjugate gradient, projection, genetic algorithms, etc. These methods implement some iterative search procedures, which significantly increases the time required to find the necessary solution and the load on the signal processor.

Aim. To develop a direct algorithm for restoring the antenna pattern of a digital antenna array in presence of failed elements.

Materials and methods. The developed recovery algorithm is based on the estimation of the spatial frequency of the received wave using signals in antenna elements by the least squares method.

Results. A simple, non-iterative algorithm for timely restoring the antenna pattern of a digital antenna array is proposed. The conducted computer simulation showed that for the signal-to-noise ratio of 20 dB in the antenna elements, the algorithm restores the directivity, antenna beamwidth, and the first side lobe level with an accuracy of no worse than 2, 5, and 1 %, respectively, of the values of these parameters in the absence of failed elements

Conclusion. The proposed algorithm for restoring the antenna pattern of a digital antenna array can be used in software of a signal processor controlling the operation of an antenna system to compensate for the influence of failed elements.

Introduction. Methods for assessing the reliability of communication networks require simple and effective calculation tools. Although reduction methods allow the analysis of complex systems to be simplified, their application is limited by certain conditions.

Aim. To investigate a reduction method based on the sequential transformation of networks with serial and parallel connections into equivalent circuits. Bipolar connectivity that implies a path between two dedicated nodes is considered, in contrast to multipolar connectivity that evaluates connectivity between several critical nodes and all-pole connectivity that requires paths between all nodes of the network.

Materials and methods. Purely sequential and purely parallel structures, as well as their combinations, are considered. For sequential systems, the probability of operability is defined as the product of the serviceability probabilities of the elements, for parallel systems – through the probability of failure of all components.

Results. For mixed structures, a reduction algorithm for calculating their reliability using simplified formulas is proposed. The reduction procedure and the final formulas for calculating network reliability are directly derived from the rules for serial and parallel connections. A communication network was used as an example to confirm the method accuracy provided that the failures of the elements are independent.

Conclusion. The demonstrated reduction method is effective for analyzing the reliability of communication networks with series-parallel structures. The accuracy of calculations depends significantly on the assumption of the independence of failures. The advantages of the method include its simplicity and clarity; however, the method is inapplicable in cases of gradual failures and the interdependence of elements. In addition, this method processes correctly only loaded redundancy; for systems with unloaded or lightweight redundancy, the method needs to be modified. Computational difficulties for large-size networks and the possibility of information loss about the criticality of elements is noted. This is related to the loss of data on the contribution of individual components to the overall reliability of the system in the process of simplification, which impedes the analysis of weak links. The results obtained can be used in the design and optimization of communication networks, as well as for assessing their operational reliability.

Introduction. One approach to the analysis of complex structures of radioelectronic equipment is based on the construction of finite-difference models of non-stationary processes in structural elements. Such models are aimed at obtaining a convenient and easy-to-use algorithm for calculating the main strength characteristics of an object, such as displacements, deformations, and stresses. The basis for developing such an algorithm is the relationship between physical models presented in the form of discrete structures and their calculation schemes. Since the main structural elements of radioelectronic equipment are distinguished by a significant excess of two coordinates (width and height) over thickness, the calculation process is associated with certain difficulties. These are expressed in a significant volume of calculations with equal discretization steps for all coordinates, or in a decrease in the accuracy of calculations with different step values.

Aim. Research and development of an approach to strength assessment of circular cylindrical shells under dynamic external disturbances.

Materials and methods. The finite difference method was used to transfer from the equations of dynamic equilibrium in differential from to those in difference form.

Results. A method for calculating the stress–strain state of a shell using finite difference models is proposed. The resulting explicit difference scheme allows changing the boundary and initial conditions, thus enabling automatization of the calculation process. A specific example is used to consider the implementation of the proposed method for the case of a continuously acting pulsating cylindrical wave deforming the shell.

Conclusion. Future research can use the proposed method to analyze complex structures by improving the calculation models and including additional conditions and characteristics, thereby forming the basis for designing modules for engineering calculations of radioelectronic equipment.

Introduction. Conventional approaches to evaluating the electromagnetic interference (EMI) immunity of integrated circuits (ICs) focus on analyzing signals generated at their outputs. However, such methods fail to account for potential malfunctions in internal functional blocks, such as microcontrollers (MCUs). During operation, MCUs are exposed to external EMI, which can disrupt their functionality by altering data stored in their flashmemory, thereby increasing the risk of overall device failure. Consequently, there is a critical need to develop new methodologies for assessing MCU susceptibility and identifying EMI-vulnerable flash-memory locations.

Aim. To develop a comprehensive methodology for evaluating MCU susceptibility, encompassing analysis of generated signals and verification of flash-memory data integrity under EMI exposure in a TEM cell.

Materials and methods. A methodology for assessing MCU susceptibility in a TEM cell is described, including analysis of output signals and a data integrity verification algorithm for flash-memory. The approach localizes memory alterations using a checksum verification procedure.

Results. Experimental evaluation of IC signal susceptibility revealed deviations in the amplitude of the pulse-width modulated (PWM) signals, phase, and frequency of 33, 35, and 93 %, respectively, relative to baseline values. Flash-memory data corruption was observed at a clock frequency of 72 MHz under external EMI at 25 dBm (72 and 144 MHz). At 72 MHz, 40 % of the address space of the main program was modified, although the flash-memory retained its stored data. Exposure at 144 MHz altered 42.68 % of the address space and caused near-complete erasure of flash-memory data. Most flash-memory modifications occurred at the MCU’s fun-damental clock frequency and its harmonics.

Conclusion. The proposed TEM cell-based methodology for MCU susceptibility assessment, including flashmemory integrity testing, can be effectively applied to evaluate diverse MCUs.

Introduction. In conventional pulse radar systems of earlier generations that utilize magnetron generators, automatic frequency tracking and correction mechanisms are predominantly based on analog technology. These systems exhibit several inherent limitations, most notably those arising from to the limited frequency stability of the magnetron generator. Specific issues include inaccuracies in estimating the deviation between the measured frequency and its nominal value, a limited tracking range, and a slow response time. The fundamental cause of this low frequency stability lies in the magnetron design, which operates on an LC self-oscillation principle. In this paper, we propose to enhance the automatic frequency tracking and correction system by incorporating digital signal processing techniques and fast Fourier transform (FFT) algorithms. This approach enables rapid and high-precision measurement of the operating frequency within time intervals defined by the pulse width. The proposed methodology significantly improves the performance and reliability of such systems. These findings hold considerable practical importance, particularly for the modernization and sustained operation of legacy pulse radar systems. By addressing the limitations of outdated analog components, the proposed solution extends the operational lifespan of such systems. This is of importance given the scarcity of replacement parts that are no longer available on the market.

Aim. Research and presentation of a digital solution for the system of automatic frequency tracking and correction. Materials and methods. The research methodology was based on previous research findings, achievements in digital signal processing and theoretical analysis. A structural diagram of the proposed system was developed and its experimental simulation was conducted.

Results. A functional diagram of the proposed automatic frequency tracking and correction system is developed. Specific experimental results are described. The measurement error can reach 1 kHz (~0.003 %) in the mid-frequency range.

Conclusion. An automatic frequency tracking and correction system has been developed. This approach extends the current methodology in the field of pulse radars.

Introduction. This article analyzes the possibility of implementing highly efficient fault-tolerant algorithms for resolving the ambiguity of phase measurements in Russian and foreign global navigation satellite systems. Nominal values of the GLONASS carrier frequencies with code division of signals are proposed, which ensure an increase in its efficiency by implementing the technology of non-multiple scales. Algorithms for resolving the ambiguity of phase measurements are considered. These algorithms are based on a system of residual classes to calculate the integer value of the number of phase cycles of carrier frequencies in the obtained unambiguity range. The simulation results are presented, and the stability of the proposed algorithms to systematic and random errors of phase measurements is shown.

Aim. To improve the efficiency of global navigation satellite systems in determining the position of consumer navigation equipment using phase measurements.

Materials and methods. The MATLAB modeling environment was used to process phase measurements from RINEX files. This environment has proven efficient in resolving a wide range of scientific problems of varying complexity in industrial and research settings. To achieve the research aim, the mathematical apparatus of number theory and the system of residual classes were employed.

Results. For the GLONASS system with code division of signals, new nominal values of carrier frequencies are proposed; a highly efficient fault-tolerant algorithm for resolving the ambiguity of phase measurements is developed and simulated. The stability of non-multiple scales to systematic errors causing a shift of scales relative to each other is shown, and the operability and reliability of ambiguity resolution algorithms in the presence of random errors not exceeding the value of the specified limiting error of phase measurements is confirmed.

Conclusion. The conducted analysis has shown the possibility of forming non-multiple phase metric scales in consumer navigation equipment using signals with code division of GLONASS, GPS, Galileo, and BeiDou systems.

Introduction. Walking with additional load, such as a backpack, weights, or specialized equipment, has a significant effect on the musculoskeletal system. Carrying extra weight increases the load on the lower limb joints, enhances muscular activity, and modifies the spatiotemporal characteristics of gait, which is accompanied by increased energy expenditure. Notably, these effects depend not only on the mass but also on the distribution of the load. Contemporary studies are increasingly employing the integration of biomechanical, kinetic, and electromyographic data to quantitatively assess the body’s adaptation mechanisms to external loading. The development of integrated metrics for loaded walking is relevant for objective characterization of the biomechanical cost of different loading conditions, being promising for application in sports science, ergonomics, military training, and clinical practice.

Aim. To develop an integral index that quantitatively reflects changes in human gait under two external loads: 3 kg attached to the lower legs and 12 kg evenly distributed in a backpack. A functional analysis of loaded human gait, represented by a set of biomechanical and electromyographic parameters, was carried out.

Materials and methods. Seven healthy volunteers were subjected to examination using the methods of 3D optical motion capture and simultaneous surface electromyography from seven muscle groups. The primary trajectories were processed in QTM, exported to TXT/TSV, and further organized by Python scripts. The aggregated values (maximum, minimum, ROM) were automatically transferred to Excel. Inter-parameter dependencies were examined using Spearman’s correlation coefficient. The statistical significance of individual changes was assessed using the Friedman test followed by cluster analysis.

Results. An integral index (I_total) using global min–max normalization and equal weighting of the selected metrics was developed.

Conclusion. Distal loading increases double-support time and decreases step frequency, whereas proximal loading alters muscle activation patterns and pelvic positioning, partially normalizing spatiotemporal gait parameters. The proposed integral index combines changes in biomechanical and EMG parameters, enabling a quantitative assessment of the biomechanical cost associated with the applied load.