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“Digital
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Mathematical model of correlation methods of frame synchronization of LTE technology
K.Yu. Ryumshin Doctor of Technical Sciences, e-mail: e86420@yandex.ru
T.P Kiseleva, e-mail: golzev2011@yandex.ru
RTS Department of the Moscow Technical University of Communications and Informatics (MTUCI), Russia, Moscow
Keywords: mathematical model, cyclic autocorrelation function, cross-correlation function, CAZAC (multiphase) sequences, correlation synchronization method along OFDM character boundaries, time window for processing the received frame.
Abstract
The widespread use of OFDM (Orthogonal frequency division multiplexing) technology and the combination of this technology with other advanced communication technologies allows us to successfully solve the problems of increasing speed, noise immunity, spectral efficiency and customer service quality. A prerequisite for the successful solution of the tasks set is the improvement of synchronization systems of modern communication technologies using OFDM symbol construction. The correlation method of synchronization along the boundaries of the OFDM symbols of the LTE technology frame presented in [1-4] [5-7], the feature of which is to replace the basic binary data filling of the cyclic prefix (CP) and the end of the OFDM symbols of the central frequency range of the LTE frame with CAZAC (Constant Amplitude Zero AutoCorrelation – a multiphase sequence with zero autocorrelation), sequences of the same length, or their sum with binary data of the end of characters, reduces the synchronization time at the peaks of the CP autocorrelation function (ACF) by 1.5 – 2.6 times due to a decrease in the time "window" for processing the received frame and higher values of the CAZAC merit-factor of sequences compared to the basic version of filling the CP and the end of characters with binary data. This article presents a mathematical model that implements options for constructing the central frequency range of an LTE frame by filling the ends of OFDM symbols with CAZAC sequences or their sum with binary data, as well as statistical and correlation methods for processing the received LTE frame in the time domain to obtain peaks of cyclic ACF of CP that match the boundaries of OFDM symbols with a given accuracy. Then, an aperiodic correlation of a "sliding window" with a duration of one character is performed to the right and left along the time axis from the obtained boundaries of the OFDM symbols with reference primary sync signals until a correlation peak is obtained marking the boundary of the LTE half-frame with a given accuracy.
This article provides a block diagram and analytical expressions describing the functional modules of the developed mathematical model.
References
1. Kiseleva T.P. – Using Assignment sequences for synchronization along the correlation curve of the cyclic prefix of OFDM symbols of LTE technology – Digital Signal Processing, No. 4,2018, 40-44 p.
2. Kiseleva T.P. – Calculation of the time of entry into synchronism at the stage of synchronization using a cyclic prefix of symbols in LTE OFDMA technology – Digital signal processing, No. 4, 2020, 43-48 p.
3. Kiseleva T.P. The time of entering into synchronism during synchronization according to the cyclic prefix OFDM symbols formed by the sum of information and multiphase sequences. - IEEE Xplore Digital Library,March, 2023 (IEEE Conference Record #56737)
4. Ryumshin K.Y., Kiseleva T.P. Investigation of sequences for the formation of a synchro signal of the PSS frame of a low–orbit satellite communication and data transmission system / K.Y. Ryumshin, T.P. Kiseleva // Digital signal processing. – 2024. – No. 2. pp. 35-43.
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Signal processing in compact doppler-based velocity and drift angle measurement systems for autonomous navigation of unmanned aerial vehicles
L.B. Ryazantsev, e-mail: kernel386@mail.ru
Babich O.A., e-mail: oleg9mufc5fan@mail.ru
D.L. Ryazantsev, e-mail: kepke386@mail.ru
MESC «Zhukovsky–Gagarin Air Force Academy», Russia, Voronezh
LLC «ERA FPI», Russia, Anapa
Keywords: unmanned aerial vehicles, Doppler velocity sensor, autonomous navigation, orientation angles, coordinate system, accuracy assessment, Linear Frequency Modulation.
Abstract
The rapid development of unmanned aerial vehicle (UAV) and the increasing demands for their autonomous operation, including in complex electronic warfare environments, necessitate the development of devices capable of determining flight parameters (velocity vector components), spatial orientation angles, and coordinates. This information is crucial for onboard autopilots and flight control systems. Existing small-scale inertial navigation systems (INS), based on low-cost piezoelectric gyroscopes, accelerometers, and magnetometers, are prone to error accumulation and often fail to provide the required navigation accuracy, even with periodic correction from external sensors. The use of satellite navigation receivers is not always feasible due to their susceptibility to electronic jamming, limiting UAV operational autonomy.
This article examines signal processing methods applicable to miniaturized Doppler-based velocity and drift angle measurement systems (DVMS). The authors derive analytical expressions linking the Doppler characteristics of reflected signals to the motion parameters and spatial orientation of a UAV for single-beam, dual-beam, triple-beam, and quadruple-beam system configurations. The analysis is based on the fundamental relationship between the Doppler shift frequency, the radar wavelength, and the radial velocity of the carrier relative to the reflecting surface. A methodology for assessing measurement errors induced by variations in the aircraft's spatial orientation (pitch, yaw, roll) is formulated and applied.
Key findings are as follows:
Single-Beam Systems exhibit a strong dependence of velocity measurement error on the aircraft's pitch angle. Even minor pitch measurement errors from a low-cost INS can lead to significant (tens of percent) velocity errors, making them suitable only for rough estimation during stable, level flight.
Dual-Beam Systems effectively compensate for pitch angle variations, providing stable velocity and pitch angle measurements within the antenna beam coverage. However, they remain sensitive to yaw (drift) errors and cannot simultaneously measure velocity and drift angle without additional processing.
Triple- and Quadruple-Beam Systems demonstrate the highest accuracy and robustness. They provide virtually error-free measurements of velocity, drift (yaw), and pitch angles, independent of spatial orientation. While the triple-beam configuration offers sufficient accuracy with minimal hardware complexity, the quadruple-beam system provides redundancy, enhanced reliability, and reduced sensitivity to variations in ground surface reflectivity (e.g., land-to-sea transitions), which is critical for operations over heterogeneous terrain.
The article proposes that future miniaturized DVMS should employ a continuous Linear Frequency Modulation (LFM) architecture for its inherent advantages in resolution (due to large signal bandwidth) and interference immunity. The implementation of digital signal processing (DSP) enables the use of multi-beam antennas, such as Microstrip Antenna Arrays (MAA), which can reduce the number of required transceiver channels. Integrating multiple beams into a single printed circuit board enhances compactness and energy efficiency.
The analysis concludes that three- and four-beam configurations are the most practical for autonomous UAV navigation, balancing accuracy, hardware complexity, and operational robustness. Future research will focus on optimizing the structure of such systems, particularly regarding advanced antenna design and signal processing algorithms to minimize hardware requirements further.
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Signal sideband separation methods in digital down converter
Grenkov S.A., e-mail: grenkov@iaaras.ru
Fedotov L.V., e-mail: fedotov@iaaras.ru
The Institute of Applied Astronomy of the Russian Academy of Sciences (IAA RAS), Saint-Petersburg
Keywords: radio astronomy signals, digital down converter, quadrature signal processing, Field Programmable Gate Array.
Abstract
Two digital methods for sideband separation are considered for sideband separation during the processing of wideband radio astronomy signals in digital down converters (DDCs) implemented on Field-Programmable Gate Arrays (FPGAs). The traditionally used phase method, based on a 90° phase shift, has significant drawbacks: difficulties in ensuring precise phase shift across a wide frequency range, high demands on FPGA computational resources, and insufficient suppression of the opposite sideband (approximately 35–40 dB).
As an effective alternative, a method based on quadrature processing of complex signals with a subsequent transition to the real domain is proposed. This approach simplifies the DDC structure by replacing complex phase-shifting filters with simpler low-pass filters (LPFs) and significantly reduces the load on hardware resources.
The implementation of this method in an FPGA as part of the Multifunctional Digital Backend System (MDBE) for the telescopes of the “Quasar-KVO” complex demonstrated high efficiency: suppression of the opposite sideband of up to 80 dB was achieved while simultaneously reducing the utilization of multiplier blocks and other FPGA resources compared to the phase method.
The quadrature processing method demonstrates significant advantages in accuracy, resource efficiency, and is applicable not only in radio astronomy but also in other fields requiring high-precision frequency band separation.
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6. Grenkov S. A., Melnikov A. E., Fedotov L. V. Narrowband operation mode of a multifunctional digital signal conversion system // Proceedings of IAA RAS. 2025. Iss. 72. pp. 16–28. https://doi.org/10.32876/ApplAstron.72.16-28
Quality control of shaft rotation using a remote sensing device using a wavelet transform
D.V. Valuyskiy, e-mail: valuyskiy.d.v@mail.ru
The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan
Keywords: industrial shaft, vibrations, wavelet transform, Morlet wavelet, neural networks, deep learning, digital signal processing, classification, evaluation of rotation quality.
Abstract
The problem of shaft rotation control during continuous monitoring of the state of industrial equipment using a radar sensor is considered. The study examined various approaches to monitoring shaft rotation. It presented the advantages of using radar signals to detect shaft damage. Based on the theoretical concepts described, a test bench was constructed to assess the quality of shaft rotation using a remote sensing sensor. The reflections from damaged and undamaged shafts were recorded and analyzed. It was observed that the damaged shaft exhibited prominent spikes in the time domain. This observation was proposed as a basis for a wavelet signal processing algorithm in a shaft rotation quality monitoring device. The brightness of low-frequency components within one shaft rotation and repeated bright low-frequency components during all observation intervals in the frequency-time representation of the reflected signal can be used as an indicator of the unevenness of the shaft rotation.
An approach to the classification of industrial shafts by frequency-time maps using a deep learning neural network is proposed. The effectiveness of this classification was demonstrated using a test neural network trained on a set of recorded experimental signals.
It has been experimentally confirmed that the analysis of the dynamics of the reflected signal spectrum can be used to draw conclusions about the uneven rotation of the shaft. The uneven rotation of the shaft can be assessed using spectral analysis and statistical estimation methods. In particular, the use of neural networks and deep learning algorithms for classifying signals based on the "damaged" / "undamaged" shaft demonstrates an accuracy of detecting shaft rotation defects of over 99%.
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Software Implementation of Nonlinear Spectral Synthesis for Multi-Soliton Signals of the Korteweg–de Vries Equation
I.V. Grigorov, e-mail: i.grigorov@psuti.ru
V.D. Albatyrev, e-mail: albatyrevv@icloud.com
O.V. Sheruhaev, e-mail: o.sheruhaev@psuti.ru
Povolzhskiy State University of Telecommunications and Informatic (PSUTI)
Samara, Russia
Keywords: nonlinear spectral analysis, nonlinear spectral synthesis, Korteweg-de Vries equation, nonlinear Schrodinger equation, sine-Gordon equation, Kadomtsev-Petviashvili equation.
Abstract
This article presents a software implementation of an algorithm for the nonlinear spectral synthesis of signals, specifically designed to generate multi-soliton solutions of the Korteweg–de Vries (KdV) equation. The work aims to address the need for signal generation to test corresponding nonlinear spectral analysis algorithms. The authors position their research within the broader context of nonlinear signal processing, highlighting its potential applications in fields like fiber optics, where methods such as Nonlinear Frequency Division Multiplexing (NFDM) are being developed to overcome transmission limitations.
The core methodology is based on the inverse scattering problem (ISP) for the KdV equation, utilizing the Gelfand–Levitan–Marchenko (GLM) integral equation. The paper focuses on the specialized case of a purely discrete spectrum, which corresponds to multi-soliton, or "non-reflective," signals, thereby simplifying the computationally intensive general synthesis problem. The authors propose a modified algorithm where the kernel of the GLM equation becomes degenerate, allowing it to be expressed as a finite sum of separable functions dependent on the discrete spectral data.
The modified algorithm is mathematically developed, starting from the single-soliton case (N=1) and generalizing to an arbitrary number of solitons (N). The solution is formulated in matrix terms, requiring the resolution of a linear system to reconstruct the time-domain signal. Numerical experiments were conducted to validate the software implementation, successfully generating one-, two-, and three-soliton signals. The results for the two-soliton case are noted to coincide with known theoretical formulas from established literature, confirming the algorithm's correctness.
In conclusion, the developed software provides a practical tool for the nonlinear spectral synthesis of multi-soliton KdV signals. The numerical validation against theoretical benchmarks proves the validity of the proposed algorithmic variant. This work contributes to the toolkit for nonlinear digital signal processing and supports further research and testing in areas utilizing nonlinear Fourier transform-based methods.
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Software and algorithmic module for automated estimation of statistical charac-teristics of dangerous meteorological phenomena associated with cumulonimbus clouds in weather radar complex ‘Monocle’
A.N. Saveliev, e-mail: savelyev.an@bmstu.ru
O.V. Vasiliev, e-mail: vas_ov@mail.ru
E.S. Boyarenko, e-mail: boyarenko.elvira@mail.ru
K.I. Galaeva, e-mail: ks.galaeva@mail.ru
Bauman Moscow State Technical University (BMSTU), the Russian Federation, Moscow
The Moscow State Technical University of Civil Aviation (MSTU CA), the Russian Federation, Moscow
Keywords: weather radar, dangerous weather phenomena, classification of weather phenomena, pattern recognition, feature separation function, software and algorithmic module, decision threshold.
Abstract
One of the decisive factors affecting the safety and regularity of state and civil aviation flights is the meteorological situation. Based on the developed methodology of statistical analysis of experimental data, a software and algorithmic module was created to study the recognition of dangerous meteorological phenomena "rainfall-thunderstorm-hail", which is the first step towards partially automating the process of adapting the dangerous weather phenomena of cumulonimbus clouds classification criteria to the system installation site.
Based on the data obtained as a result of statistical analysis of field experiment data, a software and algorithmic module was developed for the study of dangerous weather phenomena recognition, designed to calculate and visualize graphs of one-dimensional and two-dimensional densities and probability distribution functions of values physical quantities of dangerous weather phenomena. The software and algorithmic module is developed in the Python 3 programming language using a package of application programs for technical computing. The structure of the graphical software and algorithmic module can be divided into 4 parts: analysis parameters; saving parameters; choosing the type of construction; analyzing the results.
Weather radar complex ‘Monocle’ puts the complex into a fully automatic self-learning mode. Currently, the software and algorithmic module includes automatic calculations of probability densities of classification features, as well as decision thresholds, the correctness of which is confirmed by the corresponding complete probability matrices. The developed automated dangerous weather phenomena recognition learning technology will greatly facilitate the calculation of thresholds and generate complete probability matrices to determine the informative value of the feature space in the dangerous weather phenomena of cumulonimbus clouds classification.
Using a specific example of weather radar complex ‘Monocle’ meteorological data located at the Orlovka airfield (Tver region, the Russian Federation), it is shown that the optimization of criteria in terms of applying a combination of features for rainfall, thunderstorms, hail, proposed by the authors in the work, is successful.
Thus, in the course of the work, an automated software and algorithmic module for processing radar surveillance data was developed to form decision thresholds for the classification of dangerous weather phenomena of cumulonimbus clouds in the weather radar complex ‘Monocle’.
References
1. Vasiliev O.V., Bolelov E.A., Galaeva K.I., Boyarenko E.S. Bayesian method of radar classification of dangerous meteorological phenomena of cumulonimbus clouds // Electromagnetic waves and electronic systems. 2025. V. 30. ¹ 1. P. 55-67. DOI: https://doi.org/10.18127/j15604128-202501-06
2. Boyarenko E.S., Bolelov E.A., Vasiliev O.V., Korotkov S.S. Experimental statistical analysis of radar signals reflected from weather hazards // Civil Aviation High Technologies. 2023; vol. 26, no.5, pp.19-29. DOI: https://doi.org/10.26467/2079-0619-2023-26-5-19-29
3. Vasiliev O.V., Boyarenko E.S., Savelyev A.N., Gorbachev N.V. Analysis of informativeness of features of classification of dangerous weather events based on radar observation results // Civil Aviation High Technologies. 2024; vol. 27, no. 3, pp.8-22. DOI: https://doi.org/10.26467/2079-0619-2024-27-3-8-22
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Detection of OFDM Signals in the Gigahertz Range Using a Robust
Gromov-Hausdorff Detector
Timofeev A.V., Dr. of Engineering, e-mail: timofeev.andrey@gmail.com
EqualiZoom LLP, Astana, Kazakhstan
Keywords: Gromov-Hausdorff detector, OFDM signal, robust detection, frequency range scanning.
Abstract
This article addresses the critical problem of reliably detecting orthogonal frequency-division multiplexing (OFDM) signal sources in the crowded and interference-prone gigahertz frequency spectrum (1–6 GHz). In modern wireless environments, the presence of numerous communication devices, industrial equipment, and impulsive noise sources severely degrades the performance of conventional detection methods, which often rely on assumptions of Gaussian noise and stationary conditions. To overcome these limitations, the authors propose a novel, robust detection algorithm based on a median-stabilized version of the Gromov–Hausdorff (GH) metric. This new detector is specifically designed to maintain high sensitivity to OFDM signals while being resilient to non-Gaussian and impulsive interference. The core innovation lies in the application of the Gromov–Hausdorff metric—a tool from metric geometry that measures the distance between two sets by comparing their intrinsic shapes—to the problem of spectrum analysis. Unlike simple energy or power detectors, the GH metric captures complex structural differences between a reference noise spectrum and an observed spectrum. It is sensitive to global shifts, local peaks, and distortions caused by the presence of a signal. To enhance its robustness against isolated outliers and heavy-tailed noise, the authors introduce a median version of the metric. This modification calculates the median of the minimal distances between spectral bins of the two sets, effectively filtering out sporadic, high-amplitude noise bursts that would otherwise distort the measurement. The resulting decision rule declares a signal present when the median GH distance between the current spectrum and a calibrated background model exceeds a dynamically adapted threshold. A comprehensive theoretical framework supports the detector's design. The authors analyze the performance of robust detectors under Huber's ε-contamination noise model, which mixes a primary Gaussian distribution with a contaminating heavy-tailed distribution (e.g., Cauchy). They demonstrate that classical detectors, such as those based on average power, become highly susceptible to false alarms under such conditions. To mitigate this, the study explores and compares three robust detection structures:
1) a Censored Median Power Detector, which uses trimmed statistics;
2) a Hodges-Lehmann Detector, based on the robust Hodges-Lehmann estimator of location; and
3) the proposed Gromov–Hausdorff Detector.
Theoretical expressions for probability of detection (PD) and probability of false alarm (PFA) are derived for the first two, while the GH detector's performance is evaluated numerically due to the complexity of its statistic. Furthermore, the article tackles the practical system-level challenge of efficiently scanning wide frequency ranges. The authors formulate an optimization problem that determines the optimal scanning step size for each predefined sub-band. The objective is to maximize the overall probability of detection while minimizing total scan duration, taking into account prior Bayesian probabilities of signal presence in different bands. The solution, obtained via sequential quadratic programming, rationally allocates finer scanning steps to bands with higher prior probability, thereby optimizing resource usage. Experimental validation was conducted using a physical prototype built on a HackRF One software-defined radio platform controlled by a Raspberry Pi. Field tests were performed in a realistic, interference-rich office environment. Three different emission sources were used: two OFDM-based drones (Autel and DJI Mavic Mini) and one non-OFDM jammer (TG-120G-Pro). The results were unequivocal: the Gromov–Hausdorff detector consistently outperformed both the median power and Hodges-Lehmann detectors. It achieved a superior balance, maintaining a high probability of detection (Pd > 0.92 across all tests) while drastically reducing the false alarm rate (PFA as low as 0.01). Numerical simulations of the Area Under the ROC Curve (AUC) further confirmed the GH detector's superior discriminative capability. In conclusion, this work presents a significant advancement in robust RF signal detection. The Gromov–Hausdorff detector, combined with an intelligent scanning strategy, offers a powerful and practical solution for detecting OFDM signals in complex electromagnetic environments. Its demonstrated performance makes it a promising candidate for deployment in radio monitoring systems, electromagnetic compatibility assurance, cognitive radio networks, and security applications operating in the gigahertz spectrum.
References
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Wavelet-based despeckling of radar images using spatially oriented trees and transformer neural network architecture
Y.S. Bekhtin, e-mail: yuri.bekhtin@yandex.ru
V.T. Trinh, e-mail: vantoan.vkhk92@gmail.com
The Ryazan State Radio Engineering University (RSREU) named after V.F. Utkin,
Russia, Ryazan
Keywords: radar images, speckle noise, despeckling, multi-scale wavelet transform, spatially oriented trees, neural network, transformer.
Abstract
The paper is devoted to the filtering of speckle noise which is caused by coherent microwave radiation interference in synthetic aperture radars (SAR) and degrades quality of the formed SAR image by masking true textural and geometric characteristics of scenes, thereby hindering visual interpretation and automatic analysis tasks such as segmentation, classification, and object recognition.
The paper proposes a novel approach which combines multi-scale wavelet analysis with attention mechanisms in the transformer neural network architecture to effectively model both local and global dependencies within so-called spatially oriented trees (SOT). Each SOT represents hierarchical relationships between wavelet coefficients across different decomposition levels and orientations (horizontal, vertical, diagonal) and is processed as a sequence of tokens by the modified transformer architecture. It allows avoiding critical limitations of traditional wavelet-based denoising techniques which process wavelet coefficients independently without accounting for inter-scale correlations, resulting in either excessive smoothing or insufficient noise suppression.
The suggested SOT_TRANS model consists of three independent encoder channels for each orientation incorporating multi-head attention mechanisms with four heads and a hidden dimension of 64, followed by a cross-channel aggregator that enables inter-orientation information exchange. Training employs residual learning with L1-norm hierarchical loss functions and adaptive weighting that prioritizes fine scale coefficients containing both noise and important structural details.
The results of computing simulation experiments have shown that the proposed method outperforms significantly other despeckling methods across some quality metrics: mean square error (MSE), peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM). Visual analysis of real SAR imagery from the StriX-1 satellite confirms superior noise suppression while preserving edge sharpness and structural details compared to competing methods.
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