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“Digital
Signal Processing” No. 2-2025 |
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Correlogram estimation of power spectral density based on simulation of one-bit analog-stochastic quantization in processing a uniformly sampled signal sequence
Yakimov V.N., e-mail: yvnr@hotmail.com
Samara State Technical University (SSTU), Russia, Samara
Keywords: power spectral density, correlogram, one-bit stochastic quantization, fast algorithms.
Abstract
The article considers the problem of increasing the digital spectral analysis efficiency of a uniformly sampled signal by the correlogram method. The basis for solving this problem was the preprocessing of a uniformly sampled signal, which imitates the procedure of primary one-bit analog-stochastic signal quantization. As a result, a transition was made from processing multi-bit signal samples to processing sequences of samples with values equal to plus one or minus one. This approach made it possible to develop mathematical software for calculating the correlogram estimate of the power spectral density (PSD), the practical implementation of which leads to the execution of recurrent computational procedures. The main operations of these calculations are summation and subtraction. This reduces the multiplicative complexity of calculating the PSD estimation by the correlogram method. The practical result was the development of algorithmic support for calculating the correlogram estimate of the PSD. It is implemented in the form of a metrologically significant software module. Testing of this module confirmed that the proposed approach to calculating the correlogram estimate of the PSD allows for high-resolution spectral analysis against the background of additive noise and without shifting the harmonic components in frequency. The use of this module does not require the direct execution of one-bit analog-stochastic quantization of the analyzed signal. Therefore, it can be used as part of metrologically significant software designed for complex processing of uniformly sampled signals.
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16. Yakimov V.N., Mashkov À.V. Algoritm vychisleniya otsenki spektral'noy plotnosti moshchnosti na osnove obrabotki znakovykh signalov s ispol'zovaniyem vremennykh vesovykh funktsiy (Algorithm to Compute Estimate of a Power Spectral Density Based on Sign Signal Processing Using Time-Weighting Functions) // Tsifrovaya obrabotka signalov (Digital Signal Processing). 2016. no. 4. pp. 3-8. (In Russian).
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The algorithm for probabilistic-optimal addition of incoherent signals under fading conditions
V.V. Egorov,
M.L. Maslakov , e-mail: maslakovml@gmail.com
JSC «Russian institute for power radioengineering»; Saint-Petersburg State University of Aero-space Instrumentation, Russia, Saint-Petersburg
Keywords: signal-to-noise ratio, diversity reception algorithms, fading.
Abstract
The use of spaced signal reception is one of the ways to improve the quality of radio communication in channels with fading in conditions of low values of the signal-to-noise ratio (SNR). The problem of summing modulated signals in a fading channel with spatially-spaced reception in case of one transmitting antenna and several receiving antennas spaced apart from each other at a distance of several wavelengths is considered.
As a solution to this problem, a fast algorithm for probabilistic-optimal addition of modulated signals with spatially spaced reception is proposed. The proposed addition algorithms do not require a large amount of calculations.
The idea of the algorithm is to add signals in conditions of a limited number of phase shift variants and select the most preferable hypothesis that ensures maximum SNR. The energy gain provided in this case is probabilistic in nature. The probability densities functions of the SNR gain and the dependences of the probability of an increase in SNR by a given X dB when adding two and four signals are obtained. The simulation was carried out for the cases of an AWGN channel and a fading channel.
The presented algorithms do not require significant processing of reception devices, and also do not impose requirements for additional signal processing, for example, compensation of phase distortions of signals received by different branches of diversity. The number of diversity branches can vary from 2 to 4, and if necessary, it can easily be increased to 8 with a slight increase in implementation complexity.
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Selection of adaptive algorithm for digital antenna array of land-based equipment for global satellite navigation systems
Djigan V.I., e-mail: dzhigan_vi@nrcki.ru
Department for Design Problems in Microelectronics of National Research Center “Kurchatov Institute”
Keywords: adaptive antenna array, Global Navigation Satellite Systems, Side Lobe Canceller, Liner Constraint, Signal-to-Noise Ratio, Recursive Least Squares.
Abstract
This paper considers a technique for assessing the possibility of the receiving signals from the Global Navigation Satellite Systems (GNSS) using the Adaptive Antenna Arrays (AAA) as the antennas in the ground-based equipment. This technique is based on assessing the Signal-to-Noise Ratio (SNR) at the AAA output in its steady state. The SNR is assessed with a uniform discrete step over the entire set of the angles of the possible positions of the informational signal source (satellite) around the AAA. Based on these assessments, a map is formed showing the areas in the directions of which the reception of the satellite signals is possible or impossible. The simulation has demonstrated, that such reception is possible in the directions where, according to international standards, the SNR value of at least –20 dB is ensured at the output of the antenna or the AAA in use. The technique is demonstrated using the examples of two the AAA widely used in the ground-based equipment for the modern GNSS: a Side Lobe Canceller and an AAA with a Linear Constraint of the radiation pattern. The simulation has demonstrated that when using a rectangular equidistant AAA with eight wide-beam antennas, after the suppressing of the signals from 7 interference sources, the satellite signals can be received from approximately 30% of the directions of the surrounding space (in the vicinity of the zenith). This value is approximately 10% greater than that of the AAA before the adaptation. If such estimates are made only for the upper hemisphere of space, these values are doubled. In the experiment, both considered the AAA demonstrate approximately the same efficiency in terms of interference suppression and reception of information signals, although their radiation patterns in the steady state differ somewhat. For the AAA of other configurations and when operating in other interference environments, these estimates may differ and have different numerical values. Using the proposed technique, these estimates can be easily obtained for the desired operating conditions of the receiving AAA. The paper also presents the architectures and the computational procedures for calculation the weighs and the output signal of the considered AAA. These procedures are based on the use of the Recursive Least Squares algorithm for the adaptive filtering of the signals.
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A Method of Dual Domain Differential Orthogonal Matching Pursuit for MIMO Channel Estimation
A.A. Solomkin, e-mail: solomkin.aa@phystech.edu
S.V. Shatilov, e-mail: shatilov.sv@ict-lab.ru
V.A. Lyashev, e-mail: lyashev.va@mipt.ru
Moscow Institute of Physics and Technology (national research university)
Keywords: MIMO-OFDM, vector quantization, channel estimation, spatial multiplexing, dual basis representation.
Abstract
Today, active antenna arrays are increasingly being used in wireless communication. The systems become highly selective in space, which makes them sensitive to errors in channel estimations. The paper considers the main problems of MIMO systems in which it is not possible to evaluate the channel using direct methods based on pilot signals. Implicit estimation methods require a compressed representation of channel state information, which imposes limitations on their accuracy. A method of dual domain iterative recovery of channel information from a compressed representation is proposed, which has an improved efficiency of channel matrix acquisition and the effect of error smoothing. A specific of the proposed approach is mutual channel information recovery in antenna and frequency domains.
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Iterative Method for Reducing the Peak-to-Average Power Ratio of OFDM Signal Based on Clipping Noise Processing
Hoang Van Tuan, e-mail: khoang.vt@phystech.edu
Dvorkovich A.V., e-mail: dvork.alex@gmail.com
Department of Multimedia Technologies and Telecommunications, MIPT, Russia
Keywords: OFDM, PAPR, peak-to-average power ratio, CAF, clipping and filtering, ACE, active constellation extension.
Abstract
The OFDM (Orthogonal Frequency Division Multiplexing) technology plays a crucial role in modern wireless communication systems. Thanks to its ability to efficiently utilize the spectrum, resist distortions caused by multipath propagation, and provide high data transmission rates, OFDM has become the foundation for numerous telecommunications standards. These include first- and second-generation digital television (DVB-T, DVB-T2) [1,2], fourth- and fifth-generation mobile networks (4G, 5G), as well as wireless local area networks (Wi-Fi) [3]. However, one of the most serious challenges of OFDM remains the high Peak-to-Average Power Ratio (PAPR) of the signal. Increased PAPR imposes strict requirements on the linearity of the power amplifier (PA), necessitating a wide linear dynamic range. As a result, the amplifier operates with reduced energy efficiency – away from the saturation region. If the signal exceeds the linear range of the PA, nonlinear distortions are introduced, severely degrading the transmission quality.
This paper addresses the problem of reducing the peak-to-average power ratio (PAPR) in OFDM systems, which is one of the key challenges in broadband signal transmission. To tackle this issue, an iterative method is proposed that reduces the PAPR of OFDM signals by processing clipping noise, combining the advantages of amplitude clipping and active constellation extension techniques. A distinguishing feature of the proposed approach is the use of clipping noise to generate a peak-correction signal, which is processed in two directions – by limiting the spectral amplitude and by controlled extension of constellation points. Analytical and simulation results demonstrate that the proposed method effectively reduces the PAPR value. Compared to clipping and filtering (CAF) and active constellation extension (ACE) methods, the proposed technique achieves the highest PAPR reduction gain – up to 6.44 dB after three iterations. The results confirm the high efficiency and practical relevance of the proposed method for modern OFDM systems.
References
1. ETSI EN 302 755 V1.3.1, Digital Video Broadcasting (DVB); Frame structure channel coding and modulation for a second generation digital terrestrial television broadcasting system (DVB-T2), ETSI, Apr. 2012
2. Dvorkovich V. P., Dvorkovich A. V. Tsifrovye videoinformatsionnye sistemy (teoriya i praktika) // Moscow: Tekhnosfera, 2012. – 1008p.
3. Tekhnologiya OFDM. Uchebnoe posobie dlya vuzov / M. G. Bakulin, V. B. Kreindelin, A. M. Shloma, A. P. Shumov. – Goryachaya liniya – Telekom, 2017.
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Vibration detection of a rotating shaft using a non-contact sensor and linear discriminant analysis
D.V. Valuyskiy, e-mail: valuyskiy.d.v@mail.ru
The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan
Keywords: industrial shaft, vibrations, linear discriminant analysis, digital signal processing, classification, evaluation of rotation quality.
Abstract
The article is devoted to the study of problems of quality control of industrial machine shaft rotation using radar monitoring tools. Radar signals are reflected from a rotating industrial shaft, processed and then analyzed using a short-term Fourier transform. The signals are classified by the degree of uniformity of shaft rotation using the linear discriminant analysis method.
Within the framework of the conducted research, a number of approaches to assessing the quality of rotation of industrial rollers are considered. A method for evaluating the quality of roller rotation using a linear discriminant analysis algorithm is proposed. The theoretical aspects of the implementation of the LDA algorithm are considered.
A testbed has been implemented. A set of signals has been recorded for a roller rotating without distortion and for a roller with simulated damage. For a set of received signals, classification by the LDA method was carried out.
It has been experimentally confirmed that the dynamics of changes in the spectrum of the reflected signal shows an uneven rotation of the roller and can be estimated using spectral analysis and statistical methods. In particular, the application of the LDA method to classify signals based on the "damaged-undamaged roller" mark demonstrates the accuracy of detecting roller rotation defects at the level of 98%.
References
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Fine-tuning the Whisper neural network encoder using promt vectors and adaptation blocks for heart murmur detection
A.I. Topnikov, e-mail: a.topnikov@uniyar.ac.ru
T.A. Smirnova, e-mail: t.smirnova9@stud.uniyar.ac.ru
P.G. Demidov Yaroslavl State University (YarSU), Russia, Yaroslavl
Keywords: phonocardiogram, heart murmurs, neural network, deep learning, transfer learning, audio signals classification.
Abstract
Recent advancements in neural network methods for detecting heart murmurs in phonocardiograms have been significantly driven by the introduction of The CirCor DigiScope Phonocardiogram Database and the organization of The George B. Moody PhysioNet Challenge 2022. In parallel, transformer-based neural architectures have gained traction in speech and audio processing. However, training such large-scale models typically requires extensive datasets. For tasks with limited data, transfer learning techniques offer a viable solution.
This study investigates the feasibility of constructing a heart sound classification system for murmur detection using the Whisper ("base" model) encoder. Prior to computing 80-channel mel-spectrograms, input signals were upsampled to 16 kHz, with mixup augmentation applied during training. During fine-tuning, the original Whisper encoder weights (excluding LayerNorm parameters) were frozen. To aggregate information from hidden representations, a trainable classification token was prepended to the input sequence, processed by the transformer blocks, and subsequently fed into a task-specific fully connected classification head. Additional approaches, including prompt-based tuning and adapters (similar to the WhisPAr approach), were also investigated.
Training employed class-weighted cross-entropy (with class weights: 1 – for "Absent", 5 – for "Present", 3 – for "Unknown"), the AdamW optimizer and batch size 16. All models were trained for 100 epochs. The primary evaluation metric was weighted accuracy, using identical class weights to those in the loss function.
The baseline approach (frozen encoder with LayerNorm tuning) achieved a validation weighted accuracy of 0.800. Incorporating prompts (additional 3 vectors) and adapters (with bottleneck dimension 32) improved signal-level weighted accuracy to 0.832. On the test set, this configuration yielded weighted accuracies of 0.833 (per signal) and 0.822 (per patient).
These findings highlight the potential of transformer-based architectures, especially when employing parameter-efficient fine-tuning strategies, for accurate heart murmur detection from phonocardiogram recordings.
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Modified Pan-Tompkins algorithm with adaptive definition of the boundaries of the qrs complex
K.M.Demushkina, e-mail: riabova.ksenija@yandex.ru
A.V. Kuzmin, e-mail: a.v.kuzmin@pnzgu.ru
Penza State University, Russia, Penza
Keywords: ECG, R-peak, Pan-Tompkins algorithm, Neurokit library, PhysioNet database.
Abstract
Currently, ECG is a widely used method of cardiological examination. The amplitude-time ECG analysis, performed manually by specialists, consists in estimating the duration of each of the events occurring during the cardiac cycle, in particular, the waves P, Q, R, S, T. One of the most common ways to programmatically determine the R wave is the Tompkins Pan algorithm. The classical algorithm is not resistant to noise and vibrations, and shifts during filtering do not give accurate results, hence the task of modifying the algorithm.
The main idea of the modification is to determine the boundaries of the assumed R-peak. To do this, all the peaks are located in the integrated signal to get a starting point for defining the boundary. After that, the boundaries from a certain peak are set at a distance of 5 ms from the peak to the right and left along the time axis. Then, within a given window, the real location of the R-peak is determined by searching for the maximum amplitude in a given interval.
Testing of the modified Pan-Tompkins algorithm was performed using data from open databases of digital ECG signals from the PhysioNet resource. According to the test results, the modified algorithm has a sensitivity of 79%, a specificity of 76%, and an accuracy of about 74% in lead V2. For the V6 lead, the results were as follows: sensitivity 99%, specificity 90%, accuracy 91%. The relatively low specificity in the V6 lead is less critical for the modified algorithm, which indicates that the probability of detecting a peak where it is not present in the modified algorithm is slightly higher than in the Neurokit analog, so the analog is more likely to miss the R peak in the signal.
References
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