Russian
Scientific & Technical
Journal

Improved design of pulse-shaping FIR filters for digital communication systems
Mingazin A.T., e-mail: alexmin@radis.ru
RADIS Ltd, Russia, Moscow

Keywords: pair of identical pulse-shaping linear-phase FIR filters, weighted Chebyshev approximation, Remez algorithm, additional control points in transition band, stopband attenuation, inter-symbol interference, peak-to-average power ratio, quantization of coefficients, 2D- and 3D-graphics.

Abstract
The design method of pulse-shaping linear-phase FIR filters for digital communication systems is investigated. The system's transmitter and receiver filters are identical. The method is based on a weighted Chebyshev approximation using the Remez algorithm with additional control of the frequency response levels at a given number of frequency points in the transition band and iterative weight selection for the level in the stop band. The method of calculating frequency response levels at all these frequencies using only one auxiliary parameter, which is determined iteratively during design is proposed. Thus, with a fixed number of points, the optimal solution, according to the selected criterion, corresponds to certain values of mentioned weight and auxiliary parameter. Design criteria related to obtaining the desired values of stopband attenuation, peak inter-symbol interference and the peak-to-average power ratio are considered. The example shows that by proper selection of the number of control points (3, 5, 7 or 9) and their location in the transition band, it is possible to significantly increase stopband attenuation and/or reduce intersymbol interference compared to previously published values. This choice allows to slightly reduce the peak-to-average power ratio. The problem of quantization of filter coefficients in the process of finding solutions is touched upon. In this case, the optimal solution can be improved by introducing additional variable affecting the filter gain. The design method of pulse-shaping linear-phase FIR filters, including those with quantized coefficients, is widely illustrated by 2D- and 3D-graphics, as well as the data obtained.

References
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2. Farhang-Boroujeny B. A square-root Nyquist (M) filter design for digital communication systems// IEEE Trans on SP, 2008, vol. 56, no. 5, pp. 2127-2132.

3. Ashrafi A. Optimized linear phase square-root Nyquist FIR filters for CDMA IS-95 and UMTS standards// Signal Processing, 2013, vol. 93, no. 4, pp. 866-873.

4. Traverso S. A family of square-root Nyquist filter with low group delay and high stopband attenuation// IEEE Commun. Letters, 2016, vol. 20, no. 6, pp. 1136-1139.

5. Xiao R., Lei Q., Guo X., Du W., Zhao Y. A design of two sub-stage square-root Nyquist matched filter// IEEE Access, 2018, vol. 6, may, pp. 23292-23302.

6. Mingazin A. T. Design quantized pulse-shaping FIR filters for digital communication system// Digital Signal processing. Russian Scientific and Technical Journal, 2021, no. 4, pp. 3-15.

7. Mingazin A. T. Weighted Chebyshev approximation in design of pulse-shaping FIR filters for digital communication system// Digital Signal processing. Russian Scientific and Technical Journal, 2022, no. 2, pp. 3-11.

Adaptive polynomial filtering algorithms in the time domain
Shcherbakov M.A., e-mail: mashcherbakov@yandex.ru
The Penza State University (PSU), Russia, Penza

Keywords: adaptive nonlinear filtering, polynomial filters, discrete Volterra series.

Abstract
Adaptive nonlinear filtering algorithms for the class of polynomial filters (Volterra filters) in the time domain are considered. The property of linearity of polynomial filters with respect to their coefficients allows, on the one hand, to use the principles of constructing adaptation algorithms for linear filters, and on the other hand, it has a number of features associated with the choice of adaptation parameters for various nonlinear components of the filter.

It is shown that for nonlinear filters, the range of the adaptation parameters of gradient algorithms narrows compared to the linear case and is determined by high-order correlation moments. To speed up the convergence rate of gradient adaptation algorithms for processes with a symmetric probability distribution density, instead of carrying out a time-consuming orthogonalization operation, an algorithm based on separate adaptation of even and odd nonlinear components of the filter is proposed. This approach is considered using the example of a third-order nonlinear filter, for which estimates of the permissible limits of the adaptation parameters were obtained.

In order to equalize the rate of convergence of individual nonlinear components of the filter, a sequential adaptation algorithm is proposed, based on performing iterations in the direction of increasing the order of nonlinearity of the filter components. The convergence of such an algorithm is proven and estimates for the choice of its parameters are obtained. It is shown that, along with increasing the speed of convergence, the sequential adaptation algorithm at the same time does not guarantee convergence to the optimal point. To achieve the required accuracy without a significant loss of adaptation speed, a combined scheme is proposed, based on the joint use of sequential and parallel adaptation algorithms, using the latter to refine the current vector of filter coefficients. Another possible solution is to add additional feedback to the sequential circuit, the periodic closure of which leads to a decrease in the systematic adaptation error.

Increasing and leveling the speed of convergence of the adaptation process can be achieved through the use of Newton-type algorithms (recursive least squares algorithms). A recursive algorithm for adapting polynomial filters with exponential weighting is proposed, which, along with increasing the convergence rate, ensures smoothing of random fluctuations when approaching the optimal point, as well as equalization of the convergence rate relative to the nonlinear components of the filter.

References
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Optimization of signal detection systems with non-recursive rejection filters
D.I. Popov, e-mail: adop@mail.ru
The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

Keywords: probabilistic criterion, doppler phase, optimization, passive interference, rejection filter, signals, detection system.

Abstract
The article considers the optimization of systems for detecting signals of moving targets against the background of passive interference by a probabilistic criterion. The object of the study is detection systems that carry out coherent interference rejection with subsequent coherent or incoherent accumulation of rejection residues.

The aim of the work is to optimize the weight coefficients of non–recursive rejection filters depending on the correlation properties of passive interference according to the probability criterion. Expressions are obtained for the probabilistic characteristics of detection systems with coherent interference rejection and subsequent coherent or non-coherent accumulation of rejection residues, respectively.

These expressions establish a functional relationship between the probability of correct detection averaged over the Doppler phase of the signal and the correlation parameters of the passive interference and the characteristics of the detection system. The criteria for the optimization of the weight vector of the rejection filter are given. These criteria make it possible to establish the relationship of the optimal weight vector with the interference parameters based on nonlinear programming methods. A quasi-Newtonian iterative procedure for finding the optimal vector is given. In order to achieve a unimodal extremum, restrictions on the frequency response of the rejection filter are introduced.

Numerical results of optimization of a system with coherent rejection and subsequent incoherent equilibrium accumulation according to a probabilistic criterion are considered. Their comparison with similar results of optimization of the rejection filter according to the energy criterion is carried out. The proposed method of optimization of detection systems by probabilistic criterion makes it possible to obtain significant gains in the efficiency of signal detection compared to optimization by energy criterion and to realize the marginal efficiency for the class of systems under consideration.

References
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Reconstitution of an object image based on a series of its images distorted in a random environment
O.V.Goryachkin, e-mail: o.goryachkin@psuti.ru
A.V. Borisenkov, e-mail: a.borisenkov@psuti.ru
Povolzhskiy State University of Telecommunications and Informatics, 23 L. Tolstoy Str., 443010 Samara, Russia

Keywords: blind image deconvolution, SIMO, matrix factorization, polynomial statistics.

Abstract
The article considers an algorithm for blind deconvolution of images distorted in a random environment and registered as a set of random implementations, i.e. the case of multichannel blind deconvolution of images, which is also known as multi-frame blind deconvolution (MFBD). It is assumed that the image-distorting random impulse response of a linear medium is described by a random discrete field with independent nonstationary random coefficients. The proposed approach is based on polynomial representations of random signals and the use of polynomial moments and cumulants to describe them. Within the framework of this approach, we reduce the problem of image deconvolution to the problem of factorization of the covariance matrix of a given structure obtained from a set of random realizations. The use of second-order polynomial statistics generated by random polynomials allows you to select sections on manifolds of a given correlation so that infinite values are excluded in the estimation of the covariance matrix, which significantly improves the noise immunity of the algorithm. However, such a solution has a price, namely the need to perform calculations with large degrees, which quickly becomes a problem when the image dimension increases. To overcome these difficulties, the article proposes an algorithm based on reducing the two-dimensional problem of image identification to the one-dimensional problem of identifying signals with polynomial values. The article presents the results of modeling this image deconvolution algorithm using dimensionality reduction. The algorithm can be used to solve the problem of image reconstruction that occurs in astronomy using the speckle interferometry method, technical television.

References
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8. Zhang, Haichao, David Wipf, and Yanning Zhang. " Reconstruction of single image from multiple blurry measured images " IEEE transactions on pattern analysis and machine intelligence 36.8 (2014): 1628-1643.

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13. P. Zhu, C. Xie and Z. Gao, "Multi-Frame Blind Restoration for Image of Space Target With FRC and Branch-Attention," in IEEE Access, vol. 8, pp. 183813-183825, 2020, doi: 10.1109/ACCESS.2020.3029356.

14. P. Zhu, C. Xie and Z. Gao, "Multi-Frame Blind Restoration for Image of Space Target With FRC and Branch-Attention," in IEEE Access, vol. 8, pp. 183813-183825, 2020, doi: 10.1109/ACCESS.2020.3029356.

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TIME-FREQUENCY PROCESSING OF RADIO SIGNALS FROM SEVERAL MOVING OBJECTS
V.K. Klochko, e-mail: klochkovk@mail.ru
B. H. Vu, e-mail: ronando2441996@gmail.com
Ryazan State Radio Engineering University, Russia, Ryazan

Keywords: radio signal processing, time processing, frequency processing, time-frequency processing, object detection, estimates of angular coordinates.

Abstract
The problem of detection and estimation the angular coordinates of several moving objects in multi-channel Doppler radar is being solved. Three approaches to processing reflection signals from several moving objects are considered in comparison - processing in the time domain, in the frequency domain and joint time-frequency signal processing. For processing in the time domain, a new approach is proposed to select signals from each object from a mixture of signals based on extrapolation of initially isolated signals, their subtraction from the smoothed mixture of signals and phase estimation using the Kalman filter. For processing in the frequency domain, the known approach for selection of spectral components in a signal mixture in several processing channels with the following determination of angular coordinates by the phase method is considered. To be able to detect objects moving with similar velocity vectors and time points of arrival of reflected signals, the time-frequency processing is proposed based on comparing the number of objects detected in time and frequency domains and angular coordinates found in these regions. The results of computer modeling of algorithms that realize approaches are presented. The advantage of time-frequency approach is shown. It is recommended to use the proposed approach in existing finding systems for detecting several moving objects.

References
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4. Klochko V. K., Vu B. H. Time-frequency signal processing in Doppler radios // Digital signal processing. 2023. No. 2. pp. 15-21.

5. Klochko V. K., Kuznetsov V. P., Vu B. H. Estimation of parameters of radio signals from mobile low-altitude objects // Bulletin of the Ryazan State Radio Engineering University. 2022. Issue 80. pp. 12-23.

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7. Klochko V. K., Vu B. H.. Detection of mobile sources by a radio receiver system // Digital signal processing. 2022. № 4. Pp. 50-55.

Modeling of the Nakagami random process with given parameters and correlation function
M.L. Maslakov, e-mail: maslakovml@gmail.com
Saint-Petersburg State University of Aerospace Instrumentation, Russia, Saint-Petersburg

Keywords: random process, probability density function, Nakagami m-distribution, fading, correlation function.

Abstract
When modeling fading channels, it is necessary to obtain random processes according to Rice's or Nakagami's laws. The Nakagami distribution allows a more detailed description of the energy parameters of a radio link at low SNR values, in contrast to the Rice distribution. Therefore, it is of practical interest to model the correlated random Nakagami process with given parameters.

Goal: development of an algorithm for modeling a random process obeying the Nakagami m-distribution with given parameters m and Ω and a correlation function.

Results: the algorithm for modeling random numbers with the Nakagami distribution was substantiated for parameter values m multiples of 0.5. This algorithm is adapted for any values of the parameters m and Ω. For the resulting sample, tests were performed using the Kolmogorov and Pearson Chi-square tests. Using the example of a random process with an exponential correlation function, the operation of the algorithm for modeling a correlated random process with the Nakagami distribution is shown. It is shown that it is possible to obtain a random process with the Nakagami distribution with any given positive definite correlation function.

Practical significance: the problem of modeling a correlated random process with the Nakagami distribution with given parameters is relevant when simulating signal transmission over non-stationary fading channels. The results of the work can be used, for example, in simulating high-frequency and satellite communication systems.

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Neural network Earth object identification based of hyperspectral imaging systems and knowledge about their video information path
V.A. Eremeev, A.A. Makarenkov, e-mail: foton@rsreu.ru
The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

Keywords: remote sensing, hyperspectral images (HSI), radiometric and spectral resolution of HSI, reduction of HSI redundancy, neural network objects identification using HSI.

Abstract
Over the past 20 years, aerospace systems for hyperspectral imaging of the Earth have been actively developed. Hyperspectral data allows getting spectral signature for each point of image. Knowledge about spectral signature creates broad possibilities for object identification procedures automation.

The article analyzes video information path in aerospace hyperspectral imaging systems of Earth and describes ways to usage this knowledge for improve neural network object identification performance. The video information path is represented as multiply of two functions, one of which depends only on solar radiation wavelength, and the other on coordinates of scanned point and solar radiation wavelength. Based on video information path representation some important practical tasks were generated: 1) estimation of spectral reflectance coefficient; 2) clarification of atmospheric transmission coefficients; 3) clarification of parameters of video information path during flight of satellite. This study focuses on solving the first task.

An analyze of radiometric quality of the hyperspectral sensor was performed. The issue of reducing the redundancy of hyperspectral output data for neural network processing is considered. For experimental research, data from the aviation system «AVIRIS» and the Russian space system «Resurs-P» are used. Some experiments are presented for demonstrating the effect of reducing data redundancy with principle component method. Quality metrics of neural network object identification were obtained.

References
1. M. D. Lewis et al., "The Hyperspectral Imager for the Coastal Ocean (HICO): Sensor and data processing overview," OCEANS 2009, Biloxi, MS, USA, 2009, pp. 1-9.

2. H. Kaufmann et al., "EnMAP A Hyperspectral Sensor for Environmental Mapping and Analysis," 2006 IEEE International Symposium on Geoscience and Remote Sensing, Denver, CO, USA, 2006, pp. 1617-1619.

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4. Eremeev V.V.. Egoshkin N.A.. Makarenkov A.A.. Moskvitin A.E.. Ushenkin V.A. Problemnyye voprosy obrabotki dannykh ot kosmicheskikh sistem giperspektralnoy i radiolokatsionnoy syemki Zemli // Vestnik Ryazanskogo gosudarstvennogo radiotekhnicheskogo universiteta. 2017. №60. pp. 54-64.

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Recovery of a discrete time signal using an orthogonal polynomials system of a discrete argument
V.N. Yakimov, e-mail: yvnr@hotmail.com
Samara State Technical University (SSTU), Russia, Samara

Keywords: discrete time signal, sampled sequence, signal recovery, approximation, polynomial.

Abstract
The article discusses the development of mathematical software for recovery the numerical values of samples of a discrete sequence of a uniformly sampled continuous signal in time. The development was carried out on the basis of the approximation method and the construction of a basic polynomials system for a discrete argument. The basic polynomials system is constructed depending on the order of the approximating model, taking into account the fact that each subsequent polynomial must be orthogonal with the two previous polynomials. The values of the model weighting coefficients are calculated based on the criterion of minimum square error. The resulting mathematical solution reduces the amount of computational procedures by half in relation to the number of sequence samples to be recovery. This is achieved due to the possibility of calculating estimates of the values of the samples simultaneously both forward and backward in the process of recovery the problem section of the sequence. The practical result was the development of algorithmic support. It is implemented as a functionally complete software module. This module was developed in accordance with regulatory requirements for the development of software components that affect the accuracy characteristics of computing procedures. The module is designed to operate in asynchronous control mode without interrupting the execution of the main application program that performs the current signal processing. Numerical experiments to evaluate the metrological and functional capabilities of the developed algorithmic support and software module were carried out using simulation modeling. The results of numerical experiments have shown that the recovery of the samples is carried out with a fairly low error.

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Methodology for optimizing the topology of the differential correction field when constructing a network of reference integrity monitoring stations
S.F. Shakhnov, e-mail: shahnovsf@gumrf.ru
S.V. Smolentsev, e-mail: SmolencevSV@gumrf.ru
A.A. Butsanets, e-mail: butsanetsaa@gumrf.ru
A.A. Ivanova, e-mail: uid@gumrf.ru
Admiral Makarov State University of Maritime and Inland Shipping, Russia, Saint-Petersburg

Keywords: river information services, RIS, differential correction, control and correction station, reference station, reference integrity monitoring station, system for distributing and monitoring corrective information, calculation algorithm, reference stations network, probability of error.

Abstract
River information services (RIS) on inland waterways (IWW) of Russia are designed to ensure safe and cost-effective navigation by providing navigators, shipowners and inland waterway basins Administrations with a standard set of information services. One of the conditions for the technical implementation of the RIS concept is the coverage of inland waterways with a continuous differential correction field, the creation of which requires the construction of an optimal topology of a network of reference integrity monitoring stations (RS) of local differential subsystems (LDSS) of GNSS GLONASS. To build it, it is also necessary to take into account factors affecting the reference stations range. One of these factors, namely, noises of various natures is examined in the paper.

A methodology for calculating the reference stations range is presented. An approach that takes into account the dependences of the electric-field strength on frequency for various types of noises has been demonstrated. Using the approach it becomes possible to simplify the algorithm for calculating the reference stations range. It is noted that when implementing the presented algorithm, it is particularly difficult to determine an attenuation function.

An example of the application of the developed algorithm in calculating the coverage areas of the reference integrity monitoring stations network in the Krasnoyarsk region in the Yenisei basin is given. As a result, the presented methodology for calculating the reference integrity monitoring stations range, taking into account noises of various natures, makes it possible to optimize the topology of the differential field when constructing a telecommunication system for distributing and monitoring corrective information.

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Algorithms of interaction of cognitive maps in the procedure of permutational decoding of binary codes
Anatoly A. Gladkikh, Ulyanovsk State Technical University, Ulyanovsk, Russia, e-mail: a_gladkikh@mail.ru
Ovinnikov A.A. Ryazan State Radio Engineering University, Ryazan, Russia, e-mail: ovinnikov.a.a@yandex.ru
Nichunaev A.A. Ulyanovsk State Technical University Ulyanovsk, Russia, e-mail: ni4unaev_art@mail.ru
Brynza A.A. Ulyanovsk State Technical University Ulyanovsk, Russia, e-mail: abrynza73@gmail.com
Attabi A. L. Kh. Ulyanovsk State Technical University Ulyanovsk, Russia, e-mail: aqeel.attaby@gmail.com

Keywords: permutational decoding, cognitive map of resultative permutations, cognitive map of non-productive permutations, interval estimation of numerators, interaction of cognitive maps of the decoder.

Abstract
The article provides a detailed description of algorithms for implementing the method of permutational decoding of binary redundant codes in conditions where, for objective reasons, not all permutations of symbols after their ranking within the receiver's accepted combination result in a transition to an equivalent analogue due to the degeneracy of the permuted matrix. Studies have shown that this phenomenon significantly reduces the efficiency of redundant coding as the length of code vectors increases, as the total volume of resultative permutations of numerators steadily aligns with the volume of non-resultative permutations of numerators. By using the property of degeneracy of a certain subset of permuted matrices, it was proven that the options of resultative and non-resultative permutations of numerators do not intersect. This opens up the possibility for most of the latter, through targeted replacement of just one numerator, to be converted into the set of resultative permutations. This procedure unequivocally excludes the trial and error method in decoding. It was proposed to explicitly indicate in the cognitive map the a priori unfavorable outcomes of correcting a non-resultative permutation. This allowed reducing the volume of such permutations from approximately 40% to 50% to around 10% of the total number of similar unsuccessful outcomes. At the same time, in previous works, the volumes of memory of cognitive maps were not evaluated, which could decisively affect the constructive and temporal parameters of the decoder. The aim of this work is to develop rational approaches to implementing algorithms for processing permutations of numerators under conditions of their diversity with constructive and computational constraints imposed on cognitive maps.

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The results of experiments on recording and post-processing a mixture of a spread spectrum signal and intense CW interference converted by a radio frequency front-end
E.V. Kuzmin, e-mail: ekuzmin@sfu-kras.ru
A.Yu. Taranenko, e-mail: ataranenko@sfu-kras.ru
Siberian Federal University (SibFU), Russia, Krasnoyarsk

Keywords: spread spectrum signals, continuous wave interference, signal acquisition, interference rejection, spectral-weight estimation, signals simulator, radio frequency front-end, post-processing.

Abstract
An experimental laboratory study of the suppression effectiveness of in-band intense continuous wave (CW) interference for radio electronic systems with spread spectrum signals has been carried out. Digital recording of an additive mixture of spread spectrum signals and CW interference at the output of the receiver radio frequency front-end (RF front-end) has been performed. Spectral pre-correlation algorithms of CW interference suppression and spread spectrum signals searching by delay procedures was carried out by post-processing of the recorded mixture samples. Spread spectrum signals simulator was used. The RF front-end is formed by a typical amplifying and filtering links. Recording of the mixture samples is performed into external memory by a digitally recording samples device. The post-processing of the mixture samples included a Fourier procedure for spread spectrum signals searching in the absence and presence of CW interference suppression algorithms. Spectral ranked element-by-element rejection and compensation based on spectral-weight estimation of CW interference parameters was used. The output effects of the spread spectrum signals searching procedure are presented in case of presence and absence of CW interference suppression. The effectiveness of the spectral pre-correlation algorithms for intense CW interference suppression was experimentally confirmed.

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