Digital Signal Processing

Scientific & Technical

“Digital Signal Processing” No. 2-2022

In the issue:

- pulse-shaping fir filters synthesis

- simplified adaptive filters
- continuous wave interference neutralizing
- radio navigation systems working areas estimation
- probability density function estimation
- air targets classification
- quasi-optimal processing systems adaptation
- design of adaptive correlator
- speech signal digital coding
- analysis of parity-check LDPC codes matrices properties

Weighted Chebyshev approximation in design of pulse-shaping FIR filters for digital communication systems
A.T. Mingazin, e-mail:

RADIS Ltd, Russia, Moscow

Keywords: matched pulse-shaping linear-phase FIR filter pair, weighted Chebyshev approximation, Remez algorithm, transition band requirements, trade-off curves, stopband attenuation and inter-symbol interference.

The use of a pair of identical pulse-shaping linear-phase FIR filters in digital communication systems is most preferred due to the ease of implementation and a number of other known reasons. Although such filters do not allow zero inter-symbol interference (ISI) inherent in a matched pair of pulse-shaping non-linear phase FIR filters, they can nevertheless provide a sufficiently low level thereof. The widely used analytical synthesis of linear-phase FIR filters with a frequency response of the form square root raised cosine (SRRC) in an acceptable order does not always meet the specified requirements, especially with a small roll-off factor. For this reason, a large number of numerical design methods have been developed differing in the degree of complexity and the results obtained.

This paper discusses the problem of design of a pair of matched pulse shaping linear-phase FIR filters. The design involves obtaining a predetermined attenuation of the magnitude response in the stopband and a minimum level of ISI. The known design method based on the weighted Chebyshev approximation using the Remez algorithm with additional control of the transition band at one point and weight selection for the magnitude response level in the stopband is compared with several alternative approaches namely the SRRC function, nonlinear programming, convex optimization and semi-analytical procedure. Examples of pulse-shaping filters taken from the literature show that this method does not always result in repetition or improvement of known solutions. However, the modification proposed in the paper, related to the addition of several more conditions for the control of the transition band, can contribute to a significant improvement in these solutions both for stopband attenuation at the same ISI value and for each of these parameters.


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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.

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Simplified Adaptive Filters Based on Recursive Least Squares algorithms
V.I. Djigan, e-mail:

Institute for design problems in microelectronics of Russian Academy of Sciences Moscow, Russia

Keywords: linear system identification, adaptive filters, cascaded adaptive filter, simplified adaptive filter, Recursive Least Squares, RLS algorithm, Matrix Inversion Lemma, correlation matrix, matrix diagonalization.


This paper presents two adaptive filters with reduced computational complexity. They are the cascade adaptive filter and the adaptive filter with a diagonalized correlation matrix of the input signal. The weights of these filters are computed using the Recursive Least Squares (RLS) algorithms. Computational complexity, i.e. the number of the arithmetic operations required to perform one iteration, is less in the both filters compared to the traditional implementation of the adaptive filter. The reducing of the computational complexity is achieved only if the RLS algorithms with quadratic complexity are used. Therefore, the gradient algorithms or the fast RLS algorithms with linear computational complexity are not considered in the paper. The computational complexity of the considered adaptive filters is the same, but the efficiency is different. The cost of the computational complexity reducing is some degradation of the adaptive filter characteristics. The paper presents the characteristics of the considered adaptive filters obtained by simulation. They are the echo return loss enhancement and the mismatch. The first characteristics is the ratio of the energy of the desired signal to the energy of the error signal of the adaptive filter, and the second one is the Euclidean distance between the vector of the weights of the identified system (linear filter) and the vector of the weights of the adaptive filter. The simulation results demonstrate the superiority of the adaptive filter with a diagonalized correlation matrix over the cascade adaptive filter in terms of above specified characteristics in steady-state. However, this improvement is achieved by the increased duration of the adaptive filter transient response. It is shown, that in case of the correlated signal processing the dimension of the nonzero matrices over the diagonal correlation matrix of the adaptive filter is determined by the half-width of the signal autocorrelation function. The paper presents the RLS algorithms based on the matrix inversion lemma. However, the results and conclusions are valid for any RLS algorithms with quadratic computational complexity, such as ones based on the QR decomposition or Householder transform.

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Neutralizing intensive continuous wave interference by spectral-weight estimation of its parameters
E.V. Kuzmin, e-mail:
Siberian Federal University (SibFU), Russia, Krasnoyarsk

Keywords: spectral-weight estimation, signal processing, continuous wave interference, discrete Fourier transform.

The necessary auxiliary expressions are obtained analytically for the procedure of spectral-weight estimation of the parameters of a harmonic signal from the samples of the complex spectrum of its temporal realization, "weighted" using the cubic variation of the Hanning weight (window) function. The heuristic generalization of the expressions of the spectral-weight estimation procedure for the nearest integer cases of variations in the degree of this weight function is carried out and tested. The comparison of the signal parameters estimation accuracy is carried out and the efficiency of the obtained solutions is demonstrated. On the basis of spectral-weight estimation, a compensation algorithm for neutralizing harmonic interference is implemented and compared with a frequency notch based on the discrete Fourier transform.

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Working areas estimation of pulse-phase radio navigation systems when using signals from two chains together

A.P. Grunin, e-mail:
S.V. Sai, e-mail:
Pacific National University (PNU), Russia, Khabarovsk

Keywords: navigation, positioning, accuracy, coordinates, working zones, iterative algorithm, minimization.

In this paper, an iterative position search algorithm considered, based on the use of the differences in the arrival times of radio pulses from all radio navigation stations operating at the receiving point.

The error in determining the location by the proposed algorithm compared with the existing hyperbolic method at 8178 points in the Asia-Pacific region. The data obtained made it possible to simulate and evaluate the working zones of two jointly used chains of pulse-phase radio navigation systems according to both algorithms. It shown that the use of the iterative position search method significantly expands the working area of chains when they used together.

In addition, in most areas, the position determination error is significantly lower than in the hyperbolic method. A method introduced for quantitative assessment of the effectiveness of the iterative position search method in comparison with the hyperbolic method.

Modeling the working area of several chains allows you to improve the efficiency of determining the deployment locations and formats of new systems.

A quantitative analysis of the effectiveness of the proposed method allows us to conclude that when using the iterative position search algorithm, the size of the zone in which the position error is below 20 meters is approximately 11 times larger than the zone in which the hyperbolic method provides the same error. For an error below 40 meters, the size of the working area increases by a factor of 2.86. For an error below 60 meters, 2.7 times.

The iterative position search algorithm is able to work with signals from two or more radio navigation circuits. The use of the results of the study will make it possible to determine the optimal deployment sites and formats for the operation of new combined radio navigation systems.

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Estimation of the probability density function of the envelope signals with modulation in cases of fading
Maslakov M.L., Ph.D., assistant professor, e-mail:
Saint-Petersburg State University of Aerospace Instrumentation

probability density function, envelope signal, fading, quadrature amplitude modulation, phase shift-keying modulation, noise variance.

Estimation of the radiolink characteristics, such as the probability of bit error rate and the signal-to-noise ratio is one of the most important tasks of the operation of an adaptive radio communication system. To obtain these estimates, as well as to analyze the state of the channel, one often proceeds to the complex envelopes of the received signals are considered.

At the same time, in non-stationary communication channels, as well as in case signal fading and/or hard signal-interference conditions, it is required to obtain appropriate estimates quickly enough, which significantly limits the possible size of the analyzed sample and the applicability of some known methods.

The purpose of this work is to estimation of an empirical probability density function of the complex envelope coefficients of modulated signals received from a non-stationary channel with fading.

To estimation an empirical two-dimensional probability density function of the complex envelope coefficients of modulated signals received from a channel with fading, the Parzen method or the method of kernel functions was used in the work. As shown in the work, the obtained empirical probability density function are smooth, independent of the probability of individual symbols, and also allow one to draw conclusions about the “depth” and nature of fading in the communication channel.

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Classification of aerial targets based on a system with a random jump-like structure using information from neural network classifiers
L.B. Ryazantsev:

MESC «Zhukovsky–Gagarin Air Force Academy», Russia, Voronezh

Keywords: unmanned aerial vehicles (UAVs), Recognition, radar characteristics, aircraft-type UAVs, multirotor-type UAVs, prevent overloading, Doppler portrait, inverse aperture synthesis, Bayesian classifier, neural networks, synthetic aperture radar, resolution, trajectory instability, phase errors, optimal aperture synthesis time, autofocus.

The article is devoted to the study of the classification of small-sized aerial targets by their trajectory characteristics and radar portraits obtained by the method of inverse aperture synthesis. An approach based on the integration of information from Bayesian and neural network classifiers is considered. The integration is proposed to be carried out using the provisions of the theory of systems with a random jump-like structure. Simulation results are presented, including an assessment of the probabilistic and temporal characteristics of the proposed classifier.

Recognition of small UAVs is not an easy task due to the similarity of the radar characteristics of such targets and the parameters of their movement both among themselves.

The recognition of targets can be carried out on the basis of the following features: the nature of the Doppler portrait of the reflected signal due to the peculiarities of the rotation of the propellers of a particular type of aircraft or the flapping of the wings of birds; radar image of the target formed by methods of inverse aperture synthesis; trajectory signs of the flight of the target, etc.

The Bayesian classifier uses observable features as a basis and correlates objects to a certain class based on the maximum likelihood principle, which consists in assessing the degree of discrepancy between the statistical characteristics of the obtained samples of parameter values with their a priori values. Classifiers based on neural networks have high performance, however, the addition of a new class leads to the need to repeat the procedure of full network training on the entire existing set.

The approach that allows combining the advantages of neutron and Bayesian methods can be based on the representation of the classification object as a system with a random jump-like structure. Evaluation of the parameters of such systems is carried out by Bayesian methods, and neural classifiers act as so-called indicators that ensure the formation of a final solution, taking into account their probabilistic characteristics for the correlation of an object to a given class.

The neural network indicator is a deep learning neural network based on the SqueezeNet architecture and implemented using the Neural Networks Toolbox extension of the Matlab software package. As a training sample, the radar of the DJI Matrice S900 multicopter aircraft, the Orlan-10 and Bayraktar TB2 UAVs, as well as the Tomahawk BGM-109 cruise missile were used. The radar was formed in the CST Microwave Studio electrodynamic modeling environment using the inverse aperture synthesis method implemented in it. The training sample was a set of 700 radar images for each aircraft, obtained from various viewing angles. The images are formed for horizontal polarization of the electromagnetic wave using the monostatic radar method and the average wavelength of the probing signal is 5.5 cm. The width of the spectrum of the probing signal is 1 GHz, which provides a horizontal range resolution (x coordinate) of about 15 cm.

The use of the proposed classifier in radar means will increase the efficiency of choosing a priority for counteraction, taking into account the degree of danger of targets and exclude secondary targets from processing to prevent overloading of radar and counteraction channels.

1. Vorobyev E.N. Investigation of signal signs of recognition of small UAVs in semi-active radar // Bulletin of Novgorod State University, 2019. No. 4 (116). pp. 72-77.

2. Ryazantsev L.B. Multimodel Bayesian estimation of the state vector of a maneuverable aerial target in discrete time // Bulletin of TSTU, 2009. No. 4. pp. 729-739.

3. Jiekong Jiao, Chibiao Ding, Longyun Chen, Fubo Zhang. A three-dimensional visualization method for an ISAR array based on sparse Bayesian inference // Sensors, 2018. DOI:10.3390/s18103563.

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Synthesis of real discrete bandpass and rejector filters by the billinear z-transform method
S.I. Ziatdinov, e-mail:
St. Petersburg State University of Aerospace Instrumentation (GUAP), Russia, St. Petersburg

Keywords: discrete filters, frequency characteristics, z-transform, weight coefficients. The question of constructing real discrete band-pass and notch filters based on given continuous filters-analogues of low and high frequencies using a bilinear z-transform is considered. The aim of the work is to create a technique for the synthesis of real tunable band-pass and notch filters with the same shape and width of the amplitude-frequency characteristics, regardless of the filter tuning frequency.

The synthesis is based on the representation of the mathematical frequency transfer function of the real filter separately in the region of positive and negative frequencies, for each of which a bilinear z-transform shifted by the tuning frequency is applied. Based on the given frequency transfer functions of real continuous filters analogs of low and high frequencies, using a bilinear z-transform, the weight coefficients of the difference equations are found that determine the operation of real discrete band-pass and notch filters that have a constant shape and width of the amplitude-frequency characteristics under conditions of a variable filter tuning frequency . Bilinear z-transforms shifted by filter tuning frequencies are presented. The transfer functions of discrete filters are obtained in the ranges of positive and negative frequencies. By summing the transfer functions for the regions of positive and negative frequencies and multiplying these transfer functions, the final transfer functions for real discrete bandpass and notch filters are obtained. Expressions for the frequency transfer functions of the synthesized real discrete band-pass and notch filters are given. Their amplitude-frequency characteristics are calculated.

It is shown that the shape and width of the amplitude-frequency characteristics of the synthesized filters remain constant when the filter tuning frequency is changed. The developed technique for the synthesis of tunable discrete band-pass and notch filters with a constant shape and width of the amplitude-frequency characteristic will be very useful in the construction of adaptive systems and signal processing devices, such as systems for detecting and filtering signals with an unknown frequency, Doppler velocity meters under varying Doppler frequency, systems for selecting moving targets in the presence of reflections from the earth's surface and moving hydrometeors. Keywords: discrete filters, frequency characteristics, z-transform, weight coefficients.

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Adaptation of quasi-optimal signal processing systems against the background of clutter
D.I.Popov, e-mail:

Keywords: adaptation, quasi-optimal processing, coherent storage, optimization, clutter, restructuring of the structure, rejection filter, signal.

Quasi-optimal processing systems that carry out coherent accumulation of cutting residues are considered. It is shown that systems of this type follow from the procedure of statistical synthesis, which generally leads to matrix processing and subsequent coherent accumulation. With Markov approximations of interference, the adaptive matrix filter is transformed into a vector adaptive vector filter (RF), leading to the traditional quasi-optimal structure of the "vector filter - coherent storage".

Based on the introduced criterion, a two-stage optimization problem has been solved. At the first stage, the optimal RF vector is determined, at the second stage - a multichannel filter (MF) of coherent accumulation. Optimization results are presented depending on the correlation properties of the interference and a comparison is made with the efficiency of optimal processing.

The dependences of the optimal RF order on the magnitude of the dynamic range of interference in relation to the level of intrinsic noise are obtained. having a directly proportional character. The conditions are established under which a system of a fixed structure, the scheme of which is given, is achieved close to potential efficiency. The conditions for the use of tunable structure systems are considered, in which it is possible to approach the potential efficiency when changing the interference parameters in a relatively wide range only when optimizing the RF order by appropriate restructuring of the structure.

A method for choosing the RF and MF orders is proposed, based on the relationship of the optimal RF order with the increment of the interference transmission coefficient at the RF output when its order changes. As a result of the analysis of the dependences of the increments of the passage coefficient, the condition for choosing the optimal order of the RF is established. A block diagram of the adaptive processing system of the transferred structure is given.

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Digital coding of wideband speech signal on telephony task
A.A. Rybolovlev, e-mail:

Keywords: speech signal, speech coding, codebook, linear prediction coefficients.

The article describes the adaptive multirate wideband (AMR-WB) speech codec, which was used by the International Telecommunication Union – Telecommunication Sector (ITU-T) for wideband speech coding around 16 kbit/s (Recommendation G.722.2). AMR-WB uses an extended speech bandwidth from 50 Hz to 7 kHz, gives high speech quality and voice naturalness, adds a feeling of transparent communication and eases speaker recognition. Codec operates at a 16 kHz sampling rate and on nine speech coding modes with bit-rates from 6,6 kbit/s to 23,85 kbit/s. The bit rate may be changed at any 20-ms frame boundary. The paper details AMR-WB algorithmic description. The block diagrams of the encoding and decoding algorithms are shown.

The AMR-WB speech codec is based on the algebraic code excited linear prediction technology (ACELP). Two frequency bands, 50 – 6400 Hz and 6400 – 7000 Hz, are coded separately.

The input signal of the lower frequency band is pre-processed using a high-pass filter and a pre-emphasis filter. Linear Prediction (LP) analysis is performed on each frame. The set of LP parameters is converted to immittance spectrum pairs and vector quantized using split-multistage vector quantization. The speech frame is divided into four subframes of 5 ms each. The adaptive and fixed codebook parameters and pitch lag are transmitted every subframe. The bit allocation of the codec at different bit rates is shown.

The higher frequency band is reconstructed in the decoder using the parameters of the lower band and a random excitation. No information about the higher band is transmitted, except in the 23,85 kb/s mode, where the higher band gain is transmitted. In other modes, the gain of the higher band is adjusted relative to the lower band using voicing information. The spectrum of the higher band is reconstructed by using a wideband LP filter generated from the lower band LP filter.

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Analysis of properties of parity-check matrices of LDPC codes intended for satellite and space communications
A.A. Ovinnikov, e-mail:
E. A. Likhobabin, e-mail:
A. V. Kharin, e-mail:
M. O. Isaev, e-mail:
The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

Keywords: channel coding, iterative decoding, low density parity check (LDPC) codes, Tanner graph, girth, Extrinsic Message Degree (EMD), coding gain.

In this paper, the analysis of codes with a low-density parity checks (LDPC) of the currently most common standards of satellite and space communications is carried out. Approaches are considered for the operational evaluation of the coding gain in the area of rapid change in the probability of error from the signal-to-noise ratio, as well as decoding error floor. A comparison of simulation modeling in the communication channel for LDPC codes taken from various standards with two methods of static physics is presented in order to compare relative coding gain and conclusions are drawn about the expediency of using such qualitative assessments. In the area of saturation of the decoding error probability, it is proposed to introduce an indirect criterion for assessing the presence of a slowdown in the decline in the frequency of errors, based on the properties of cycles of different lengths in Tanner graphs. A comparison is made between the extrinsic message degree (EMD) of the simulation results for a number of high-speed MPP codes, R > 0.5. The key result of the work is a large set of experimental data, which were obtained on the basis of specialized software developed, among others, by the authors of the publication. In the future, it is planned to continue research in this direction in order to establish clearer patterns linking the properties of codes with the results obtained during simulation.

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