Digital Signal Processing

Scientific & Technical

“Digital Signal Processing” No. 2-2020

22 International Scientific Research Conference “Digital Signal Processing and its Application - DSPA-2020”

In the issue:

- adaptive filtering in fractionally spaced equalizers

- allpass transformed filter banks
- signal transmission methods in satellite communications systems
- synchronizing a cellular base station
- spread spectrum signal searching procedure
- convolutional neural networks application

Peculiarities of RLS adaptive filtering algorithms application in fractionally spaced equalizers
Djigan V.I. Institute for design problems in microelectronics of Russian Academy of Sciences, Moscow, Russia, e-mail:

Keywords: equalizer, Fractionally Spaced (FS), Feed Forward (FF) equalizer, Feed Backward (FB) equalizer, multichannel adaptive filter, fast Recursive Least Squares (RLS) algorithms, Fast Kalman (FK) algorithm, Fast Transversal Filter (FTF) algorithm, Fast a Posteriori Error Sequential Technique (FAEST) algorithm, stabilized FAEST algorithm.

Adaptive signal processing is an important part of modern digital signal processing. Today adaptive filters are widely used in applications, where the filters with fixed weights cannot be designed in advance. The well-known examples of these applications are the adaptive antenna and acoustic arrays, active noise control, acoustic and electrical echo cancellation, digital predistortion of power amplifiers and channel equalization. Channel equalizer is an essential part of modern communication system. Its role is to equalize the amplitude-frequency response of a non-flat communication channel, that allows to receive digital data, sent via the channel, without intersymbol interference. There are two sorts of adaptive equalizers: Feed Forward (FF) and Feed Backward (FB). Usually, sampling rate of the equalizer input signal is the same as data rate. This allows to save the implementation resources, but does not satisfy the sampling theorem. Due to the aliasing, the sampled signal becomes noisy, but the noise is tolerable, if data symbols and samples are well synchronized. Equalizers, with the same sampling rate as the symbol rate, are called Symbol Spaced (SS) ones. Another sort of equalizers are Fractionally Spaced (FS) ones. They use input signal sampling rate, which a few times (actually an integer value) higher of symbols rate. FS equalizers do not suffer of aliasing problem and do not require a precise synchronization of data symbols and sampling. The price of the solution is a higher arithmetic complexity because FF part of FS equalizer has to contain a larger number of weights. However today, the achievements in modern microelectronic technologies and progress in integrated circuit design allow to produce the high performance Digital Signal Processors (DSP) and Field-Programmable Gate Arrays (FPGA), which ensure efficient implementation of different signal processing algorithms, including algorithms for adaptive filtering. Adaptive filtering algorithms are conditionally separated into two groups: gradient search based and least squares method based. The most efficient are last ones, called Recursive Least Squares (RLS). The RLS adaptive filters are characterized by the quadratic arithmetic complexity. However, these algorithms also exist in the fast, i.e. computationally efficient form with a linear arithmetic complexity, that allows to implement simultaneously efficient and low complexity adaptive filters. The paper considers the peculiarities of the fast RLS algorithms application in FS FF and FS FF/ FB equalizers. Such equalizers are viewed as the multichannel adaptive filters with unequal number of weights in channels. The architectures and computational procedures of such equalizes, based on fast Kalman adaptive filtering algorithm, Fast Transversal Filter (FTF) algorithm, Fast a Posteriori Error Sequential Technique (FAEST) algorithm and stabilized FAEST algorithm are presented. The simulation results demonstrate the proposed equalizer efficiency.


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Comparison of time-frequency transforms: Fourier analysis, wavelets and allpass transformed filter banks
M.I. Vashkevich, e-mail:
I.S. Azarov, e-mail:

Belarusian State University of Informatics and Radioelectronics (BSUIR), Belarus, Minsk

Keywords: time-frequency transform, filter bank, allpass transform, constant Q analysis.


The article presents a comparative analysis of three time-frequency signal representation methods including 1) short-time Fourier transform (STFT), 2) wavelet transform, 3) decomposition based on allpass transformed filter bank. Attention is given to study time-frequency tiling associated with these methods. In order to consider the methods within an integrated framework we treat time-frequency transform as a filter bank. We also give attention to explaining the basic principle of allpass transform by showing its relation to decomposition of the signal into discrete orthonormal Laguerre sequences. The application of allpass transform to the DFT-modulated filter bank is considered. In order to visualize configuration of time-frequency tiling for considered transforms Heisenberg rectangles were calculated using numerical integration of the corresponding expressions.

Based on the obtained results, it can be concluded that the STFT and the corresponding DFT-modulated filter bank should be used when it is required to decompose the signal into "atoms" uniformly covering the time-frequency plane. The wavelet filter bank as well as the allpass transformed DFT filter bank are well suited for constant Q analysis. Such analysis is especially important in applications where it is necessary to model the auditory perception. However, the allpass transformed DFT filter bank has some advantage over the wavelet-based filter bank in that it allows better frequency localization in the low-pass region. In addition, it should be noted the flexibility of the approach based on the allpass transform. The degree of deformation of the frequency axis depends on one parameter, changing which time-frequency tilling can be smoothly controlled.

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Effective signal transmission methods in satellite communications systems
M.A. Bykhovskiy, e-mail:

Keywords: satellite communications, signal transmission methods, spectral and energy efficiency, message coding.

The article is devoted to the study of the characteristics of satellite communications systems (SCS) that use multidimensional surface-spherical signal ensembles (SSSE) to transmit messages. It is shown that such systems are significantly superior to systems created in accordance with the DVB-S2 standard, providing high reliability of the reception of transmitted messages with the highest possible spectral and energy efficiency.

It was noted that SSSE systems are simpler in technical implementation compared to SCS of the DVB-S2 standard. The use of multidimensional SSSE also simplifies the implementation of different operating modes, allowing you to adapt the transmission of messages with high reliability to possible changes in the propagation conditions of radio waves in the satellite communication channel. This is due to the fact that in systems with SSSE there is no need to use noise-resistant codes of large length and very complex decoders.

It is shown that in systems with SSSE the length of transmitted signals is significantly less than the length of code combinations in SCS standard DVB-S2. Therefore, the use of communication systems with SSSE is especially attractive in cases where it is necessary to transmit short informational messages and the transmission time should be minimally possible.

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Algorithm for synchronizing a cellular base station with a mobile user based on the correlation function of the primary sync signal in LTE technology

Kiseleva Tatyana, post-graduate student of the Department of radio systems of the Moscow technical University of communication and Informatics (MTUCI), Moscow, Russia, e-mail:

Keywords: Zadoff-Chu sequence (ZC), primary synchronization signal (PSS), LTE OFDMA technology, intercorrelation function , additive Gaussian noise, Doppler frequency offset.

The article provides a brief algorithm for synchronizing the base station with a mobile user when the user first connects to the station. The structure of the algorithm covers the synchronization stage along the correlation curve of the primary synchro signal (PSS) transmitted by the base station in the direction of the user when it is initialized. In contrast to the classical algorithm for FFT processing and frequency alignment of the accepted PSS, it is proposed to synchronize the PSS correlation curve only in the time domain without switching to the frequency domain. The algorithm is based on preliminary simulation in the MATLAB operating environment using a channel model with additive white Gaussian noise and Doppler carrier frequency offset.

To form PSS, we use sequences with Good correlation characteristics – ZC(u, n), where u is the indices (roots) of the sequences (u= 25, 29 ,34), and n=62 is the number of elements. The LTE standard regulates OFDM technology, and 62 Central subcarriers are allocated for the distribution of sequence elements that form synchro signals to accommodate elements of the corresponding sequences.

The article defines the conditions for forming a normalized threshold for analyzing the peaks of PSS correlation functions, and develops a mathematical model of the transmitted multi – frequency OFDM symbol of the primary PSS sync signal formed on the basis of the ZCi(u,n) sequence, according to the LTE technology standard. The results of modeling all combinations of normalized correlation functions are summarized in a table. The structure of the classical version of the algorithm for processing received OFDM symbols is given, and the algorithm for processing PSS correlation functions in the time domain, without switching to the frequency domain, is described. An approximate calculation of the reduction of calculations when using the algorithm in the time domain of PSS processing is performed.

Based on the results of simulation in the MATLAB operating environment, a 3D software model of the correlation function of the PSS synchro signal was developed based on the ZC(25,62) set sequence, in coordinates (time x frequency x normalized amplitude). The 3D model graph is based on a resource matrix (256x20) of elements; the time grid step– 0,52*10-6s, frequency grid step – 50 Hz.

One of the main tasks of designing mobile user systems is to reduce the hardware and software resources of the systems. In terms of this problem, the PSS correlation function is modeled for a quantized sequence ZC(25.62) with a quantization step Q=1/32.

The analysis of the obtained data for a quantized sequence with a step of Q = 1/32 and a non-quantized sequence ZC(25.62) allows us to conclude that synchronization along the correlation curve of the primary multi-frequency synchro signal (PSS) in the time domain is possible without passing into the frequency compensation region of the Doppler shift. The synchronization accuracy on the correlation function of the PSS, in case of constructing a multifrequency PSS symbol as unquantized and quantized with quantization step Q = 1/32 sequence ZC(of 25.62) equal to ± 0,52*10-6, and for correlation of the curve of the ZC sequence(of 25.62), obtained by the classical treatment of a received PSS symbol, i.e. the transition in the frequency region processed with FFT and frequency equalization by the equalizer. In this case, the accuracy of frequency synchronization for PSS based on non – quantized ZC(25.62) is about ±50 Hz; for PSS based on quantized ZC(25.62) – about ±100 Hz, which is quite acceptable for carrier frequency values with f0 = 100 MHz and higher based on the permissible carrier frequency detuning of 0.1 ppm.

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Efficiency of the spread spectrum signal searching procedure in case of continuous wave interference and quantization effect
E.V. Kuzmin, e-mail:

Siberian Federal University (SibFU), Russia, Krasnoyarsk

Keywords: spread spectrum signal, continuous wave interference, spread spectrum signal searching, correct searching probability, n-bit quantization, quantization noise, discrete Fourier transform.

This paper deals with the characteristics of the non-threshold spread spectrum signal search-ing by the delay procedure in case of continuous wave interference influence and quantization ef-fect. This study applied the method of statistical modeling to obtain curves of correct searching probability vs. the reception conditions for various versions of the bit-width of the analog-to-digital conversion. The article presents estimation of possible losses in efficiency of the spread spectrum signal searching procedure occurring due to the quantization effect.

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Three-dimensional graphics in analysis problem of quantized FIR filters
Mingazin A.T., RADIS Ltd, Russia, Moscow, e-mail:

optimum FIR filters, halfband FIR filters, analysis of direct structure, one and three-step coefficient quantization, variation of initial parameters, three-dimensional graphics.

ΐ simple and clear direct method for the analysis/synthesis of FIR filters with quantized coefficients (quantized FIR filters) is often used. In this case the degree of influence of the coefficient quantization on the change of the filter magnitude response is estimated for only one set of initial parameters. However, by using one or even several sets of initial parameters, it is not always correct to judge the advantage of one or another approximation of a magnitude response or filter structure. By variation of the initial parameters (VIP), the results of the direct method can be improved. In particular, for the analysis (VIP analysis) of the degree of influence of coefficient quantization, the built-in dependencies of the controlled parameters of the magnitude response on the selected initial parameter can be used. Earlier this approach is applied to optimal FIR filters synthesized using the Remez-Parks-McClellan algorithm (see, for example, the cremez (...) function in MATLAB). Thus, for low-pass filters of a direct structure with continuous and quantized coefficients, options for plotted dependencies of controlled parameters from initial ones are presented and discussed. In addition, an analysis of the plotted dependencies of the maximum relative error of magnitude response on the initial ratio of ripple levels in the passband and stopband for the four structures of FIR filters was carried out.

In this paper, another effort is made in order to improve VIP analysis, namely, it is proposed to plotting the dependence of the controlled parameter of the magnitude response of optimal FIR filters not from one as earlier, but immediately from two selected initial parameters. This involves MATLAB three-dimensional graphics. After description of controlled and initial parameters some examples of analysis of presented dependencies for optimal halfband FIR filter of direct structure with one and three quantization steps of its coefficients are given. It is shown that the use of three quantization steps, instead of one-step, makes it possible to significantly simplify multipliers in the filter when it is implemented on VLSI. It saves the chip area and power consumption.

The presented three-dimensional graphical analysis in addition to the two-dimensional analysis allows better understand the problems of designing quantized FIR filters, since it is a convenient visual means to find the best combination of the initial parameter values, the approximation method of magnitude response and filter structure.

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The problem of personality recognition using facial images and audio signals with speech recordings

Stefanidi A.F., Priorov A.L., Topnikov A.I., Hryashev V.V., e-mail:

Keywords: digital speech processing, digital image processing, machine learning, speaker identification, face recognition, convolutional neural network, bimodal biometrics.

Currently, biometric identification systems are often used in mobile applications, banking systems, access control and management systems as well as for the management of mobile robots. In this paper, we consider the problem of personality recognition using facial images and audio signals with speech recordings. The results of the research will be used to create a system of multimodal biometric identification. Since convolutional neural networks demonstrate the highest results regarding the problems of detection, segmentation and classification of objects, this paper also proposes an approach to person identification based on convolutional neural networks. The research was carried out using modern audiovisual database VoxCeleb1. To decrease the computational capability of the experiment, the researchers reduced the number of classes from 1251 to 200. The development results showed the possibility of using the proposed algorithm as a part of a multimodal identity identification system.

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