Digital Signal Processing

Scientific & Technical

“Digital Signal Processing” No. 1-2020

In the issue:

- digital processing in SDR

- spread spectrum signal searching
- synchronization of OFDM-symbols in LTE technology
- analysis of the international standard DVB-S2
- measuring nonlinear distortion
- correlator with adaptive threshold
- modeling in speech recognition systems
- multivariable data qualification
- detection of changes in the observed scene

- inverse filtering in conditions of uncertainty

Digital processing of non-linear signal distortion in a software-defined radio (SDR)
Tikhonov V. Y., Shinakov Y. S., Tymoshenko A. S., Bakhtin A. A., e-mail:

Keywords: nonlinear inertial device, nonlinear signal distortion, digital predistortion, OFDM technology.

The model of digital predistortion device for compensation of nonlinear signal distortions arising in the power amplifier of the transmission system with the use of OFDM technology is considered. The model is implemented in the form of a software and hardware module and is interfaced with laboratory equipment NI USRP 2943R, containing the receiving and transmitting parts of the transmission system. The results of experimental measurements of nonlinear distortions of OFDM signals in a power amplifier without and using the proposed digital pre-distortion device are presented, confirming a significant expansion of the linear part of the dynamic range of the power amplifier.


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2. R. Marsalek, P. Jardin, and G. Baudoin, “From post-distortion to predistortion for power amplifiers linearization,” IEEE Commun. Lett., vol. 7, no. 7, pp. 308–310, Jul. 2003.

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5. G. Baudoin, P. Jardin, and R. Marsalek, “Power amplifier linearisation using predistortion with memory,” in Proc. 13th Int. Czech—Slovak Scientific Conf. RADIOELEKTRONIKA, Brno, Czech Republic, May 6–7, 2003, pp. 193–196.

6. L. Ding, G. T. Zhou, D. R. Morgan, Z. Ma, J. S. Kenney, J. Kim, and C. R. Giardina, “A robust digital baseband predistorter constructed using memory polynomials,” IEEE Trans. Commun., vol. 52, no. 1, pp. 159–165, Jan. 2004.

7. A. Zhu and T. J. Brasil, “An adaptive Volterra predistorter for the linearization of RF high power amplifiers,” in Proc. Conf. IEEE MTT, 2002, pp. 461–464.

8. Y. Ding, H. Ohmori, and A. Sano, “Adaptive predistortion for high power amplifier with linear dynamics,” in Proc. IEEE Int. MidWest Symp. Circuits and Syst., Hiroshima, Japan, Jul. 2004, pp. 121–124.

9. V. Y. Tikhonov and Y. S. Shinakov, "COMPENSATION OF NONLINEAR DISTORTION IN INERTIAL DEVICES," 2018Systems of Signal Synchronization, Generating and Processing in Telecommunications (SYNCHROINFO), Minsk, 2018, pp. 1-4.

10. A. G. Timoshenko, N. K. Osipenko, A. A. Bakhtin and E. A. Volkova, "5G Communication Systems Signal Processing PAPR Reduction Technique," 2018Systems of Signal Synchronization, Generating and Processing in Telecommunications (SYNCHROINFO), Minsk, 2018, pp. 1-4.

11. NI USRP-2943 Software Defined Radio Reconfigurable Device,

Efficiency of the non-threshold spread spectrum signal searching procedure in case of quantization of the incoming observations
Kuzmin E.V., e-mail:

Siberian Federal University (SibFU), Russia, Krasnoyarsk

Keywords: n-bit quantization, quantization noise, spread spectrum signal searching, correct searching probability, cross-correlation function.


The characteristics of the non-threshold spread spectrum signal searching by the delay procedure in case of quantization effect are studied. The results of the statistical modeling are presented: curves of correct searching probability vs. the reception conditions for various versions of the bit-width of the analog-to-digital conversion. The paper presents estimation of possible losses in noise immunity of the signal searching procedure due to the quantization effect.

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9. Kuzmin E.V., Zograf F.G. Povyshenie verojatnosti pravil'nogo poiska shumopodobnogo signala po vremeni zapazdyvanija na fone tonal'noj pomehi (Enhancement of the probability of spread-spectrum signal correct searching in case of narrow-band interference) // Uspekhi sov-remennoi radioelektroniki (Achievements of Modern Radioelectronics). 2016. no 11. pp. 137–140.

10. A statistical theory for GNSS signal acquisition. PhD thesis / D. Borio. Politecnico di Torino. Marzo. 2008. 291 p.

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Using Zadov - Chu sequences for synchronization along the correlation curve of the cyclic prefix OFDM-symbols 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: LTE OFDM, Zadov-Chu sequence (ZC), correlation function, OFDM–symbol, cyclic prefix.

In this paper, the criteria for the selection of complex sequences of Zadov-Chu (ZC) for their use in the formation of cyclic prefix OFDM-symbols in LTE technology at the stage of synchronization on the correlation curve of the cyclic prefix of symbols of the frame transmitted from the base station to the mobile user are determined. The use of ZC sequences to fill the time interval of the cyclic prefix increases the speed and efficiency of synchronization, which is confirmed by the results of modeling in the MATLAB operating environment. The studied ZC sequences as part of a cyclic symbol prefix can be used to analyze subcarriers modulated by elements of these sequences, which are used by the mobile station as control ones, when detecting selective frequency distortions in the channel with fading.

Initial synchronization of the database with the user includes standard steps:
- clock synchronization, in this case – determination of the boundaries of the OFDM symbol by the correlation curve CP;
- loop synchronization – in this case, it is synchronization along the correlation curve of the PSS signal located in the 7th OFDM symbol of the 0th and 10th slots of the transmitted frame;
- frame synchronization – in this case, it is synchronization along the correlation curve of SSS built on 2 31-element M-sequences and their cyclic shifts, placed in the 6th OFDM symbol of the 0th and 10th slots of the transmitted frame.

In this paper, we study ways to improve synchronization efficiency along the correlation curve of the cyclic prefix. This is the first stage of synchronization, which allows you to get a temporary binding to the borders of the OFDM symbol and the beginning of the slot. When passing a communication channel with Rayleigh fades, the information data during the duration of the OFDM symbol, especially with "fast" fades, may change so much that the CP and the final interval of the symbol from which the information was copied when transmitting the frame, do not form an explicit peak of the mutual correlation function (VCF).

The author suggests using as cyclic prefixes OFDM symbols located in the Central frequency band and not involved in information exchange with other subscribers, short sequences of ZC that are not used in the group of standards allocated in the 36th series of 3GPP technical specifications.

To test the assumption of increasing the efficiency of the synchronization process along the CP correlation curve when using short ZC sequences instead of CP bit data, simulations were performed in the MATLAB operating environment for characters with CP from complex sequences ZC(5,9), ZC(9,19), ZC(15,31), ZC (25,37) and random complex bit sequences with the same number of n elements.

As a result, the energy gain values are obtained when using ZC(u,n) to form the CP of the OFDM symbol within (1.67...2.94) dB for sequences with the number of elements 9,19,31,37, considered in this paper.

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6. Bykov V. V., al-Mershahi S. M. improvement of synchronization of OFDM signals in DVB-T2 system / / T-Comm: telecommunications and transport. - 2016. - Volume 10. - No. 6. Pp. 21-26.

7. Kiseleva T. P.-Investigation of the properties of the cyclic autocorrelation function of the Zadov – Chu sequence depending on the quantization characteristics of the sequence elements.- Digital signal processing, No. 4,2018. 40-44C.

Analysis of the international standard DVB-S2, defining parameters modern satellite communications systems

Bykhovskiy Mark, PhD, Professor MTUSI, e-mail:

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

In this paper, we analyze the DVB-S2 standard, on the basis of which satellite communication systems (SCS) are currently being created. A theoretical method for determining the reception quality of communication systems built according to the DVB-S2 standard is presented. The article provides a comparison of the noise immunity estimates of the reception of SCS systems obtained by the method of statistical modeling given in the DVB-S2 standard with those obtained on the basis of theoretical analysis. The comparison showed that the results of theoretical analysis are close to those obtained by statistical modeling.

Thus, the proposed theoretical research method makes it possible to obtain analytical formulas that determine the dependence of the reliability of receiving messages in satellite communication systems on their system parameters (on the modulation parameters of the transmitted signals, the type and parameters of the codes used in the SCS).

The next part of the article presents the results of a study of the possibilities of using optimal multidimensional surface-spherical signal ensembles. These results showed that systems in which multidimensional signals are used to transmit messages in their characteristics are significantly superior to systems created in accordance with the standard DVB-S2.

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The correlator with adaptive threshold
V.G.Bartenev, Russian technological university, RTU(MIREA), e-mail:

signal correlation detection, adaptive threshold, constant false alarm rate, probability of false alarm and probability of detection.

The problem of detecting correlated signals in noise is considered. Two correlation detectors are introduced. One detector may be realized using multiplication and coherent addition with constant threshold. Another just the same, but with adaptive threshold. Numerical study is presented analytically for false alarm probability but detection probability obtained using models of correlators in MATLAB.

The detection of correlated signals against the uncorrelated random processes using discrete samples of finite volume arises in many technical applications. A method of correlation detection of received signals is known, when two samples of observations received at two carrier frequencies are multiplied, their product is accumulated and the module of the accumulated product is compared with a fixed threshold [1]. The resulting estimate of the envelope of the inter-frequency correlation coefficient is compared with the threshold, on the basis of which a decision is made about the presence of the received correlated signals. Although this method allows effective detection of correlated signals, however, this method has a disadvantage, which is in the lack of stabilization of false alarms when the noise level changes, against which the detection is performed. In order to ensure the stabilization of false alarms in correlation detection, a method is proposed that includes forming an estimate of the correlation coefficient module based on samples of observations taken at two carrier frequencies and comparing this estimate with a threshold that is made adaptive in order to stabilize false alarms when the noise level changes, formed as the product of a coefficient that determines the probability of a false alarm on the total noise power estimate at two carrier frequencies. As a rule, their analysis of the effectiveness of such devices was performed using statistical modeling, since the nonlinear multiplication operation leads to a change in the type of distributions at the output of these devices and significantly complicates their analysis using analytical calculations, especially for small observation samples and low probability of false alarms. That is why numerical study in the first of time is presented analytically for false alarm probability.

A correlator with an adaptive threshold was compared with a correlator with a fixed threshold by calculating the characteristics of detecting a fluctuating correlated signal. This was done using simulations in the MATLAB system. The results show that the efficiency in the threshold signal for the probability of correct detection is 0.5 and the probability of false alarm of 0.1 and 0.0001 slightly higher in correlator without stabilization false alarm. This is a kind of payment for the invariant properties of the adaptive correlator to changes in noise power, providing stabilization of the probability of a false alarm at the output.

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Acoustic and language modeling in end-to-end speech recognition systems
Chuchupal V.J., leading scientist, Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, e-mail:

Keywords: automatic speech recognition, deep neural networks, end to end speech recognition systems, acoustic modeling, language models.

End-to-end speech recognition systems have appeared recently, but they already have recognition accuracy comparable to the conventional state-of-the-art hybrid systems based on hidden Markov models and deep neural networks. The use of homogeneous network structures for acoustic, pronunciation, and language modeling in end-to-end systems, simplification of decoding algorithms, and replacement of expert knowledge with those obtained by machine learning greatly simplified the architecture of speech recognition systems. The presence of open tools and datasets greatly facilitated the entry of new teams into this scientific and technical field. As a fee for simplifying the architecture of recognition systems, one can consider the need to use a very big, accordingly to the usual concepts, datasets for training models. Collection, annotating and augmentation audio and text data has become an important task. The lack of theoretical results to justify the optimality of the choice of models and training methods significantly complicates the development of systems Nevertheless, the existing results give reason to believe that in the nearest future this technology will become a standard for building speech recognition systems.

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Dispersion minimization approaches in biomedical multivariable data qualification
Ya.A. Turovskyi, S.V. Borzunov, V.A. Belobrodskyi, e-mail:

Keywords: digital processing of signals, customized principal component analysis, biomedical signal classification.

The focus of this article is an innovative method of digital data processing based on factor analysis, developed and tested to solve the task of data categorization using customized principal component analysis (PCA). The method searches the n-space for a new coordinate system, where component variance of a class is minimal. The result is that a data cluster is formed, in which probability density of a given class data is significantly higher than the one of the data belonging to other classes.

The accuracy of the method was verified by sequential enumeration of all possible angles of a data cloud rotation in a given coordinate system.

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