Digital Signal Processing

Scientific & Technical

“Digital Signal Processing” No. 4-2016

In the issue:

- digital algorithm based on sign signal processing
- estimate of a power spectral density
- novel approach to the construction of the orthogonal system
- offset estimation for OFDM systems in MIMO channels
- decoding of LDPC codes
- detecting a correlated signals in noise
- recognition of scanned handwritten texts
- interfaces of multiprocessor system

Digital algorithm to compute estimate of a power spectral density based on sign signal processing using time-weighting functions
V.N. Yakimov, e-mail:
A.V. Mashkov,

Samara State Technical University (SSTU), Russia, Samara

Keywords: random process, power spectral density, time-weighting function, stochastic quantization, sign signal, time readout.

The developed Digital algorithm for estimating of a power spectral density random process based on sign signal processing. These signals are the result of the transformation of the investigated random process using the sign-function analog stochastic quantization. This type of quantization is a very rough binary conversion, which is based on a comparison of the investigated random process with uniformly distributed auxiliary random signal acting as a threshold quantization. Such quantization allows very rough two-level quantization of random process without systematic error. Using of a sign-analog stochastic quantization has given analytical calculation of Fourier cosine transformation of time-weighting functions in going from the continuous represent spectral estimates to implement it in digital form. That approach eliminates the systematic error caused by the implementation of the operations of integration in digital form. As a result of analytical calculations of the cosine-Fourier transform operation of multiplication is converted to procedures that require performing logical and simple arithmetic operations of addition and subtraction. As a result, developed a digital algorithm increases the computational efficiency and reduces the complexity of the digital estimation of power spectral density. The results of numerical experiment estimating the power spectral density using the algorithm developed for some of the most used time-weighting function. Model of the investigated realization of a random process represented statistically independent harmonic components in the presence of additive noise.


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8. Yakimov V.N. Strukturnoe proektirovanie tsifrovykh korrelometrov dlya operativnogo korrelyatsionnogo analiza na osnove znakovogo analogo-stokhasticheskogo kvantovaniya [The structural design of digital correlators for operative correlation analysis based on the sign-analog stochastic quantization]. Izmeritelnaya tekhnika [Measuring equipment]. 2007. ¹ 4. P. 6-11.

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Pulse random processes spectral density estimation using selected characteristic functions
V.S. Parshin, e-mail:
The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

Keywords: : spectral analysis, pulse random process, characteristic function, statistic characteristics.


Many objectives arising in the processing of the signals in radar, radio-navigation, related systems are reduced to the analysis of pulse random processes. Pulse sequence can act both as a carrier of useful information, and be a hindrance. Considering, that the signal processing is often performed in the spectral domain, relevant is the assessment of the spectral power densities of pulse sequence, at that in practice often have to evaluate the spectral power for one implementation of the process. It is know, that the evaluation of the spectral density of the power pulse sequences, obtained using fast or discrete Fourier in one implementation of the process is manque. To obtain well-founded estimates commonly used smoothing selective spectra by means spectral windows. For the pulse sequences occurring at random times, it is possible to obtain well-founded and nonadjacent spectral density estimation for one implementation without the smoothing procedure. This are explained by the fact that for many types of pulsed random processes common property is the dependence of the form of the spectral density from the square modulus of the characteristic function of the parameters of the pulse train. In work it was carried out assessment of statistical analysis of a square of the module of characteristic function of accidental stationary processes. Were received ratios for mathematical expectation and dispersion of assessment of a square of the module of characteristic function, the accuracy of which is confirmed by the simulation results. It is shown that this estimate is asymptotically unbiased and well-founded (in the mean square sense). Therefore, knowing the model of the pulse sequence in the time domain always possible to estimate the characteristic function of parameters of pulse sequences and on its basis to calculate the spectral density. The simulation results of two types of stationary pulse sequences are given – pulse sequences with identical durations and amplitudes, arising in accidental random time and the sequences, consisting of pulses with the accidental amplitudes arising in accidental random time. Results of simulation completely confirm theoretical calculations.

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A metod of constructing compactly supported ortogonal wavelets

R. A. Rafikov, e-mail:
The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

Keywords: wavelet, scaling function, symmetry, high-order moments.

The novel approach to the construction of the orthogonal system of compactly supported scaling and wavelet functions is suggested. This approach allows construction of functions without the requirement on vanishing high-order moments for functions.

Construction of wavelets with compactly supported functions includes determination of the coefficients hn of the refinement equation:

There are fundamental requirements on scaling φ(x) and wavelet ψ(x) functions lead to the main equations for the coefficients hn of the refinement equation:

The fundamental requirements allow N+1 equations for the coefficients hn, while the total number of coefficients equals 2N. N+1 coincides with 2N only if N=1. If N>1, to generate N-1 equation, the fundamental requirements should be supplemented with additional demands on functions φ(x) and ψ(x). These demands are referred to as secondary. Ingrid Daubechies has suggested secondary demand on wavelet moments [1]:

In paper instead of demands on moments for functions introduced symmetry of the coefficients hn relative to the coefficients hN-1 (or hN) as a secondary demand. This condition links the coefficients of the refinement equation ( hi= h2(n-1)-i).

1. I. Daubechies, Ten lectures on wavelets, SIAM, Philadelphia, PA, 1992.

Method for increasing the accuracy of timing and frequency offset estimation for OFDM systems in MIMO channels
A.V. Bakke, e-mail
I.V. Lukashin, e-mail:
The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

Keywords: OFDM, time and frequency synchronization.

For most communication system MIMO-OFDM synchronization algorithms’ is unsolved of the quality of functioning problem in non-stationary multipath channel at low signal-to-noise ratios. The degradation of the quality is evident in significant decrease of accuracy timing and frequency offset estimation.

The paper is proposed a method to improve the accuracy of timing and frequency offset estimation synchronization algorithm Schmidl&Cox. The algorithm Schmidl&Cox is based on the use of two preamble symbols. The first symbol is used for detection the preamble and estimation the fractional frequency offset, the second symbol – to estimate the integer frequency offset. Detection and symbol timing estimation is based on finding the likelihood function. The presence of the second symbol provides the possibility of implementing additional components in the likelihood function. This will reduce the risk of making false decisions in the presence of inter-symbol interference at the stage of symbol timing estimation.

In the proposed method, an additional component of the likelihood function is defined in the frequency domain based on calculations of cross-correlation functions of first and second symbol preamble reference spectrum’s and analyzed block spectrum’s. The resulting likelihood function is based on a weighted application of likelihood function Schmidl & Cox algorithm and additional components.

The research of proposed method effect’s on the accuracy timing and frequency offset estimation for various values of weight coefficient in non-stationary multipath channel is produced. As model of multipath the COST 259 (Typical Urban) was used. The simulation showed that the proposed method for different configurations spatial diversity MIMO can significantly improve the accuracy of timing and frequency offset estimation in non-stationary multipath channel at low signal-to-noise ratios.

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Images of cycles of cyclic liftings in the base graph of protograph LDPC codes
A.A. Ovinnikov, e-mail:
The Ryazan State Engineering University (RSREU), Russia, Ryazan

error-correction coding, LDPC, protograph, cyclic liftings, base graph, girth.

This report describes the problem of identifying the possible intersections of cycles in the protographs of quasi-cyclic LDPC codes. The performance of an LDPC code is related to the short cycle structure of the Tanner graph. Numerous publications have used the cycle structure of the Tanner graph as an important measure of the efficiency of LDPC codes, with the general belief that for good performance, short cycles should be avoided in the Tanner graph of the code. It was shown that in addition to the girth, the number and statistics of short cycles are also important performance metric of the code. The close relationship between the performance of message passing decoders and the cycle structure of the graph, motivates the search for efficient algorithms that can enumerate cycles of different length in the graph, as well as finding their relationships to the other structures which affect the performance of such coding schemes. For structured LDPC codes, resulted from a lifting process, it is also important to know the relationship between the girth of the LDPC code and other code parameters such as lifting degree and the size of base matrix. It is worth noting that all the LDPC codes currently adopted in standards are structured QC protograph LDPC codes. In this paper we analyze the relationship between short cycles in the base graph and make a list of cycle identification rules, which can be used as a part of algorithms of synthesis of quasi-cyclic codes with low density parity checks. We closely examine the relationships among the subgraphs of the base graph that rise to short cycles in the lifted graph. As a result of this study, we derive relevant rules on the required cycle metric of the protograph. The list of such rules can be used as a part of algorithms of synthesis of quasi-cyclic codes with low density parity checks.

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UMP-APP decoding of LDPC Codes with self-correction modifie
Volkov I.Y., Dryakhlov A.A., Likhobabin E.A., Mirokhin E.I., Terekhov K.G.

Keywords: forward error correction, LDPC codes, UMP-APP algorithm, self-correction.

In this paper we propose self-correction modifier for the UMP-APP decoding of LDPC codes. Like self-corrected “min-sum” decoding our method modifies the variable nodes processing by erasing unreliable messages. As shown by Monte-Carlo simulations, self-corrected UMP-APP decoding performs better then common UMP-APP decoding.

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Analysis of correlated signals in noise detection performance for small observation samples
Bartenev V.G., e-mail:

Moscow Technological University (MIREA)

Keywords: signal detection, correlated signals, maximum likelihood correlation estimate, probability of false alarm and probability of detection.

The problem of detecting a correlated signals in noise is considered. The detector optimal for this problem is the maximum likelihood type. Unfortunately, the amount of computations required to design this optimal detector can be quite substantial. For this reason, two suboptimal detectors are introduced, which much easier to design than the optimal detector. One suboptimal detector may be realized only using multiplication and coherent addition. Another suboptimal detector very simple using after the multiplication a binary decision device. Numerical study is presented which indicates that suboptimal detector with multiplication and coherent addition more effective, than optimal detector in detection probability but optimal detector not sensitive to changes in noise power. Simple detector with multiplication and binary decision device shows much worse results.

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Evaluation of processor word length required for solving stochastic signals processing problems
M.V. Ratynsky, e-mail:
A.K. Kiryakmasov, e-mail:
JSC "Russian Scientific-Research Institute of Radiotechnology" (VNIIRT), Russia, Moscow

Keywords: processor word length, stochastic signals, signal processing.

The required processor word length (the number of mantissa bits for floating-point calculations) is evaluated for four stochastic signal processing problems: detection, enumeration and directions of arrival estimation and adaptive space filtering. The evaluation is carried out by computer simulation, with mantissa of each intermediate result (for each quadrature component when the numbers are complex) being cut off to the desired number of bits, while the number of bits is changed over sufficiently wide limits. For each of the problems the algorithm of solution is outlined, and criterion of required word length evaluation is determined.

The results of evaluation are as follows. Detection problem requires 16...18 bit word length, the latter being limited by false alarm probability increase. Enumeration problem requires 19...21 bit word length, the latter being limited by arising of enumeration errors. Directions of arrival estimation problem requires 10...12 bit word length, the latter being limited by false directions of arrival arising. Adaptive space filtering problem requires 14...16 bit word length, the latter being limited by signals suppression decrease.

Three problems of the four considered (namely detection, enumeration and adaptive space filtering problems) are solved without explicit forming and inverting covariance matrix of input signals, those steps being substituted by essentially equivalent finding filter that orthogonalizes the rows of input signal matrix. Such a solution has higher numerical stability, i.e. it needs smaller processor word length against explicit forming and inverting covariance matrix, which is demonstrated by direct verification for adaptive space filtering problem as an example.


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The decrease in the number of recognition errors of scanned handwritten texts
I.Ya. Lvovich1, e-mail:
Ya.E. Lvovich2, e-mail:
A.A.Mozgovoy2, e-mail:
A.P.Preobrazhenskiy2, e-mail:
O.N.Choporov2, e-mail:
1Paneuropean university, Slovakia, Bratislava
Voronezh institute of high technologies (ANOO VO VIVT), Russia, Voronezh

Keywords: OCR, optical recognition, handwriting, HMM.

One of the popular approaches used for handwriting recognition, is the representation of images of full words as in a sequence of symbols of the Markov chain. A set of symbols derived from images is analyzed for compliance with the pre-arranged word models (models-templates). The word, the model of which has the maximum probability of the analyzed pattern generation, is recognized as the desired. Variations of handwritten words writing necessitate analyzing the sequence of symbols derived from images by means of models, developed for the words consisting of a different number of symbols. In case when the analyzed word differs from the word used for the model - template only in the ending, the model - template of a longer word obtains mathematical precedence over the model of the shorter word, resulting in recognition errors. The solution to the described problem based on normalization of horizontal dimensions of handwritten words images is provided in the article.

Normalization is necessary not only for the images for recognition but also for the images for model development. Equaliy of number of states in the analyzed image with the model dimension ensures the non-existence of the above-noted problem.

The analysis of 800 graphic images of handwritten words written in twenty different handwritings was performed for the purpose of estimation of normalization parameters.

The analysis of graphic images proved a linear dependence of the mean square deviation of the word length from the average value of its length. Thus, the necessity of the increase of the overlap area of linear dimensions of recognizable words by several word model dimensions. This will ensure that the largest number of word models developed from the handwritten words written in different handwritings is involved in determination of the best model.

The conducted experiment showed a significant effect of normalization. The average increase in the percentage of recognition was 7.7 percent in comparison with the algorithms (neural networks), where skeletonization was not used.


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