Signal Processingö No. 2-2014
parametric energy Fourier spectrums;
- empirical mode decomposition;
- waveform envelope extraction;
- adaptive signal processing;
- algorithm of matching pursuit;
- analysis of time relation;
- analysis of signals on multicore processors.
of Hartley Transform to Solve the Integral Equation of Convolution Type
V.V., JSC "Russian institute for power radiobuilding"
Maslakov M.L., JSC "Russian institute for power radiobuilding", email@example.com
Keywords: integral equation of convolution type, ill-posed problem,
calculation of impulse response of the communication channel, correction,
Fourier transform, Hartley transform.
The calculation of unknown impulse response of the communication channel
is one of the most important task for adaptive signal correction. Consider
a signal S(t) transmitted through the system with the impulse response
h(t), where the received output signal U(t) is presented by
the following formula:
The above shown equation
refers to a linear integral equation of convolution type, or it is also
called a Fredholm integral equation of the first kind, where there the
function h(t) is unknown.
Various methods of solving this equation, concerning time or frequency
domain, are practically known. One of the most effective methods for the
numerical solution of integral equations of convolution type are those
based on the transition to frequency domain. For this purpose it is supposed
to use the discrete Fourier transform (DFT), for there are a variety of
algorithms for the fast Fourier transform (FFT). This significantly reduces
the computational cost. However, the Fourier transform uses complex numbers,
that is why it is recommended to use Hartley transform, which makes possibility
to avoid complex numbers in calculation. Unfortunately, the Hartley transform
is rarely used in practice.
The authors have presented the new formulae provided for the solution
of the integral equation of convolution type in the Hartley basis. The
advantage of discrete Hartley transform (DHT) compared to the DFT is proved
and illustrated. The results of the simulation and computational efficiency
evaluation of the algorithms are presented.
The calculation of the impulse response of the communication channel is
provided using DHT for adaptive signal correction. The provided numerical
solution of integral equations using DHT is more effective than the DFT,
since there are algorithms fast Hartley transform (FHT), which can be
easily implemented and require lower computational cost, moreover, all
the performed operations are real. At the same time the obtained numerical
results practically are not worse than the results obtained using the
Fourier transform. Therefore, the use of FHT allows to reduce the number
of operations for the solution of integral equation as good as twice.
1. Gahov F.D., Cherskii Yu.E. Equations of convolution type. -
Moscow: Nauka, 1978. - 296 p.
2. Manjirov A.V.,
Polianin A.D. Reference book on integral equations: the methods of
solving. - Moscow: Faktorial Press, 2000. - 384 p.
3. Tihonov A.N.,
Arsenin V.Ya. The methods solving of ill-posed problems. - Third
edition. - Moscow: Nauka, 1986. - 285 p.
4. Bracewell R.N.
The Hartley transform. - New York: Oxford University Press, 1986.
- 175 p.
5. Egorov V.V., Kolomiec
E.V. The Solving of linear equation system with circulant matrix the
method of discrete Harley transform. Electronic modeling, 1991, V.3,
╣ 6. P. 99-100.
6. Egorov V.V., Maslakov
M.L., Mingalev A.N. Highrate single-tone HF radiomodems. 13th International
Conference "Digital Signal Processing and Application - DSPA 2011". -
Moscow, 2011. P. 183-186.
7. Nussbaumer H.J.
Fast Fourier transform and convolution algorithms. - New York:
Springer-Verlag, 1982. - 248 p.
8. Vlasenko V.A.,
Lappa Yu.M., Yaroslavskii L.P. The methods design of fast convolution
algorithms and spectral analysis of signals. - Moscow: Nauka, 1990.
- 180 p.
Invariance of Current Parametric Energy Fourier Spectrums of Discrete
Real Signals on Finite Intervals
Ponomareva O.V. Ph.D. (technical science), associate professor
of Kalashnikov Izhevsk State Technical University, firstname.lastname@example.org
discrete signal, finite interval, sliding spectral measurement, basis,
parametric discrete exponential functions, non-invariance, energy Fourier
spectrum, tonal components.
In such fields of research as radar, speech recognition and synthesis,
passive sonar, biomedicine, it is often necessary to solve the problem
of detection and measurement of tonal components (problem of detecting
the hidden periodicities). One of the effective methods of detecting hidden
periodicities in the signals of such kind is a measurement of their sliding
Fourier spectra on finite intervals. In this case, the method of discrete
Fourier transform (DFT) uses basis of discrete exponential functions (DEF).
While method of parametric DFT (DFT-P), proposed by the author, uses basis
of parametric DEF (DEF-P). The essence of measurement of sliding Fourier
spectra of signals on finite intervals is to determine the Fourier spectrum
of the signal in the time window (having N samples), which shifted by
one sample before spectral re-measurement. Papers on digital spectral
analysis relies, by default, that the sliding energy Fourier spectrum
of tone signal in the DEF basis is invariant to time shift of tone signal.
Experimental researches on simulated signals, made by the author of this
paper, showed that the assumption of the invariance of the sliding energy
Fourier spectrum of tone signal to its time shift is generally untrue
in both DEF basis and DEF-P basis.
We have studied the relationship of discrete-time Fourier transform (DTFT)
and DFT-P signal defined on a finite interval with DFT signal defined
on a finite interval and zero padded. For real applications it is important
that the DFT of sequence
defining the DTFT values at points
does not answer the question, what are values of DTFT between these points,
creating so-called stockade effect. To avoid this unwanted effect
in the spectral digital signal processing (DSP) (of both one-dimensional
and multidimensional sequences), the operation of zero padding (OZP) has
been widely used. However, despite the undoubted advantages of this operation,
it has two major drawbacks. Practical use of OZP requires significant
additional memory and significant useless computational operations due
to the need for a large number of operations with zero samples. DFT-P
(proposed by the author) allows while calculating Fourier spectra with
OZP, not to increase the amount of required memory, to reduce extra computational
operations and to find the DTFT signal at any frequency, varying parameter
of DFT-P. This makes it possible to increase significantly (compared to
OZP) distinguishing harmonics in the frequency domain. We studied
the methods and algorithms of sliding spectral measurements on finite
intervals. The theoretical principles of measurement of sliding energy
Fourier spectra of digital signals in the basis of discrete exponential
functions and parametric discrete exponential functions. We got theoretical
and practical results of the evaluation of non-invariance of sliding energy
Fourier spectra of tonal components on finite intervals in the DEF-P basis.
The results allow: to increase the spectral efficiency of the DSP in solving
problems on the detection and identification of hidden periodicities,
to further develop a methodology to determine the errors of spectral
measurements of tone signals on finite intervals, taking into account
the effect of the non-invariance.
1. M. G. Serebrennikov and A. A. Pervozvanskii, Detection of Hidden
Periodicities (Nauka, Moscow, 1965) [in Russian].
2. E. Oppenheim,
Digital Signal Processing (Mir, Moscow, 1980). [Russian translation].
3. G. Lyons, Understanding
Digital Signal Processing (Binom-Press, Moscow, 2007) [Russian translation].
4. L. Rabiner, B.
Gold. Theory and application digital signal proctssing (Mir, Moscow,
1978). [Russian translation].
5. Petrovsky, Alexey.
Hydrid signal decomposition dased on instantaneous harmonic parameters
and perceptually motivated wavelet packets for scalable audio coding / Alexey Petrovsky, Elias Azarov, Alexander Petrovsky, Elsiver, Signfl
Processng, Special issue "Fourier Related Transform for Non-Stationary
Signals"/- Vol. 91/-Issue 6/-June 2011.- P/ 1489-1504.
6. ╬. V. Ponomareva,
"Development of the Theory of Spectral Analysis of Discrete Signals
on Finite Intervals in the Basis of Parametric Exponential Functions,"
Tsifrovaya Obrabotka Signalov, No. 2, 7-12 (2010).
7. ╬. V. Ponomareva,
"Probabilistic Properties of Spectral Estimates Obtained by Parametric
Discrete Fourier Transform," Intellektual'nye Sistemy v Proizvodstve,
No. 2(10), 36-42 (2010).
8. V. A. Ponomarev
and ╬. V. Ponomareva, "Theory and Application of the Parametric Discrete
Fourier Transform," Tsifrovaya Obrabotka Signalov, No. 1, 2-6 (2011).
9. ╬. V. Ponomareva,
"Fast Parametric Discrete Fourier Transform of Real Sequences," Tsifrovaya
Obrabotka Signalov, No. 2, 2-5 (2012).
10. ╬. V. Ponomareva,
A. V. Ponomarev, and N. V. Ponomareva, "Sliding Parametric DFT in Detecting
Tonal Components," Tsifrovaya Obrabotka Signalov, No. 4, 2-7 (2012).
11. V. A. Ponomarev
and ╬. V. Ponomareva, "Modification of the Discrete Fourier Transform
for Solving Problems of Interpolation and Convolution of Functions," Radiotekhnika
i Elektronika, 29 (8), 1561-1570 (1984).
12. Ponomarev V.A.,
Ponomareva O.V. Generalization of discrete Fourier transform for interpolation
in time domen, Electronic and Electrical Engineering. 1984 no 3, pp
13. V. A. Ponomarev,
╬. V. Ponomareva, "A Generalization of the Discrete Fourier Transform
for Interpolation in the Time Domain," Izv. Vuzov, Radioelektronika
XXVI (9), 67-68 (1983).
14. ╬. V. Ponomareva,
A. V. Ponomarev, and N. V. Ponomareva, "A Fast Method for. Computing
the Discrete Fourier Transform of Real Sequences," Tsifrovaya Obrabotka
Signalov, No. 2,10-15 (2013).
15. V. A. Alekseev,
V. A. Ponomarev, and ╬. V. Ponomareva, "Methodology for Determining
Measurement Errors of Probability Characteristics of Random Processes
Implemented by Measuring Processing Means" Intellektul,nye Sistemy
v Proizvodstve, No.2(10), 91-99 (2010).
16. ╬. V. Ponomareva,
V. A. Alekseev, and V. A. Ponomarev, "Digital Periodogram Analysis
and Problems of its Practical Application," Vestn. IzhGTU, No 2, 130-133
17. ╬. V. Ponomareva
and N. V. Ponomareva, "Modification of a Filter Based on Frequency
Sampling for Solving Problems of Digital Processing of Stochastic Processes
with Hidden Periodicities," Intellektual'nye Sistemy v Proizvodstve,
No. 2(20), 122-129 (2012).
18. ╬. V. Ponomareva,
A. V. Ponomarev, and V. A. Ponomarev, "Generalization of the Goertzel
Algorithm for Detecting Hidden Periodicities," Intellektual'nye Sistemy
v Proizvodstve, No. 1(21), 41-46 (2013).
19. V. A. Ponomarev
and ╬. V. Ponomareva, "Vibroacoustic Diagnostics of the Machine Gearboxes
by Digital Methods," Stanki i Instrument, No. 9, 18-21 (1983).
20. ╬. V. Ponomareva
and N. V. Ponomareva, "Improving the Accurace and Extending the Functionalite
of Digital Filters Based on Frequency Sampling," Pribory Metody Izmerenii,
No. 2, (5), 114-119 (2013)
21. ╬. V. Ponomareva
and V. A. Ponomarev, "Measurement of current energy Fourier spectrum
of complex and real discrete signals on finite intervals," Intellektual'nye
Sistemy v Proizvodstve, No. 2(22), 149-157 (2013).
22. ╬. V. Ponomareva,
V. A. Ponomarev and A. V. Ponomarev, Hierarchical morphlogicflly-information
model diagnosis of functional objects based on digital signal processing,
Sensors and Systems, 2014, No.1(176), 2-8.
23. V. A. Ponomarev,
╬. V. Ponomareva, A. V. Ponomarev and N. V. Ponomareva, "The summary
of the Goertzel algorithm and the sliding parametric discrete Fourier
transform," Tsifrovaya Obrabotka Signalov, No. 1, 3-11 (2014).
24. V. A. Ponomarev,
╬. V. Ponomareva and A. V. Ponomarev, "Method for Effective Measurement
of a Sliding Parametric Fourier Spectrum," Avtometria. 2014, Vol 50,
25. V. A. Ponomarev
and ╬. V. Ponomareva, "The invariance of current energy Fourier spectrums
of discrete real signals on finite intervals," Technology and Design
in Electronic Equipment, 2014, No.1, pp.15-22
Loss in Signal-to-Noise Ratio for Communication System with Binary
Differential Shift Keying and Orthogonal Coding
Zaytsev G.V., email@example.com
Keywords: binary differential phase shift keying, orthogonal code,
soft metrics, bit error probability, loss in signal-to-noise ratio.
The paper analyzes digital communication system which uses binary differential
phase shift keying and orthogonal coding with Hadamard matrix. The system
is intended for transmission of short messages. In the channel additive
white Gaussian noise is present. The purpose of the paper is to estimate
loss caused by differential modulation/demodulation.
Several algorithms for soft differential demodulation are deduced from
the concept of logarithm likelihood ratio. Formula for exact calculation
of log-likelihood ratio is derived but it requires calculation of Bessel
function and proved to be rather complex for practical purposes. Two simple
approximations are described as follows. Let ,
be the sequence of numbers at the demodulator input, resulting from optimal
reception of transmitted bits. Then simple forms of soft differential
demodulation are given by the formula
Nonlinear operations in these formulae cause loss in signal-to-noise ratio.
It is shown that this loss can be evaluated by the expression
signal-to-noise power ratio in the sequence Z. For small signal-to-noise
ratio this loss may be up as high as 10 dB. For considered orthogonal
codes, optimal correlation reception is possible, additional losses are
absent, and presented formula is valid for decoder output.
Computer simulation of the considered communication system was performed
in C++ language. The method of simulation is described and main parameters
of the program are given. Bit error rate Pb vs signal-to-noise
ratio is calculated and is displayed graphically for Pb>10-8
. The simulation confirmed that performance of simple demodulation
method, described above, is in close agreement with performance of exact
method. It is also shown that total code gain in described communication
system is rather small (2 3 dB) for the range Pb>10-8
and code lengths n≤1024.
From the results of the paper it is obvious that the above mentioned heavy
loss may take place for any code with large redundancy. For different
reception methods, other than correlation, some additional losses may
arise. Analytical estimation of these losses is difficult because probability
density function of the noise after differential demodulation is not Gaussian.
1. Bernard Sklar. Digital Communications: Fundamentals and Applications.
New Jersey: Prentice Hall PTR. 2001. 1011 p.
2. Use and Performance
of the AHA4501 Turbo Product Code Encoder/Decoder with Differential Phase
Shift Keying (DPSK). // AHA Application Note ANTPC04_0100. URL: http://www.aha.com.
3. Harmuth H.F. Sequency
theory. NY: Academic Press. 1977. 574 p.
4. Channel Coding
in Communication Networks. / Ed. Alain Glavieux / London: ISTE Ltd.
2007. 418 ˝.
5. Gladkikh └.└.
Fundamentals of Soft Decoding Theory for Redundancy Codes in Erasing
6. Fuqin Xiong.
Digital Modulation Techniques. New York: Artech House. 2006. 1017
7. Levin B.R. Fundamentals
of Statistical Radio Engineering. v. 1. ╠.: Sov. Radio. 1966. 728
8. Anger Fog. Instructions
for the Random Number Generator Libraries. 2010. URL: http://www.agner.org.
9. Matsumoto ╠.,
Nishimura T. Mersenne Twister: A 623-dimensionally Equidistributed
Uniform Pseudo-Random Number Generator. // ACM Transactions on Modeling
and Computer Simulation. 1998. ╣ 8. P. 3-30.
10. Devroye L. Non-Uniform
Random Variate Generation. New York: Springer. 1986.
11. Venttsel E.S.
Probability Theory. ╠.: Vysshaja Shkola (Higher School). 1999.
Problems and Methods of Communication Systems Spectral Efficiency Increasing:
Bakulin M.G, Kreindelin V.B., Shumov A.P.
Keywords: spectral efficiency, wireless communication systems,
OFDM, many carriers, multicarrier modulations, inter-carrier interference.
Spectral efficiency is a key design issue for all wireless communication
systems. Orthogonal frequency division multiplexing (OFDM) is a very well-known
technique for efficient data transmission over many carriers overlapped
in frequency. Recently, several papers have appeared which describe spectrally
efficient techniques for multi-carrier systems where the condition of
orthogonality is dropped. Proposed techniques suffer from high complexity
or high error rates because of the inter-carrier interference. This work
addresses to problems of transmitter and receiver architectures whose
design is based on using high efficient OFDM technologies.
There can be several approaches to realize transmission of FTN modulated
symbols. One approach is considering in the first part of the article.
Efficient implementations for multicarrier modulations already exist in
the form of IFFT, as used in OFDM-based systems. Hence an effort is made
to retain this attractive option. However, using only the IFFT introduces
complexity in a different dimension. In order to use IFFT for multicarrier
modulation the Gaussian pulses are to be represented in an orthonormal
set of basis functions. Each FTN symbol is represented on the basis functions
spanning both time and frequency. The number of basis functions required
in time can be different. The process of representing the FTN symbols
in the orthogonal basis is referred to as mapping and a block realizing
it is referred to as a mapper. The mapper produces outputs by processing
the incoming FTN symbols. Data processing at the receiver is implemented
in a reverse way. This approach allows spectral efficiency increasing.
Another approach is considering in the second part of the work. Recently
many authors have proposed non-orthogonal systems or Spectrally Efficient
Frequency Division Multiplexing (SEFDM) systems. OFDM symbols are sent
on carrier frequencies separated by F and the symbols remain constant
for time T (the symbol period) with TF = 1. This ensures no sub-channel
interference. For SEFDM, TF < 1 and, while there will necessarily be sub-channel
interference, the key advantage is that the available spectrum can be
used more efficiently. This approach suggests design for a simple to implement
transmitter and receiver/decoder for SEFDM systems. The transmitter design
and the decoder design are interlinked. The key insight is to see SEFDM
as a small number of interleaved OFDM systems. The design can increase
spectral efficiency by 20% using similar techniques to traditional OFDM
and with little compromise to the required signal to noise ratio for the
system. The designs require only slightly more complexity in the receiver
1. Bakulin M.G, Kreindelin V.B., Shumov A.P. Some Issues of Communication
Systems Spectral Efficiency Increasing: Nonorthogonal Transmission
// Digital Signal Processing. 2013, ╣4, pp. 55-64.
2. Fredrik Rusek
and John B. Anderson, "Multistream Faster than Nyquist Signaling,"
IEEE Trans. Commun., vol. 57, no. 5, May 2009, pp. 1329-1340.
3. J.E. Mazo, "Faster-than-Nyquist
Signaling," Bell Syst. Tech.J., vol. 54, pp. 1451-1462, Oct. 1975.
4. F. Rusek and J.B.
Anderson, "The Two Dimensional Mazo Limit," Proc., 2005 IEEE Int.
Symp. Information Theory, Adelaide, pp. 970-974, Sept. 2005.
5. R. W. Chang. High-speed
multichannel data transmission with bandlimited orthogonal signals.
Bell System Technical Journal, 45:1775-1796, Dec 1966.
6. B. Saltzberg.
Performance of an efficient parallel data transmission system.
IEEE Trans. on Communication Technology, 15(6):805-811, Dec. 1967.
7. M. Bellanger and
J. Daguet. TDM-FDM Transmultiplexer: Digital Polyphase and FFT.
IEEE Trans. on Communications, 22(9):1199-1205, Sep. 1974.
8. H. Bolcskei. Orthogonal
Frequency Division Multiplexing based on offset QAM, pages 351-352.
9. B. Le Floch, M.
Alard, and C. Berrou. Coded Orthogonal Frequency Division multiplex. Proceedings of the IEEE, 83(6):982-996, Jun. 1995.
10. P.K. Remvik and
N. Holte. Carrier frequency offset robustness for OFDM systems with
different pulse shaping filters. In IEEE Global Telecommunications
Conference (GLOBECOM), volume 1, pages 11-15, Nov. 1997.
11. D. Dasalukunte,
Multicarrier Faster-than-Nyquist Signaling Transceivers. Ph.D.
dissertation, Lund University, 2012.
12. P. Siohan, C.
Siclet, and N. Lacaille. Analysis and design of OFDM/OQAM systems based
on filterbank theory. IEEE Trans. on Signal Processing, 50(5):1170-1183,
13. M. Muck and J.
P. Javaudin. Advanced OFDM modulators considered in the IST-WINNER
framework for future wireless systems. In 14th IST Mobile and Wireless
Communications Summit conference, 2005.
14. J. G. Proakis
and D. G. Manolakis. Digital Signal Processing: Principles, Algorithms,
and Applications. Prentice-Hall, Inc., 3 edition, 2004.
15. J. P. Javaudin
and D. Lacroix. Technical description of the OFDM/IOTA modulation. Technical Report R1-03-168, France Telecom R&D, 2003.
16. 3GPP. Feasibility
Study for Orthogonal Frequency Division Multiplexing (OFDM) for UTRAN
enhancement. Technical Report TR 25.892 V6.0.0, 3rd Generation Partnership
Project, Jun. 2004.
17. S. Verdu. Multiuser
Detection. Cambridge University Press, 1998.
18. M.C. Reed, C.B.
Schlegel, P.D. Alexander, and J.A. Asenstorfer. Iterative multiuser
detection for CDMA with FEC: near-singleuser performance. IEEE Trans.
on Communications, 46:1693-1699, Dec. 1998.
19. X. Wang and H.
V. Poor. Iterative (turbo) soft interference cancellation and decoding
for coded CDMA. IEEE Trans. on Communications, 47:1046-1061, Jul.
20. S. Lin and D.
J. Costello. Error Control Coding. Prentice-Hall, Inc., 2 edition,
21. F. Rusek. Partial
response and faster-than-Nyquist signaling. PhD thesis, Dept. of Electrical
and Information Technology, Lund University, 2007.
22. I. Lee. The
effect of a precoder on serially concatenated coding systems with an ISI
channel. IEEE Transactions on Communications, 49(7):1168-1175, Jul.
23. Clegg, R. G.,
Isam, S., Kanaras, I., & Darwazeh, I. (2012). A practical system for
improved efficiency in frequency division multiplexed wireless networks.
IET Communications, 6 (4), 449-457. doi:10.1049/iet-com.2011.0365
24. S. I. A. Ahmed
and I. Darwazeh, "IDFT Based Transmitters for Spectrally Efficient
FDM System," in London Communication Symposium, Sep. 2009.
25. M. R. Perrett
and I. Darwazeh, "Flexible hardware architecture of SEFDM transmitters
with real-time non-orthogonal adjustment," Proc. of Int. Conference
on Telecommunications, 2011.
26. S. Weinstein
and P. Ebert, "Data Transmission by Frequency-Division Multiplexing
Using the Discrete Fourier Transform," IEEE Transactions on Communications,,
vol. 19, no. 5, pp. 628-634, Oct 1971.
27. V. Pammer, Y.
Delignon,W. Sawaya, and D. Boulinguez, "A low complexity suboptimalMIMO
receiver: The combined ZF-MLD algorithm," 14th IEEE Proceedings on
Personal, Indoor and Mobile Radio Communications, 2003. PIMRC 2003, vol.
3, pp. 2271-2275 vol.3, 7-10 Sept. 2003.
28. I. Kanaras, A.
Chorti, M. Rodrigues, and I. Darwazeh, "A combined MMSE-ML detection
for a spectrally efficient non orthogonal FDM signal," 5th International
Conference on Broadband Communications, Networks and Systems, 2008. BROADNETS
2008., pp. 421-425, Sept. 2008.
29. Y.-P. Lin and
S.-M. Phoong, "MMSE OFDM and prefixed single carrier systems: BER analysis,"
in International Conference on Acoustics, Speech, and Signal Processing,
2003, ICASSP '03, IEEE, Hong Kong, Apr. 2003, pp. 229-232.
30. E. Viterbo and
J. Boutros, "A universal lattice code decoder for fading channels,"
IEEE Transactions on Information Theory, vol. 45, no. 5, pp. 1639-1642,
31. I. Kanaras, A.
Chorti, M. Rodrigues, and I. Darwazeh, "Spectrally Efficient FDM Signals:
Bandwidth Gain at the Expense of Receiver Complexity," IEEE International
Conference on Communications. ICC 2009. Proceedings, June 2009.
32. W.-K. Ma, P.-C.
Ching, and Z. Ding, "Semidefinite relaxation based multiuser detection
for M-ary PSK multiuser systems," IEEE Transactions on Signal Processing,
vol. 52, no. 10, pp. 2862-2872, Oct. 2004.
33. I. Kanaras, A.
Chorti, M. Rodrigues, and I. Darwazeh, "An Investigation of Semidefinite
Programming Detection for a non orthogonal FDM system," 20th Personal,
Indoor and Mobile Radio Communications Symposium 2009, IEEE PIMRC'09,
Japan, Tokyo, September 2009.
34. I. Kanaras, A.
Chorti, M. Rodrigues, and I. Darwazeh, "A New Quasi-Optimal Detection
Algorithm for a Non Orthogonal Spectrally Efficient FDM," in 9th International
Symposium on Communications and Information Technologies 2009, IEEE ISCIT
2009, Incheon, Korea, September 2009.
35. I. Kanaras, A.
Chorti, M. R. D. Rodrigues, and I. Darwazeh, "A Fast Constrained Sphere
Decoder for Ill Conditioned Communication Systems," IEEE Communications
Letters, vol. 14, no. 11, pp. 999-1001, 2010.
36. S. Isam and I.
Darwazeh, "Design and Performance Assessment of Fixed Complexity Spectrally
Efficient FDM Receivers," in IEEE 73rd Vehicular Technology Conference
(IEEE VTC'11), 2011.
37. S. Isam, I. Kanaras,
and I. Darwazeh, "A Truncated SVD Approach for Fixed Complexity Spectrally
Efficient FDM Receivers," in IEEE Wireless Communications & Networking
Conference (IEEE WCNC'11), 2011.
38. B. Hassibi and
H. Vikalo, "On the sphere-decoding algorithm I. Expected complexity,"
IEEE Transactions on Signal Processing, vol. 53, no. 8, pp. 2806-2818,
39. J. Jalden and
B. Ottersten, "On the complexity of sphere decoding in digital communications,"
IEEE Transactions on Signal Processing, vol. 53, no. 4, pp. 1474-1484,
Empirical Mode Decomposition in Geophysical Multivariate Time Series Short-Term
Zaporozhtsev Ivan Fedorovich, Murmansk State Technical University,
Department of Higher Mathematics and Computers Software, postgraduate
Sereda Algirdas-Vladimir Ignatyevich, Murmansk State Technical University,
Department of Higher Mathematics and Computers Software, Doctor of Engineering,
Keywords: short-term forecast, spatial distribution of geophysical
characteristics, clustering, sea level anomalies, Arctic.
The article is concerned with multivariate time series forecasting based
on multivariate singular spectrum analysis and preprocessing with empirical
mode decomposition concepts. We assume that particular time series originates
from the observations of geophysical parameters with time-based variety.
Geophysical characteristic values are calculated in planar uniform grid
nodes on basis of regularly obtained satellite and/or surface measured
data. Each node provides time series with the same start point, time step
and length (time points number). These conditions are necessary to form
multivariate time series. The problem is to make accurate short-term forecast
of grid nodes values while input data is multivariate time series of the
same characteristic and the same grid for previous time span.
Main forecast tool is K-continuation technique described by D.A. Stepanov
and N.E. Golyandina. It is developed in connection with multivariate singular
spectrum analysis (MSSA).
Forecast accuracy can be enhanced by applying appropriate preprocessing
steps to multivariate time series already constructed. In processing raw
data it is advantageous and often necessary to make abnormal values removal,
smoothing, numerical differentiation, etc. It is also important to mention
additive decomposition: original multivariate time series is to be replaced
with a system of new multivariate time series each of which is obtained
as a result of combination of additive components with the same number
extracted from different original univariate series. It should be noted
that linear regression models, such as MSSA, are extremely efficient for
stationary time series. Therefore, most univariate time series of new
multivariate series have to indicate greater stationarity than original
ones. According to previous statements, authors of this article choose
suggested by N.E. Huang empirical mode decomposition (EMD) to be essential
preforecast step. The so-called sifting process as iteratively repeated
EMD stage is intended to extract orthogonal additive components (with
predetermined accuracy) except last summand being a time series residue
with arbitrary properties. Sifting requires construction of upper and
lower time series envelopes interpolating its local extrema. Current time
series analysed is renovated at each stage.
Being originally designed for univariate time series, the EMD technique
was widely accepted as promising treatment in multivariate series processing.
The method is unreasonable to use for each univariate series separately
because it is not supposed to insure the same number of additive components
extracted. Furthermore, the main obstacle of the EMD generalization is
that multivariate series being referred to as vector-function of time
is not provided with extremum definition.
Some possibilities analysed in details by some authors for method adoption
in multivariate case are used in the article. The obvious concept (principle
1, P1) is discarding of sifting (and the refusal of orthogonality)
to replace it with some procedure finishing on predetermined number of
component extracted criterion. Another idea (principle 2, P2) is
formulated by J. Fleureau et al and is based on the so-called oscillation
extrema definition. They are local minima of vector-function time derivative
norm. The latter provides usage of the same joint points for envelopes
construction in the meaning of univariate EMD. This fact is crucial to
obtain the same number of additive components for all the univariate time
series as a result of applying numeric method called multivariate EMD
Both EMD and MEMD problem that arises in connection with interpolation
features is named end effect. Some experts suggest to use the first and
the last envelopes joint points outside the analysed time series domain.
Obviously, the concept is questionable in case of forecast task solution.
Therefore in this article two variants of spline end conditions (additional
principle, PA) are used: zero value of the first or the second univariate
time series derivative.
According to principles mentioned, there are three preforecast EMD based
methods (two for P1 and one for P2) in the article. In addition, PA branching
doubles the number of methods used in the article. The series of numerical
experiments is carried out with a set of sea level anomalies maps corresponding
to particular area in the Barents Sea. A map is defined as spatial distribution
of the characteristics reconstructed in specified grid nodes at chosen
time point. Thus, maps time array is exactly the same as multivariate
time series. Area is restricted by 71░N - 76.4░N and 25░E - 44.7░E. Time
period to deal with contains 365 sequential time points ended with August,
12th, 2013. Data source is international project Aviso which have been
distributing altimetry data worldwide since 1992. Nowadays reference portal
located in France provides data, articles, news and tools to satisfy users
requests concerning altimetry domain. Particular sea level anomalies can
be obtained if you know the mapping between degrees and Aviso counters.
In our research, we used 764 - 823 for latitude and 75 - 134 for longitude
(60 by 60 nodes uniform grid). Grid nodes are divided into clusters according
to its definition (set of nodes corresponding to simply connected subregion
of area studied which time series have similar temporal variability) and
clustering method suggested by authors of this article. Time series values
vary from -15 to +15 with precision of one hundred-thousandths. Calculations
are made for 4 multivariate time series. Each series is constructed as
cluster time series corresponding to stable cluster of grid nodes. These
clusters have 21,15,15 and 25 nodes respectively.
In conclusion, error values estimated via experiments are analysed and
some proposals are formulated concerning applying models assembly based
on MSSA and EMD/MEMD combination.
1. Ashik I.M. Numerical Hydrodynamic Method of Sea Level Anomalies
Variability Forecasting in the South-Eastern Part of the Barents Sea and
in the South-Western Part of the Kara Sea, http://method.hydromet.ru/publ/sb/sb31/sb31.html,
2. Verbitskaya O.G.
Hydrodynamic Forecasting Method of of Sea Level and Current Synoptical
Variability in the Caspian Sea, Ph.D. Thesis, 2009, 175 p.
3. Orlov U.N., Osminin
K.P. Non-Stationary Time Series. Forecasting Methods with Financial
and Materials Markets Analysis Examples, Moscow, 2011, 384 p.
4. Chuchueva I.A.
Time Series Forecasting Model over Maximum Likelihood Sample, Ph.D.
Thesis, 2012, 153 p.
5. Zagoruyko N.G.
Applied Aspects of Data and Knowledge Analysis, Novosibirsk, 1999,
6. Ngongolo H.K.
Tropical Precipitation Statistical Forecasting on Basis of Ocean Surface
Temperature and Quasi-Biennial Oscillation of Zonal Flow Applied to the
Eastern Africa Datasets, Ph.D. Thesis, 2011, 156 p.
7. Stepanov D.A.,
Golyandina N.E. SSA-Caterpillar Method Variants for Multivariate Time
Series Forecasting. Proceedings of SICPRO'05, Moscow, 2005.
8. Höppner F.,
Klawonn F. Compensation of Translational Displacement in Time Series
Clustering Using Cross Correlation. Lecture Notes in Computer Science.
Advances in Intelligent Data Analysis, vol.5772, pp.71-82, 2009.
9. Liao T.W. Clustering
of Time Series Data - a Survey. Pattern Recognition, vol. 38, pp.
10. Huang N. E.
The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear
and Non-Stationary Time Series Analysis, http://keck.ucsf.edu/~schenk/Huang_etal98.pdf,
11. Yang P. at al.
The Prediction of Non-Stationary Climate Time Series Based on Empirical
Mode Decomposition. Advances in Atmospheric Sciences, vol. 27, pp.
12. Davidov V.A.,
Davidov A.V. End Effects Reduction for Signals Empirical Mode Decomposition
of Hilbert-Huang Transformation, http://www.actualresearch.ru/nn/2011_1/Article/physics.../
13. Fleureau J. at
al. Multivariate Empirical Mode Decomposition and Application to Multichannel
Filtering. Signal Processing, vol. 91, pp. 2783-2792, 2011.
14. Rehman N., Mandic
D.P. Multivariate Empirical Mode Decomposition. Proceedings of
the Royal Society A., vol. 466, no. 2117, pp. 1291-1302, 2010.
15. Aviso. Satellite
Altimetry Data, http://www.aviso.altimetry.fr/en/home.html.
Error Decreasing Method of Waveform Envelope Extraction in Digital
Spatial Correlation Processing Chain
Oroshchuk I. M., professor , firstname.lastname@example.org
Suchkov A. N., suchkov-Andreyemail@example.com
Vasilenko A.M., firstname.lastname@example.org
Keywords: spatially-correlation signal processing, noise-immunity,
cross-correlation function, time delay, digital detector, quadrature component,
phasing error, pulsation, pulsation averaging, root-mean-square error,
The paper deals with the operation principle of spatial correlation of
signal processing chain (SCSPC) in a decameter range. This processing
chain consists of the antenna array (AA), multichannel direct amplifier
and analog-to-digital converter (ADC), time delay unit, correlation processing
chain, decision taken device.
The mapping is carried out by introducing compensation time delay in the
input signals. It virtually locates the AA elements on one line orthogonally
to the signal arrival direction that results to ensuring high spatial
selectivity of the whole signal processing chain.
Then in the correlation processing chain the signal cross-correlation
function (CCF) is being assessed from the outputs of all the couple elements
of array antenna. After that the output voltage is summed up. The decision
on signal detection is made in the decision taken unit, depending on the
assigned probability characteristics.
Spatially-correlation signal processing chain is characterized by enhanced
noise immunity and spatial resolution selectivity at low level signal.
The antenna array comprises 30-40 identical direct amplifier. To make
them identical is difficult. In case of partial identities of array antenna
elements and amplifier tracks, or if phasing minor errors occur in signal
time delay unit CCF significance can be reduced to a great value. This
phasing hardware error results in significant reduction of spatially-correlation
signal processing chain noise-immunity.
To eliminate such errors the evaluation of CCF based on waveform envelope
is proposed. Waveform envelope computation is carried out with the Hilbert's
transform by the adjustment of a quadrature component. To exclude additional
phase distortions in the SCSPC direct amplifiers are used. In this kind
of receivers signal carrier frequency changes within a decameter range
at a fixed sampling frequency of ADC. As a result errors while adjusting
the quadrature signal component occur. This is displayed in the form of
pulsations in the specified envelope. The amplitude of pulsations enhances
with the increase of the quadrature component errors. Pulsations also
result in inaccurate evaluation of the CCF that in general reduces noise-immunity
and other characteristics of SCSPC.
To reduce the impact on the above-mentioned drawbacks the error decrease
method of specifying waveform envelope in the spatial correlation processing
chain is offered. The method is based on smoothing pulsations due to averaging
samplings massif within pulsations period. It leads to the fact that the
envelope has become smoothed, but the constant deviation from the maximum
values of amplitudes is observed depending on the ratio of the signal
carrier frequency to the sampling frequency of ADC. To eliminate these
deviations compensating coefficient at the evaluation of final values
of cross-correlation function is used with the analytical method. As a
result, the final inaccuracy of cross-correlation function of the specified
waveform envelope is not more than 0.1%.
The application of this method allows to reduce the phasing inaccuracy
emerging due to incomplete identity of array antenna channels and pulsations
compensation error. This results in SCSPC use that will have the greatest
noise-immunity at processing low-level signal.
The proposed method can be used in other digital radio engineering systems
of direct amplifying as well as for the channels with signal phase jitter.
1. Dolgikh V.N., Oroshchuk I.M., Prishchepa M.N. Probabilistic characteristics
of signal detection by a spatial correlation filter // Acoustical
Physics. 2007. Ď. 53. ╣ 2. Đ. 190-196.
2. Oroshchuk I.M.,
Dolgikh V.N., Suchkov A.N. Spatial correlation method probabilistic
characteristics of signal acquisition in decameter range // Journal
of radio electronics. 2013. ╣ 12. http://jre.
3. Oroshchuk I.M.,
Dolgikh V.N., Suchkov A.N. The measuring device for estimating spatially
- and frequency-correlation properties of signals and disturbances in
decameter range // Izvestiya Volgogradskogo gosudarstvennogo tehnicheskogo
universiteta. 2013. ╣ 23 (126). Đ. 95-99.
4. Oroshchuk I.M.,
Suchkov A.N. Spatial correlation method of signal processing in decameter
range // The 16th International Conference "Digital signal processing".
Section 4 "Signal processing in radio engineering system". March 26 -
March 28, 2014 Moscow, Russia.
5. Oroshchuk I.M.,
Suchkov A.N. Error estimate of waveform envelope extraction in digital
processing chains // The International Conference "The radio-electronic
devices and systems for the infocommunication technologies. May 21 - May
23, 2014 Moscow, Russia.
Detecting Changes of State of the Complex Source in the Absence of
Chuvilina E. V.,
Gryzlova T. P., Solovyev Rybinsk State Aviation Technical University,
states of bearings of transmission, detecting changes, threshold algorithm,
measure of the complexity of the signal's blocks.
Technical state of GTE largely determines reliability and safety of the
aircrafts. Device IVU-1M is used in operating tests of aircraft engines
D30/KU for transmission bearings control. It is an analog meter of vibration's
amplitude . If level of the amplitude exceeds value, determined by
the test method, engine has to be taken out of service. A large number
of engines are removed unjustifiably, that leads to economic loss. Digital
processing of diagnostic signals is implemented in device VDK-44(MIC -
200), but its quality is not enough for introduction into service .
Development of algorithms of digital signal processing (DSP) for diagnostics
states of bearings of transmission GTE is actual not only for practical
issues. Its solution based on structural analysis, detecting local inhomogeneities
leads to new class of algorithms DSP, the theory of which is currently
being actively developed .
For evaluation of informativity of features it is selected the ratio of
the average interclass distances to the average intra-distance .
Problem of detecting changes in the properties of random processes formulated
by VV Mottl , was used for detecting changes of the source state. It
is required to detect in realization of a random process
G moments of abrupt change in the parameter,and estimate its moments:
Detecting a change of state of the source is performed using a threshold
algorithm based on the calculating of the change the measure of the complexity
of the signal's blocks. Realization is
represented as a sequence of overlapping blocks length b. For each
measure of the complexity of the block of the signal in accordance with
an algorithm coating which is commonly used for calculating the fractal
The change of the measure of complexity between adjacent blocks ΔRi=Ri-Ri-1is
compared to value of measure of complexity in previous clock. It is considered
that local heterogeneity is detected if
where hR - predetermined threshold.
Separately calculated the total number of inhomogenities and the number
of inhomogenities associated with increasing or decreasing of measure
of complexity - we call them positive and negative, respectively.
It is proposed to use as diagnostic sequences the frequency of conditional
and unconditional increment signal modules within blocks . The set
of values of the entire signal S is partitioned into n ordered
ranges, the range of modules divided into m increments ranked ranges.
For each block at a fixed level signal the matrix of conditional increments
calculated, then rows of the matrix are summed, so we have unconditional
frequency increments: vector drift coefficients for
the block of the signal.
Investigated sample are provided by "NPO" Saturn "and the center of Intelligent
Maintenance Systems, University of Cincinnati .
The first sample is divided into three classes: B - faulty, C - conditioning,
(correctly recognized using the device IVU-1M) and N - wrongly taken (conditioning,
but incorrectly identified as a bad bearing device IVU-1M).
The second sample was obtained in the tests on the reliability of the
bearings. The sample is split into two classes: B - faulty, C - conditioning.
The results show that the use of algorithms for detecting local inhomogeneities
in the vibrosignal provides more informative features. Informativity of
features depends on the block's size, threshold, matrix's growth statistics
size. It is sufficient for linear separability wrongly taken and faulty
bearings. The most informative are combinations of the dissimilar features,
ie results of nonparametric processing and estimating parameters of rough
In  proposed a segmentation signal based nonparametric approach to
the problem of detecting moments of change of probability characteristics
of random processes.
It has been shown that the detection of any changes in the distribution
function or any other characteristics of the probability can be reduced
to the detection of changes in expectation of some new random sequence
generated from the original (diagnostic sequence). In this paper it is
offered to use sequences of local measures of complexity as diagnostic
In the absence of parametric models, like the fractal dimension, measure
of the complexity of the signal's blocks are estimated. Under the assumption
that within a block can be taken a linear model of the signal, the algorithms
of rough statistical estimation of its parameters are developed. Change
conditional and unconditional statistics increment signal is more informative
than the known solution of bearings diagnostics. It is Shown that the
complex processing of diagnostic signals is effective for the analysis
of signals of bearings. Algorithms can be adapted for the analysis of
signals in a wide class of applications, such as medical.
1. Kuzmenko M. L., Porter A. M., Komarov B. I., Karasev V. A. Vibrodiagnostics
of bearings of D30KU-family engines: scientific and technological collection
edited M. L. Kuzmenko, V. F. Bezyazichny, V. N. Vernigor, A. L. Mikhailov.
M.: CIAM. 2001. part. 4. Non-destructive testing of materials and structures
of damage GTE. - p. 221.
2. Shepel V. T.,
Komarov B. I., Gryzlova T. P. Feature selection for the diagnosis of
the technical state of transmission bearings GTE // Aerospace Engineering
and Technology. - 2005. - ╣8(24). - Pp. 97-100.
3. Kolesnikova S.
I. Problem-oriented model recognition and estimation of states of complex
objects: dissertation of the doctor of technical sciences: 05.13.01/Kolesnikova
S.I; [place of defense: Tomsk State University].-Tomsk, 2011. - 364 p.
4. Glyzlova T. P. Methods of evaluation of the informative digital
signal processing in tasks of classification analysis. - 15-th International
Conference "Digital Signal Processing and its Applications" - DSPA - 2013",
Moscow, Russia. Pp.149 - 152.
5. Mottl V.V., Muchnik
I. B. Hidden Markov models in the structural analysis of signals.
- M.: FIZMATLIT, 1999. - 352 p.
6. Chuvilina E.V.
Informative features for diagnostics of bearings by detection of local
inhomogeneities // Machine learning and data analysis. 2013. V. 1,
╣ 6. Pp. 695-704.
7. J. Lee, H. Qiu,
G. Yu, J. Lin, and Rexnord Technical Services 'Bearing Data Set', IMS,
University of Cincinnati. NASA Ames Prognostics Data Repository URL: http://ti.arc.nasa.gov/tech/dash/pcoe/prognostic-data-repository/.
8. Brodsky B.E.,
Darkhovsky B.S., Kaplan A.Ya., Shishkin S.L. Nonparametric segmentation
of brain electrical signals. - Automatics and teleautomatics. - 1998.
- ╣ 2. - Pp. 23-32.
Adaptive Refining Matching Pursuit Algorithm For Combined Dictionaries
In The Analysis Of The Geoacoustic Emission Signals
Tristanov A.B, Lukovenkova O.O., email@example.com
Keywords: sparse approximation; matching pursuit; geoacoustic emission;
time-frequency analysis; geophysical signals.
investigation of geoacoustic emission (GAE) at different stages of seismic
activity has been carried out at Kamchatka peninsular since 1999. GAE
characteristic signal is compound of a sequence of relaxation pulses with
the length of not more than 200 ms, 0.1-1 Pa amplitude, with shock excitation
and the basic frequency from units to the first tens of kHz. Besides pulses,
GAE signals may contain noise of different nature, acoustic noise hereafter.
In 2011 a method of sparse approximation was suggested for the analysis
of GAE signal inner structure at the Laboratory of Acoustic Research in
the Institute of Cosmophysical Research and Radio Wave Propagation (IKIR)
FEB RAS. The task of sparse approximation was to construct a signal model
containing the least number of elements.
In general case, minimization of L0-norm is a computationally intensive
task which is not solved within the polynomial time. Algorithms of pursuit
decrease the computational complexity of the task and allow us to find
an effective solution for ||RN|| minimization, but not an optimal one.
In the course the experiments, the authors showed that the algorithm of
Matching Pursuit, suggested by Mallat S and Zhang S., is the most appropriate
from the algorithms of sparse approximation to analyze GAE signals.
In comparison to the methods of classical time-and-frequency analysis
which result in redundant decomposition of signals, including all atoms
of a dictionary, the sparse approximation constructs compact presentations
composed of only the most significant dictionary elements, not loosing
the accuracy. One more advantage of the sparse approximation approach
is the possibility to make signal decomposition into nonorthogonal dictionaries,
in general case, described by different mathematic functions, which gives
wider possibilities to interpret signal models and to explain the physics
of signal generation processes. The quality of approximation, further
analysis, and interpretation depend on the choice of a dictionary D.
In the first approximation, GAE signal elements may be described by modulated
functions. It was shown, that the dictionary composed of scaled, modulated
and shifted Berlage functions is the most adequate in comparison to Gabor
dictionary, since Berlage functions have a similar structure with GAE
elementary pulses, thus, they approximate better the parts of a signal
containing a pulse. To improve the quality of GAE signal approximation,
we decided to apply a joint dictionary including both Berlage and Gauss
In the course of a series of the experiments, parameter distributions
the most frequently occurring in atom decompositions were analyzed, and
the ranges of dictionary parameters were chosen so to ensure the appropriate
quality of approximation. Application of a joint dictionary reduced the
approximation error by about 5-10%.
The most laborious part of the Matching Pursuit algorithm is the calculation
of scalar products of dictionary atoms with a signal on every iteration.
One of the ways to improve the quality of approximation in the conditions
of limited calculation resources, not requiring dictionary growth, is
to add a refinement in the parameter space of the algorithm. The essence
of the Matching Pursuit adaptive algorithm with a refinement is to find
a new, more significant element of decomposition at every algorithm iteration
in the vicinity of the selected atom. The detected atom and all its shifts
are added into the dictionary, adopting it to the specific features of
Application of a refinement allows us to decrease the size of computational
Modification of the classical Matching Pursuit applying joint dictionaries
and algorithms of refinement in parameter space considerably improves
the quality of GAE signal approximation. It is reasonable and effective
to use the suggested algorithm in the systems for GAE signal processing
1. Mallat S. A Wavelet Tour of Signal Processing: The Sparse Way.
2009 // Acad. Burlingt. 2009.
2. Marapulets Yu.V.,
Tristanov A.B. Using The Sparse Approximation Method For The Problems
Of Geoacoustic Emission Analysis //Digital Signal Processing. 2011,
╣2, P.13-17 (in Russian)
3. Marapulets Yu.V.,
Tristanov A.B. Acoustic Time Series Sparse Approximation with Berlage's
time-series dictionary // Proceedings of RNTORES. Digital Signal Processing.
2012. ╣XIV, Vol. 1, P. 91-94 (in Russian)
4. Marapulets Yu.V.,
Shevtsov B.M. Mesoscale Acoustic Emission. - Vladivostok: Dalnauka,
2012 (in Russian)
of the Two Autoregressive Methods in Computing Weighting Coefficients
for the Adaptive MTI
Bartenev V. G., Kutepov V. E. , firstname.lastname@example.org.
Keywords: adaptive Doppler filtering, autoregressive methods, moving
One of the most important design stages of modern radar is development
of the MTI system working in severe clutter environment. The classical
solution of this problem using MTI with constant binomial weighting coefficients
on the base of a small number processed impulses is not effective. It
is possible to consider alternative option of the multichannel Doppler
filtering with more number processed impulses using FFT algorithm and
weighing for example, Hamming's function . However both simple MTI
and multichannel Doppler filter having fixed weighting coefficients, give
insufficient efficiency of suppression of echo signals from multimode
clutter, with Doppler shift.
The progress in the field of the parametric spectral analysis with high
resolution and high-performance means of digital processing of signals
gave the chance to approach to the realization of more perfect algorithms.
The purpose of this article is the comparative analysis of two methods
of realization of adaptive MTI system on the basis of autoregressive approach.
Two methods were considered: adaptive filtering with weight coefficients
estimated with use of Yule-Walker method  and adaptive filtering with
weight coefficients estimated using Burg's method .
The mathematical modeling which has been carried out in MATLAB system,
gave the chance to compare two options of realization of adaptive system
based on autoregressive approach.
Results of modeling show that adaptive MTI system using autoregressive
coefficients calculated by Burg's method most preferable.
1 . Bartenev V. G., Tanygin A.A. "Radar radio control systems". M,
2 . Sergiyenko A.B. "Digital processing of signals". St. Petersburg, 2003.
3 . Bassem R. Mahafza
& Atef Z. Elsherbeni "MATLAB simulations for radar systems design". Chapman & Hall/CRC Press LLC, 2000 N.W. Corporate Blvd. Boca Raton, Florida
4 . Gaspare Galati.
"Advanced radar techniques and systems". Peter Peregrinus Ltd.,
on behalf of Institution of Electrical Engineers, London, UK, 1993.
5 . Vyacheslav Tuzlukov
"Signal processing in radar systems" Talor & Francis Group LLC/CRC
Press LLC, 2000 N.W. Corporate Blvd. Boca Raton, Florida 33431, 2013.
Parallel Algorithm of Matching Pursuit and its Application for the
Analysis of Acoustic Emission Signals
Marapulets Yu. V., email@example.com
Kim A. A., firstname.lastname@example.org
acoustic emission, time-and-frequency analysis, sparse approximation,
parallel algorithm of matching pursuit.
During the last years, methods of sparse approximation have been
actively used for time-and-frequency analysis of signals. They are widely
applied in the studies of complicated processes of different nature, in
particular, in the analysis of seismic signals , hydro-acoustics ,
tasks of nondestructive testing [3, 4]. The results have been obtained
which show the efficiency of application of sparse approximation for the
analysis of acoustic emission (AE) signals in the sound frequency range
[5, 6]. Investigation of emission in this range is urgent to evaluate
the hardness of landscapes, mountain slopes, glaciers, snow mantles and
large technical constructions. They are very important in the study of
the physics of earthquake precursors . An acoustic emission signal
consists of a series of relaxation oscillations (geoacoustic pulses) with
shock excitation, 0.1-1 Pa amplitude, with the length of not more than
200 ms, and the frequencies from units to the first tens of kilohertz
. Pulse repetition frequency is determined by rock deformations and
changes within a wide range, from single pulses on some second time interval
during calm periods to tens and even hundreds per a second during anomalies
before earthquakes . One of the main tasks of AE signal processing
is the automatic detection and time-and-frequency analysis of geoacoustic
signals, the frequencies of which contain the data on their source size
and dynamics. Sparse approximation methods with basic dictionaries constructed
on Gabor  and Berlage [6, 8] functions were used for that purpose.
To realize the sparse approximation, a matching pursuit method, suggested
by Mallat S. and Zhang Z [9, 10] was applied, it was considered in detail
in [5, 6].
The significant disadvantage of the matching pursuit method is its computational
complexity; time for signal analysis is dozens of times longer than the
signal length. To make the calculation faster, it is reasonable to apply
the methods of parallel estimations in SIMD (Single Instruction stream/Multiple
Data stream) architecture format, which allows one to perform one arithmetic
step for much data at once . One of the most popular technologies,
based on SIMD conception, is CUDA hardware-software platform used to organize
parallel calculations on graphic processors (GPU) . The basics notion
of CUDA program model is the Thread. Threads are joined into blocks and
blocks, in their turn, form a grid. Grid and blocks may be one-, two-
and three-dimensional. The number and the size of grid components are
determined by a video card family and version. Application of such a group
allows one to launch millions of threads, and it saves the programmer
from the necessity to scale the computed blocks. If a GPU does not have
enough resources, blocks are processed sequently. It is just necessary
to determine the size of a launching grid. Let the number of threads
nt, launching in every block, be 256. This number gives
the optimal relation of memory and delays . Consequently, the number
of blocks nb, necessary to calculate the covariance
matrix is determined as nb = k/256.
To realize the parallel algorithm for matching pursuit method, MS
Visual Studio 2010 programming environment and CUDA 5.0 package were used.
A fragment of geoacousstic emission record with the length of 400 counts
was sent to the input of a standard matching pursuit method (sequential
algorithm) and of the developed parallel algorithm. A laptop with Intel
Core i3-2330M, 2.2 GHz central processor and NVIDIA GeForce 410M (48 kernel
CUDA, 73 Gflops performance) video card was used in the experiment. In
the result of tests it was established that computational time decreased
by more than 10 times, when applying the parallel algorithm. The results
of time-and-frequency analysis for geoacoustic emission signals were the
same. We should note that, in spite of CUDA platform support, the applied
video card has quite low performance. Application of a more powerful card,
for example, NVIDIA GeForce GTX 760 (1152 kernel CUDA, 2258 Gflops performance)
will allow us to decrease the time of calculation more significantly and
to synthesize a system for time-and-frequency analysis of acoustic emission,
operating in real-time regime.
1. Chakraborty A., Okaya D. Frequency-time decomposition of seismic
data using wavelet-based methods// Geophysics. Vol.60, 6, P.1906-1916.
2. Josso N. F., Zhang
J. J., Papandreou-Suppappola A. et al. On the Characterization of time-scale
underwater acoustic signal using matching pursuit decomposition //
Proceedings of the IEEE of OCEANS Conference. P. 6, Biloxi, Miss, USA,
3. Ebenezer S. P.,
Papandreou-Suppappola A., Suppappola S. B. Classification of acoustic
emissions using modified matching pursuit // EURASIP Journal on Applied
Signal Processing. N.3, P. 347-357.
4. Kovvali N., Das
S., Chakraborty D., Cochran D., Papandreou-Suppappola A., Chattopadhyay
A. Time-frequency based classification of structural damage //AIAA/ASME/ASCE/AHS/ASC
Structures, Structural Dynamics, and Materials Conference, 23 - 26 April
2007, Honolulu, Hawaii, P. 2007-2055.
5. Marapulets Yu.V.
Tristanov A.B. Application of sparse approximation method in the tasks
of analysis of geoacoustic emission signals // Digital Signal Processing.
2011. ╣2. P.13-17
6. Afanaseva A. A.,
Lukovenkova O. O., Marapulets Yu. V., Tristanov A. B. Using the sparse
approximation and clustering methods for the time series structure description
of acoustic emission // Digital Signal Processing. 2013. ╣2. P.30-34.
7. Marapulets Yu.
V., Shevtsov B. M. Mesoscale acoustic emission. Vladivostok: Dal'nauka,
2012, 125 p.
8. Afanaseva A. A.,
Lukovenkova O. O. Application of matching pursuit method to detect
acoustic emission pulses in the sound range // Proceedings of 15-th
International Scientific Research Conference "Digital Signal Processing
and its Applications" (DSPA'2013). Moscow, Russia, Issue: XV., V. 1.,
2013. P. 86-89.
9. Mallat S., Zhang
Z. Matching pursuits with time-frequency dictionaries. IEEE Transactions
on Signal Processing. N. 41(12), P.3397-3415.
10. Mallat S. A
Wavelet Tour of Signal Processing. Academic Press; 3rd edition, 2008.
11. Voevodin V. V.,
Voevodin Vl. V. Parallel computations. St.Petersburg.: BVH-Peterburg,
2002. 608 p.
12. Boreskov A. V.,
Kharlamov A. A. Operation basis for CUDA technologies. M.: DMK
Press, 2010. 232 p.
13. Sanders J., Kandrot
E. CUDA by Example: An Introduction to General-Purpose GPU Programming.
Addison-Wesley Professional, 2010. 312 p.
The features of data plotting in MATLAB
Rybolovlev A. A., Associate Professor, Ph. D. The Academy of Federal
Security Guard Service of the Russian Federation, email@example.com
Rybolovlev D. A., research associate, Ph. D. The Academy of Federal Security
Guard Service of the Russian Federation, firstname.lastname@example.org
Keywords: processing of results, plot, diagram, MATLAB, Russian
unified system for design documentation.
At the final stage of any research work, special attention is paid
to the presentation of the results in one form or another. There are different
ways of presenting information: verbal form (text, speech), symbolic (signs,
formula), graphics (charts, diagrams, graphs), subject-shaped (layouts,
models, movies, etc.).
This paper is devoted to processing the calculation results obtained in
the MATLAB computing environment. The authors believe that the visibility
(and hence clarity, persuasiveness) of presented plots and diagrams is
determined not only by possession of elementary methods of processing
the calculation results, but also by researcher ability to use MATLAB
Special attention is paid to the issue of compliance with plotting rules
that are defined in the recommendations of Russian unified system for
design documentation (ESKD) P 50-77-88. As in other systems, such information
is not found in the general case. So, it is specially noted that the construction
of plots should be guided by the rules of ESKD. It should be emphasized
that the research works (according to Russian national standard GOST 7.32-2001
and GOST 2.105-95), dissertations and theses (according to GOST 7.0.11-2011)
are also performed in accordance with the ESKD standards.
All samples are prepared in MATLAB R2012a computing environment. Plots
and diagrams are performed in a rectangular coordinate system of two dimensions
(plotting in other coordinate systems is described in detail in ESKD).
The initial data used to plot the curves includes the basis functions
(carrier waves) of VDSL communication system (Very high speed Digital
Mastering this method will help the researcher to enhance the visibility
and readability of presented plots and diagrams. In addition it will help
to get a general appreciation of the work by the experts.
1. Vlasov V. G. New Encyclopedic Dictionary of Fine Arts. St. Petersburg
: ABC Classics, 2007. 591 p.
2. Great Soviet Encyclopedia.
Moscow : Soviet Encyclopedia, 1969-1978.
R 50-77-88. Unified system for design documentation. Rules for
making diagrams. Moscow : Standards Press, 1989. 9 p.
4. GOST 7.32-2001.
System of standards on information, librarianship and publishing.
Report on the research work. Structure and design rules. Moscow
: Publishing House of Standards, 2001. 21 p.
5. GOST 2.105-95.
Unified system for design documentation. General requirements for text
documents. Moscow : Standards Press, 1996. 31 p.
6. GOST 7.0.11-2011.
System of standards on information, librarianship and publishing. Thesis
and dissertation. Structure and design rules. Moscow : Standartinform,
2012. 12 p.
7. Squires G. L.
Practical Physics. London : McGRAW Hill, 1968. 244 p.
8. Svetozarov V.
V. Elementary analysis of measurements. Moscow : MIFI Publishing
House, 1983. 52 p.
9. G.993.1 ITU-T
Recommendation. Very high speed digital subscriber line transceivers
10. GOST 2.307-2011.
Unified system for design documentation. Dimensioning and tolerances.
Moscow : Standartinform, 2012. 37 p.
Analysis of Time Relation for Signals in Design Digital Modules
and Availability Estimation
Kuzin A.A., email@example.com
Pluzhnikov A.D., firstname.lastname@example.org
Pribludova E.N., email@example.com
Sidorov S.B., firstname.lastname@example.org
Keywords: multiprocessor systems; high-speed; route; synchronous
Technique of route singularity accounting with analysis of time relation
for signals propagating in high-speed digital modules with synchronous
data exchange is devised. The matrix route definition for the system highway
and the system clocking is proposed. The application example of devised
technique for the analysis of multiprocessor cluster designed with purpose
of the use for advanced processing of the large information volume is
For the choosen example, cluster contains the four advanced digital signal
processors, the four SDRAM chips and the flash memory chip. The listed
cluster components are connected among themselves by system highway that
contains three multiplexed system buses: address bus and con-trol bus,
high-order bit transfer bus (from 63th to 32th) of datum and low-order
bit transfer bus (from 31th to 0) of datum. Though four processors are
connected to all three system buses and every of the rest five components
is connected to two of three system buses only (every to own).
Singularity of route such that the system highway may imagine as closed
in the ring formally. Formality of such presentation defines with what
none of three highway buses above physically do not close in the ring,
i.e., every form these bus is opened or it is the opened ring. However,
a mutual displacement of the three similar closed ring (three buses) in
point of fact a mutual displacement of the sections their opening with
sufficiently near placement of the printed conductors (lines) of the three
bus on multilayer board allows to tell about the system highway structurally
closed (formally, but no physically) in the ring.
So far as the current task is assigned so that should analyze the synchronous
data exchange, in which flash memory does not share, when this component
ignores with an analysis. For realization of synchronous exchange serves
the synchronization buffer containing in cluster and connected with eight
components (four processors and four SDRAM chips) lines of the unilateral
transfer of the clock pulses from the synchronization buffer to the listed
Singularity of the considered multiprocessor cluster is the possibility
of interprocessor data ex-change when any from four processors (master
processor, Master) has access to internal memory and registers of other
(slave, Slave) or all other (in the regime of broadcast exchange, Broadcast).
The timing analysis made for comparing project variants will allow to
avoid the crude errors in the design process.
The made analysis shows that the route of system highway is potential
source of system nonser-viceability as a whole.
Developed in the given work the technique of route singularity accounting
with the timing analy-sis for signals propagating in high-speed digital
modules with synchronous data exchange ensures the availability estimation
capability for the selected design variant.
1. Kyle Castille. TMS320C6000 EMIF-to-External SDRAM Interface.
Application Report SPRA433D. Texas Instruments, March 2004. P. 76.
Data Sheet. Texas Instruments, May 2010. P. 2.
Spectrum analysis of signals on multicore processors
Musayev M.M., email@example.com
Kardashev M.S., firstname.lastname@example.org
Keywords: multi-core processors, algorithms of spectral analysis
of signals, parallel processing cycles, the matrix-vector calculation,
thread processing, the acceleration of parallel algorithms.
This article focuses on the implementation procedures of spectral
analysis of signals on multicore processors. To estimate the resulting
acceleration of calculations a few basic systems of the Fourier transform
are taken: a fast Fourier transform, discrete cosine transform and Hadamard
Acceleration of digital signal processing procedures can be achieved both
by optimizing algorithms or recursive computation in the fast Fourier
transforms, and by using of threads on multicore processors.
Thread processing in the signal processing tasks should be considered
as a new technology, including the following elements of the preparation
and execution of programs:
- analysis of the numerical methods and algorithms for the creation of
independent computational threads;
- choice of effective programming language for writing programs;
- implementation of forming threads technologies using modern tools;
- estimation of parallel solutions efficiency.
Performance of the parallel algorithm depends on the software implementation
environment: processor parameters, mechanisms for creating computational
threads in the operating system, the number of threads.
In this paper the parameters of the acceleration of parallel algorithms
performed for various numbers of threads on processors Intel Core i3,
i5 are discussed. As a tool for the implementation of created parallel
algorithms of spectral analysis the library of Open MP, Intel TBB and
API Win32 Native Threads is used.
To compare the efficiency of these algorithms the graphs of acceleration
of each parallel algorithm are shown relative to the sequential version
of the same algorithm, as well as a parallel algorithm is shown relative
to another at different numbers of threads.
Research results show that the main parameter that affects the scalability
and final acceleration of application when migrating to multi-core platform
is the number of source signal samples. Usually dependence of acceleration
from number of samples has the character of a power function with horizontal
axis, thus this maximum value of acceleration tends to the number of processors.
Another important estimation parameter is a minimum amount of data, which
can be processed without a loss of performance. The optimal value for
this parameter is the quotient obtained by dividing the total number of
iterations to a number of computing threads.
Comparison of programming libraries shows when the number of samples in
the signal fragment is a small, the usage of compiler directives Open
MP is more efficient (acceleration occurs when the number of samples of
signal fragment is from 16 to 64) and when the number of samples in the
processed fragment is more than 128, the usage of Intel TBB algorithms
is more efficient.
The best areas of using developed parallel processing algorithms are speech
processing algorithms, spectra construction of small plots of the signals,
spectrogram, digital filters.
1. Shameem Akhter, Jason Roberts "Multi-Core Programming", Intel
2. Jonson S.G., Frigo
M. Implementing FFTs in practice, ch.11.- Rice University, Houston
TX: Connexion, 2008
S., Stokes A. Parallel Programming with Intel Parallel Studio XE.-
Indianapolis, Indiana: "John Wiley @ Sons, Inc.", 2012 -556p
4. Reinders J. Intel
Threading Building Blocks. Outfitting C++ for Multi-Core Processor Parallelism.-
Sebastopol, California: "O'Reilly Media, Inc.", 2007.-334p 5. Shpakovsky
G.I. Implementation of parallel calculations.- Minsk: Belarus State University.-
you have any question please write: email@example.com