Digital Signal Processing 
Russian 
Hyperphase Modulation  the optimal method of message transmission
(Part 2)
Abstract It is noted that operations of signal formation by using HPM in a modulator at transmission and demodulation at reception, as well as algorithms of message coding and decoding, could be rather simply implemented using modern digital signal processing equipment. The results of the conducted research show that application in the modern communication systems of HPM signals is rather promising. The article review example of technical processing of a coder and a modulator for the signals with HPM in threedimensional space. These examples illustrate application of the results received in Part I of this article for the solution of practical problems. 2. Van Trees H.L. Detection Estimation and Modulation Theory. N.Y.: Wiley, 2013.  1176p. 3. Byhovskiy M.A. Pomekhoustoychivost priema optimalnyh signalov, raspolozhennyh na poverhnosti Nmernogo shara // Elektrosvyaz ¹ 3, 2016. 4. Byhovskiy M.A. Teoreticheskie osnovy proektirovaniya sistem svyazi s vysokoy energeticheskoy effektivnost'yu // Cifrovaya obrabotka signalov, ¹2, 2017. 5. A. G. Zyuko, A. I. Fal’ko, I. P. Panfilov, et al., Interference Immunity and Efficiency of the Information Transmission Systems, Ed. by A. G. Zyuko // Radio i Svyaz, Moscow, 1985 6. John Proakis. Digital Communications// McGrawHill Education, 2000 7. Peterson W., Weldon E. J. Jr. Errorcorrecting codes, Moscow, Mir, 1976, 593 p. 8. Clark, George C. Jr. and J. Bibb Cain. ErrorCorrection Coding for Digital Communications. New York: Plenum Press, 1981 9. V.A. Varguasin, I.A. Cikin. Methods of Increase of Power and Spectral Efficiency of a Digital Radio Communication. SPb.: BHBPeterburg, 2013, p. 352.
Hyperphase Modulation  the optimal method of message transmission
(Part 3) Keywords: : energy efficiency of telecommunication systems, multidimensional signal ensemble, noise immunity code, telecommunication systems’ design References 2. Byhovskiy M.A. Propusknaya sposobnost' kanala svyazi pri peredache signalov ogranichennoy dlitelnosti // Elektrosvyaz ¹ 8, 2016. 3. Byhovskiy M.A. Teoreticheskie osnovy proektirovaniya sistem svyazi s vysokoy energeticheskoy effektivnost'yu // Cifrovaya obrabotka signalov, ¹2, 2017. 4. Fink L.M. The theory of transmission of discrete messages, Moscow, Sovetskoe radio, 1970, 728 p. 5. John Proakis. Digital Communications// McGrawHill Education, 2000 6. Clark, George C. Jr. and J. Bibb Cain. ErrorCorrection Coding for Digital Communications. New York: Plenum Press, 1981 7. Byhovskiy M.A. Giperfazovaya modulyaciya – optimalnyy metod peredachi cifrovyh soobscheniy (Chast 1) // Cifrovaya obrabotka signalov. ¹1, 2018, pp. 817. 8. Byhovskiy M.A. Giperfazovaya modulyaciya – optimanyy metod peredachi cifrovyh soobscheniy (Chast 2) // Cifrovaya obrabotka signalov. ¹ 2, 2018, pp. 310. 9. V.A. Varguasin, I.A. Cikin. Methods of Increase of Power and Spectral Efficiency of a Digital Radio Communication. SPb.: BHBPeterburg, 2013, p. 352.
Development of the hybrid scheme using tone reservation and clippingandfiltering methods for peaktoaverage power ratio reduction of OFDM signals Abstract The modified TR method is proposed based on an discrete Fourier transform (DFT)/ inverse DFT (IDFT) pair to suppress simultaneously all peaks, as hardware scheme of the CAF methods, while in the gradientbased TR methods, the largest peak is reduced. Therefore, it improves the efficiency of reducing PAPR and possesses relatively simple hardware implementation. The modified TR method extracts clipping noise on reserved subcarriers to generate an “antipeak” signal instead of using the impulselike kernel. In the modified CAF method, the clipping noise is generated and used to design a correction signal, as in TR methods. It keeps the clipping noise on the reserved subcarriers, resets to zero the frequency samples of the clipping noise associated with the pilot subcarriers and sets bounds to the inband distortion and the outofband radiation to satisfy an error rate below the specified level and a given spectral mask. The clipping noise is used in analysis instead of using the clipped OFDM signal to transform the original CAF algorithm into an equivalent form. Modifications of the original TR and CAF methods are very important to introduce a novel low complexity high efficiency hybrid algorithm which can be implemented in a common hardware architecture. The proposed hybrid algorithm has a low computational complexity because its hardware architecture is almost similar to that of the constrained clipping method and does not require a modification in the demodulation of the OFDM signal. The simulation results show that the proposed method offers a high performance in term of PAPR reduction capability. Its FPGA implementation has been tested and evaluated in the DVBT2 modulator. 2. ESTI EN 302 755 V1.4.1. Digital video broadcasting (DVB); Frame structure channel coding and modulation for a second generation digital terrestrial television broadcasting system // European Standard, July 2015. 3. ETSI TS 102 831 V1.2.1. Digital Video Broadcasting (DVB); Implementation guidelines for a second generation digital terrestrial television broadcasting system (DVBT2) // European Standard, Aug. 2012. 4. Han S.H. and Lee J.H. An overview of peaktoaverage power ratio reduction techniques for multicarrier transmission // IEEE Wireless Communications, vol. 12, no. 2, pp. 56–65, April 2005. 5. Jiang T. and Wu Y. An Overview: PeaktoAverage Power Ratio Reduction Techniques for OFDM Signals // IEEE Transactions on Broadcasting, vol. 54, no. 2, pp. 257–268, June 2008. 6. Anoh K., Tanriover C. and Adebisi B. On the Optimization of Iterative Clipping and Filtering for PAPR Reduction in OFDM Systems // IEEE Access, vol. 5, pp. 12004–12013, June 2017. 7. Baxley R.J., Zhao C., and Zhou G.T. Constrained clipping for crest factor reduction in OFDM // IEEE Transactions on Broadcasting, vol. 52, no. 4, pp. 570–575, Dec. 2006. 8. Tellado J. Peak to average power reduction for multicarrier modulation // Ph.D. dissertation, Stanford Univ., Stanford, CA, 2000. 9. Wang Y., Xie S., and Xie Z. FISTABased PAPR Reduction Method For Tone Reservation’s OFDM System // IEEE Wireless Communications Letters, vol. PP, no. 99, pp. 1–1, Nov. 2017. 10. Tran V.N. and Le H.N. Reconfigurable Complex Filtering Methods for PAPR Reduction of OFDM Signals with Low Computational Complexity // 2017 IVth International Conference on Engineering and Telecommunication (EnT), Moscow, Russia, pp. 59–63, Dec. 2017. 11. Pg109. Fast Fourier Transform v9.0 // Xilinx LogiCORE IP Product Guide, Nov. 2015.
Abstract Taking into account the asymptotic efficiency and asymptotic normality of the maximum likelihood estimations of the unknown interference parameters, the accuracy of the estimation is characterized by the variance of the estimate determined by the CramerRao expression indicating the lower bound of the variance of the estimate. On the basis of the CramerRao expression, formulas are obtained for the variance of estimates of the coefficients of interperiod correlation and the Doppler shift of the phase of the interference, taking into account the volume of the training sample and the spectral parameters of the interference. The presence of uncorrelated noise leads to a noticeable decrease in accuracy at a relatively high level. The main factors determining the accuracy of the estimation are the volume of the training sample and the spectral parameters of the interference. It is shown that the use of interchannel and interperiod averaging leads to a corresponding increase in the accuracy of estimating the coefficients of interperiod correlation and the Doppler phase shift of the interference. The resulted results of calculations and simulation statistical modeling of estimation algorithms have confirmed the asymptotic efficiency of the obtained estimates, the accuracy of which approaches the limit with a relatively small volume of the training sample. References 2. Richards M.A., Scheer J.A., Holm W.A. (Eds.). Principles of Modern Radar: Basic Principles. New York: SciTech Publishing, IET, Edison. 2010. – 924 p. 3. Popov D.I. Statisticheskaja teorija radiotehnicheskih system: ucheb. posobie (Statistical theory of radio engineering systems: Textbook. allowance). Ryazan': RGRTU, 2011. 80 p. (in Russian). 4. Melvin W.L., Scheer J.A. (Eds.). Principles of Modern Radar: Advanced Techniques. New York: SciTech Publishing, IET, Edison, 2013. 846 p. 5. Radar Handbook / Ed. by M.I. Skolnik. 3rd ed. McGraw–Hill, 2008. 1352 p. 6. Richards M.A. Fundamentals of Radar Signal Processing, Second Edition. New York: McGraw–Hill Education, 2014. – 618 p. 7. Cifrovaja obrabotka signalov v mnogofunkcional'nyh radiolokatorah. Metody. Algoritmy. Apparatura: monografija / pod red. G. V. Zajceva (Digital signal processing in multifunctional radars. Methods. Algorithms. Equipment: monograph / ed. G. V. Zaitseva). Moscow, Radiotehnika, 2015. 376 p. (in Russian). 8. Lozovskij I.F. Cifrovaja obrabotka signalov v RLS obzora: monografija (Digital processing of signals in the radar survey: monograph). Novosibirsk, Izdvo NGTU, 2016. 270 p. (in Russian). 9. Popov D.I. Adaptive notch filter with complex weight // Vestnik Kontserna PVO «Almaz – Antej». 2015. no 2 (14). pp. 2126. (in Russian). 10. Popov D.I. Autocompensation of the Doppler phase of clutter // Cifrovaja obrabotka signalov. 2009. no 2. pp. 30–33. (in Russian). 11. Popov D.I. Adaptive suppression of clutter // Cifrovaja obrabotka signalov. 2014. no. 4. pp. 3237. (in Russian). 12. Popov D.I. Adaptivnije pegektornjie filtrij kaskadnogo tipa // Cifrovaya obrabotka signalov. 2016. no. 2. pp. 5356. (in Russian). 13. Popov D.I. Adaptive notch filter with real weights // Cifrovaya obrabotka signalov. 2017. no. 1. pp. 2226. (in Russian). 14. Popov D. I. Measurements of Characteristics of Clutter // Measurement Techniques. May 2017. Vol. 60. No 2. – P. 190–195. 15. Cramer G. Matematicheskie metolji statistiki (Mathematical methods of statistics) / per. s angl. pod red. A.N. Kolmogorova. Moscow: Mir, 1975. 648 p. (in Russian).
Abstract References 2. Kondratenkov, G.S. and Frolov, A.Yu., (Radiovision: Radar Systems for Remote Sensing of the Earth, Moscow: Radiotekhnika, 2005. 3. Levin B.R. «Teoreticheskie osnovy statisticheskoy radiotekhniki» kniga 1ya, izd. 2e, M., «Sov. Radio», 1974, pp. 59 – 60. 4. Shirman, Ya. D. Theoretical foundations of radiolocation. M.: Sov.radio, 1970, 560 p.
Abstract More exactly the method minimizes the rootmeansquare sidelobes level for a rectangular set of points in the suppression zone. Variation of points density allows adjusting the resulting value of sidelobes suppression. Let s be a modulation sequence of the phasecoded pulse, expressed by row vector and x be a modulation sequence of the receiver reference. The filter output is a crosscorrelation function of the sequences s and x. It is shown in the paper that for a given s the optimal vector x, minimizing rootmeansquare sidelobes level in the twodimensional zone, is given by the formula x = sR^{1}, where R is a matrix (specified in the paper) which is a function of s, parameters of suppression zone, and user parameters. The paper investigates main parameters of the filter output for the optimal solution: rootmeansquare sidelobes level, maximum sidelobes level and losses in signaltonoise ratio. It is shown that the described method allows achieving high sidelobes suppression (hundreds of dB) for the zone with relatively small area if abovementioned points density for synthesis is set to be high. Great suppression leads to high losses in signaltonoise ratio. For practical radar applications such a great suppression in not realizable because of other restrictions in the signal flow path. It makes it possible to set a tradeoff between small suppression and large losses in signaltonoise ratio. The paper describes necessary points density for the given suppression level. In the paper all examples are calculated for Legendre modulation sequences [6] and 50 dB maximum sidelobe suppression level in the zone. In this case resulting losses L may be estimated by the formula L = 10S + 0.1 dB where S is the zone area. It is also shown that for the fixed losses and fixed zone configuration maximum possible area of the suppression zone is increased with increasing distance of the zone from the origin. The proposed method is applicable for the zone with arbitrary configuration particularly for the zone containing several connected regions. The paper describes the case of two connected regions in the zone. The resulting performance of the proposed method of filtering meets requirements of many practical problems. References 2. A.A. Trukhachev. Radiolokatsionnye signaly i ih primenenie (Radar signals and their applications). Ì. Voenizdat. 2005. 320 p. 3. P. Stoica, J. Li, and M. Xue. Transmit codes and receive filters for radar. IEEE Signal Processing Magazine. vol. 25. pp. 94–109. November 2008. 4. G.V. Zaytsev, N.S. Kondranina, D.M. Litvinov. Otsenka characteristic metoda nesoglasovannoy filtratsii, minimizirujuschego integral’niy uroven’ bokovih lepestkov fazokodomanipulirovannih signalov (Characterization of mismatched filtering, minimizing integrated sidelobe level for phasecoded pulse). Tsifrovaya obrabotka signalov (Digital signal processing). ¹ 1, 2017. 5. R. A. Horn and C. R. Johnson. Matrix Analysis. Cambridge University Press. 1985. 652 p. 6. J. Jedwab. A Survey of the Merit Factor Problem for Binary Sequences. Sequences and Their Applications. Proceedings of SETA 2004. ed. T. Helleseth et al. Lecture Notes in Computer Science. vol. 3486. pp. 30–55. SpringerVerlag. Berlin Heidelberg. 2005.
2. Sandia National Laboratories // URL: http://www.sandia.gov 3. ImSAR LLC [Ýëåêòðîííûé ðåñóðñ] // URL: http://www.imsar.com (äàòà îáðàùåíèÿ: 04.04.2018). 4. Shkolnyiy L.A., Radar systems aerial reconnaissance, interpretation of radar images. Moscow, VVIA im. N.E. Zhukovskogo, 2008, 531 p. 5. Duersch M. Backprojection for Synthetic Aperture Radar. Thesis for Ph.D. Brigham Young University, 2013. 6. Duersch M., Long D. Analysis of timedomain backprojection for stripmap SAR // International Journal of Remote Sensing, 2015. Vol. 36, No. 8, pp. 2010–2036. 7. Doerry À. Basics of Backprojection Algorithm for Processing Synthetic Aperture Radar Images. Sandia National Laboratories, 2016.
Abstract The article is described the basic principles of digital implementation of the algorithm for processing quasiperiodic pulse signals using the GaussianHermite functions (FGH). Using this algorithm it is possible not only to detect a defect, but also to trace its dynamics throughout the process under investigation. The algorithm is based on the basic properties of the Hermite transformation. The change in the scale of GaussHermite functions is borrowed from the theory of wavelet transform. The parent function is formed as series of the GaussHermite functions associated with an orthogonal filter bank. The signal detection is realized by means of crosscorrelation function processing. The decision on the presence of a signal is made on the basis of the maxima of the correlation function, which corresponds to the classical theory of optimal filtration. As a result, the developed algorithm allows us to detect features of the signal, based on which the filter is constructed. The filtering scheme can be reduced to a matrix form, where each column is characterized by a particular defect or pathology. This form of representation has a flexible structure, i.e. it is sufficient to record the matrix of the filter weights in the memory of the programmable logic integrated circuit to form the final signal analysis device. Also, there is the possibility of parallel processing, which increases the computational speed. 2. Janke E., Emde F., Lesch F. Spetsialnie functsii (Special functions), M.: Nauka, 1964. 344 p. 3. Balakin, D. A., Shtykov, V. V. Postroenie ortogonalnogo banka filtrov na osnove preobrazovania Ermita dlia obrabotki signalov (The construction of orthogonal filters bank based on Hermit transform for signal processing) // Zurnal radioelectroniki (Journal of radio electronics), 2014, no. 9. 4. Gradshtein, I. S., Ryzhik, I. M. Tablitsa integralov, sum riadov i proizvedenii (Tables of integrals, sums of series and products), M.: Fizmat, 1963. 1100 p. 5. Baskakov, S., I. Radiotekhnicheskie tsepi i signali (Radio circuits and signals), M.: Vish. shkola, 2000. 450 p.
Abstract 2. Kahaner D., Mouler K., Nesh S.: Numerical Methods and Software. Prentice Hall, New York. 1988, 575 p. 3. Krylov, V.I. and Shul’gina, L.T., Handbook of Numerical Integration, Moscow: Nauka, 1966, 372 p. 4. Ignat'ev N.K. Discretization and its applications. Moscow: Svyaz, 1980, 284p. 5. P. A. M. Dirac The Principles of Quantum Mechanics. Snowball Publishing, 1960, 480p. 6. I.N. Bronshtein, K.A. Semendyayev, Handbook of mathematics for engineers and students of higher technical schools, Moscow: Nauka, 1986, 544 p.
Abstract 2. N. Takahashi and K. Suyama, Design of CSD coefficient FIR filters based on branch and bound method, Proc. of ISCIT2010, pp.575578, 2010. DOI: 10.1109/ISCIT.2010.5665055 3. Y. Arie and K. Suyama, Evolutionary stagnation avoidance for design of CSD coefficient FIR filters using GA, Proc. of ITCCSCC 2016, 2016. 4. R. Baudin and G. Lesthievent. Design of FIR Filters with Sum of PowerofTwo Representation Using Simulated Annealing, 2014 7th Advanced Satellite Multimedia Systems Conference and the 13th Signal Processing for Space Communications Workshop (ASMS/SPSC). DOI: 10.1109/ASMSSPSC.2014.6934565 5. T. Sasahara and K. Suyama, An ACO approach for design of CSD coefficient FIR filters, Proc. of APSIPA ASC 2015, pp.463468, 2015. DOI: 10.1109/APSIPA.2015.7415314 6. T. Sasahara and K. Suyama, Verification of search process in CSD coefficient FIR filter design, 2016 International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS). DOI: 10.1109/ISPACS.2016.7824710 7. Alan V. Oppenheim, Ronald W. Schafer DiscreteTime Signal Processing (3rd Edition). PrenticeHall Signal Processing Series, 2009, 1144 p. 8. M. Dorigo and G. D. Caro, Ant colony optimization: a new metaheuristic, Proc. of Congress on Evolutionary Computation 99, Vol.2, 1999, pp.14701477. DOI: 10.1109/CEC.1999.782657 9. G. Rui and L. S. DeBrunner, A novel fast canonicalsigneddigit conversion technique for multiplication. Proc. Of IEEE Conference pn Acoustics, Speech and Signal Processing, ICASSSP2011, pp. 16371640, 2011. DOI: 10.1109/ICASSP.2011.5946812 10. T. Sasahara and K. Suyama, An Effectiveness of ACO Approach in Design of CSD Coefficient FIR Filters. Intelligent Signal Processing and Communication Systems (ISPACS), 2015 International Symposium on. DOI: 10.1109/ISPACS.2015.7432839 If you have any question please write: info@dspa.ru
