Digital Signal Processing 
Russian 
Hyperphase Modulation the optimal method of message transmission Abstract The article explores dependence of the speed of message transmission with the use of HPM on minimal phase distance between SPs in this multidimensional SE. It is shown that by applying HPM method it is possible to achieve a substantial net energy gain as compared with other twodimensional SEs, such as QAM. Such gain grows with the increase of N and can be quite significant. The author develops an effective, from a calculation standpoint, coding algorithm of the transmitted message – by using the transmitted message number (m) to calculate phase coordinates of signals’ SPs. The values of those coordinates are then used for formation of transmitted signals with HPM. The major difference of this coding method from those that are used in modern telecommunication systems is that that method, while improving noise immunity, it does not contribute additional (excessive) symbols into a sequence of informational symbols of a transmitted message. 2. Shannon C. Probability of error for optimal codes in Gaussian channel. Bell SystemTechn. J., May, 1959. 3. Weinstein S.B., Ebert P.M. Data transmission by frequency division multiplexing using the discrete Fourier transform. IEEE Trans. COM19, ¹ 10, 1971 4. Bykhovskiy M.A. Veroyatnost oshibki dlya optimalnyh mnogomernyh kodov v gaussovom kanale svyazi i ih osnovnye harakteristiki. Elektrosvyaz ¹ 2, 2016 5. Bykhovskiy M.A. Pomekhoustoychivost priema optimal'nyh signalov, raspolozhennyh na poverhnosti Nmernogo shara. Elektrosvyaz ¹ 3, 2016 6. John Proakis. Digital Communications// McGrawHill Education, 2000 7. Clark, George C. Jr. and J. Bibb Cain. ErrorCorrection Coding for Digital Communications. New York: Plenum Press, 1981 8. Ungerboeck G. TrellisCoded Modulation with Redundant Signal Sets. PartIandII, IEEECommun.Mag., vol. 25,¹ 2,1987 9. Forney G. D., Gallager R.G., Lang G.R., Longstaff F.M., Qureshi S.U. Efficient Modulation for Bandlimited Channels. IEEE J. Se1ectd Areas in Commun., vol. SAC2, n. 5, ¹ 9, 1984 10. Forney G.D., Wei L.F. Multidimensional constellationsPart I: Introduction, figures of merit, and generalized cross constellations. IEEE I. Select. Areas Commun., vol. 7, ¹ 8, 1989 11. Forney G.D. Multidimensional constellationsPart II: Voronoi constellations. IEEE I. Select. Areas Commun., vol. 7, ¹ 8, 1989 12. Gallager, R. G., Low Density Parity Check Codes, Monograph, M.I.T. Press, 1963 13. Nsphere. https://en.wikipedia.org/wiki/Nsphere
Recurrent neural networks as behavioral models of nonlinear dynamic systems Keywords: : neural networks, recurrent, models of nonlinear dynamical systems, classification of neural networks, model characteristics. Depending on the feedback location affecting the neurons interaction, two classes of recurrent neural networks are distinguished. The first class is globally recurrent networks, in which feedback is allowed between the neurons of the same layer or different layers. Basically, four kinds of networks can be distinguished: fully recurrent networks, partially recurrent networks (the Elman structure, the Jordan structure, the recurrent multilayer perceptron), statespace networks and cellular neural networks. The second class is locally recurrent networks, which contain feedback inside neurons and have the following structures: the networks consisting of static feedforward and, socalled, dynamic neurons, as well as the blockoriented neural networks of Wiener, Hammerstein, WienerHammerstein, etc. The structures, properties, advantages and disadvantages of different types of recurrent networks are considered. The presented analysis is useful for choosing the mathematical model of a nonlinear dynamical system a priori, when it is necessary to evaluate which of the known neural network structures meets the requirements for model characteristics, such as accuracy, computational complexity, robustness, hardware implementation, more than others do. References 2. Janczak A. Identification of nonlinear systems using neural networks and polynomial models. A BlockOriented Approach. – Berlin: SpringerVerlag Berlin Heidelberg, 2005. 3. Speech, audio, image and biomedical signal processing using neural networks / Ed.: B. Prasad, S. R. Mahadeva Prasanna. – Berlin: SpringerVerlag Berlin Heidelberg, 2008. 4. Patan K. Artificial neural networks for the modelling and fault diagnosis of technical processes. – Berlin: SpringerVerlag Berlin Heidelberg, 2008. 5. Tang H., Tan K. C., Yi Z. Neural networks: computational models and applications. – Berlin: SpringerVerlag Berlin Heidelberg, 2007. 6. Dreyfus G. Neural networks: methodology and applications. – Berlin: SpringerVerlag Berlin Heidelberg, 2005. 7. Neural Networks. STATISTICA Neural Networks: Methodology and technologies of modern data analysis / Ed.: V. P. Borovikov. – M.: Gorjachaja linija–Telekom, 2008. 8. Osovsky S. Neural networks for information processing. – M.: Finansi i statistika, 2002. 9. Medvedev V.S., Potemkin V.G. Neural networks. MATLAB 6. – M.: DIALIGMIFI, 2002. 10. Bianchini M., Maggini M., Jain L. C. Handbook on neural information processing. – Berlin: SpringerVerlag Berlin Heidelberg 2013. 11. Michel A. N., Liu D. Qualitative analysis and synthesis of recurrent neural networks. – New York: Marcel Dekker, 2002. 12. Mandic D. P., Chambers J. A. Recurrent neural networks for prediction: learning algorithms, architectures and stability. – New York: John Wiley & Sons, Inc., 2001. 13. Solovyeva E. B. Polynomial and neural models of nonlinear discrete systems. – St. Petersburg: Izdatelstvo SPbGETU “LETI”, 2014. 14. Bichkov U. A., Inshakov U. M., Solovyeva E. B., Scherbakov S. A. Analysis of mathematical models of continuous and discrete nonlinear systems. – St. Petersburg: Izdatelstvo SPbGETU “LETI”, 2017. 15. Solovyeva E. Types of recurrent neural networks for nonlinear dynamic system modelling // Proceedings of 2017 XX IEEE International Conference on Soft Computing and Measurements (SCM2017). – St. Petersburg: SaintPetersburg Electrotechnical University “LETI”. Russia, St. Petersburg, May 2426, 2017, P. 1–4. 16. Chaos, CNN, Memristors and beyond. A festschrift for Leon Chua. / Ed.: A. Adamatzky, G. Chen. – World Scientific Publishing Co. Pte. Ltd., 2013. 17. Chen W. K. Feedback, nonlinear and distributed circuits. – New York: Taylor & Francis Group, LLC., 2009. 18. Yalcin M. E., Suykens J. A. K., Vandewalle J. P. L. Cellular neural networks, multiscroll chaos and synchronization. – Singapore: World Scientific Publishing Co. Pte. Ltd., 2005. 19. Slavova A. Cellular neural networks: dynamics and modelling. – Dordrecht: Springer Science + Business Media, 2003. 20. Dogaru R. Universality and emergent computation in cellular neural networks. – Singapore: World Scientific Publishing Co. Pte. Ltd., 2003. 21. Chua L. O., Roska T. Cellular neural networks and visual computing: foundations and applications. – Cambridge: Cambridge Univ. Press, 2002. 22. Du K.L., Swamy M. N. S. Neural networks in a softcomputing framework. – London: SpringerVerlag London Ltd, 2006. 23. Goodfellow I., Bengio Y., Courville A. Deep Learning. – M.: DMK Press, 2017. 24. Nikolenko S., Kadurin A., Arhangelskaja E. Deep lerning. – St. Petersburg: Piter, 2018.
Abstract 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. Melvin W. L., Scheer J.A. (Eds.). Principles of Modern Radar: Advanced Techniques. New York: SciTech Publishing, IET, Edison, 2013. – 846 p. 4. Merrill I. Skolnik. Radar Handbook // McGrawHill Professional Publishing, 1970 5.Popov D.I. Adaptivnaya obrabotka signalov na fone passivnyh pomekh // Izvestiya vuzov. Radioelektronika. – 2000. – T. 43, ¹ 1 (451). – pp. 5968. 6. Popov D.I. Optimalnaya obrabotka mnogochastotnyh signalov // Izvestiya vuzov Rossii. Radioelektronika. – 2013. – Vyp. 1. – pp. 32–39. 7. Popov D.I. Adaptivnye rezhektornye filtry s kompleksnymi vesovymi koefficientami // Vestnik Koncerna PVO «Almaz – Antey». – 2015. – ¹ 2 (14). – pp. 2126. 8. Popov D.I. Avtokompensaciya doplerovskoy fazy passivnyh pomekh // Cifrovaya obrabotka signalov. – 2009. – ¹ 2. – pp. 30–33. 9. Popov D.I. Adaptivnoe podavlenie passivnyh pomekh // Cifrovaya obrabotka signalov. – 2014. – ¹ 4. – pp. 3237. 10. Popov D.I. Adaptivnye rezhektornye filtry kaskadnogo tipa // Cifrovaya obrabotka signalov. – 2016. – ¹ 2. – pp. 5356. 11. Popov D.I. Adaptivnye rezhektornye filtry s deystvitelnymi vesovymi koefficientami // Cifrovaya obrabotka signalov. – 2017. – ¹ 1. – pp. 2226.
Abstract References 2. Natalia Olifer, Victor Olifer. Computer Networks: Principles, Technologies and Protocols for Network Design. // SPb.: Piter, 2004. 864 p. 3. Leonard Kleinrock, “Queueing Systems Volume I: Theory”, New York: Wiley, 19751976. 432 p. 4. Kucheryavyy E.A. Upravlenie trafikom i kachestvo obsluzhivaniya v seti Internet. – SPb.: Nauka i Tekhnika, 2004. – 336 p.
Abstract The second algorithm is based on independent handling inphase and quadrature components of described signal type by means of a filter which impulse response matched with “average” elementary impulse. This approach needs low computational costs but it has a low level of noise immunity. To combine features of two described approach in this article a handling algorithm for bandwidthefficient radio signal is offered. The algorithm uses the Viterbi’s procedure too, but a unit of handling metrics is replaced with a filter module. This algorithm is obtained as result of using in receiver as a reference signal a signal without components that provides controlled coupling between inphase and quadrature components. This assumption made possible to create two circuits of quasi optimal demodulator that used two and threechannel filtration of an inphase and quadrature components. Conducted research showed that the proposed algorithm has a maximum loss in noise immunity less 0.3 dB as compared with optimal algorithm based on common Viterbi’s procedure at BER = 1e4. At the same time, the proposed algorithm provides to reduce necessary computational costs by to four times. A gain in noise immunity as compared with onechannel algorithm that uses filtration achieves 2.6 dB at same conditional. References 2. Sun H. et al. Wideband spectrum sensing for cognitive radio networks: a survey // IEEE Wireless Communications. 2013. Vol. 20. No. 2. pp. 7481. 3. Wygliski A.M., Nekovee M. Hou Y.Th. Cognitive Radio Communications and Networks. Principles and Practice. – London: Elsevier, 2010 – 714 p. 4. Kirillov S.N., Berdnikov V.M., Pokrovskij P.S, Semin D.S. Problemnoorientirovannye platformy dlja realizacii universal'nyh, adaptivnyh, strukturnozashhishhennyh radiosistem peredachi informacii // Radiotehnika. 2015. No. 5. pp. 612. 5. Simon M.K. BandwidthEfficient Digital Modulation with Application to DeepSpace Communications. Jet Propulsion Laboratory. California Institute of Technology. URL: https://descanso.jpl.nasa.gov/monograph/series3/complete1.pdf 6. Kirillov S.N., Pokrovskij P.S. Programmnoupravljaemyj formirovatel' radiosignalov s nelinejnymi vidami moduljacii // Nelinejnyj mir. 2013. No. 3. pp. 150157. 7. Pokrovskij P.S. Procedura detektirovanija radiosignalov s upravljaemoj svjaz'ju mezhdu kvadraturnymi sostavljajushhimi // Vestnik Rjazanskogo gosudarstvennogo radiotehnicheskogo universiteta. 2013. No. 3 (45). pp. 110113. 8. Pokrovskij P.S. Sintez kvazioptimal'nogo algoritma detektirovanija spektral'nojeffektivnyh radiosignalov // Proceedings of Russian conf. «Novye informacionnye tehnologii v nauchnyh issledovanijah (NIT2017)». Ryazan: RSREU, 2017. pp. 113114. 9. Prokis Dzh. Cifrovaja svjaz'. Per s angl. / Edited by D.D. Klovskogo. – M.: Radio i svjaz', 2000 – 800 p. 10. Kirillov S.N., Pokrovskij P.S. Dvuhkriterial'nyj sintez shestnadcatipozicionnyh radiosignalov s upravljaemoj svjaz'ju mezhdu sinfaznoj i kvadraturnoj sostavljajushhimi // Uspehi sovremennoj radiojelektroniki. 2014. No. 6. pp. 1825. 11. Pokrovskij P.S. Procedura sinteza radiosignalov s upravljaemoj svjaz'ju mezhdu kvadraturnymi sostavljajushhimi po dvum pokazateljam kachestva // Vestnik Rjazanskogo gosudarstvennogo radiotehnicheskogo universiteta. 2015. No 2 (issue 52). 2015. pp. 4955. 12. Feer K. Besprovodnaja cifrovaja svjaz'. Metody moduljacii i rasshirenija spektra.  M.: Radio i svjaz', 2000. – 520 p.
Abstract References 2. Shchemelinin V.L., Simonchik K.K. Issledovanie ustoychivosti golosovoy verifikacii k atakam, ispolzuyuschim sistemu sinteza // Izvestiya vysshih uchebnyh zavedeniy. Priborostroenie. 2014. T. 57, No 2. pp. 84–88. 3. Shchemelinin V., Kozlov A., Lavrentyeva G., Novoselov S., Simonchik K. Vulnerability of Voice Verification System with STC Antispoofing Detector to Different Methods of Spoofing Attacks // Speech and Computer. SPECOM 2015. Lecture Notes in Computer Science. 2015. Vol. 9319. P. 480–486. 4. Tupicin G.S., Topnikov A.I., Priorov A.L. Modifikaciya dvuhstupenchatogo algoritma shumopodavleniya dlya uluchsheniya kachestva identifikacii diktora v usloviyah shumov // Informacionnye sistemy i tekhnologii. 2015. T. 6, ¹ 92. pp. 39 47. 5. Tupicin G.S., Kravcov S.A., Topnikov A.I., Priorov A.L. Modifikaciya algoritma ocenki binarnoy maski v zadache podavleniya shuma dlya sistemy identifikacii diktora // Proektirovanie i tekhnologiya elektronnyh sredstv. 2015. ¹ 3. pp. 32–37. 6. Tupicin G.S., Topnikov A.I., Priorov A.L. Predobrabotka zashumlennyh rechevyh signalov s pomosch'yu binarnyh masok v zadache identifikacii diktora // Naukoemkie tekhnologii. 2015. T. 16, ¹ 11. pp. 56–61. 7. Tupicin G.S., Topnikov A.I., Priorov A.L. Metodika ocenki myagkoy maski dlya zadachi predobrabotki zashumlennyh rechevyh signalov v sistemah identifikacii diktora // Uspekhi sovremennoy radioelektroniki. 2016. ¹ 6. pp. 73–80. 8. Cummins F., Grimaldi M., Leonard T., Simko J. The CHAINS Speech Corpus: CHAracterizing INdividual Speakers // Proc of SPECOM. 2006. P. 1–6. 9. Varga A., Steeneken H.J.M. Assessment for automatic speech recognition: II. NOISEX92: A database and an experiment to study the effect of additive noise on speech recognition systems // Speech Communication. 1993. V. 12, No 3. P. 247–251. 10. International Telecommunication Union. P.862: Perceptual evaluation of speech quality (PESQ), an objective method for endtoend speech quality assessment of narrowband telephone networks and speech codecs / International Telecommunication Union // ITUT Recommendation. 2001. 11. Klatt D. Prediction of perceived phonetic distance from criticalband spectra: A first step // ICASSP ’82. IEEE International Conference on Acoustics, Speech, and Signal Processing. – Institute of Electrical and Electronics Engineers. 1982. V. 7, P. 1278–1281. 12. Crochiere R., Tribolet J., Rabiner L. An interpretation of the log likelihood ratio as a measure of waveform coder performance // IEEE Transactions on Acoustics, Speech, and Signal Processing. 1980. V. 28, N. 3. P. 318–323. 13. Tupicin G.S. Ispolzovanie rasstoyaniya mezhdu melchastotnymi kepstralnymi koefficientami dlya ocenki tochnosti identifikacii diktorov // Doklady 18y mezhdunarodnoy nauchnotekhnicheskoy konferencii «Problemy peredachi i obrabotki informacii v setyah i sistemah telekommunikaciy». Ryazan', 2015. pp. 98–99. 14. Boll S. Suppression of acoustic noise in speech using spectral subtraction // IEEE Transactions on Acoustics, Speech, and Signal Processing. 1979. V. 27, No 2. P. 113–120. 15. Ephraim Y., Malah D. Speech enhancement using a minimummean square error shorttime spectral amplitude estimator // IEEE Transactions on Acoustics, Speech, and Signal Processing. 1984. V. 32. No 6. P. 1109–1121. 16. Lim J., Oppenheim A. Enhancement and bandwidth compression of noisy speech // Proceedings of the IEEE. 1979. V. 67, No 12. P. 1586–1604. 17. Ephraim Y., Malah D. Speech enhancement using a minimum meansquare error logspectral amplitude estimator // IEEE Transactions on Acoustics, Speech, and Signal Processing. 1985. V. 33, No 2. P. 443–445. 18. Plapous C., Marro C., Mauuary L., Scalart P. A twostep noise reduction technique // IEEE International Conference on Acoustics, Speech, and Signal Processing. 2004. V. 1. P. 289 92. 19. Hu Y., Loizou P. Evaluation of objective quality measures for speech enhancement // IEEE Transactions on Speech and Audio Processing. V. 16. Is. 1. 2008. P. 229–238.
2. Farwell L.A., Donchin E. Talking off the top of your head: towards mental prosthesis utilizing eventrelated brain potentials // Electroenceph. Clin. Neurophysiol. – 1988. – V. 70. – P. 510523. 3. Wang Yu., Wang Yi., Cheng Ch., Jung T. Developing Stimulus Presentation on Mobile Devices for a Truly Portable SSVEPbased BCI. http://ieeexplore.ieee.org/document/6610738/?section=abstract. 4. Volosyak I. SSVEP based BremenBCI boosting information transfer rates // Journ. Neural Eng. – 2011. – V. 8(3). – P. 036020. DOI: 10.1088/17412560/8/3/036020. 5. Resalat S.N., Setarehdan S.K. An Improved SSVEP Based BCI System Using Frequency Domain Feature Classification // American Journal of Biomedical Engineering. – 2013. – V. 3(1). – P. 18. DOI: 10.5923/j.ajbe.20130301.01. 6. Boycova YU.A., Dan'ko S.G., Medvedev S.V. Dinamika moschnosti EEG v beta i gammadiapazonah v usloviyah normal'noy i oslablennoy elektromiogrammy licevyh myshc // Fiziologiya cheloveka. 2016. T. 42. ¹ 6. pp. 517. 7. Zenkov L.R. Clinical electroencephalography with elements epileptology. Moscow. 2002; 356 p. 8. High frequency SSVEPs for BCI applications G. Garcia // http://hmi.ewi.utwente.nl/chi2008/chi2008_files/garcia.pdf 9. Multivariate synchronization index for frequency recognition of SSVEPbased braincomputer interface / Ya. Zhang, P. Xu, K. Cheng, D. Yao // Journal of Neuroscience Methods. – 2014. – 221. – P. 32– 40. 10. Comparison of the influence of stimuli color on SteadyState Visual Evoked Potentials / R. Tello, S. Muller, A. Ferreira, T. Freire // Bastos Res. Biomed. Eng. – 2015. – V. 31(3). – Ð.218231. 11. Belobrodskiy, V.A. Razrabotka geneticheskogo algoritma dlya konstruirovaniya cifrovyh filtrov, klassificiruyuschih biomedicinskie signaly, i ego aprobaciya na signalah s izvestnymi parametrami/V.A. Belobrodskiy, S.D. Kurgalin, YA.A. Turovskiy i dr.//Biomedicinskaya radioelektronika.  2015. ¹ 2. pp. 5664 12. Èññëåäîâàíèå âûçâàííûõ ïîòåíöèàëîâ ãîëîâíîãî ìîçãà íà îñíîâå àäàïòèâíîãî âàðèàíòà îáðàòíîãî âåéâëåòïðåîáðàçîâàíèÿ Òóðîâñêèé ß.À., Êóðãàëèí Ñ.Ä., Âàõòèí À.À., Áîðçóíîâ Ñ.Â., Áåëîáðîäñêèé Â.À.Áèîôèçèêà. 2015. Ò. 60. ¹ 3. pp. 547554. 13. Turovskiy YA.A. Obrabotka signala elektroenncefalogrammy na osnove analiza chastotnyh zavisimostey i veyvletpreobrazovaniya / YA.A.Turovskiy S.D.Kurgalin, A.A.Vahtin // Biomedicinskaya radioelektronika. – 2012. – ¹2. – pp.3945
Abstract 2. I. Koren, Computer Arithmetic Algorithms (Second ed.), A.K. Peters, Ltd. (Ed.), 2002. 3. Milic L. D., Lutovac M. D. Design of multiplierless elliptic IIR filters with a small quantization error. // IEEE Trans. Signal Proc. 1999. Vol. 47. ¹ 2. P. 469–479. 4. Lutovac M. D., Milic L.D. Approximate linear phase multiplierless IIR halfband filter. // IEEE Trans. Signal Proc. Lett. 2000. Vol. 7. ¹ 3. P. 52–53. 5. M. D. Lutovac and Lj. D. Milic, “Design of multiplierless elliptic IIR halfband filters and Hilbert transformers,” in Proc. EUSIPCO, ’98 Rodos, Greece, Sept. 1998, pp. 291–294. 6. YliKaakinen J., Saramaki T. An algorithm for the design of multiplierless approximately linearphase lattice wave digital filters. // ISCAS. 2000. May. P. 77–80. 7. Persson P., Nordebo S., Claesson I. A multimode mean field annealing technique to design recursive digital filters. // IEEE Trans. Circuits and Syst.: II. 2001. 8. YliKaakinen J., Saramaki T. A systematic algorithm for the design of multiplierless lattice wave digital filters. // ISCCSP. 2004. Mar. P. 393–396. 9. Milic L. D., Lutovac M. D. Efficient algorithm for the design of highspeed elliptic IIR filters. // Int. J. Electron. Commun. (AEU). 2003. Vol. 57. ¹ 4. P. 255–262. 10. Mingazin A.T. Sintez cifrovyh fil'trov na osnove fazovyh cepey s konechnoy dlinoy slova koefficientov. // II Mezhdunarodnaya konferenciya «Cifrovaya obrabotka signalov i ee primeneniya» (DSPA). 1999. T. 1. Sentyabr. pp. 112–116. 11. Mingazin A.T. Sintez polupolosnyh cifrovyh filtrov bez umnozhiteley na osnove fazovyh cepey. // VI Mezhdunarodnaya konferenciya «Cifrovaya obrabotka signalov i ee primeneniya» (DSPA). 2004. T. 1. Mart–Aprel. pp. 39–41. 12. Aleshin D.V. Algoritm sinteza celochislennyh umnozhiteley dlya cifrovyh KIHfiltrov. 9ya mezhdunarodnaya konferenciya "Cifrovaya obrabotka signalov i ee primenenie". DSPA2007. pp. 96 – 98. 13. Emmanuel Ifeachor, Barrie Jervis, 2nd Edition.Prentice Hall, 2001. 960 p. 14. Antoniou A. Digital filters: analysis and design. McGrawHill Science/Engineering/Math, 2000. 15. Bugrov V.N. Proektirovanie cifrovyh filtrov metodami celochislennogo nelineynogo programmirovaniya // Vestnik NNGU, 2009, ¹ 6. pp. 61 – 70. 16. Artem'ev V.V., Bugrov V.N. Sintez cifrovyh rekursivnyh filtrov s lineynoy fazoy // Komponenty i tekhnologii, 2013, ¹ 7. pp. 60 – 62. 17. Artem'ev V.V., Bugrov V.N., Proydakov V., SHkelev E.I., Celochislennye cifrovye filtry – effektivnoe reshenie dlya 8bitovyh cifrovyh platform // Komponenty i tekhnologii, 2013, ¹ 10. pp. 104 – 110.
Abstract To increase the PAPR reduction performance, we introduce a modified method of the TR technique and propose two combinational algorithms of the modified TR technique and the clippingandfiltering (CAF) method, as well as two reconfigurable filters to implement these algorithms on FPGA. In the first objective of the proposed filter configuration, the modified TR method suppresses simultaneously all peaks like CAF methods, while in the traditional TR method, the largest peak is reduced. The modified TR method extracts clipping noise on reserved subcarriers to generate an “antipeak” signal instead of using the impulselike kernel. This configuration of the filter does not introduce inband distortion and outofband radiation into the transmitted signal. Therefore, this filter configuration can be iteratively used to suppress significantly peaks of OFDM signals. After reconfiguring, the new filter configuration keeps the clipping noise on the data bearing subcarriers and resets to zero the frequency samples of the clipping noise associated with the reserved subcarrier indices. In this filter configuration, the CAF method is used. Therefore, clipping noise is added to the transmit signal. The proposed filters are based on the discrete Fourier transform (DFT)/ inverse DFT (IDFT) pair and finite impulse response (FIR) filters. Simulation results on Matlab show that the proposed algorithms significantly reduced PAPR after the first iteration and the signal peaks can achieve the desired threshold after 2–4 iterations. Both algorithms give similar results in terms of PAPR reduction capability, the expense of system interference MER and the increase in the mean power. FPGA implementation of the FFT/IFFTbased complex filter is suite for long OFDM symbols. It provides fast processing speed, low hardware resource utilisation and flexibility to reconfigure. The complex FIRfilter utilises great hardware resources, especially DSP48E1s. It gives a low processing delay. 2. J. Armstrong. New OFDM peaktoaverage power reduction scheme // Proc. IEEE, VTC2001 Spring, Rhodes, Greece, pp. 756–760, Aug. 2002. 3. ShangKang Deng , MaoChao Lin. Recursive Clipping and Filtering With Bounded Distortion for PAPR Reduction // IEEE Transactions on Communications, vol. 55, no. 1, pp. 227–230, Jan. 2007. 4. S. H. Muller and J. B. Huber. OFDM with reduced peak to average power ratio by optimum combination of partial transmit sequences // Electronics Letters, vol. 33, no. 5, pp. 368369 February 1997. 5. R. W. Bauml, R. F. H. Fischer, and J. B. Huber. Reducing the peaktoaverage power ratio of multicarrier modulation by selected mapping // IEEE Electronics Letters, vol. 32, no. 22, pp. 2056–2057, Sep. 1996. 6. 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. 7. V.P. Dvorkovich, A.V. Dvorkovich. Digital video information systems (theory and practice) // Moscow: Technosphere, 2012, 1008p. 8. B. S. Krongold and D. L. Jones. PAR reduction in OFDM via active constellation extension // IEEE Trans. Broadcast., vol. 49, no. 3, pp. 258–268, Sep. 2003. 9. K. Bae, J.G. Andrews, and E.J. Powers. Adaptive active constellation extension algorithm for peakto average ratio reduction in OFDM // IEEE Commun. Lett., vol. 14, no. 1, pp. 39–41, Jan. 2010. 10. J. Tellado. Peak to average power reduction for multicarrier modulation // Ph.D. dissertation, Stanford Univ., Stanford, CA, 2000. 11. Pg109. Fast Fourier Transform v9.0 // Xilinx LogiCORE IP Product Guide, 97p., Nov. 2015. 12. F. Dinechin, H. Takeugming, and J.M. Tanguy. A 128tap complex FIR filter Processing 20 gigasamples/s in a single FPGA // 2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers (ASILOMAR), Pacific Groove, CA, USA, pp. 841–844, Nov. 7–10, 2010. 13. Pg149. FIR Compiler v7.2 // Xilinx LogiCORE IP Product Guide, 131p, Nov. 2015. 14. H. Chen and M. Haimovish. Iterative Estimation and Cancellation of Clipping Noise for OFDM Signals // IEEE Commun. Lett., vol. 7, no. 7, pp. 305–307, July 2003.
Abstract Another choice is to linearize a nonlinear power amplifier so that overall we have a linear and reasonably effcient device. Digital predistortion is one of the most cost effective ways among all linearization techniques. However, most of the existing designs treat the power amplifier as a memoryless device. For wideband or high power applications, the power amplifier exhibits memory effects, for which memoryless predistorters can achieve only limited linearization performance. Presently there are many effective methods for nonlinearity compensation of digital radio signal power amplifier. In this paper we analyze several wellknown algorithms and propose a new variant of nonlinearity compensation of power amplifier. Computer simulation results confirms the effectiveness of the proposed method. 2. Eun, C. and Powers, E. J., “A new Volterra predistorter based on the indirect learning architecture,” IEEE Trans. Signal Processing, vol. 45, pp. 223–227, Jan. 1997. 3. Kang, H. W., Cho, Y. S., and Youn, D. H., “On compensating nolinear distortions of an OFDM system using effcient adaptive predistorter,” IEEE Trans. Commun., vol. 47, pp. 522–526, Apr. 1999. 4. Eskinat, E., Johnson, S. H., and Luyben, W. L., “Use of Hammerstein models in identification of nonlinear systems,” AIChE J., vol. 37, pp. 255–267, Feb. 1991. 5. Bai, E. W., “An optimal two stage identification algorithm for HammersteinWiener nonlinear systems,” in Proc. American Contr. Conf., pp. 2756–2760, June 1998. 6. Ding, L., Zhou, G. T., Morgan, D. R., Ma, Z., Kenney, J. S., Kim, J., and Giardina, C. R., “Memory polynomial predistorter based on the indirect learning architecture,” in Proc. IEEE Global Telecommun. Conf., pp. 967–971, Nov. 2002. If you have any question please write: info@dspa.ru
