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FPAA DESIGN OF FRACTIONAL CHAOS BASED COMMUNICATION SYSTEMS

Year 2023, Volume: 26 Issue: 1, 191 - 202, 15.03.2023

Gökçenur Kaya , Kenan Altun

https://doi.org/10.17780/ksujes.1194619

Abstract

Chaotic signals are difficult to predict signals that have an order in themselves but exhibit disordered behavior. One of the most important usage areas of chaotic signals is secure communication systems. The reliability of the communication system depends on the complexity of the chaotic signal. Communication systems are implemented with many methods that increase the complexity of chaotic signals. It has increased the reliability of the system rather than increasing the BER/SNR performance of these methods. It is thought that fractional chaotic signals may have a positive effect on increasing both communication reliability and BER/SNR performance in chaos-based communication systems. For this reason, numerical analysis of the dynamic system was carried out by computer simulation of the BER/SNR performance of fractional chaotic based communication systems. In addition, the simulation was repeated experimentally using analog based FPAA structures. The obtained simulation and experimental results were compared with similar studies of integer-order.

Keywords

chaotic communication fractional analysis FPAA bit error rate

References

  • Abdullah, H. N., & Valenzuela, A. A. (2011). Performance evaluation of FM-COOK chaotic communication system. Journal of Signal and Information Processing, 2(3), 175-177.
  • Altun, K. (2021). FPAA implementations of fractional-order chaotic systems. Journal of Circuits, Systems and Computers, 30(15), 2150271.
  • Baccigalupi, A., & Liccardo, A. (2007). Field programmable analog arrays for conditioning ultrasonic sensors. IEEE Sensors Journal, 7(8), 1176-1182.
  • Chua, L. O., & Yang, L. (1988). Cellular neural networks: Theory. IEEE Transactions on Circuits and Systems, 35(10), 1257-1272.
  • Chua, L. O., Desoer, C. A., & Kuh, E. S. (1987). Linear and nonlinear circuits. McGraw-Hill College. Cuomo, K. M., Oppenheim, A. V., & Strogatz, S. H. (1993). Synchronization of Lorenz-based chaotic circuits with applications to communications. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 40(10), 626-633.
  • Dedieu, H., Kennedy, M. P., & Hasler, M. (1993). Chaos shift keying: modulation and demodulation of a chaotic carrier using self-synchronizing Chua's circuits. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 40(10), 634-642.
  • Günay, E., & Altun, K. (2017). A performance comparison study of programmable platforms: FPAA and FPGA implementation of COOK communication system. In 2017 European Conference on Circuit Theory and Design (ECCTD).
  • Günay, E., & Altun, K. (2018). Switched state controlled-CNN: an alternative approach in generating complex systems with multivariable nonlinearities using CNN. International Journal of Bifurcation and Chaos, 28(06), 1830019.
  • Hall, T. S., Twigg, C. M., Gray, J. D., Hasler, P., & Anderson, D. V. (2005). Large-scale field-programmable analog arrays for analog signal processing. IEEE Transactions on Circuits and Systems I: Regular Papers, 52(11), 2298-2307.
  • Hasler, J., & Shah, S. (2017). VMM+ WTA embedded classifiers learning algorithm implementable on SoC FPAA devices. IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 8(1), 65-76.
  • Herzallah, M. A. (2014). Notes on some fractional calculus operators and their properties. J. Fract. Calc. Appl, 5(19), 1-10.
  • Holmes, P. (1990). Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports, 193(3), 137-163.
  • Jin, Y., Chen, Y. Q., & Xue, D. (2011). Time-constant robust analysis of a fractional order [proportional derivative] controller. IET Control Theory & Applications, 5(1), 164-172.
  • Kennedy, M. P., & Kolumban, G. (2000). Digital communications using chaos. Signal Processing, 80(7), 1307-1320.
  • Kolumbán, G. (1997). Performance improvement of chaotic communication systems. In Proc. ECCTD'97 (pp. 284-289).
  • Kolumbán, G., Kennedy, M. P., & Chua, L. O. (1998). The role of synchronization in digital communications using chaos. II. Chaotic modulation and chaotic synchronization. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 45(11), 1129-1140.
  • Kolumbán, G., Vizvári, B., Schwarz, W., & Abel, A. (1996). Differential chaos shift keying: A robust coding for chaos communication. In Proc. NDES (Vol. 96, pp. 87-92).
  • Koziol, S. (2020). Multi-Objective Path Planning for Autonomous Robots Using Reconfigurable Analog VLSI. IEEE Access, 8, 80134-80147.
  • Li, C. B., Thio, W. J. C., Sprott, J. C., Zhang, R. X., & Lu, T. A. (2017). Linear synchronization and circuit implementation of chaotic system with complete amplitude control. Chinese Physics B, 26(12), 120501. Linsay, P. S. (1981). Period doubling and chaotic behavior in a driven anharmonic oscillator. Physical Review Letters, 47(19), 1349.
  • Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of Atmospheric Sciences, 20(2), 130-141. Ma, S., Zheng, J., & Li, Y. (2014). Chaos control and synchronization of a new fractional order chaotic system. Journal of Informatıon &Computatıonal Scıence, 11(10), 3469-3479.
  • Moreno, D. G., Del Barrio, A. A., Botella, G., & Hasler, J. (2021). A cluster of FPAAs to recognize images using neural networks. IEEE Transactions on Circuits and Systems II: Express Briefs, 68(11), 3391-3395.
  • Nishimoto, K. (1984). Fractional Calculus, Decartess Press, Koriama.
  • Oldham, K., & Spanier, J. (1974). The fractional calculus theory and applications of differentiation and integration to arbitrary order. Elsevier.
  • Ott, E., Grebogi, C., & Yorke, J. A. (1990). Controlling chaos. Physical Review Letters, 64(11), 1196.
  • Oustaloup, A., Levron, F., Mathieu, B., & Nanot, F. M. (2000). Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 47(1), 25-39.
  • Parlitz, U., Chua, L. O., Kocarev, L., Halle, K. S., & Shang, A. (1992). Transmission of digital signals by chaotic synchronization. International Journal of Bifurcation and Chaos, 2(04), 973-977.
  • Pecora, L. M., & Carroll, T. L. (1990). Synchronization in chaotic systems. Physical Review Letters, 64(8), 821. Peitgen, H. O., Jürgens, H., Saupe, D., & Feigenbaum, M. J. (1992). Chaos and fractals: new frontiers of science (Vol. 7). New York: Springer.
  • Petráš, I. (2011). Fractional-order nonlinear systems: modeling, analysis and simulation. Springer Science & Business Media.
  • Petráš, I., & Bednárová, D. (2011). Control of fractional-order nonlinear systems: A review. Acta Mechanica et Automatica, 5(2), 96-100.
  • Podlubny, I. (1999). Fractional differential equations. Mathematics in Science and Engineering, 198, 41-119. Salih, T. A. (2021). Design and Implementation of a Low Power Consumption of ASK, FSK PSK, and QSK Modulators Based on FPAA Technology, Int. J. Adv. Sci. Eng. Inf. Technol., 11(4), 1288.
  • Schlottmann, C. R., & Hasler, J. (2013). High-level modeling of analog computational elements for signal processing applications. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 22(9), 1945-1953. Sprott J. C., (1994). Some simple chaotic flows. Physical Review E, 50(2):R647.
  • Sushchik, M., Tsimring, L. S., & Volkovskii, A. R. (2000). Performance analysis of correlation-based communication schemes utilizing chaos. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 47(12), 1684-1691.
  • Tolba, M. F., Said, L. A., Madian, A. H., & Radwan, A. G. (2018). FPGA implementation of the fractional order integrator/differentiator: Two approaches and applications. IEEE Transactions on Circuits and Systems I: Regular Papers, 66(4), 1484-1495.
  • Udita, N. K. (2014). A new approach to generalized fractional derivatives. Bulletin of Mathematical Analysis and Applications, 6(4), 1-15.
  • Yong, Y. K., Bhikkaji, B., & Moheimani, S. R. R. (2012). Design, modeling, and FPAA-based control of a high-speed atomic force microscope nanopositioner. IEEE/ASME Transactions on Mechatronics, 18(3), 1060-1071.

KESİR DERECELİ KAOS TABANLI HABERLEŞME SİSTEMLERİNİN FPAA TASARIMI

Year 2023, Volume: 26 Issue: 1, 191 - 202, 15.03.2023

Gökçenur Kaya , Kenan Altun

https://doi.org/10.17780/ksujes.1194619

Abstract

Kaotik sinyaller kendi içerisinde bir düzeni olan ancak düzensiz davranış sergileyen tahmin edilmesi zor sinyallerdir. Kaotik sinyallerin en önemli kullanım alanlarından biri güvenli haberleşme sistemleridir. Haberleşme sisteminin güvenilirliği kaotik işaretin karmaşıklığına bağlıdır. Kaotik sinyallerin karmaşıklığını artıran birçok yöntem ile haberleşme sistemleri gerçekleştirilmektedir. Bu yöntemlerin BER/SNR performansına artırmaktan çok sistemin güvenilirliğini artırmıştır. Kesir dereceli kaotik sinyallerin kaos tabanlı haberleşme sistemlerinde hem haberleşme güvenilirliğinin hem BER/SNR performansının artmasına olumlu etkisi olabileceği düşünülmektedir. Bu nedenle çalışmada kesir dereceli kaotik tabanlı haberleşme sistemlerinin BER/SNR performansının bilgisayar benzetimi ile dinamik sistemin nümerik analizi gerçekleştirilmiştir. Ayrıca benzetim analog tabanlı FPAA yapılar kullanılarak deneysel olarak tekrarlanmıştır. Elde edilen benzetim ve deneysel sonuçlar tam dereceli benzer çalışmalarla karşılaştırılmıştır.

Keywords

Kaotik Haberleşme Kesir Dereceli Analiz FPAA Bit Hata Oranı

References

  • Abdullah, H. N., & Valenzuela, A. A. (2011). Performance evaluation of FM-COOK chaotic communication system. Journal of Signal and Information Processing, 2(3), 175-177.
  • Altun, K. (2021). FPAA implementations of fractional-order chaotic systems. Journal of Circuits, Systems and Computers, 30(15), 2150271.
  • Baccigalupi, A., & Liccardo, A. (2007). Field programmable analog arrays for conditioning ultrasonic sensors. IEEE Sensors Journal, 7(8), 1176-1182.
  • Chua, L. O., & Yang, L. (1988). Cellular neural networks: Theory. IEEE Transactions on Circuits and Systems, 35(10), 1257-1272.
  • Chua, L. O., Desoer, C. A., & Kuh, E. S. (1987). Linear and nonlinear circuits. McGraw-Hill College. Cuomo, K. M., Oppenheim, A. V., & Strogatz, S. H. (1993). Synchronization of Lorenz-based chaotic circuits with applications to communications. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 40(10), 626-633.
  • Dedieu, H., Kennedy, M. P., & Hasler, M. (1993). Chaos shift keying: modulation and demodulation of a chaotic carrier using self-synchronizing Chua's circuits. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 40(10), 634-642.
  • Günay, E., & Altun, K. (2017). A performance comparison study of programmable platforms: FPAA and FPGA implementation of COOK communication system. In 2017 European Conference on Circuit Theory and Design (ECCTD).
  • Günay, E., & Altun, K. (2018). Switched state controlled-CNN: an alternative approach in generating complex systems with multivariable nonlinearities using CNN. International Journal of Bifurcation and Chaos, 28(06), 1830019.
  • Hall, T. S., Twigg, C. M., Gray, J. D., Hasler, P., & Anderson, D. V. (2005). Large-scale field-programmable analog arrays for analog signal processing. IEEE Transactions on Circuits and Systems I: Regular Papers, 52(11), 2298-2307.
  • Hasler, J., & Shah, S. (2017). VMM+ WTA embedded classifiers learning algorithm implementable on SoC FPAA devices. IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 8(1), 65-76.
  • Herzallah, M. A. (2014). Notes on some fractional calculus operators and their properties. J. Fract. Calc. Appl, 5(19), 1-10.
  • Holmes, P. (1990). Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports, 193(3), 137-163.
  • Jin, Y., Chen, Y. Q., & Xue, D. (2011). Time-constant robust analysis of a fractional order [proportional derivative] controller. IET Control Theory & Applications, 5(1), 164-172.
  • Kennedy, M. P., & Kolumban, G. (2000). Digital communications using chaos. Signal Processing, 80(7), 1307-1320.
  • Kolumbán, G. (1997). Performance improvement of chaotic communication systems. In Proc. ECCTD'97 (pp. 284-289).
  • Kolumbán, G., Kennedy, M. P., & Chua, L. O. (1998). The role of synchronization in digital communications using chaos. II. Chaotic modulation and chaotic synchronization. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 45(11), 1129-1140.
  • Kolumbán, G., Vizvári, B., Schwarz, W., & Abel, A. (1996). Differential chaos shift keying: A robust coding for chaos communication. In Proc. NDES (Vol. 96, pp. 87-92).
  • Koziol, S. (2020). Multi-Objective Path Planning for Autonomous Robots Using Reconfigurable Analog VLSI. IEEE Access, 8, 80134-80147.
  • Li, C. B., Thio, W. J. C., Sprott, J. C., Zhang, R. X., & Lu, T. A. (2017). Linear synchronization and circuit implementation of chaotic system with complete amplitude control. Chinese Physics B, 26(12), 120501. Linsay, P. S. (1981). Period doubling and chaotic behavior in a driven anharmonic oscillator. Physical Review Letters, 47(19), 1349.
  • Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of Atmospheric Sciences, 20(2), 130-141. Ma, S., Zheng, J., & Li, Y. (2014). Chaos control and synchronization of a new fractional order chaotic system. Journal of Informatıon &Computatıonal Scıence, 11(10), 3469-3479.
  • Moreno, D. G., Del Barrio, A. A., Botella, G., & Hasler, J. (2021). A cluster of FPAAs to recognize images using neural networks. IEEE Transactions on Circuits and Systems II: Express Briefs, 68(11), 3391-3395.
  • Nishimoto, K. (1984). Fractional Calculus, Decartess Press, Koriama.
  • Oldham, K., & Spanier, J. (1974). The fractional calculus theory and applications of differentiation and integration to arbitrary order. Elsevier.
  • Ott, E., Grebogi, C., & Yorke, J. A. (1990). Controlling chaos. Physical Review Letters, 64(11), 1196.
  • Oustaloup, A., Levron, F., Mathieu, B., & Nanot, F. M. (2000). Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 47(1), 25-39.
  • Parlitz, U., Chua, L. O., Kocarev, L., Halle, K. S., & Shang, A. (1992). Transmission of digital signals by chaotic synchronization. International Journal of Bifurcation and Chaos, 2(04), 973-977.
  • Pecora, L. M., & Carroll, T. L. (1990). Synchronization in chaotic systems. Physical Review Letters, 64(8), 821. Peitgen, H. O., Jürgens, H., Saupe, D., & Feigenbaum, M. J. (1992). Chaos and fractals: new frontiers of science (Vol. 7). New York: Springer.
  • Petráš, I. (2011). Fractional-order nonlinear systems: modeling, analysis and simulation. Springer Science & Business Media.
  • Petráš, I., & Bednárová, D. (2011). Control of fractional-order nonlinear systems: A review. Acta Mechanica et Automatica, 5(2), 96-100.
  • Podlubny, I. (1999). Fractional differential equations. Mathematics in Science and Engineering, 198, 41-119. Salih, T. A. (2021). Design and Implementation of a Low Power Consumption of ASK, FSK PSK, and QSK Modulators Based on FPAA Technology, Int. J. Adv. Sci. Eng. Inf. Technol., 11(4), 1288.
  • Schlottmann, C. R., & Hasler, J. (2013). High-level modeling of analog computational elements for signal processing applications. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 22(9), 1945-1953. Sprott J. C., (1994). Some simple chaotic flows. Physical Review E, 50(2):R647.
  • Sushchik, M., Tsimring, L. S., & Volkovskii, A. R. (2000). Performance analysis of correlation-based communication schemes utilizing chaos. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 47(12), 1684-1691.
  • Tolba, M. F., Said, L. A., Madian, A. H., & Radwan, A. G. (2018). FPGA implementation of the fractional order integrator/differentiator: Two approaches and applications. IEEE Transactions on Circuits and Systems I: Regular Papers, 66(4), 1484-1495.
  • Udita, N. K. (2014). A new approach to generalized fractional derivatives. Bulletin of Mathematical Analysis and Applications, 6(4), 1-15.
  • Yong, Y. K., Bhikkaji, B., & Moheimani, S. R. R. (2012). Design, modeling, and FPAA-based control of a high-speed atomic force microscope nanopositioner. IEEE/ASME Transactions on Mechatronics, 18(3), 1060-1071.
There are 35 citations in total.

Details

Primary Language Turkish
Subjects Electrical Engineering
Journal Section Electrical and Electronics Engineering
Authors

Gökçenur Kaya 0000-0001-5768-4659

Kenan Altun 0000-0001-7419-1901

Publication Date March 15, 2023
Submission Date October 25, 2022
Published in Issue Year 2023Volume: 26 Issue: 1

Cite

APA Kaya, G., & Altun, K. (2023). KESİR DERECELİ KAOS TABANLI HABERLEŞME SİSTEMLERİNİN FPAA TASARIMI. Kahramanmaraş Sütçü İmam Üniversitesi Mühendislik Bilimleri Dergisi, 26(1), 191-202. https://doi.org/10.17780/ksujes.1194619
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