Year 2023,
Volume: 5 Issue: 3, 141 - 152, 30.11.2023
Vyacheslav Rybin
,
Ivan Babkin
,
Dmitriy Kvitko
,
Timur Karimov
,
Lucas Nardo
,
Erivelton Nepomuceno
,
Denis Butusov
References
- Abib, G. A. and M. Eisencraft, 2015 On the performance of a digital
chaos-based communication system in noisy channels. IFACPapersOnLine
48: 976–981.
- Afraimovich, V., N. Verichev, and M. I. Rabinovich, 1986 Stochastic
synchronization of oscillation in dissipative systems. Radiophysics
and Quantum Electronics 29: 795–803.
- Alexander, P., S. Emiro˘ glu, S. Kanagaraj, A. Akgul, and K. Rajagopal,
2023 Infinite coexisting attractors in an autonomous hyperchaotic
megastable oscillator and linear quadratic regulatorbased
control and synchronization. The European Physical Journal
B 96: 12.
- Arslan, H. and S. Reddy, 2003 Noise power and snr estimation
for ofdm based wireless communication systems. In Proc. of 3rd
IASTED International Conference on Wireless and Optical Communications
(WOC), Banff, Alberta, Canada, pp. 1–6.
- Babajans, R., D. Cirjulina, F. Capligins, D. Kolosovs, J. Grizans,
et al., 2023 Performance analysis of vilnius chaos oscillator-based digital data transmission systems for iot. Electronics 12: 709.
- Babajans, R., D. Cirjulina, D. Kolosovs, and A. Litvinenko, 2022
Quadrature chaos phase shift keying communication system
based on vilnius chaos oscillator. In 2022 Workshop on Microwave
Theory and Techniques in Wireless Communications (MTTW), pp.
5–8, IEEE.
- Bai, C., H.-P. Ren, M. S. Baptista, and C. Grebogi, 2019 Digital
underwater communication with chaos. Communications in
Nonlinear Science and Numerical Simulation 73: 14–24.
- Bai, C., H.-P. Ren, C. Grebogi, and M. S. Baptista, 2018 Chaosbased
underwater communication with arbitrary transducers
and bandwidth. Applied Sciences 8: 162.
- Carroll, T. L. and L. M. Pecora, 1995 Synchronizing chaotic circuits.
In Nonlinear Dynamics in Circuits, pp. 215–248,World Scientific.
Cirjulina, D., R. Babajans, D. Kolosovs, and A. Litvinenko, 2022
- Experimental study on frequency modulated chaos shift keying
communication system. In 2022 Workshop on Microwave Theory
and Techniques inWireless Communications (MTTW), pp. 1–4, IEEE.
- Cordesses, L., 2004a Direct digital synthesis: A tool for periodic
wave generation (part 1). IEEE Signal processing magazine 21:
50–54.
- Cordesses, L., 2004b Direct digital synthesis: a tool for periodic
wave generation (part 2). IEEE Signal Processing Magazine 21:
110–112.
- Dedieu, H., M. P. Kennedy, and M. Hasler, 1993 Chaos shift keying:
modulation and demodulation of a chaotic carrier using selfsynchronizing
chua’s circuits. IEEE Transactions on Circuits and
Systems II: Analog and Digital Signal Processing 40: 634–642.
- Dmitriev, A. and A. Panas, 2002 Dynamic chaos: novel type of
information carrier for communication systems. Izdatel’stvo
Fiziko–matematicheskoj literatury 252.
- Emiroglu, S., A. Akgül, Y. Adıyaman, T. E. Gümü¸s, Y. Uyaroglu,
et al., 2022 A new hyperchaotic system from t chaotic system:
dynamical analysis, circuit implementation, control and synchronization.
Circuit World 48: 265–277.
- Fujisaka, H. and T. Yamada, 1983 Stability theory of synchronized
motion in coupled-oscillator systems. Progress of theoretical
physics 69: 32–47.
- Gaspard, P., 2005 Rössler systems. Encyclopedia of nonlinear science
231: 808–811.
- Hasan, A. N. and T. Shongwe, 2017 Impulse noise detection in
ofdm communication system using machine learning ensemble
algorithms. In International Joint Conference SOCO’16-CISIS’16-
ICEUTE’16: San Sebastián, Spain, October 19th-21st, 2016 Proceedings
11, pp. 85–91, Springer.
- Hedayatipour, A., R. Monani, A. Rezaei, M. Aliasgari, and
H. Sayadi, 2022 A comprehensive analysis of chaos-based secure
systems. In Silicon Valley Cybersecurity Conference: Second Conference,
SVCC 2021, San Jose, CA, USA, December 2–3, 2021, Revised
Selected Papers, pp. 90–105, Springer.
- Kaddoum, G., 2016 Wireless chaos-based communication systems:
A comprehensive survey. IEEE Access 4: 2621–2648.
- Kaddoum, G., M. Coulon, D. Roviras, and P. Chargé, 2010 Theoretical
performance for asynchronous multi-user chaos-based
communication systems on fading channels. Signal Processing
90: 2923–2933.
- Karimov, A., V. Rybin, E. Kopets, T. Karimov, E. Nepomuceno,
et al., 2023 Identifying empirical equations of chaotic circuit from
data. Nonlinear Dynamics 111: 871–886.
- Karimov, T., O. Druzhina, A. Karimov, A. Tutueva, V. Ostrovskii,
et al., 2021a Single-coil metal detector based on spiking chaotic
oscillator. Nonlinear Dynamics pp. 1–18.
- Karimov, T., V. Rybin, G. Kolev, E. Rodionova, and D. Butusov,
2021b Chaotic communication system with symmetry-based
modulation. Applied Sciences 11: 3698.
- Khan, A. M., V. Jeoti, M. Rehman, and M. Jilani, 2017 Noise
power estimation for broadcasting ofdm systems. In 2017 IEEE
30th Canadian Conference on Electrical and Computer Engineering
(CCECE), pp. 1–6.
- Kharel, R., 2011 Design and implementation of secure chaotic communication
systems. Ph.D. thesis, Northumbria University.
- Koronovskii, A. A., O. I. Moskalenko, and A. E. Hramov, 2009 On
the use of chaotic synchronization for secure communication.
Physics-Uspekhi 52: 1213.
- Liao, T.-l., 1998 Adaptive synchronization of two lorenz systems.
Chaos, Solitons & Fractals 9: 1555–1561.
- Liu, S.-H., D.-S.Wang, and L. Chen, 2007 Analysis of the ambiguity
characteristic of digital synthesis signals with chaotic frequency
modulation. ACTA ELECTONICA SINICA 35: 1784.
- Lukin, K. A. and O. V. Zemlyaniy, 2016 Digital generation of wideband
chaotic signal with the comb-shaped spectrum for communication
systems based on spectral manipulation. Radioelectronics
and Communications Systems 59: 417–422.
- Lyu, Y., L. Wang, G. Cai, and G. Chen, 2015 Iterative receiver for
m-ary dcsk systems. IEEE Transactions on Communications 63:
3929–3936.
- Minati, L., M. Frasca, P. Os´wiecimka, L. Faes, and S. Droz˙dz˙ , 2017
Atypical transistor-based chaotic oscillators: Design, realization,
and diversity. Chaos: An Interdisciplinary Journal of Nonlinear
Science 27: 073113.
- Moysis, L., C. Volos, I. Stouboulos, S. Goudos, S. Çiçek, et al.,
2020 A novel chaotic system with a line equilibrium: Analysis
and its applications to secure communication and random bit
generation. In Telecom, volume 1, pp. 283–296, MDPI.
- Pecora, L. M. and T. L. Carroll, 1990 Synchronization in chaotic
systems. Physical review letters 64: 821.
- Rajagopal, K., S. Çiçek, A. J. M. Khalaf, V.-T. Pham, S. Jafari, et al.,
2018 A novel class of chaotic flows with infinite equilibriums and
their application in chaos-based communication design using
dcsk. Zeitschrift Für Naturforschung A 73: 609–617.
- Rybin, V., D. Butusov, E. Rodionova, T. Karimov, V. Ostrovskii, et al.,
2022a Discovering chaos-based communications by recurrence
quantification and quantified return map analyses. International
Journal of Bifurcation and Chaos 32: 2250136.
- Rybin, V., T. Karimov, O. Bayazitov, D. Kvitko, I. Babkin, et al., 2023
Prototyping the symmetry-based chaotic communication system
using microcontroller unit. Applied Sciences 13: 936.
- Rybin, V., G. Kolev, E. Kopets, A. Dautov, A. Karimov, et al., 2022b
Optimal synchronization parameters for variable symmetry discrete
models of chaotic systems. In 2022 11th Mediterranean Conference
on Embedded Computing (MECO), pp. 1–5, IEEE.
- Rybin, V., A. Tutueva, T. Karimov, G. Kolev, D. Butusov, et al.,
2021 Optimizing the synchronization parameters in adaptive
models of rössler system. In 2021 10th Mediterranean Conference
on Embedded Computing (MECO), pp. 1–4, IEEE.
- Shannon, C. E., 1984 Communication in the presence of noise.
Proceedings of the IEEE 72: 1192–1201.
- Türkben, Ö. Ü. A. K. and V. S. A. Al-Akraa, 2022 Snr estimation in
communication systems using cognitive radio. In 2022 5th International
Conference on Engineering Technology and its Applications
(IICETA), pp. 477–481, IEEE.
- Tutueva, A., L. Moysis, V. Rybin, A. Zubarev, C. Volos, et al., 2022
Adaptive symmetry control in secure communication systems.
Chaos, Solitons & Fractals 159: 112181.
- Volos, C., I. Kyprianidis, and I. Stouboulos, 2013 Image encryption
process based on chaotic synchronization phenomena. Signal
Processing 93: 1328–1340.
- Voznesensky, A., D. Butusov, V. Rybin, D. Kaplun, T. Karimov,
et al., 2022 Denoising chaotic signals using ensemble intrinsic
time-scale decomposition. IEEE Access 10: 115767–115775.
- Wang, L., X. Mao, A. Wang, Y. Wang, Z. Gao, et al., 2020 Scheme of
coherent optical chaos communication. Optics Letters 45: 4762–
4765.
- Willsey, M. S., K. M. Cuomo, and A. V. Oppenheim, 2011 Quasiorthogonal
wideband radar waveforms based on chaotic systems.
IEEE Transactions on Aerospace and Electronic Systems
47: 1974–1984.
- Yang, T. and L. O. Chua, 1996 Secure communication via chaotic parameter
modulation. IEEE Transactions on Circuits and Systems
I: Fundamental Theory and Applications 43: 817–819.
- Yang, Z., L. Yi, J. Ke, Q. Zhuge, Y. Yang, et al., 2020 Chaotic optical
communication over 1000 km transmission by coherent
detection. Journal of Lightwave Technology 38: 4648–4655.
Estimating Optimal Synchronization Parameters for Coherent Chaotic Communication Systems in Noisy Conditions
Year 2023,
Volume: 5 Issue: 3, 141 - 152, 30.11.2023
Vyacheslav Rybin
,
Ivan Babkin
,
Dmitriy Kvitko
,
Timur Karimov
,
Lucas Nardo
,
Erivelton Nepomuceno
,
Denis Butusov
Abstract
It is known, that coherent chaotic communication systems are more vulnerable to noise in the transmission channel than conventional communications. Among the methods of noise impact reduction, such as extended symbol length and various digital filtering algorithms, the optimization of the synchronization coefficient may appear as a very efficient and simple straightforward approach. However, finding the optimal coefficient for the synchronization of two chaotic oscillators is a challenging task due to the high sensitivity of chaos to any disturbances. In this paper, we propose an algorithm for finding the optimal synchronization parameter K_opt for a coherent chaos-based communication system affected by various noises with different signal-to-noise ratios (SNR). It is shown, that under certain conditions, optimal $K$ provides the lowest possible bit error rate (BER) during the transmission. In addition, we show that various metrics applied to the message demodulation task propose different noise immunity to the overall system. For the experimental part of the study, we simulated and physically prototyped two chaotic communication systems based on well-known Rossler and Lorenz chaotic oscillators. The microcontroller-based prototype of a chaotic communication system was developed to investigate the influence of noise in the real transmission channel. The experimental results obtained using the designed hardware testbench are in good correspondence with the theoretical propositions of the study and simulation results. The suggested evaluation metrics and optimization algorithms can be used in the design of advanced chaos-based communication systems with increased performance.
References
- Abib, G. A. and M. Eisencraft, 2015 On the performance of a digital
chaos-based communication system in noisy channels. IFACPapersOnLine
48: 976–981.
- Afraimovich, V., N. Verichev, and M. I. Rabinovich, 1986 Stochastic
synchronization of oscillation in dissipative systems. Radiophysics
and Quantum Electronics 29: 795–803.
- Alexander, P., S. Emiro˘ glu, S. Kanagaraj, A. Akgul, and K. Rajagopal,
2023 Infinite coexisting attractors in an autonomous hyperchaotic
megastable oscillator and linear quadratic regulatorbased
control and synchronization. The European Physical Journal
B 96: 12.
- Arslan, H. and S. Reddy, 2003 Noise power and snr estimation
for ofdm based wireless communication systems. In Proc. of 3rd
IASTED International Conference on Wireless and Optical Communications
(WOC), Banff, Alberta, Canada, pp. 1–6.
- Babajans, R., D. Cirjulina, F. Capligins, D. Kolosovs, J. Grizans,
et al., 2023 Performance analysis of vilnius chaos oscillator-based digital data transmission systems for iot. Electronics 12: 709.
- Babajans, R., D. Cirjulina, D. Kolosovs, and A. Litvinenko, 2022
Quadrature chaos phase shift keying communication system
based on vilnius chaos oscillator. In 2022 Workshop on Microwave
Theory and Techniques in Wireless Communications (MTTW), pp.
5–8, IEEE.
- Bai, C., H.-P. Ren, M. S. Baptista, and C. Grebogi, 2019 Digital
underwater communication with chaos. Communications in
Nonlinear Science and Numerical Simulation 73: 14–24.
- Bai, C., H.-P. Ren, C. Grebogi, and M. S. Baptista, 2018 Chaosbased
underwater communication with arbitrary transducers
and bandwidth. Applied Sciences 8: 162.
- Carroll, T. L. and L. M. Pecora, 1995 Synchronizing chaotic circuits.
In Nonlinear Dynamics in Circuits, pp. 215–248,World Scientific.
Cirjulina, D., R. Babajans, D. Kolosovs, and A. Litvinenko, 2022
- Experimental study on frequency modulated chaos shift keying
communication system. In 2022 Workshop on Microwave Theory
and Techniques inWireless Communications (MTTW), pp. 1–4, IEEE.
- Cordesses, L., 2004a Direct digital synthesis: A tool for periodic
wave generation (part 1). IEEE Signal processing magazine 21:
50–54.
- Cordesses, L., 2004b Direct digital synthesis: a tool for periodic
wave generation (part 2). IEEE Signal Processing Magazine 21:
110–112.
- Dedieu, H., M. P. Kennedy, and M. Hasler, 1993 Chaos shift keying:
modulation and demodulation of a chaotic carrier using selfsynchronizing
chua’s circuits. IEEE Transactions on Circuits and
Systems II: Analog and Digital Signal Processing 40: 634–642.
- Dmitriev, A. and A. Panas, 2002 Dynamic chaos: novel type of
information carrier for communication systems. Izdatel’stvo
Fiziko–matematicheskoj literatury 252.
- Emiroglu, S., A. Akgül, Y. Adıyaman, T. E. Gümü¸s, Y. Uyaroglu,
et al., 2022 A new hyperchaotic system from t chaotic system:
dynamical analysis, circuit implementation, control and synchronization.
Circuit World 48: 265–277.
- Fujisaka, H. and T. Yamada, 1983 Stability theory of synchronized
motion in coupled-oscillator systems. Progress of theoretical
physics 69: 32–47.
- Gaspard, P., 2005 Rössler systems. Encyclopedia of nonlinear science
231: 808–811.
- Hasan, A. N. and T. Shongwe, 2017 Impulse noise detection in
ofdm communication system using machine learning ensemble
algorithms. In International Joint Conference SOCO’16-CISIS’16-
ICEUTE’16: San Sebastián, Spain, October 19th-21st, 2016 Proceedings
11, pp. 85–91, Springer.
- Hedayatipour, A., R. Monani, A. Rezaei, M. Aliasgari, and
H. Sayadi, 2022 A comprehensive analysis of chaos-based secure
systems. In Silicon Valley Cybersecurity Conference: Second Conference,
SVCC 2021, San Jose, CA, USA, December 2–3, 2021, Revised
Selected Papers, pp. 90–105, Springer.
- Kaddoum, G., 2016 Wireless chaos-based communication systems:
A comprehensive survey. IEEE Access 4: 2621–2648.
- Kaddoum, G., M. Coulon, D. Roviras, and P. Chargé, 2010 Theoretical
performance for asynchronous multi-user chaos-based
communication systems on fading channels. Signal Processing
90: 2923–2933.
- Karimov, A., V. Rybin, E. Kopets, T. Karimov, E. Nepomuceno,
et al., 2023 Identifying empirical equations of chaotic circuit from
data. Nonlinear Dynamics 111: 871–886.
- Karimov, T., O. Druzhina, A. Karimov, A. Tutueva, V. Ostrovskii,
et al., 2021a Single-coil metal detector based on spiking chaotic
oscillator. Nonlinear Dynamics pp. 1–18.
- Karimov, T., V. Rybin, G. Kolev, E. Rodionova, and D. Butusov,
2021b Chaotic communication system with symmetry-based
modulation. Applied Sciences 11: 3698.
- Khan, A. M., V. Jeoti, M. Rehman, and M. Jilani, 2017 Noise
power estimation for broadcasting ofdm systems. In 2017 IEEE
30th Canadian Conference on Electrical and Computer Engineering
(CCECE), pp. 1–6.
- Kharel, R., 2011 Design and implementation of secure chaotic communication
systems. Ph.D. thesis, Northumbria University.
- Koronovskii, A. A., O. I. Moskalenko, and A. E. Hramov, 2009 On
the use of chaotic synchronization for secure communication.
Physics-Uspekhi 52: 1213.
- Liao, T.-l., 1998 Adaptive synchronization of two lorenz systems.
Chaos, Solitons & Fractals 9: 1555–1561.
- Liu, S.-H., D.-S.Wang, and L. Chen, 2007 Analysis of the ambiguity
characteristic of digital synthesis signals with chaotic frequency
modulation. ACTA ELECTONICA SINICA 35: 1784.
- Lukin, K. A. and O. V. Zemlyaniy, 2016 Digital generation of wideband
chaotic signal with the comb-shaped spectrum for communication
systems based on spectral manipulation. Radioelectronics
and Communications Systems 59: 417–422.
- Lyu, Y., L. Wang, G. Cai, and G. Chen, 2015 Iterative receiver for
m-ary dcsk systems. IEEE Transactions on Communications 63:
3929–3936.
- Minati, L., M. Frasca, P. Os´wiecimka, L. Faes, and S. Droz˙dz˙ , 2017
Atypical transistor-based chaotic oscillators: Design, realization,
and diversity. Chaos: An Interdisciplinary Journal of Nonlinear
Science 27: 073113.
- Moysis, L., C. Volos, I. Stouboulos, S. Goudos, S. Çiçek, et al.,
2020 A novel chaotic system with a line equilibrium: Analysis
and its applications to secure communication and random bit
generation. In Telecom, volume 1, pp. 283–296, MDPI.
- Pecora, L. M. and T. L. Carroll, 1990 Synchronization in chaotic
systems. Physical review letters 64: 821.
- Rajagopal, K., S. Çiçek, A. J. M. Khalaf, V.-T. Pham, S. Jafari, et al.,
2018 A novel class of chaotic flows with infinite equilibriums and
their application in chaos-based communication design using
dcsk. Zeitschrift Für Naturforschung A 73: 609–617.
- Rybin, V., D. Butusov, E. Rodionova, T. Karimov, V. Ostrovskii, et al.,
2022a Discovering chaos-based communications by recurrence
quantification and quantified return map analyses. International
Journal of Bifurcation and Chaos 32: 2250136.
- Rybin, V., T. Karimov, O. Bayazitov, D. Kvitko, I. Babkin, et al., 2023
Prototyping the symmetry-based chaotic communication system
using microcontroller unit. Applied Sciences 13: 936.
- Rybin, V., G. Kolev, E. Kopets, A. Dautov, A. Karimov, et al., 2022b
Optimal synchronization parameters for variable symmetry discrete
models of chaotic systems. In 2022 11th Mediterranean Conference
on Embedded Computing (MECO), pp. 1–5, IEEE.
- Rybin, V., A. Tutueva, T. Karimov, G. Kolev, D. Butusov, et al.,
2021 Optimizing the synchronization parameters in adaptive
models of rössler system. In 2021 10th Mediterranean Conference
on Embedded Computing (MECO), pp. 1–4, IEEE.
- Shannon, C. E., 1984 Communication in the presence of noise.
Proceedings of the IEEE 72: 1192–1201.
- Türkben, Ö. Ü. A. K. and V. S. A. Al-Akraa, 2022 Snr estimation in
communication systems using cognitive radio. In 2022 5th International
Conference on Engineering Technology and its Applications
(IICETA), pp. 477–481, IEEE.
- Tutueva, A., L. Moysis, V. Rybin, A. Zubarev, C. Volos, et al., 2022
Adaptive symmetry control in secure communication systems.
Chaos, Solitons & Fractals 159: 112181.
- Volos, C., I. Kyprianidis, and I. Stouboulos, 2013 Image encryption
process based on chaotic synchronization phenomena. Signal
Processing 93: 1328–1340.
- Voznesensky, A., D. Butusov, V. Rybin, D. Kaplun, T. Karimov,
et al., 2022 Denoising chaotic signals using ensemble intrinsic
time-scale decomposition. IEEE Access 10: 115767–115775.
- Wang, L., X. Mao, A. Wang, Y. Wang, Z. Gao, et al., 2020 Scheme of
coherent optical chaos communication. Optics Letters 45: 4762–
4765.
- Willsey, M. S., K. M. Cuomo, and A. V. Oppenheim, 2011 Quasiorthogonal
wideband radar waveforms based on chaotic systems.
IEEE Transactions on Aerospace and Electronic Systems
47: 1974–1984.
- Yang, T. and L. O. Chua, 1996 Secure communication via chaotic parameter
modulation. IEEE Transactions on Circuits and Systems
I: Fundamental Theory and Applications 43: 817–819.
- Yang, Z., L. Yi, J. Ke, Q. Zhuge, Y. Yang, et al., 2020 Chaotic optical
communication over 1000 km transmission by coherent
detection. Journal of Lightwave Technology 38: 4648–4655.