Abstract
Due to the inherent noise-like characteristic of chaotic signals and their sensitivity to the initial value, chaotic direct sequence spread spectrum (CD3S) signals have the advantages of a low probability of intercept (LPI) and a high level of security. Demodulation of non-cooperated CD3S signals is then a challenging issue. If the signal is sent though multipath channels, it is even more difficult for the receiver to demodulate it blindly. Based on the existing theories and methods, we focus more on signals passing through multipath channels. This paper presents an approach to achieve blind equalization and demodulation of CD3S signals through multipath channels. Multiple unscented Kalman filters (UKFs) are used to equalize and demodulate the CD3S signals for the unknown channel. This method can effectively demodulate the signals without any knowledge of the chaotic transmitter’s parameters, initial value, state equation, or the channel coefficients, even when the signal is severely distorted by the multipath channel. Simulation results demonstrate that this method gives faster convergence and better demodulation performance than existing methods for various channel conditions.
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References
S. Azou, C. Pistre, L. Duff, G. Burel, Sea trial results of a chaotic direct sequence spread spectrum under water communication system, in IEEE-OCEANS’03, San Diego, CA (2003)
L. Bai, J. Guo, Breakability of chaotic direct sequence spreading spectrum secure system under multi-path fading channel. Acta Phys. Sin. 60(7), 070504 (2011)
C. Chi, C. Feng, C. Chen, C. Chen, Blind Equalization and System Identification: Batch Processing Algorithm, Performance and Applications (Springer, Berlin, 2006)
K.M. Cuomo, A.V. Oppenheim, S.H. Strogatz, Synchronization of Lorenz-based chaotic circuits with applications to communications. IEEE Trans. Circuits Syst. II 40(10), 626–633 (1993)
H. Dedieu, M.P. Kennedy, M. Hasler, Chaos shift keying: modulation and demodulation of a chaotic carrier using self-synchronizing Chua’s circuits. IEEE Trans. Circuits Syst. II 40(10), 634–642 (1993)
G. Heidari-Bateni, C.D. McGillem, A chaotic direct sequence spread spectrum communication system. IEEE Trans. Commun. 42(2–4), 1524–1527 (1994)
J. Hu, J. Guo, Breaking a chaotic secure communication scheme. Chaos 18, 013121 (2008)
R. Johnson Jr., P. Schniter, T. Endres, J. Behm, D. Brown, R. Casas, Blind equalization using the constant modulus criterion: a review. Proc. IEEE 86(10), 1927–1950 (1998)
S.J. Julier, J.K. Uhlmann, A new extension of the Kalman filter to nonlinear systems, in Proc. of AeroSense: The 11th Int. Symp. A.D.S.S.C, (1997)
G. Kolumban, M.P. Kennedy, L.O. Chua, The role of synchronization in digital communications using chaos-Part II: chaotic modulation and chaotic synchronization. IEEE Trans. Circuits Syst. I 45(4), 1129–1140 (1998)
H. Leung, J. Lam, Design of demodulator for the chaotic modulation communication system. IEEE Trans. Circuits Syst. I 44(3), 262–267 (1997)
H. Leung, H. Yu, K. Murali, Ergodic chaos-based communication schemes. Phys. Rev. E 66(3), 036203 (2002)
M.B. Luca, S. Azou, E. Hodina, Pseudo-blind demodulation of chaotic DSSS signals through exact Kalman filtering, in IEEE Communications Conf., Bucharest, Romania (2006)
K. Murali, H. Leung, H. Yu, Design of noncoherent receiver for analog spread-spectrum communication based on chaotic masking. IEEE Trans. Circuits Syst. I 50(3), 432–441 (2003)
U. Parlitz, S. Ergezinger, Robust communication based on chaotic spreading sequences. Phys. Lett. A 188(2), 146–150 (1994)
L.M. Pecora, T.L. Carroll, Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821–824 (1990)
D.N. Vizireanu, R.O. Preda, Is “five-point” estimation better than “three-point” estimation? Measurement 46(1), 840–842 (2013)
F. Wang, Z. Wang, J. Guo, Extracting weak harmonic signals from strong chaotic interference. Circuits Syst. Signal Process. 21(4), 427–448 (2002)
K. Xiong, H. Zhang, C. Chan, Performance evaluation of UKF-based nonlinear filtering. Automatica 42, 261–270 (2006)
X. Xu, J. Guo, A novel unified equalization and demodulation of chaotic direct sequence spread spectrum signal based on state estimation. Acta Phys. Sin. 60(2), 020510 (2011)
T. Yang, L. Yang, C. Yang, Breaking chaotic switching using generalized synchronization: examples. IEEE Trans. Circuits Syst. I 45(10), 1062–1067 (1998)
T. Yang, L.O. Chua, Secure communication via chaotic parameter communication. IEEE Trans. Circuits Syst. I 43(9), 817–819 (1996)
H. Zhao, J. Zhang, P. Zeng, Adaptive neural Legendre orthogonal polynomial nonlinear channel equalization for chaos-based communications systems. Acta Phys. Sin. 56(4), 1975–1982 (2007)
H. Zhao, J. Zhang, Adaptive nonlinear channel equalization based on combination neural network for chaos-based communication systems. Acta Phys. Sin. 57(7), 3996–4006 (2008)
Z. Zhu, H. Leung, Adaptive blind equalization for chaotic communication systems using extended-Kalman filter. IEEE Trans. Circuits Syst. I 48(8), 979–989 (2001)
Z. Zhu, H. Leung, Combined demodulation with adaptive blind-channel equalization for chaotic-modulation communication systems. IEEE Trans. Circuits Syst. I 49(12), 1811–1820 (2002)
Z. Zhu, H. Leung, Channel equalization and timing recovery technique for chaotic communications systems, in ISCAS, Seoul, Korea (2012)
Acknowledgements
This work was partially supported by the National Natural Science Foundation of China (Grant No. 51277100) and the State Key Laboratory of Control and Simulation of Power System and Generation Equipments, Tsinghua University, China (Grant No. SKLD09M25).
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Xu, X., Guo, J. Combined Equalization and Demodulation of Chaotic Direct Sequence Spread Spectrum Signals for Multipath Channels. Circuits Syst Signal Process 32, 2957–2969 (2013). https://doi.org/10.1007/s00034-013-9599-y
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DOI: https://doi.org/10.1007/s00034-013-9599-y