Complex-Valued Neural Networks for Blind Equalization of Time-Varying Channels
Most of the commonly used blind equalization algorithms are based on the minimization of a nonconvex and nonlinear cost function and a neural network gives smaller residual error as compared to a linear structure. The efficacy of complex valued feedforward neural networks for blind equalization of linear and nonlinear communication channels has been confirmed by many studies. In this paper we present two neural network models for blind equalization of time-varying channels, for M-ary QAM and PSK signals. The complex valued activation functions, suitable for these signal constellations in time-varying environment, are introduced and the learning algorithms based on the CMA cost function are derived. The improved performance of the proposed models is confirmed through computer simulations.
[1] J. G. Proakis, Digital Communications. Third Edition, Singapore,
McGraw Hill, 1995.
[2] S. Haykin (Editor). Blind Deconvolution. Englewood Cliffs, New
Jersey: Prentice-Hall, 1994.
[3] S. I. Amari and A. Cichocki, "Adaptive blind signal processing - Neural
network approaches," Proceedings of IEEE, vol. 86, no. 10, pp. 2026 -
2048, Oct. 1998.
[4] T. W. S. Chow and Y. Fang, "Neural blind deconvolution of MIMO
noisy channels," IEEE Trans. Circuits and Systems-I, vol. 48, no. 1, pp.
116 - 120, Jan. 2001.
[5] H. Lin and M. Amin, "A dual mode technique for improved blind
equalization for QAM signals," IEEE Signal Processing Letters, vol.
10, no. 2, pp. 29 - 31, Feb. 2003.
[6] N. Thirion Moreau and E. Moreau, "Generalized criterion for blind
multivariate signal equalization," IEEE Signal Processing Letters, vol.
9, no. 2, pp. 72 - 74, Feb. 2002.
[7] J. B. Destro Filho, G. Favier and J. M. Travassos Romano, "Neural
networks for blind equalization," Proceedings of IEEE Globcom, 1996,
pp. 196 - 200.
[8] Y. Fang and T. W. S. Chow, "Blind equalization of a noisy channel by
linear neural network," IEEE Trans. Neural Networks, vol. 10, no. 4,
pp. 925 - 929, July 1999.
[9] R. Pandey, "Blind equalization and signal separation using neural
networks," Ph. D. thesis, I.I.T. Roorkee, India, 2001.
[10] S. Haykin, Adaptive Filter Theory, Third Edition. Upper Saddel River,
New Jersey: Prentice Hall, 1996.
[11] M. Ghosh, "Blind decision feedback equalization for terrestrial
television receivers," Proceedings of IEEE, vol. 86, no. 10, pp. 2070 -
2081, Oct. 1998.
[12] J. Labat, O. Macchi and C. Laot, "Adaptive decision feedback
equalization: Can you skip the training period?," IEEE Trans.
Communications, vol. 46, no. 7, pp. 921 - 930, July 1998.
[13] C. You and D. Hong, "Nonlinear blind equalization schemes using
complex valued multilayer feedforward neural networks," IEEE Trans.
Neural Networks, vol. 9, no. 6, pp. 1442 - 1455, Nov. 1998.
[14] A. Cichocki, R. Unbehauen, Neural Networks for Optimization and
Signal Processing, Chichester: John Wiley & Sons, 1994.
[15] S. Haykin, Neural Networks: A Comprehensive Foundation, Upper
Saddle River, New Jersey: Prentice -Hall, 1994.
[16] F. L. Luo, and R. Unbehauen, Applied Neural Networks for Signal
Processing, Cambridge: University Press, 1997.
[17] S. Haykin, Neural networks expand SP-s horizons, IEEE Signal
Processing Magazine, issue 3, pp. 24 - 49, 1996.
[18] G. Kechriotis, E. Zervas and E. S. Manolakos, "Using recurrent neural
networks for adaptive communication channel equalization," IEEE
Trans. Neural Networks, vol. 5, no. 2, pp. 267 - 278, March 1994.
[19] R. Parisi, C. D. Di Elio, G. Orlandi and B. D. Rao, "Fast adaptive
digital equalization by recurrent neural network," IEEE Trans. Signal
Processing, vol. 45, no. 11, pp. 2731 - 2739, Nov. 1997.
[20] S. Ong, C. You, S. Choi and D. Hong, "A decision feedback recurrent
neural equalizer as an infinite impulse response filter," IEEE Trans.
Signal Processing, vol. 45, no. 11, pp. 2851 - 2858, Nov. 1997.
[21] N. Benvenuto and F.Piazza, "On the complex backpropagation
algorithm," IEEE Trans. Signal Processing, vol. 40, pp. 967 - 969, Apr.
1992.
[22] C. R. Johnson Jr. et al., "Blind equalization using the constant modulus
criterion: A review," Proceedings of IEEE, vol. 86, no. 10, pp. 1927 -
1950, Oct. 1998.
[23] T. J. Endres, B. D. O. Anderson, C. R. Johnson Jr. and M. Green,
"Robustness to fractionally-spaced equalizer length using the Constant
Modulus Criterion," IEEE Trans. Signal Processing, vol. 47, no. 2, pp.
544 - 548, Feb. 1999.
[24] P. Schniter and C. R. Johnson Jr., "Dithered signed error CMA: Robust,
computationally efficient blind adaptive equalization," IEEE Trans.
Signal Processing, vol. 47, no. 6, pp. 1592 - 1603, June 1999.
[1] J. G. Proakis, Digital Communications. Third Edition, Singapore,
McGraw Hill, 1995.
[2] S. Haykin (Editor). Blind Deconvolution. Englewood Cliffs, New
Jersey: Prentice-Hall, 1994.
[3] S. I. Amari and A. Cichocki, "Adaptive blind signal processing - Neural
network approaches," Proceedings of IEEE, vol. 86, no. 10, pp. 2026 -
2048, Oct. 1998.
[4] T. W. S. Chow and Y. Fang, "Neural blind deconvolution of MIMO
noisy channels," IEEE Trans. Circuits and Systems-I, vol. 48, no. 1, pp.
116 - 120, Jan. 2001.
[5] H. Lin and M. Amin, "A dual mode technique for improved blind
equalization for QAM signals," IEEE Signal Processing Letters, vol.
10, no. 2, pp. 29 - 31, Feb. 2003.
[6] N. Thirion Moreau and E. Moreau, "Generalized criterion for blind
multivariate signal equalization," IEEE Signal Processing Letters, vol.
9, no. 2, pp. 72 - 74, Feb. 2002.
[7] J. B. Destro Filho, G. Favier and J. M. Travassos Romano, "Neural
networks for blind equalization," Proceedings of IEEE Globcom, 1996,
pp. 196 - 200.
[8] Y. Fang and T. W. S. Chow, "Blind equalization of a noisy channel by
linear neural network," IEEE Trans. Neural Networks, vol. 10, no. 4,
pp. 925 - 929, July 1999.
[9] R. Pandey, "Blind equalization and signal separation using neural
networks," Ph. D. thesis, I.I.T. Roorkee, India, 2001.
[10] S. Haykin, Adaptive Filter Theory, Third Edition. Upper Saddel River,
New Jersey: Prentice Hall, 1996.
[11] M. Ghosh, "Blind decision feedback equalization for terrestrial
television receivers," Proceedings of IEEE, vol. 86, no. 10, pp. 2070 -
2081, Oct. 1998.
[12] J. Labat, O. Macchi and C. Laot, "Adaptive decision feedback
equalization: Can you skip the training period?," IEEE Trans.
Communications, vol. 46, no. 7, pp. 921 - 930, July 1998.
[13] C. You and D. Hong, "Nonlinear blind equalization schemes using
complex valued multilayer feedforward neural networks," IEEE Trans.
Neural Networks, vol. 9, no. 6, pp. 1442 - 1455, Nov. 1998.
[14] A. Cichocki, R. Unbehauen, Neural Networks for Optimization and
Signal Processing, Chichester: John Wiley & Sons, 1994.
[15] S. Haykin, Neural Networks: A Comprehensive Foundation, Upper
Saddle River, New Jersey: Prentice -Hall, 1994.
[16] F. L. Luo, and R. Unbehauen, Applied Neural Networks for Signal
Processing, Cambridge: University Press, 1997.
[17] S. Haykin, Neural networks expand SP-s horizons, IEEE Signal
Processing Magazine, issue 3, pp. 24 - 49, 1996.
[18] G. Kechriotis, E. Zervas and E. S. Manolakos, "Using recurrent neural
networks for adaptive communication channel equalization," IEEE
Trans. Neural Networks, vol. 5, no. 2, pp. 267 - 278, March 1994.
[19] R. Parisi, C. D. Di Elio, G. Orlandi and B. D. Rao, "Fast adaptive
digital equalization by recurrent neural network," IEEE Trans. Signal
Processing, vol. 45, no. 11, pp. 2731 - 2739, Nov. 1997.
[20] S. Ong, C. You, S. Choi and D. Hong, "A decision feedback recurrent
neural equalizer as an infinite impulse response filter," IEEE Trans.
Signal Processing, vol. 45, no. 11, pp. 2851 - 2858, Nov. 1997.
[21] N. Benvenuto and F.Piazza, "On the complex backpropagation
algorithm," IEEE Trans. Signal Processing, vol. 40, pp. 967 - 969, Apr.
1992.
[22] C. R. Johnson Jr. et al., "Blind equalization using the constant modulus
criterion: A review," Proceedings of IEEE, vol. 86, no. 10, pp. 1927 -
1950, Oct. 1998.
[23] T. J. Endres, B. D. O. Anderson, C. R. Johnson Jr. and M. Green,
"Robustness to fractionally-spaced equalizer length using the Constant
Modulus Criterion," IEEE Trans. Signal Processing, vol. 47, no. 2, pp.
544 - 548, Feb. 1999.
[24] P. Schniter and C. R. Johnson Jr., "Dithered signed error CMA: Robust,
computationally efficient blind adaptive equalization," IEEE Trans.
Signal Processing, vol. 47, no. 6, pp. 1592 - 1603, June 1999.
@article{"International Journal of Electrical, Electronic and Communication Sciences:52970", author = "Rajoo Pandey", title = "Complex-Valued Neural Networks for Blind Equalization of Time-Varying Channels", abstract = "Most of the commonly used blind equalization algorithms are based on the minimization of a nonconvex and nonlinear cost function and a neural network gives smaller residual error as compared to a linear structure. The efficacy of complex valued feedforward neural networks for blind equalization of linear and nonlinear communication channels has been confirmed by many studies. In this paper we present two neural network models for blind equalization of time-varying channels, for M-ary QAM and PSK signals. The complex valued activation functions, suitable for these signal constellations in time-varying environment, are introduced and the learning algorithms based on the CMA cost function are derived. The improved performance of the proposed models is confirmed through computer simulations.
", keywords = "Blind Equalization, Neural Networks, Constant
Modulus Algorithm, Time-varying channels.", volume = "1", number = "9", pages = "1267-8", }
