Complex-Valued Neural Networks for Blind Equalization of Time-Varying Channels

Authors: Rajoo Pandey

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.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1331087

References:

[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.