Convergence Analysis of a Prediction based Adaptive Equalizer for IIR Channels
This paper presents the convergence analysis
of a prediction based blind equalizer for IIR channels.
Predictor parameters are estimated by using the recursive
least squares algorithm. It is shown that the prediction
error converges almost surely (a.s.) toward a scalar
multiple of the unknown input symbol sequence. It is
also proved that the convergence rate of the parameter
estimation error is of the same order as that in the iterated
logarithm law.
[1] D. N. Godard, "Self recovering equalization and carrier tracking
in the two dimensional data communication systems," IEEE
Trans. Commun., vol. COMM-28, pp. 1867-1875, November
1980.
[2] O. Shalvi and E. Weinstein, "New criterion for blind deconvolution
of minimum phase system (channels)," IEEE Trans. Inform.
Theory, vol. 36, pp. 312-321, March 1990.
[3] C. R. Johnson, P. Schniter, T. J. Endres, J. D. Behm, D. R. Brown
and R. A. Casas, "Blind equalization using the constant modulus
criterion: a review," Proc. of the IEEE, vol. 86, no. 10, pp. 1927-
1949, Oct. 1998.
[4] L. Toug, G. Xu and T. Kailath, "Blind identification and
equalization based on a second order statics: a time domain
approach," IEEE Trans. Inform. Theory, vol. 40, pp.340-349,
March 1994.
[5] E. W. Bai and M. Fu, "Blind system identification and channel
equalization of IIR system without statistical information," IEEE
Trans. Signal Processing, vol. 47, pp. 1910-1920, July 1999.
[6] D. Gesbert and P. Duhamel, "Unbiased blind adaptive channel
identification and equalization," IEEE Trans. Signal Processing,
vol. 48, pp.148-158, Jan. 2000.
[7] L. Tong and S. Perrean, "Multichannel blind identification: from
subspace to maximum likelihood methods," Proc. IEEE, vol. 86,
no. 10, pp.1951-1968, 1998.
[8] K. Abed-Meriau, E. Mouliues and P. Loubaton "Prediction
error method for second-order blind identification," IEEE Trans.
Signal Processing, vol. 45, pp. 694-705, 1997.
[9] J. Tugnait, "Multistage linear prediction based blind equalization
of FIR/IIR single-input multiple-output channels with common
zeros," IEEE Trans. Signal Processing, vol. 47, pp. 1689-1700,
1999.
[10] S. Haykin, "Adaptice Filter Theory," Prentice Hall, 2002.
[11] Y. S. Chow and H. Teicher, "Probability theory, indepdedence,
interchangibility, martingles," Springer-Verlag, New York, 1978.
[1] D. N. Godard, "Self recovering equalization and carrier tracking
in the two dimensional data communication systems," IEEE
Trans. Commun., vol. COMM-28, pp. 1867-1875, November
1980.
[2] O. Shalvi and E. Weinstein, "New criterion for blind deconvolution
of minimum phase system (channels)," IEEE Trans. Inform.
Theory, vol. 36, pp. 312-321, March 1990.
[3] C. R. Johnson, P. Schniter, T. J. Endres, J. D. Behm, D. R. Brown
and R. A. Casas, "Blind equalization using the constant modulus
criterion: a review," Proc. of the IEEE, vol. 86, no. 10, pp. 1927-
1949, Oct. 1998.
[4] L. Toug, G. Xu and T. Kailath, "Blind identification and
equalization based on a second order statics: a time domain
approach," IEEE Trans. Inform. Theory, vol. 40, pp.340-349,
March 1994.
[5] E. W. Bai and M. Fu, "Blind system identification and channel
equalization of IIR system without statistical information," IEEE
Trans. Signal Processing, vol. 47, pp. 1910-1920, July 1999.
[6] D. Gesbert and P. Duhamel, "Unbiased blind adaptive channel
identification and equalization," IEEE Trans. Signal Processing,
vol. 48, pp.148-158, Jan. 2000.
[7] L. Tong and S. Perrean, "Multichannel blind identification: from
subspace to maximum likelihood methods," Proc. IEEE, vol. 86,
no. 10, pp.1951-1968, 1998.
[8] K. Abed-Meriau, E. Mouliues and P. Loubaton "Prediction
error method for second-order blind identification," IEEE Trans.
Signal Processing, vol. 45, pp. 694-705, 1997.
[9] J. Tugnait, "Multistage linear prediction based blind equalization
of FIR/IIR single-input multiple-output channels with common
zeros," IEEE Trans. Signal Processing, vol. 47, pp. 1689-1700,
1999.
[10] S. Haykin, "Adaptice Filter Theory," Prentice Hall, 2002.
[11] Y. S. Chow and H. Teicher, "Probability theory, indepdedence,
interchangibility, martingles," Springer-Verlag, New York, 1978.
@article{"International Journal of Electrical, Electronic and Communication Sciences:49814", author = "Miloje S. Radenkovic and Tamal Bose", title = "Convergence Analysis of a Prediction based Adaptive Equalizer for IIR Channels", abstract = "This paper presents the convergence analysis
of a prediction based blind equalizer for IIR channels.
Predictor parameters are estimated by using the recursive
least squares algorithm. It is shown that the prediction
error converges almost surely (a.s.) toward a scalar
multiple of the unknown input symbol sequence. It is
also proved that the convergence rate of the parameter
estimation error is of the same order as that in the iterated
logarithm law.", keywords = "Adaptive blind equalizer, Recursive leastsquares, Adaptive Filtering, Convergence analysis.", volume = "2", number = "8", pages = "1572-5", }