An Approximated Expression for the Residual ISI Obtained by Blind Adaptive Equalizer and Biased Input Signals

Nissim Panizel, Monika Pinchas

Department of Electrical and Electronic Engineering, Ariel University, Ariel, Israel.

DOI: 10.4236/jsip.2014.54018                

Abstract

Recently, two expressions (for the noiseless and noisy case) were proposed for the residual inter-symbol interference (ISI) obtained by blind adaptive equalizers, where the error of the equalized output signal may be expressed as a polynomial function of order 3. However, those expressions are not applicable for biased input signals. In this paper, a closed-form approximated expression is proposed for the residual ISI applicable for the noisy and biased input case. This new proposed expression is valid for blind adaptive equalizers, where the error of the equalized output signal may be expressed as a polynomial function of order 3. The new proposed expression depends on the equalizer’s tap length, input signal statistics, channel power, SNR, step-size parameter and on the input signal’s bias. Simulation results indicate a high correlation between the simulated results and those obtained from our new proposed expression.

Keywords

Blind Adaptive Equalizers, Deconvolution, Inter-Symbol Interference (ISI), Convolutional Noise, Residual ISI

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Pinchas, M. (2013) Two Blind Adaptive Equalizers Connected in Series for Equalization Performance Improvement. Journal of Signal and Information Processing, 4, 64-71. http://dx.doi.org/10.4236/jsip.2013.41008
[2]	Pinchas, M. (2013) Residual ISI Obtained by Blind Adaptive Equalizers and Fractional Noise. Mathematical Problems in Engineering, 2013, Article ID: 972174.
[3]	Pinchas, M. and Bobrovsky, B.Z. (2006) A Maximum Entropy Approach for Blind Deconvolution. Signal Processing (Eurasip), 86, 2913-2931. http://dx.doi.org/10.1016/j.sigpro.2005.12.009
[4]	Pinchas, M. and Bobrovsky, B.Z. (2007) A Novel HOS Approach for Blind Channel Equalization. IEEE Transactions on Wireless Communications, 6, 875-886. http://dx.doi.org/10.1109/TWC.2007.04404
[5]	Pinchas, M. (2009) Blind Equalizers by Techniques of Optimal Non-Linear Filtering Theory. VDM Verlagsservice gesellschaft mbH.
[6]	Pinchas, M. (2012) The Whole Story behind Blind Adaptive Equalizers/Blind Deconvolution. e-Books Publications Department, Bentham Science Publishers, Sharjah.
[7]	Godard, D.N. (1980) Self Recovering Equalization and Carrier Tracking in Two-Dimensional Data Communication System. IEEE Transactions on Communications, 28, 1867-1875. http://dx.doi.org/10.1109/TCOM.1980.1094608
[8]	Im, G.H., Park, C.J. and Won, H.C. (2009) A Blind Equalization with the Sign Algorithm for Broadband Access. IEEE Communications Letters, 5, 70-72.
[9]	Reuter, M. and Zeidler, J.R. (1999) Nonlinear Effects in LMS Adaptive Equalizers. IEEE Transactions on Signal Processing, 47, 1570-1579. http://dx.doi.org/10.1109/78.765126
[10]	Makki, A.H.I., Dey, A.K. and Khan M.A. (2010) Comparative Study on LMS and CMA Channel Equalization. 2010 International Conference on Information Society (i-Society), London, 28-30 June 2010, 487-489.
[11]	Tucu, E., Akir, F. and Ozen, A. (2013) A New Step-Size Control Technique for Blind and Non-Blind Equalization Algorithms. Radioengineering, 22, 44-51.
[12]	Wang, J.F. and Zhang, B. (2010) Design of Adaptive Equalizer Based on Variable Step LMS Algorithm. Proceedings of the 3rd International Symposium on Computer Science and Computational Technology, Jiaozuo, 14-15 August 2010, 256-258. http://www.academypublisher.com/proc/iscsct10/papers/iscsct10p256.pdf
[13]	Nikias, C.L. and Petropulu, A.P. (1993) Chapter 9. Higher-Order Spectra Analysis A Nonlinear Signal Processing Framework. Prentice-Hall, Englewood Cliffs, 419-425.
[14]	Im, G.H and Won, H.C. (2001) RF Interference Suppression for VDSL System. IEEE Transactions on Consumer Electronics, 47, 715-722. http://dx.doi.org/10.1109/30.982781
[15]	Pinchas, M. (2010) A Closed Approximated Formed Expression for the Achievable Residual Intersymbol Interference Obtained by Blind Equalizers. Signal Processing (Eurasip), 90, 1940-1962. http://dx.doi.org/10.1016/j.sigpro.2009.12.014
[16]	Pinchas, M. (2010) A New Closed Approximated Formed Expression for the Achievable Residual ISI Obtained by Adaptive Blind Equalizers for the Noisy Case. IEEE International Conference on Wireless Communications, Networking and Information Security WCNIS 2010, Beijing, 25-27 June 2010, 26-30. http://dx.doi.org/10.1109/WCINS.2010.5541879
[17]	Shalvi, O. and Weinstein, E. (1990) New Criteria for Blind Deconvolution of Nonminimum Phase Systems (Channels). IEEE Transactions on Information Theory, 36, 312-321. http://dx.doi.org/10.1109/18.52478
[18]	Pinchas, M. (2011) A MSE Otimized Polynomial Equalizer for 16QAM and 64QAM Constellation. Signal, Image and Video Processing, 5, 29-37. http://dx.doi.org/10.1007/s11760-009-0138-z
[19]	Nandi, A.K. (1999) Blind Estimation Using Higher-Order Statistics. Chapter 2, Kluwer Academic Publishers, Boston, 78-79.
[20]	Fiori, S. (2001) A Contribution to (Neuromorphic) Blind Deconvolution by Flexible Approximated Bayesian Estimation. Signal Processing (Eurasip), 81, 2131-2153. http://dx.doi.org/10.1016/S0165-1684(01)00108-6
[21]	Pinchas, M. (2013) A Novel Expression for the Achievable MSE Performance Obtained by Blind Adaptive Equalizers. Signal, Image and Video Processing, 7, 67-74. http://dx.doi.org/10.1007/s11760-011-0208-x
[22]	Shalvi, O. and Weinstein, E. (1993) Super-Exponential Methods for Blind Deconvolution. IEEE Transactions on Information Theory, 39, 504-519. http://dx.doi.org/10.1109/18.212280
[23]	Arslan, G., Ding, M., Lu, B., Milosevic, M., Shen, Z. and Evans, Brian, L. (2005) UT Austin Multicarrier Equalizer Design Toolbox for Matlab. http://users.ece.utexas.edu/~bevans/projects/adsl/dmtteq/dmtteq.html