# AN APPROXIMATED EXPRESSION FOR THE CONVERGENCE TIME OF ADAPTIVE BLIND EQUALIZERS

### Monika Pinchas

#### Abstract

In this paper, closed-form approximated expressions are proposed for the convergence time (or number of iterations required for convergence) and for the Intersymbol Interference (ISI) as a function of time valid during the stages of the iterative deconvolution process. The new derivations are valid for the noiseless, real and two independent quadrature carrier case and for type of blind equalizers where the error that is fed into the adaptive mechanism which updates the equalizer’s taps can be expressed as a polynomial function of order three of the equalized output like in Godard’s algorithm. Up to now, the equalizer’s performance (convergence time and ISI as a function of time) could be obtained only via simulation when the channel coefficients were known. The new proposed expressions are based on the knowledge of the initial ISI and channel power (which is measurable) and eliminate the need to carry out any more the above mentioned simulation.

#### References

- Fiori, S. (2001). A contribution to (neuromorphic) blind deconvolution by flexible approximated bayesian estimation. In Signal Processing 81, 2131-2153. Elsevier.
- Godard, D. (1980). Self recovering equalization and carrier tracking in two-dimentional data communication system. In IEEE Transaction Communication 28 (11) 1867-1875. IEEE.
- Lee, E. A. and Messerschmitt, D. G. (1997). Adaptive Equalization, in: E. A. Lee and D. G. Messerschmitt, Digital Communication. Kluwer Academic Publisher, third printing, 2nd edition.
- Pinchas, M. (2009). A closed approximated formed expression for the achievable residual intersymbol interference obtained by blind equalizers. In Signal Processing Journal (Eurasip), DOI: 10.1016/j.sigpro.2009.12.014.
- Pinchas, M. (2011). A mse optimized polynomial equalizer for 16qam and 64qam constellation. In Signal, Image and Video Processing, Volume 5, Issue 1, DOI 10.1007/s11760-009-0138-z.
- Shalvi, O. and Weinstein, E. (1990). New criteria for blind deconvolution of nonminimum phase systems (channels). In IEEE Trans. Information Theory 36 (2), 312- 321.

#### Paper Citation

#### in Harvard Style

Pinchas M. (2011). **AN APPROXIMATED EXPRESSION FOR THE CONVERGENCE TIME OF ADAPTIVE BLIND EQUALIZERS** . In *Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 978-989-8425-74-4, pages 411-414. DOI: 10.5220/0003529204110414

#### in Bibtex Style

@conference{icinco11,

author={Monika Pinchas},

title={AN APPROXIMATED EXPRESSION FOR THE CONVERGENCE TIME OF ADAPTIVE BLIND EQUALIZERS},

booktitle={Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

year={2011},

pages={411-414},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003529204110414},

isbn={978-989-8425-74-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,

TI - AN APPROXIMATED EXPRESSION FOR THE CONVERGENCE TIME OF ADAPTIVE BLIND EQUALIZERS

SN - 978-989-8425-74-4

AU - Pinchas M.

PY - 2011

SP - 411

EP - 414

DO - 10.5220/0003529204110414