Abstract
In this paper, I propose for the noiseless, real and two independent quadrature carrier case some approximated conditions on the step-size parameter, on the equalizer’s tap length and on the channel power, related to the nature of the chosen equalizer and input signal statistics, for which a blind equalizer will not converge anymore. These conditions are valid for type of blind equalizers where the error that is fed into the adaptive mechanism that updates the equalizer’s taps can be expressed as a polynomial function of the equalized output of order three like in Godard’s algorithm. Since the channel power is measurable or can be calculated if the channel coefficients are given, there is no need anymore to carry out any simulation with various step-size parameters and equalizer’s tap length for a given equalization method and input signal statistics in order to find the maximum step-size parameter for which the equalizer still converges.
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References
Nikias, C.L., Petropulu, A.P. (eds): Higher-Order Spectra Analysis A Nonlinear Signal Processing Framework, Chapter 9, pp. 419–425. Prentice-Hall, Englewood Cliffs (1993)
Godard D.N.: Self recovering equalization and carrier tracking in two-dimensional data communication system. IEEE Trans. Commun. 28(11), 1867–1875 (1980)
Sato Y.: A method of self-recovering equalization for multilevel amplitude-modulation systems. IEEE Trans. Commun. 23, 679–682 (1975)
Pinchas, M.: A MSE optimized polynomial equalizer for 16QAM and 64QAM constellation. Signal Image Video Process. doi:10.1007/s11760-009-0138-z, Oct. (2009)
Bellini, S.: Bussgang techniques for blind equalization. In: Proceedings of IEEE Global Telecommunication Conference Records, pp. 1634–1640. December (1986)
Bellini S.: Blind equalization. Alta Frequenza 57, 445–450 (1988)
Pinchas M., Bobrovsky B.Z.: A maximum entropy approach for blind deconvolution. Signal Process. 86, 2913–2931 (2006)
Haykin, S. : Blind deconvolution. In:Haykin, S. Adaptive Filter Theory, Chapter 20, Prentice-Hall, Englewood Cliffs (1991)
Lee E.A., Messerschmitt D.G.: Digital Communication, 2nd edn, Chapter 11, pp. 517–538. Kluwer Academic, Boston (1997)
Nandi, A.K. (eds): Blind Estimation Using Higher-Order Statistics, Chapter 2, pp. 66. Kluwer Academic, Boston (1999)
Lazaro M., Santamaria I., Erdogmus D., Hild K.E., Pantaleon C., Principe J.C.: Stochastic blind equalization based on pdf fitting using Parzen estimator. IEEE Trans. Signal Process. 53(2), 696–704 (2005)
Shalvi O., Weinstein E.: New criteria for blind deconvolution of nonminimum phase systems (channels). IEEE Trans. Inf. Theor. 36(2), 312–321 (1990)
Gi-Hong Im., Park C.J., Won H.C.: A blind equalization with the sign algorithm for broadband access. IEEE Comm. Lett. 5(2), 70–72 (2001)
Pinchas M.: A closed approximated formed expression for the achievable residual intersymbol interference obtained by blind equalizers. Signal Process. J. (Eurasip) 90(6), 1940–1962 (2010). doi:10.1016/j.sigpro.2009.12.014
Fiori S.: A contribution to (neuromorphic) blind deconvolution by flexible approximated Bayesian estimation. Signal Process. 81, 2131–2153 (2001)
Godfrey R., Rocca F.: Zero memory non-linear deconvolution. Geophys. Prospect. 29, 189–228 (1981)
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Pinchas, M. What are the analytical conditions for which a blind equalizer will loose the convergence state?. SIViP 6, 325–340 (2012). https://doi.org/10.1007/s11760-011-0221-0
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DOI: https://doi.org/10.1007/s11760-011-0221-0