Abstract
This work is devoted to asymptotic properties of a sign-error adaptive filtering algorithm with constant step size. Under much weaker conditions than those that appear in the literature, we obtain convergence and rate of convergence by using weak convergence methods. An example is provided to demonstrate the performance of the algorithm.
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References
Eweda, E., Macchi, O., Quadratic mean and almost-sure convergence of unbounded stochastic approximation algorithms with correlated observations, Ann. Henri Poincaré, 1983, 19: 235–255.
Gersho, A., Adaptive filtering with binary reinforcement, IEEE Trans. Inform. Theory, 1984, IT-30: 191–199.
Widrow, B., Stearns, S.D., Adaptive Signal Processing, Englewood Cliffs, NJ: Prentice-Hall, 1985.
Kushner, H. J., Yin, G., Stochastic Approximation Algorithms and Applications, New York: Springer-Verlag, 1997.
Chen, H.F., Zhu, Y.M., Stochastic Approximation (in Chinese), Shanghai: Shanghai Scientific and Technical Publishers, 1996.
Eweda, E., Convergence of the sign algorithm for adaptive filtering with correlated data, IEEE Trans. Inform. Theory, 1991, IT-37: 1450–1457.
Chen, H.F., Zhu, Y.M., Stochastic approximation procedure with randomly varying truncations, Scientia Sinica, Ser. A, 1986, 29: 914–926.
Chen, H.F., Stochastic approximation and its new applications, Proc. 1994 Hong Kong International Workshop on New Directions of Control and Manufacturing, 1994, 2–12.
Kushner, H. J., Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic Systems Theory, Cambridge, MA: MIT Press, 1984.
Benveniste, A., Gooursat, M., Ruget, G., Analysis of stochastic approximation schemes with discontinuous and dependent forcing terms with applications to data communication algorithms, IEEE Trans. Automatic Control, 1980, AC-25: 1042–1058.
Eweda, E., A tight upper bound of the average absolute error in a constant step size sign algorithm, IEEE Trans. Acoust. Speech Signal Proc., 1989, ASSP-37: 1774–1776.
Kwong, C.P., Dual signal algorithm for adaptive filtering, IEEE Trans. Comm., 1986, COM-34: 1272–1275.
Verhoeckx, N.A.M., van den Elzen, H.C., Snijders, F.A.M. et al., Digital echo cancellation for baseband data transmission, IEEE Trans. Acoust. Speech Signal Processing, 1979, 27: 761–781.
Eweda, E., Convergence analysis of the signalgorithm without the independence and Gaussian assumptions, IEEE Trans. Signal Processing, 2000, 48: 2535–2544.
Ethier, S.N., Kurtz, T.G., Markov Processes, Characterization and Convergence, New York: Wiley, 1986.
Billingsley, P., Convergence of Probability Measures, 2nd ed., New York: J. Wiley, 1999.
Karlin, S., Taylor, H.M., A First Course in Stochastic Processes, New York: Academic Press, 1975.
Macchi, O., Eweda, E., Convergence analysis of self-adaptive equalizers, IEEE Trans. Information Theory, 1984, IT-30: 161–176.
Kushner, H.J., Shwartz, A., Weak convergence and asymptotic properties of adaptive filters with constant gains, IEEE Trans. Inform. Theory, 1984, IT-30: 177–182.
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Yin, G., Chen, H. On asymptotic properties of a constant-step-size sign-error algorithm for adaptive filtering. Sci China Ser F 45, 321–334 (2002). https://doi.org/10.1007/BF02714090
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DOI: https://doi.org/10.1007/BF02714090