Global stabilization of the least mean fourth algorithm

IEEE Transactions on Signal Processing

Volumn 60, Issue 3, 2012, Pages 1473-1477

  Eweda, Eweda ^a  

^a AJMAN UNIVERSITY   (United Arab Emirates)

Author keywords

Adaptive filtering; least mean fourth algorithm; normalized least mean fourth algorithm

Indexed keywords

ESTIMATION ERRORS; FILTER INPUT; FILTER WEIGHTS; FOURTH ORDER; GLOBAL SOLUTIONS; GLOBAL STABILIZATION; LEAST MEAN FOURTH; NOISE VARIANCE; SECOND ORDERS; STABILITY PROBLEM; WEIGHT INITIALIZATION; WEIGHT VECTOR;

ADAPTIVE FILTERING; ADAPTIVE FILTERS; SPURIOUS SIGNAL NOISE; STABILIZATION;

ALGORITHMS;

EID: 84857225179     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2011.2177976     Document Type: Article

References (20)

1. B. Widrow and S. D. Stearns, Adaptive Signal Processing. Engle-wood Cliffs, NJ: Prentice-Hall, 1985.
2. A. H. Sayed, Fundamentals of Adaptive Filtering. New York: Wiley-Interscience, 2003.
3. E. Walach and B. Widrow, "The least mean fourth (LMF) adaptive algorithm and its family," IEEE Trans. Inf. Theory, vol. IT-30, pp. 275-283, Feb. 1984. (Pubitemid 14564534)
4. A. Gersho, "Some aspects of linear estimation with non-mean-square error criteria," presented at the Asilomar Circuits Syst. Conf., CA, Nov. 1969.
5. S. V. Narasimham, "Application of the least mean fourth (LMF) adaptive algorithm to signals associated with Gaussian noise," Int. J. Electron., vol. 62, no. 6, pp. 895-913, 1987.
6. O. Tanrikulu and J. A. Chambers, " Convergence and steady-state properties of the least mean mixed-norm (LMMN) adaptive filtering," Proc. Inst. Electr. Eng.-VIS Image Signal Process., vol. 143, no. 3, pp. 137-142, Jun. 1996. (Pubitemid 126760764)
7. S. H. Cho, S. D. Kim, and K. Y. Jen, "Statistical convergence of the adaptive least mean fourth algorithm," in Proc. Int. Conf. Signal Process. (ICSP), 1996, pp. 610-613.
8. R. Sharma, W. A. Sethares, and J. A. Buclew, "Asymptotic analysis of stochastic gradient-based adaptive filtering algorithms with general cost functions," IEEE Trans. Signal Process., vol. 44, no. 9, pp. 2186-2194, Sep. 1996. (Pubitemid 126776504)
9. A. Zerguine, C. F. N. Cowan, and M. Bettayeb, "Adaptive echo cancellation using least mean mixed-norm algorithm," IEEE Trans. Signal Process., vol. 45, pp. 1340-1343, May 1997. (Pubitemid 127766079)
10. S. Koike, "Stability conditions for adaptive algorithms with non-quadratic error criteria," in PROC. EUSIPCO, Tempere, Finland, Sep. 5-8, 2000, pp. 131-134.
11. Zerguine, "Convergence behavior of the normalized least mean fourth algorithm," in Proc. 34th Annu. ASILOMAR Conf. Signals, Syst., Comput., Pacific Grove, CA, Oct. 29-Nov. 1 2000, pp. 275-278. (Pubitemid 32371359)
12. T. Al-Naffouri and A. Sayed, "Transient analysis of adaptive filters," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), 2001, vol. 6, pp. 3869-3872. (Pubitemid 32838465)
13. P. I. Hübscher and J. C. M. Bermudez, "An improved statistical analysis of the least mean fourth (LMF) adaptive algorithm," IEEE Trans. Signal Process., vol. 51, no. 3, pp. 664-671, Mar. 2003.
14. M. K. Chan and C. F. N. Cowan, "Using a normalised LMF algorithm for channel equalisation with co-channel interference," in Proc. EU-SIPCO, Toulouse, France, Sep. 3-6, 2002, pp. 48-51.
15. V. H. Nascimento and J. C. M. Bermudez, "Probability of divergence for the least-mean fourth algorithm," IEEE Trans. Signal Process., vol. 54, no. 4, pp. 1376-1385, Apr. 2006.
16. P. I. Hübscher, J. C. M. Bermudez, and V. H. Nascimento, "A mean-square stability of the least mean fourth adaptive algorithm," IEEE Trans. Signal Process., vol. 55, no. 8, pp. 4018-4028, Aug. 2007. (Pubitemid 47261524)
17. A. Zerguine, "Convergence and steady-state analysis of the normalized least mean fourth algorithm," Digit. Signal Process., vol. 17, no. 1, pp. 17-31, Jan. 2007. (Pubitemid 44828545)
18. A. Zerguine, M. K. Chan, T. Y. Al-Naffouri, M. Moinuddin, and C. F. N. Cowan, "Convergence and tracking analysis of a variable normalised LMF (XE-NLMF) algorithm," Signal Process., vol. 89, no. 5, pp. 778-790, May 2009.
19. E. Eweda and A. Zerguine, "New insights into the normalization of the least mean fourth algorithm," Signal, Image, Video Process., 2011 [Online]. Available: http://www.springerlink.com/content/1863-1703/?k=Eweda, DOI: 10.1007/s11760-011-0231-y
20. N. Bershad and J. C. M. Bermudez, "Mean-square stability of the normalized least mean fourth algorithm for white Gaussian inputs," Digit. Signal Process. (Elsevier), vol. 21, no. 6, pp. 694-700, Dec. 2011.