New insights into the normalization of the least mean fourth algorithm

Signal, Image and Video Processing

Volumn 7, Issue 2, 2013, Pages 255-262

  Eweda, Eweda ^a   Zerguine, Azzedine ^b  

^a AJMAN UNIVERSITY   (United Arab Emirates)

^b KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS   (Saudi Arabia)

Author keywords

Adaptive filtering; LMF algorithm; Normalized LMF algorithm

Indexed keywords

ADAPTIVE FILTERS; SIGNAL TO NOISE RATIO;

ANALYTICAL RESULTS; APPROXIMATE STABILITY; FOURTH ORDER POLYNOMIAL; INPUT POWER; LEAST MEAN FOURTH ALGORITHMS; STEP SIZE; WEIGHT INITIALIZATION; WEIGHT VECTOR;

ADAPTIVE FILTERING;

EID: 84874111430     PISSN: 18631703     EISSN: 18631711     Source Type: Journal    
DOI: 10.1007/s11760-011-0231-y     Document Type: Article

References (18)

1. Walach E., Widrow B.: The least mean fourth (LMF) adaptive algorithm and its family. IEEE Trans. Inf. Theory IT-30, 275-283 (1984).
2. Gersho, A.: Some aspects of linear estimation with non- mean-square error criteria. Presented at the Asilomar Circuits Syst. Conf., Asilomar, CA, 1969.
3. Narasimham S. V.: Application of the least mean fourth (LMF) adaptive algorithm to signals associated with Gaussian noise. Int. J. Electron 62(6), 895-913 (1987).
4. Tanrikulu O., Chambers J. A.: Convergence and steady-state properties of the least mean mixed-norm (lmmn) adaptive filtering. IEE Proc.-VIS Image Signal Process. 143(3), 137-142 (1996).
5. Cho, S. H., Kim, S. D., Jean, K. Y.: Statistical convergence of the adaptive least mean fourth algorithm. In: Proceedings of the ICSP'96, pp. 610-613 (1996).
6. Sharma R., Sethares W. A., Buclew J. A.: Asymptotic analysis of stochastic gradient-based adaptive filtering algorithms with general cost functions. IEEE Trans. Signal Process. 44(9), 2186-2194 (1996).
7. Zerguine A., Cowan C. F. N., Bettayeb M.: Adaptive echo cancellation using least mean mixed-norm algorithm. IEEE Trans. Signal Process. 45, 1340-1343 (1997).
8. Koike, S.: Stability conditions for adaptive algorithms with non-quadratic error criteria. EUSIPCO-2000, Tempere, Finland, pp. 131-134 (2000).
9. Zerguine, A.: Convergence behavior of the normalized least mean fourth algorithm. In: Proceedings of Thirty Fourth Annual, ASILOMAR Conference on Signals, Systems, and Computers, Pacific Grove, California, pp. 275-278 (2000).
10. Hübscher P. I., Bermudez J. C. M.: An improved statistical analysis of the least mean fourth (lmf) adaptive algorithm. IEEE Trans. Signal Process. 51(3), 664-671 (2003).
11. Chan, M. K., Cowan, C. F. N.: Using a normalised LMF algorithm for channel equalisation with co-channel interference. EUSIPCO-2002, Toulouse, France, pp. 48-51 (2002).
12. Nascimento V. H., Bermudez J. C. M.: Probability of divergence for the least-mean fourth algorithm. IEEE Trans. Signal Process. 54(4), 1376-1385 (2006).
13. Hübscher P. I., Bermudez J. C. M., Nascimento V. H.: A mean-square stability of the least mean fourth adaptive algorithm. IEEE Trans. Signal Process. 55(8), 4018-4028 (2007).
14. Zerguine A.: Convergence and steady-state analysis of the normalized least mean fourth algorithm. Digital Signal Process. 17(1), 17-31 (2007).
15. Imam, S. A. A., Zerguine, A., Moinuddin, M.: A noise constrained least mean fourth (SNCLMF) adaptive algorithm. ICASSP 2008, Las Vegas, USA, pp. 3817-3820 (2008).
16. Zerguine A., Chan M. K., Al-Naffouri T. Y., Moinuddin M., Cowan C. F. N.: Convergence and tracking analysis of a variable normalised LMF (XE-NLMF) algorithm. Signal Process. 89(5), 778-790 (2009).
17. Nagumo J. I., Noda A.: A learning method for system identification. IEEE Trans. Automat. Control AC-12, 282-287 (1967).
18. Eweda, E., Zerguine, A.: A normalized least mean fourth algorithm with improved stability. In: Proceedings of the 44-th Annual ASILOMAR Conference on Signals, Systems, and Computers, pp. 1002-1005, Pacific Grove, California (2010).