Output signal based combination of two NLMS adaptive filters – transient analysis; pp. 258–268Full article in PDF format | doi: 10.3176/proc.2011.4.06
A combination of two complex normalized least mean square (NLMS) adaptive filters that adapt on the same input signal at the same time is investigated. One of the filters has a large and the other one has a small step size. The outputs of the filters are combined together through a mixing parameter λ. This combination is an interesting new way of achieving simultaneously a fast initial convergence and a small steady state error of an adaptive algorithm. The mixing parameter is computed from the output signals of the individual filters. The expressions characterizing the time evolution of the mean square deviation and the excess mean square error of the combination scheme are derived. The theoretical results are verified by simulations.
1. Sayed, A. H. Adaptive Filters. John Wiley and Sons, Hoboken, NJ, USA, 2008.
2. Haykin, S. Adaptive Filter Theory, Fourth Edition. Prentice Hall, 2002.
3. Harris, R. W., Chabries, D. M., and Bishop, F. A. Variable step (vs) adaptive filter algorithm. IEEE Trans. Acoust. Speech Signal Process., 1986, 34, 309–316.
4. Kwong, R. H. and Johnston, E. W. A variable step size LMS algorithm. IEEE Trans. Signal Process., 1992, 40, 1633–1642.
5. Matthews, V. J. and Xie, Z. A stochastic gradient adaptive filter with gradient adaptive step size. IEEE Trans. Signal Process., 1993, 41, 2075–2087.
6. Arenas-Garcia, J., Figueiras-Vidal, A. R., and Sayed, A. H. A robust variable step-size LMS-type algorithm: Analysis and simulations. IEEE Trans. Signal Process., 1997, 45, 631–639.
7. Shin, H. C. and Sayed, A. H. Variable step-size NLMS and affine projection algorithms. IEEE Signal Process. Lett., 2004, 11, 132–135.
8. Martinez-Ramon, M., Arenas-Garcia, J., Navia-Vazquez, A., and Figueiras-Vidal, A. R. An adaptive combination of adaptive filters for plant identification. In Proc. 14th International Conference on Digital Signal Processing. Santorini, Greece, 2002, 1195–1198.
9. Arenas-Garcia, J., Figueiras-Vidal, A. R., and Sayed, A. H. Mean-square performance of convex combination of two adaptive filters. IEEE Trans. Signal Process., 2006, 54, 1078–1090.
10. Silva, M. T. M., Nascimento, V. H., and Arenas-Garcia, J. A transient analysis for the convex combination of two adaptive filters with transfer of coefficients. In Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing. Dallas, TX, USA, 2010, 3842–3845.
11. Bershad, N. J., Bermudez, J. C., and Tourneret, J. H. An affine combination of two LMS adaptive filters – transient mean-square analysis. IEEE Trans. Signal Process., 2008, 56, 1853–1864.
12. Mandic, D., Vayanos, P., Boukis, C., Jelfs, B., Goh, S. I., Gautama, T., and Rutkowski, T. Collaborative adaptive learning using hybrid filters. In Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing. Honolulu, Hawaii, 2007, 901–924.
13. Zhang, Y. and Chambers, J. A. Convex combination of adaptive filters for a variable tap-length LMS algorithm. IEEE Signal Process. Lett., 2006, 10, 628–631.
14. Kim, K., Choi, Y., Kim, S., and Song, W. Convex combination of affine projection filters with individual regularization. In Proc. 23rd International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC)}. Shimonoseki, Japan, 2008, 901–904.
15. Fathiyan, A. and Eshghi, M. Combining several PBS-LMS filters as a general form of convex combination of two filters. J. Appl. Sci., 2009, 9, 759–764.
16. Azpicueta-Ruiz, L. A., Figueiras-Vidal, A. R., and Arenas-Garcia, J. A normalized adaptation scheme for the convex combination of two adaptive filters. In Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing. Las Vegas, Nevada, 2008, 3301–3304.
17. Ochiai, K. Echo canceller with two echo path models. IEEE Trans. Commun., 1977, 25, 589–594.
18. Armbruster, W. Wideband acoustic echo canceller with two filter structure. In Signal Processing VI, Theories and Applications (Vanderwalle, J., Boite, R., Moonen, M., and Oosterlinck, A., eds). Elsevier Science Publishers B.V, 1992, 1611–1617.
19. Trump, T. An output signal based combination of two NLMS adaptive algorithms. In Proc. 16th International Conference on Digital Signal Processing. Santorini, Greece. IEEE 2009, 6 pp.
20. Azpicueta-Ruiz, L. A., Figueiras-Vidal, A. R., and Arenas-Garcia, J. A new least squares adaptation scheme for the affine combination of two adaptive filters combination of two adaptive filters. In Proc. IEEE International Workshop on Machine Learning for Signal Processing. Cancun, Mexico, 2008, 327–332.
21. Trump, T. Steady state analysis of an output signal based combination of two NLMS adaptive filters. In Proc. 17th European Signal Processing Conference. Glasgow, Scotland, 2009, 1720–1724.
22. Trump, T. Tracking performance of a combination of two NLMS adaptive filters. In Proc. IEEE Workshop on Statistical Signal Processing. Cardiff, UK. IEEE 2009, 181–184.
23. Trump, T. Output statistics of a line enhancer based on a combination of two adaptive filters. Central European J. Engineering, 2011, 1, 244–252.24. ITU-T Recommendation G.168 Digital Network Echo Cancellers. ITU-T, 2009; http://itu.int (accessed 27 July 2011).
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