A Family of Affine Projection Adaptive Filtering Algorithms With Selective Regressors

In this paper we present a general formalism for the establishment of the family of selective regressor affine projection algorithms (SR-APA). The SR-APA, the SR regularized APA (SR-RAPA), the SR partial rank algorithm (SR-PRA), the SR binormalized data reusing least mean squares (SR-BNDR-LMS), and the SR normalized LMS with orthogonal correction factors (SR-NLMS-OCF) algorithms are established by this general formalism. We demonstrate the performance of the presented algorithms through simulations in acoustic echo cancellation scenario.

Authors:

• Mohammad Shams Esfand Abadi
• Nader Hadizadeh Kashani
• Vahid Mehrdad

Keywords:

• Adaptive filter
• affine projection
• selective regressor.

References:

[1] S. Haykin, Adaptive Filter Theory. NJ: Prentice-Hall, 4th edition, 2002.
[2] P. S. R. Diniz, Adaptive Filtering: Algorithms and Practical Implementation,
2nd ed. Kluwer, 2002.
[3] A. H. Sayed, Fundamentals of Adaptive Filtering. Wiley, 2003.
[4] S. C. Douglas, "Analysis and implementation of the max-NLMS adaptive
filter," in Proc. 29th Asilomar Conf. on Signals, Systems, and Computers,
Pacific Grove, CA, Oct. 1995, pp. 659-663.
[5] T. Aboulnasr and K. Mayyas, "Selective coefficient update of gradientbased
adaptive algorithms," in Proc. IEEE Int. Conf. on Acoustics,
Speech, and Signal Processing, Munich, Germany, Apr. 1997, pp. 1929-
1932.
[6] ÔÇöÔÇö, "Complexity reduction of the NLMS algorithm via selective
coefficient update," IEEE Trans. Signal Processing, vol. 47, no. 5, pp.
1421-1424, May 1999.
[7] T. Schertler, "Selective block update NLMS type algorithms," in Proc.
IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, Seattle,
WA, May 1998, pp. 1717-1720.
[8] K. Do╦ÿganc┬©ay and O. Tanr─▒kulu, "Adaptive filtering algorithms with
selective partial updates," IEEE Trans. Circuits, Syst. II: Analog and
Digital Signal Processing, vol. 48, no. 8, pp. 762-769, Aug. 2001.
[9] S. Werner, M. L. R. de Campos, and P. S. R. Diniz, "Partial-update
NLMS algorithms with data-selective updating," IEEE Trans. Signal
Processing, vol. 52, no. 4, pp. 938-948, Apr. 2004.
[10] K. Y. Hwang and W. J. Song, "An affine projection adaptive filtering
algorithm with selective regressors," IEEE Trans. Circuits, Syst. II:
EXPRESS BRIEFS, vol. 54, no. 1, pp. 43-46, Jan. 2007.
[11] J. Apolinario, M. L. Campos, and P. S. R. Diniz, "Convergence analysis
of the binormalized data-reusing LMS algorithm," IEEE Trans. Signal
Processing, vol. 48, pp. 3235-3242, Nov. 2000.
[12] S. L. Gay and J. Benesty, Acoustic Signal Processing for Telecommunication.
Boston, MA: Kluwer, 2000.
[13] S. G. Sankaran and A. A. L. Beex, "Normalized LMS algorithm with
orthogonal correction factors," in Proc. Asilomar Conf. on Signals,
Systems, and Computers, 1997, pp. 1670-1673.
[14] S. G. Kratzer and D. R. Morgan, "The partial-rank algorithm for adaptive
beamforming," in Proc. SPIE Int. Soc. Opt. Eng, 1985, pp. 9-14.
[15] A. H. Sayed, Adaptive Filters. Wiley, 2008.