Sparsity-Aware and Noise-Robust Subband Adaptive Filter

This paper presents a subband adaptive filter (SAF)
for a system identification where an impulse response is sparse
and disturbed with an impulsive noise. Benefiting from the uses
of l1-norm optimization and l0-norm penalty of the weight vector
in the cost function, the proposed l0-norm sign SAF (l0-SSAF)
achieves both robustness against impulsive noise and much improved
convergence behavior than the classical adaptive filters. Simulation
results in the system identification scenario confirm that the proposed
l0-norm SSAF is not only more robust but also faster and more
accurate than its counterparts in the sparse system identification in
the presence of impulsive noise.

Authors:

• Young-Seok Choi

Keywords:

• Subband adaptive filter
• l0-norm
• sparse system
• robustness
• impulsive interference.

References:

[1] S. Haykin, Adaptive Filter Theory, 4th ed., Upper Saddle River, NJ:
Prentice Hall, 2002.
[2] A. H. Sayed, Fundamentals of Adaptive Filtering, New York: Wiley,
2003.
[3] P. S. R. Diniz, Adaptive Filtering: Algorithms and Practical
Implementations, 3rd ed. Boston: Kluwer, 2008.
[4] M. M. Sondhi, “The History of Echo Cancellation,” IEEE Transactions
on Signal Processing Magazine, vol. 23, no. 5, pp. 1730–1740, 2006.
[5] A. Gilloire and M. Vetterli, “Adaptive filtering in subbands with
critical sampling: analysis, experiments, and application to acoustic echo
cancellation,” IEEE Transactions on Signal Processing, vol. 40, no. 8,
pp. 1862–875, 1992.
[6] M. D. Couriville and P. Duhamel, “Adaptive filtering in subbands using
a weighted criterion,” IEEE Transactions on Signal Processing, vol. 46,
no. 9, pp. 2359–2371, 1998.
[7] S. S. Pradhan and V. U. Reddy, “A new approach to subband adaptive
filtering,” IEEE Transactions on Signal Processing, vol. 47, no. 3,
pp. 655–664, 1999.
[8] K. A. Lee and W. S. Gan, “Improving convergence of the NLMS
algorithm using constrained subband updates,” IEEE Signal Processing
Letters, vol. 11, no. 9, pp. 736–739, 2004.
[9] K. A. Lee and W. S. Gan, “Inherent decorrelating and least perturbation
properties of the normalized subband adaptive filter,” IEEE Transactions
on Signal Processing, vol. 54, no. 11, pp. 4475–4480, 2006.
[10] D. L. Duttweiler, “Proportionate normalized least-mean-squares
adaptation in echo cancellers,” IEEE Transactions on Speech Audio
Processing, vol. 8, no. 5, pp. 508–518, 2000.
[11] W. Li and J. C. Preisig, “Estimation of rapidly time-varying sparse
channels,” IEEE Journal of Ocean Engineering, vol. 32, no. 4,
pp. 929–939, 2007.
[12] W. F. Schreiber, “Advanced television systems for terrestrial
broad-casting: some problems and some proposed solutions,”
Proceedings of IEEE, vol. 83, no. 6, pp. 958–981, 1995.
[13] S. L. Gay, “An efficient, fast converging adaptive filter for network echo
cancellation,” in Proceedings of the Asilomar Conference on Signals,
Systems, Computer, pp. 394–398, Nov. 1998.
[14] H. Deng and M. Doroslovacki, “Improving convergence of the PNLMS
algorithm for sparse impulse response identification,” IEEE Signal
Processing Letters, vol. 12, no. 3, pp. 181–184, 2005.
[15] M. S. E. Abadi, “Proportionate normalized subband adaptive filter
algorithms for sparse system identification,” Signal Processing, vol. 89,
no. 7, pp. 1467–1474, 2009.
[16] J. Ni, and F. Li, “Variable regulaisation parameter sign subband adaptive
filter,” Electronis Letters, vol. 89, no. 7, pp. 1605–1607, 2010.
[17] L. R. Vega, H. Ray, J. Benesty, and S. Tressens, “A new robust variable
step-size NLMS algorithm,” IEEE Transions on Signal Processing,
vol. 56, no. 5, pp. 1878–1893, 2008.
[18] Z. Yang, Y. R. Zheng, and S. L. Grant, “Proportionate affine projection
sign algorithms for network echo cancellation,” IEEE Transactions on
Audio, Speech, Language Processing, vol. 19, no. 8, pp. 2273–2284,
2011.
[19] B. Liao, Z. G. Zhang, and S. C. Chan, “A new robust Kalman filter-based
subspace tracking algorithm in an impulsive noise environment,” IEEE
Transactions on Circuits and Systems II: Express Briefs, vol. 57, no. 9,
pp. 740744, 2010.
[20] D. Donoho, “Compressed sensing,” IEEE Transactions on Information
Theory, vol. 52, no. 4, pp. 1289–1306, 2006.
[21] E. Cand`es, J. Romberg, and T. Tao, “Robust uncertainty
principles: Exact signal reconstruction from highly incomplete frequency
information,” IEEE Transactions on Information Theory, vol. 52, no. 2,
pp. 489–509, 2006.
[22] R. Tibshirani, “Regression shrinkage and selection via the lasso,”
Journal of Royal statistical Society Series B, vol. 58, pp. 267–288,
1996.
[23] Y. Chen, Y. Gu, and A. O. Hero, “Sparse LMS for system identification,”
in Proceeding of the International Conference on Acoustic, Speech, and
Signal Process (ICASSP ’09), pp. 3125–3128, April 2009.
[24] Y. Gu, J. Jin, and S. Mei, “l0 norm constraint LMS algorithm for sparse
system identification,” IEEE Signal Processing Letters, vol. 16, no. 9,
pp. 774–777, 2009.
[25] J. Jin, Y. Gu, and S.Mei, “A stochastic gradient approach on compressive
sensing signal reconstruction based on adaptive filtering framework,”
IEEE Journal of Selected Topics in Signal Processing, vol. 4, no. 2,
pp. 409–420, 2010.
[26] E. M. Eksioglu and A. K. Tanc, “RLS Algorithm with convex
regularization,” IEEE Signal Processing Letters, vol. 18, no. 8,
pp. 470–473, 2011.
[27] P. S. Bradley and O. L. Mangasarian, “Feature selection via
concave minimization and support vector machines,” in Proceeding of
International Conference on Machine Learning (ICML ’98), pp. 82–90,
1998.
[28] P. P. Vaidyanathan, Multirate Systems and Filterbanks, Englewood
Cliffs, NJ: Prentice-Hall, 1993.