A Transform Domain Function Controlled VSSLMS Algorithm for Sparse System Identification
The convergence rate of the least-mean-square (LMS)
algorithm deteriorates if the input signal to the filter is correlated.
In a system identification problem, this convergence rate can be
improved if the signal is white and/or if the system is sparse. We
recently proposed a sparse transform domain LMS-type algorithm
that uses a variable step-size for a sparse system identification.
The proposed algorithm provided high performance even if the
input signal is highly correlated. In this work, we investigate the
performance of the proposed TD-LMS algorithm for a large number
of filter tap which is also a critical issue for standard LMS algorithm.
Additionally, the optimum value of the most important parameter is
calculated for all experiments. Moreover, the convergence analysis
of the proposed algorithm is provided. The performance of the
proposed algorithm has been compared to different algorithms in a
sparse system identification setting of different sparsity levels and
different number of filter taps. Simulations have shown that the
proposed algorithm has prominent performance compared to the other
algorithms.
[1] Sayed, A. H.: Fundamentals of Adaptive Filtering, Wiley, New York,
USA, 2003.
[2] Haykin, S.: Adaptive filter theory, Prentice Hall, Upper Saddle River, NJ,
2002.
[3] Bismor, D.: “Extension of LMS stability condition over a wide set of
signals,” International Journal of Adaptive Control and Signal Processing,
2014, DOI: 10.1002/acs.2500.
[4] Kwong, R. H.: “A Variable Step-Size LMS Algorithm,” IEEE Transaction
on Signal Processing, 40 (7): 1633-1641, 1992.
[5] Jamel, T. M. and Al-Magazachi, K. K.: “Simple variable step size
LMS algorithm for adaptive identification of IIR filtering system,”
IEEE International Conference on Communications, Computers and
Applications, 23-28, 2012.
[6] Wu, X., Gao, L. and Tan, Z.: “An improved variable step size LMS
algorithm,” IEEE International Conference on Measurement, Information
and Control (ICMIC), 01: 533-536, 2013.
[7] Li, M., Li, L. and Tai, H-M.: “Variable Step Size LMS Algorithm Based
on Function Control,” Springer, Circuits, Systems and Signal processing,
32 (6): 3121-3130, 2013.
[8] Schreiber, W. F.: “Advanced television systems for terrestrial
broadcasting: some problems and some proposed solutions,” Proceedings
of the IEEE, 83: 958-981, 1995.
[9] Duttweiler, D. L.: “Proportionate normalized least-mean-sqaures
adaptation in echo cancelers,” IEEE Transaction on Speech Audio
Processing, 8(5): 508-518, 2000.
[10] Chen, Y., Gu, Y. and Hero, A. O.: “Sparse LMS For System
Identification,” IEEE International Conference Acoustic, Speech and
Signal Processing, 3125-3128, 2009.
[11] Turan, C. and Salman, M. S.: “A sparse function controlled variable
step-size LMS algorithm for system identification,” Signal Processing and
Communications Applications Conference, 329-332, 2014.
[12] Madisetti, V. K. and Williams, D. B.: Digital Signal Processing
Handbook, CRC Press, 1999.
[13] Jahromi, M. N. S., Salman, M. S., Hocanin, A. and Kukrer, O.:
“Convergence Analysis of the Zero-Attracting Variable Step-Size LMS
Algorithm for Sparse System Identification,” Signal, Image & Video
Processing, Springer, 2013, DOI: 10.1007/s11760-013-0580-9.
[14] Salman, M. S.: “Sparse leaky-LMS algorithm for system identification
and its convergence analysis,” International Journal of Adaptive Control
and Signal Processing, 28: 1065-1072, 2014.
[15] Narayan, S., Peterson, A. M. and Narasimha,M. J.: “Transform domain
LMS algorithm,” IEEE Transactions on Acoustics, Speech and Signal
Processing, 31(3): 609-615, 1983.
[16] Shi, K. and Ma, X.: “Transform domain LMS algorithms for sparse
system identification,” IEEE International Conference on Acoustics,
Speech and Signal Processing, 3714-3717, 2010.
[17] Turan, C., Salman, M. S. and Haddad, H.: “A Transform Domain
Sparse LMS-type Algorithm for Highly Correlated Biomedical Signals in
Sparse System Identification” in IEEE 35th International Conference on
Electronics and Nanotechnology (ELNANO15), Kyiv, Ukraine, 711-714,
2015.
[18] Sing-Long, C. A., Tejos, C. A. and Irarrazaval, P.: “Evaluation of
continuous approximation functions for the l0 − norm for compressed
sensing” Proceedings of the International Society for Magnetic Resonance
in Medicine, 17, 2009.
[19] Strang, G.: Linear Algebra and its Applications, New York, Academic
Press, 1976.
[1] Sayed, A. H.: Fundamentals of Adaptive Filtering, Wiley, New York,
USA, 2003.
[2] Haykin, S.: Adaptive filter theory, Prentice Hall, Upper Saddle River, NJ,
2002.
[3] Bismor, D.: “Extension of LMS stability condition over a wide set of
signals,” International Journal of Adaptive Control and Signal Processing,
2014, DOI: 10.1002/acs.2500.
[4] Kwong, R. H.: “A Variable Step-Size LMS Algorithm,” IEEE Transaction
on Signal Processing, 40 (7): 1633-1641, 1992.
[5] Jamel, T. M. and Al-Magazachi, K. K.: “Simple variable step size
LMS algorithm for adaptive identification of IIR filtering system,”
IEEE International Conference on Communications, Computers and
Applications, 23-28, 2012.
[6] Wu, X., Gao, L. and Tan, Z.: “An improved variable step size LMS
algorithm,” IEEE International Conference on Measurement, Information
and Control (ICMIC), 01: 533-536, 2013.
[7] Li, M., Li, L. and Tai, H-M.: “Variable Step Size LMS Algorithm Based
on Function Control,” Springer, Circuits, Systems and Signal processing,
32 (6): 3121-3130, 2013.
[8] Schreiber, W. F.: “Advanced television systems for terrestrial
broadcasting: some problems and some proposed solutions,” Proceedings
of the IEEE, 83: 958-981, 1995.
[9] Duttweiler, D. L.: “Proportionate normalized least-mean-sqaures
adaptation in echo cancelers,” IEEE Transaction on Speech Audio
Processing, 8(5): 508-518, 2000.
[10] Chen, Y., Gu, Y. and Hero, A. O.: “Sparse LMS For System
Identification,” IEEE International Conference Acoustic, Speech and
Signal Processing, 3125-3128, 2009.
[11] Turan, C. and Salman, M. S.: “A sparse function controlled variable
step-size LMS algorithm for system identification,” Signal Processing and
Communications Applications Conference, 329-332, 2014.
[12] Madisetti, V. K. and Williams, D. B.: Digital Signal Processing
Handbook, CRC Press, 1999.
[13] Jahromi, M. N. S., Salman, M. S., Hocanin, A. and Kukrer, O.:
“Convergence Analysis of the Zero-Attracting Variable Step-Size LMS
Algorithm for Sparse System Identification,” Signal, Image & Video
Processing, Springer, 2013, DOI: 10.1007/s11760-013-0580-9.
[14] Salman, M. S.: “Sparse leaky-LMS algorithm for system identification
and its convergence analysis,” International Journal of Adaptive Control
and Signal Processing, 28: 1065-1072, 2014.
[15] Narayan, S., Peterson, A. M. and Narasimha,M. J.: “Transform domain
LMS algorithm,” IEEE Transactions on Acoustics, Speech and Signal
Processing, 31(3): 609-615, 1983.
[16] Shi, K. and Ma, X.: “Transform domain LMS algorithms for sparse
system identification,” IEEE International Conference on Acoustics,
Speech and Signal Processing, 3714-3717, 2010.
[17] Turan, C., Salman, M. S. and Haddad, H.: “A Transform Domain
Sparse LMS-type Algorithm for Highly Correlated Biomedical Signals in
Sparse System Identification” in IEEE 35th International Conference on
Electronics and Nanotechnology (ELNANO15), Kyiv, Ukraine, 711-714,
2015.
[18] Sing-Long, C. A., Tejos, C. A. and Irarrazaval, P.: “Evaluation of
continuous approximation functions for the l0 − norm for compressed
sensing” Proceedings of the International Society for Magnetic Resonance
in Medicine, 17, 2009.
[19] Strang, G.: Linear Algebra and its Applications, New York, Academic
Press, 1976.
@article{"International Journal of Electrical, Electronic and Communication Sciences:75893", author = "Cemil Turan and Mohammad Shukri Salman", title = "A Transform Domain Function Controlled VSSLMS Algorithm for Sparse System Identification", abstract = "The convergence rate of the least-mean-square (LMS)
algorithm deteriorates if the input signal to the filter is correlated.
In a system identification problem, this convergence rate can be
improved if the signal is white and/or if the system is sparse. We
recently proposed a sparse transform domain LMS-type algorithm
that uses a variable step-size for a sparse system identification.
The proposed algorithm provided high performance even if the
input signal is highly correlated. In this work, we investigate the
performance of the proposed TD-LMS algorithm for a large number
of filter tap which is also a critical issue for standard LMS algorithm.
Additionally, the optimum value of the most important parameter is
calculated for all experiments. Moreover, the convergence analysis
of the proposed algorithm is provided. The performance of the
proposed algorithm has been compared to different algorithms in a
sparse system identification setting of different sparsity levels and
different number of filter taps. Simulations have shown that the
proposed algorithm has prominent performance compared to the other
algorithms.", keywords = "Adaptive filtering, sparse system identification,
VSSLMS algorithm, TD-LMS algorithm.", volume = "11", number = "7", pages = "796-5", }
