International Science Index


10007462

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.
References:
[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.