Swastika Mishra, Jibendu Sekhar Roy

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Echo cancellation is the most essential and indispensable component of telephone networks. The impulse responses of most of the networks are sparse in nature; that is, the impulse response has a small percentage of its components with a significant magnitude (large energy), while the rest are zero or small. In these sparse environments, conventional adaptive algorithms like least mean square (LMS) and normalized LMS (NLMS) show substandard and inferior performances. In this paper, the performances of the normalized least mean square (NLMS) algorithm, the normalized least mean fourth (NLMF) and the proportionate normalized least mean fourth (PNLMF) are compared for sparse echo cancellation. The sparseness of both the echo response and the input signal is exploited in this algorithm to achieve improved results at a low computational cost. The PNLMF algorithm showed better results and faster convergence in sparse and non sparse systems, but its results in sparse environments are more impressive. The NLMF algorithm shows good results in sparse environments but not in non-sparse environments. The PNLMS algorithm can be considered superior to the NLMF and NLMS algorithms with respect to the error profile. A modified algorithm, the sparse controlled modified proportionate normalized LMF (SCMPNLMF) algorithm, is proposed, and its performances are compared with the other algorithms.


channel sparsity, echo cancellation, sparse echo, sparse adaptive algorithm, NLMF, PNLMF, SCMPNLMF

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W. H. Khong, J. Benesty and P. A. Naylor, "Stereophonic Acoustic Echo Cancellation: Analysis of the Misalignment in the Frequency Domain", IEEE Signal Process. Lett., vol. 13, no. 1, pp.33-36, 2006.

S. Haykin, Adaptive Filter Theory, Prentice-Hall, Englewood Cliffs, NJ, 2002.

P. A. Naylor, J. Cui and M. Brookes, "Adaptive Algorithms for Sparse Echo Cancellation", J. Signal Process., vol. 86, pp. 1182-1192, 2006.

C. H. Lee, B. D. Rao and H. Garudadri, "A Sparse Conjugate Gradient Adaptive Filter", IEEE Signal Process. Lett., vol.27, pp. 1000-1004, 2020.

Y. Chen, Y. Gu and A. O. Hero, "Sparse LMS for System Identification", In Proceedins of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP),vol. 3, 2009, pp. 3125-3128.

H-C. Shin, A. H. Sayed and W-J. Song, "Variable Step-Size NLMS and Affine Projection Algorithms", IEEE Signal Process. Lett., vol.11, no. 2, pp. 132-135, 2004.

S. Mishra and J. S. Roy, "Blind Channel Equalization Using Adaptive Signal Processing Algorithms", IOSR J. Eng. (IOSR-JEN), vol. 9, no. 2, pp. 74-79, 2019.

R. Chinaboina, D. S. Ramkiran, H. Khan, M. Usha, B. T. P. Madhav, K. P. Srinivas and G. V. Ganesh, "Adaptive Algorithms for Acoustic Echo Cancellation in Speech Processing", Int. J. Res. Rev. Appl. Sci., vol. 7, no. 1, pp. 38-42, 2011.

C. Ye, K. Toyoda and T. Ohtsuki, "Improved Sparse Adaptive Algorithms for Accurate Non-contact Heartbeat Detection Using Time-Window-Variation Technique", In Proceedings of the 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Honolulu, HI, USA 18-21 July 2018, pp. 1-6.

I. Hassani, A. Kedjar, M. A. Ramdane, M. Arezki and A. Benallal, "Fast Sparse Adaptive Filtering Algorithms for Acoustic Echo Cancellation", In Proceedings of the International Conference on Communications and Electrical Engineering (ICCEE), 17-18 Dec.,2018, El Oued, Algeria, pp. 1-5.

A. Zhang, P. Liu, J. Sun and B. Ning , "Block-Sparsity Log-Sum-Induced Adaptive Filter for Cluster Sparse System Identification", IEEE Access , no. 8, pp. 175265-175276, 2020.

C. Paleologu, J. Benesty and S. Ciochina, Sparse Adaptive Filters for Echo Cancellation, Springer, 2010.

D.L. Duttweiler, "Proportionate Normalized Least-Mean Squares Adaptation in Echo Cancellers", IEEE Trans. Speech Audio Process., vol. 8, no. 5 , pp. 508-518, 2002.

E. Eweda, "A Stable Normalized Least Mean Fourth Algorithm with Improved Transient and Tracking Behaviors", IEEE Trans. Signal Process., vol. 64, no. 18, pp. 4805-4816, 2016.

W. H. Khong and P. A. Naylor, "Selective-tap Adaptive Algorithms in the solution of the Non-Uniqueness Problem for Stereophonic Acoustic Echo Cancellation", IEEE Signal Process. Lett., vol. 12, no. 4, pp. 269-272, 2005.

H. Zhang, K. Tan and D. Wang, "Deep Learning for Joint Acoustic Echo and Noise Cancellation with Nonlinear Distortions", In Proceedings of the 20th Annual Conference of the International Speech Communication Association (INTERSPEECH), Graz, Austria, 2019, pp.4255-4259.

A. Akhbari and A. Ghaffar, "The Performance Comparison of Improved Continuous Mixed P-norm and Other Adaptive Algorithms in Sparse System Identification", Int. J. Adv. Intell. Paradig., vol. 16, no. 1, pp. 65-74, 2020.

M. O. Sayin, Y. Yilmaz, A. Demir and S. S. Kozat, "The Krylov-Proportionate Normalized Least Mean Fourth Approach: Formulation and Performance Analysis", J. Signal Process., vol. 109, pp. 1-13, 2015.

X. Zhang, Y. Liu and X. Wang, "A Sparsity Preestimated Adaptive Matching Pursuit Algorithm", J. Electr. Comput. Eng., vol. 2021, pp. 1-8, 2021.

Z. Habibi, H. Zayyani and Md. S. E. Abadi, "A Robust Subband Adaptive Filter Algorithm For Sparse And Block-Sparse Systems Identification", J. Syst. Eng. Electron., vol.32, no. 2, pp.487-497, 2021.

F. L. Perez, C. A. Pitz and R. Seara, "A Two-gain NLMS Algorithm for Sparse System Identification", Signal Process., vol. 200, p. 108636, 2022.

Y. Li, Y. Wang and T. Jiang, "Sparse-aware Set-membership NLMS Algorithms and Their Application for Sparse Channel Estimation and Echo Cancelation", AEÜ-Int. J. Electron. Commun., vol. 70, pp. 895-902, 2016.


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