A Novel Kernel Algorithm for Finite Impulse Response Channel Identification

• Autorzy: Fateh Rachid , Darif Anouar , Boumezzough Ahmed , Safi Said , Frikel Miloud

Identyfikatory

DOI

10.26636/jtit.2023.169823

• Języki publikacji: EN

Abstrakty

EN

Over the last few years, kernel adaptive filters have gained in importance as the kernel trick started to be used in classic linear adaptive filters in order to address various regression and time-series prediction issues in nonlinear environments.In this paper, we study a recursive method for identifying finite impulse response (FIR) nonlinear systems based on binary-value observation systems. We also apply the kernel trick to the recursive projection (RP) algorithm, yielding a novel recursive algorithm based on a positive definite kernel. For purposes, our approach is compared with the recursive projection (RP) algorithm in the process of identifying the parameters of two channels, with the first of them being a frequency-selective fading channel, called a broadband radio access network (BRAN B) channel, and the other being a a theoretical frequency-selective channel, known as the Macchi channel. Monte Carlo simulation results are presented to show the performance of the proposed algorithm.

Słowa kluczowe

EN

finite impulse response; kernel adaptive filtering; kernel recursive projection identification; nonlinear system identification

• Wydawca: Instytut Łączności - Państwowy Instytut Badawczy
• Czasopismo: Journal of Telecommunications and Information Technology
• Rocznik: 2023
• Tom: nr 2
• Strony: 84--93
• Opis fizyczny: Bibliogr. 53 poz., rys., tab., wykr.

Twórcy

autor

Fateh Rachid

• Laboratory of Innovation in Mathematics, Applications and Information Technologies (LIMATI), Polydisciplinary Faculty, Sultan Moulay Slimane University, Beni Mellal, Morocco

• https://orcid.org/0000-0002-0574-2105

autor

Darif Anouar

• Laboratory of Innovation in Mathematics, Applications and Information Technologies (LIMATI), Polydisciplinary Faculty, Sultan Moulay Slimane University, Beni Mellal, Morocco

• https://orcid.org/0000-0001-8026-9189

autor

Boumezzough Ahmed

• Laboratory of Research in Physics and Engineering Sciences, Polydisciplinary Faculty, Sultan Moulay Slimane University, Beni Mellal, Morocco

autor

Safi Said

• Laboratory of Innovation in Mathematics, Applications and Information Technologies (LIMATI), Polydisciplinary Faculty, Sultan Moulay Slimane University, Beni Mellal, Morocco

• https://orcid.org/0000-0003-3390-9037

autor

Frikel Miloud

• Laboratoire d’Automatique de Caen, UNICAEN, ENSICAEN, Normandie University, Caen, France

• https://orcid.org/0000-0003-2178-1814

Bibliografia

• [1] S. Haykin, Adaptive Filter Theory, 4th ed. Prentice Hall, Delhi, 2002 (ISBN: 9780130901262).
• [2] M.M. Sondhi, "The history of echo cancellation", IEEE Signal Processing Magazine, vol. 23, no. 5, pp. 95–102, 2006 (https://doi.org/10.1109/MSP.2006.1708416).
• [3] A.H. Sayed, Fundamentals of Adaptive Filtering. New York: John Wiley & Sons, 824 p., 2003 (ISBN: 9780471461265).
• [4] P.S.R. Diniz, Adaptive Filtering: Algorithms and Practical Implementations, 3rd ed. New York: Springer, 495 p., 2008 (https://doi.org/10.1007/978-3-030-29057-3).
• [5] R. Fateh, A. Darif, and S. Safi, "Kernel and linear adaptive methods for the BRAN channels identification", AI2SD: International Conference on Advanced Intelligent Systems for Sustainable Development, vol. 2, pp. 579–591, 2020 (https://doi.org/10.1007/978-3-030-90 633-7).
• [6] R. Fateh, A. Darif, and S. Safi, "Identification of the linear dynamic parts of wiener model using kernel and linear adaptive", AI2SD: International Conference on Advanced Intelligent Systems for Sustainable Development, vol. 2, pp. 387–400, 2020 (https://doi.org/10.1007/978-3-030-90633-7).
• [7] E. Ferrara, "Fast implementations of LMS adaptive filters", IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 28, no. 4, pp. 474–475, 1980 (https://doi.org/10.1109/tassp.19 80.1163432).
• [8] M. Zidane and R. Dinis, "A new combination of adaptive channel estimation methods and TORC equalizer in MC-CDMA systems", International Journal of Communication Systems, vol. 33, no. 11, e4429, 2020 (https://doi.org/10.1002/dac.4429).
• [9] M. Zidane, S. Safi, and M. Sabri, "Measured and estimated data of nonlinear BRAN channels using HOS in 4G wireless communications", Data in Brief, vol. 17, pp. 1136–1148, 2018 (https://doi.org/10.1016/j.dib.2018.02.005).
• [10] R. Fateh, A. Darif, and S. Safi, "Performance Evaluation of MC-CDMA Systems with Single User Detection Technique using Kernel and Linear Adaptive Method", Journal of Telecommunications and Information Technology, no. 4, pp. 1–11 2021 (https://doi.org/10.26636/jtit.2021.151621).
• [11] M. Zidane, S. Safi, and M. Sabri, "Compensation of fading channel using partial combining equalizer in MC-CDMA systems", Journal of Telecommunications and Information Technology, no. 1, pp. 5–11, 2017 [Online]. Available: https://www.il-pib.pl/czasopisma /JTIT/2017/1/5.pdf
• [12] S. Safi, M. Frikel, A. Zeroual, and M. M’Saad, "Higher order cumulants for identification and equalization of multicarrier spreading spectrum systems", Journal of Telecommunications and Information Technology, no. 2, pp. 74–84, 2011 [Online]. Available:https://www.il-pib.pl/czasopisma/JTIT/2011/2/74.pdf
• [13] L. Ljung, System Identification: Theory for the User. Upper Saddle River (NJ): Prentice Hall PTR, 1999 (ISBN: 9780136566953).
• [14] F. Ding, System Identification – Performances Analysis for Ide tification Methods. Beijing, China: Science Press, pp. 1–12, 2014 [in Chinese].
• [15] X. Zhang, F. Ding, F.E. Alsaadi, and T. Hayat, "Recursive parameter identification of the dynamical models for bilinear state space systems", Nonlinear Dynamics, vol. 89, no. 4, pp. 2415–2429, 2017 (https://doi.org/10.1007/S11071-017-3594-Y).
• [16] L. Xu, "Application of the Newton iteration algorithm to the parameter estimation for dynamical systems", Journal of Computational and Applied Mathematics, vol. 288, pp. 33–43, 2015 (https://doi.org/10.1016/j.cam.2015.03.057).
• [17] Q. Song, "Recursive identification of systems with binary-valued out-puts and with ARMA noises", Automatica, vol. 93, pp. 106–113, 2018 (https://doi.org/10.1016/j.automatica.2018.03.059).
• [18] J. Guo, X. Wang, W. Xue, and Y. Zhao, "System identification with binary-valued observations under data tampering attacks", IEEE Transactions on Automatic Control, vol. 66, no. 8, pp. 3825–3832, 2020 (https://doi.org/10.1109/TAC.2020.3029325).
• [19] R. Fateh, A. Darif, and S. Safi, "Channel identification of non-linear systems with binary-valued output observations based on positive definite kernels", E3S Web of Conferences, vol. 297, 2021 (https://doi.org/10.1051/e3sconf/202129701020).
• [20] L. Li, F. Wang, H. Zhang, and X. Ren, "A novel recursive learning estimation algorithm of Wiener systems with quantized observations", ISA Transactions, vol. 112, pp. 23–34, 2021 (https://doi.org/10.1016/j.isatra.2020.11.032).
• [21] L. Zhang, Y. Zhao, and L. Guo, "Identification and adaptation with binary-valued observations under non-persistent excitation condition", Automatica, vol. 138, 2022 (https://doi.org/10.48550/arXi v.2107.03588).
• [22] R. Fateh and A. Darif, "Mean square convergence of reproducing kernel for channel identification: Application to Bran D Channel impulse response", in International Conference on Business Intelligence, vol. 416, pp. 284–293, 2021 (https://doi.org/10.1007/978-3-030-76508-8_20).
• [23] J.F. Zhang and G.G. Yin, "System identification using binary sensors", IEEE Transactions on Automatic Control, vol. 48, no. 11, pp. 1892–1907, 2003 (https://doi.org/10.1109/TAC.2003.819073).
• [24] L.Y. Wang, G.G. Yin, and J.F. Zhang, "Joint identification of plant rational models and noise distribution functions using binary-valued observations", Automatica, vol. 42, no. 4, pp. 535–547, 2006 (https://doi.org/10.1016/j.automatica.2005.12.004).
• [25] J. Guo, Y. Zhao, C.Y. Sun, and Y. Yu, "Recursive identification of FIR systems with binary-valued outputs and communication channels", Automatica, vol. 60, pp. 165–172, 2015 (https://doi.org/10.1016/j.automatica.2015.06.030).
• [26] J. Guo and Y. Zhao, "Recursive projection algorithm on FIR system identification with binary-valued observations", Automatica, vol. 49, no. 11, pp. 3396–3401, 2013 (https://doi.org/10.1016/j.au tomatica.2013.08.011).
• [27] M. Pouliquen, E. Pigeon, O. Gehan, A. Goudjil, and R. Auber, "Impulse response identification from input/output binary measurements", Automatica, vol. 123, art. no. 109307, 2021 (https://doi.org/10.1016/j.automatica.2020.109307).
• [28] M. Pouliquen, E. Pigeon, O. Gehan, and A. Goudjil, "Identification using binary measurements for IIR systems", IEEE Transactions on Automatic Control, vol. 65, no. 2, pp. 786–793, 2019 (https://doi.org/10.1109/TAC.2019.2921657).
• [29] J. Shawe-Taylor and N. Cristianini, Kernel Methods for Pattern Analysis. Cambridge University Press, 2004 (https://doi.org/10.1017/CBO9780511809682).
• [30] W. Liu, J.C. Principe, and S. Haykin, Kernel Adaptive Filtering: A Comprehensive Introduction. John Wiley & Sons, 240 p., 2011 (ISBN: 9780470447536).
• [31] R. Fateh, A. Darif and S. Safi, "Hyperbolic functions impact evaluation on channel identification based on recursive kernel algorithm", 2022 8th International Conference on Optimization and Applications (ICOA), Genoa, Italy, pp. 1–6, 2022 (https://doi.org/10.1109/ICOA55659.2022.9934118).
• [32] J.W. Xu, A.R. Paiva, M. Park, and J.C. Principe, "A reproducing kernel Hilbert space framework for information-theoretic learning", IEEE Transactions on Signal Processing, vol. 56, no. 12, pp. 5891–5902, 2008 (https://doi.org/10.1109/TSP.2008.2005085).
• [33] F. Girosi, M. Jones, and T. Poggio, "Regularization theory and neural networks architectures", Neural Computation, vol. 7, no. 2, pp. 219–269, 1995 (https://doi.org/10.1162/neco.1995.7. 2.219).
• [34] C.K.I. Williams and C.E. Rasmussen, Gaussian Processes for Machine Learning. Cambridge: MIT Press, 2005 (https://doi.org/10.7551/mitpress/3206.001.0001).
• [35] C. Cortes, and V. Vapnik, "Support-vector networks", Machine Learning, vol. 20, no. 3, pp. 273–297, 1995 (https://doi.org/10.1007/bf00994018).
• [36] W. Liu, J.C. Principe, "Kernel affine projection algorithms", EURASIP Journal on Advances in Signal Processing, no. 1, pp. 1–12, 2008 (https://doi.org/10.1155/2008/784292).
• [37] B. Scholkopf, A. Smola, and K.R. Muller, "Kernel principal component analysis", in International Conference on Artificial Neural Networks (ICANN), Lausanne, Switzerland, pp. 583–588, 1997 (https://doi.org/10.1007/BFb0020217).
• [38] W. Liu, P. P. Pokharel, and J. C. Principe, "The kernel least-meansquare algorithm", IEEE Transactions on Signal Processing, vol. 56, no. 2, pp. 543–554, 2008 (https://doi.org/10.1109/tsp.2007 .907881).
• [39] Y. Engel, S. Mannor, and R. Meir, "The kernel recursive least-squares algorithm", IEEE Transactions on Signal Processing, vol. 52, no. 8, pp. 2275–2285, 2004 (https://doi.org/10.1109/TSP.2004. 830985).
• [40] B. Chen, S. Zhao, P. Zhu, and J.C. Principe, "Quantized kernel recursive least squares algorithm", IEEE Transactions on Neural Networks and Learning Systems, vol. 24, no. 9, pp. 1484–1491, 2013 (https://doi.org/10.1109/tnnls.2013.2258936).
• [41] B. Chen, S. Zhao, P. Zhu, and J.C. Principe, "Quantized kernel least mean square algorithm", IEEE Transactions on Neural Networks and Learning Systems, vol. 23, no. 1, pp. 22–32, 2011 (https://doi.org/10.1109/tnnls.2011.2178446).
• [42] W. Liu, I. Park, Y. Wang, and J.C. Principe, "Extended kernel recursive least squares algorithm", IEEE Transactions on Signal Processing, vol. 57, no. 10, pp. 3801–3814, 2009 (https://doi.org/10.1109/tsp.2009.2022007).
• [43] B. Chen, J. Liang, N. Zheng, and J.C. Príncipe, "Kernel least mean square with adaptive kernel size", Neurocomputing, vol. 191, pp. 95–106, 2016 (https://doi.org/10.1016/j.neucom.2016 .01.004).
• [44] Z. Qin, B. Chen, and N. Zheng, "Random Fourier feature kernel recursive least squares", in 2017 International Joint Conference on Neural Networks (IJCNN), Anchorage, AK, USA, pp. 2881–2886, 2017 (https://doi.org/10.1109/IJCNN.2017.7966212).
• [45] Q. Wu, Y. Li, Y.V. Zakharov, and W. Xue, "Quantized kernel Least lncosh algorithm", Signal Processing, vol. 189, art. no. 108255, 2021 (https://doi.org/10.1016/j.sigpro.2021.108255).
• [46] R. Fateh, A. Darif, and S. Safi, "An extended version of the proportional adaptive algorithm based on kernel methods for channel identification with binary measurements", Journal of Telecommunications and Information Technology, no. 3, pp. 47–58, 2022 (https://doi.org/10.26636/jtit.2022.161122).
• [47] J. Guo and Y. Zhao, "Identification of the gain system with quantized observations and bounded persistent excitations", Science China Information Sciences, vol. 57, no. 1, pp. 1–15, 2014 (https://doi.org/10.1007/s11432-012-4761-x).
• [48] J.D. Diao, J. Guo, C.Y. Sun, "Event-triggered identification of FIR systems with binary-valued output observations", Automatica, vol. 98, pp. 95–102, 2018 (https://doi.org/10.1016/j.automati ca.2018.09.024).
• [49] N. Aronszajn, "Theory of reproducing kernels", Transactions of the American Mathematical Society, vol. 68, no. 3, pp. 337–404, 1950 (https://doi.org/10.2307/1990404).
• [50] C.J.C. Burges, "A tutorial on support vector machines for pattern recognition", Data Mining and Knowledge Discovery, vol. 2, no. 2, pp. 121–167, 1998 (https://doi.org/10.1023/a:1009715923 555).
• [51] ETSI. Broadband Radio Access Network (BRAN); Hiperlan type 2; Physical (PHY) layer, Technical Report, December 2001.
• [52] ETSI. Broadband Radio Access Network (BRAN); Hiperlan type 2; Requirements and architectures for wireless broadband access, January, 1999.
• [53] O. Macchi, C.A. Faria da Rocha, and J.M. Travassos-Romano, "Égalisation adaptative autodidacte par rétroprédiction et prédiction", XIV Colloque GRETSI, pp. 491–493, 1993 [in French].

Uwagi

PL

W artykule błędny ORCID Boumezzough Ahmed

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).