Abstract
Herein, we propose a new class of stochastic gradient algorithm for channel identification. The proposed q-least mean fourth (q-LMF) is an extension of the least mean fourth (LMF) algorithm and it is based on the q-calculus which is also known as Jackson’s derivative. The proposed algorithm utilizes a novel concept of error correlation energy and normalization of signal to ensure a high convergence rate, better stability, and low steady-state error. Contrary to conventional LMF, the proposed method has more freedom for large step sizes. Extensive experiments show significant gain in the performance of the proposed q-LMF algorithm in comparison to the contemporary techniques.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
T. Abbas, S. Khan, M. Sajid, A. Wahab, J.C. Ye, Topological sensitivity based far-field detection of elastic inclusions. Results Phys. 8, 442–460 (2018)
J. Ahmad, M. Usman, S. Khan, I. Naseem, H.J. Syed, RVP-FLMS: a robust variable power fractional LMS algorithm, in 2016 IEEE International Conference on Control System, Computing and Engineering (ICCSCE) (IEEE, 2016)
J. Ahmad, S. Khan, M. Usman, I. Naseem, M. Moinuddin, FCLMS: fractional complex LMS algorithm for complex system identification, in 13th IEEE Colloquium on Signal Processing and its Applications (CSPA 2017) (IEEE, 2017)
U.M. Al-Saggaf, M. Moinuddin, A. Zerguine, An efficient least mean squares algorithm based on q-gradient, in 2014 48th Asilomar Conference on Signals, Systems and Computers, Nov 2014, pp. 891–894
U.M. Al-Saggaf, M. Moinuddin, M. Arif, A. Zerguine, The q-Least Mean Squares algorithm. Signal Process. 111(Suppl. C), 50–60 (2015)
H. Ammari, E. Bretin, J. Garnier, H. Kang, H. Lee, A. Wahab, Mathematical Methods in Elasticity Imaging (Princeton University Press, 2015)
S.C. Douglas, A family of normalized LMS algorithms. IEEE Signal Process. Lett. 1(3), 49–51 (1994)
T. Ernst, A Comprehensive Treatment of q-Calculus, 1st edn. (Springer, Basel, 2012)
J.M. Górriz, J. Ramírez, S. Cruces-Alvarez, C.G. Puntonet, E.W. Lang, D. Erdogmus, A novel LMS algorithm applied to adaptive noise cancellation. IEEE Signal Process. Lett. 16(1), 34–37 (2009)
S. Khan, I. Naseem, R. Togneri, M. Bennamoun, A novel adaptive kernel for the RBF neural networks. Circuits Syst. Signal Process. 1–15, (2016)
S. Khan, J. Ahmad, I. Naseem, M. Moinuddin, A novel fractional gradient-based learning algorithm for recurrent neural networks. Circuits Syst. Signal Process. 1–20, (2017)
S. Khan, N. Ahmed, M.A. Malik, I. Naseem, R. Togneri, M. Bennamoun, FLMF: fractional least mean fourth algorithm for channel estimation in non-Gaussian environment, in International Conference on Information and Communications Technology Convergence 2017 (ICTC 2017) (Jeju Island, Korea, October 2017)
S. Khan, M. Usman, I. Naseem, R. Togneri, M. Bennamoun, A robust variable step size fractional least mean square (RVSS-FLMS) algorithm, in 13th IEEE Colloquium on Signal Processing and its Applications (CSPA 2017) (IEEE, 2017)
S. Khan, M. Usman, I. Naseem, R. Togneri, M. Bennamoun, VP-FLMS: a novel variable power fractional LMS algorithm, in 2017 Ninth International Conference on Ubiquitous and Future Networks (ICUFN) (ICUFN 2017) (Italy, Milan, July 2017)
S. Khan, I. Naseem, M.A. Malik, R. Togneri, M. Bennamoun, A fractional gradient descent-based RBF neural network. Circuits Syst. Signal Process. 1–22, (2018)
S. Khan, I. Naseem, A. Sadiq, J. Ahmad, M. Moinuddin, Comments on “Momentum fractional LMS for power signal parameter estimation”. arXiv preprint arXiv:1805.07640 (2018)
S. Khan, A. Sadiq, I. Naseem, R. Togneri, M. Bennamoun, Enhanced \(q\)-least mean square. arXiv preprint arXiv:1801.00410 (2018)
S. Khan, A. Wahab, I. Naseem, M. Moinuddin, Comments on “Design of fractional-order variants of complex LMS and NLMs algorithms for adaptive channel equalization”. arXiv preprint arXiv:1802.09252 (2018)
J. Koekoek, R. Koekoek, A note on the q-derivative operator. ArXiv Mathematics e-prints (1999)
N.V. Thakor, Y.S. Zhu, Applications of adaptive filtering to ECG analysis: noise cancellation and arrhythmia detection. IEEE Trans. Biomed. Eng. 38(8), 785–794 (1991)
A. Wahab, S. Khan, Comments on “Fractional extreme value adaptive training method: fractional steepest descent approach”. arXiv preprint arXiv:1802.09211 (2018)
E. Walach, B. Widrow, The least mean fourth (LMF) adaptive algorithm and its family. IEEE Trans. Inf. Theor. 30(2), 275–283 (2006)
A. Zerguine, M.K. Chan, T.Y. Al-Naffouri, M. Moinuddin, C.F. Cowan, Convergence and tracking analysis of a variable normalised LMF (XE-NLMF) algorithm. Signal Process. 89(5), 778–790 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Sadiq, A., Usman, M., Khan, S., Naseem, I., Moinuddin, M., Al-Saggaf, U.M. (2020). q-LMF: Quantum Calculus-Based Least Mean Fourth Algorithm. In: Yang, XS., Sherratt, S., Dey, N., Joshi, A. (eds) Fourth International Congress on Information and Communication Technology. Advances in Intelligent Systems and Computing, vol 1041. Springer, Singapore. https://doi.org/10.1007/978-981-15-0637-6_25
Download citation
DOI: https://doi.org/10.1007/978-981-15-0637-6_25
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-0636-9
Online ISBN: 978-981-15-0637-6
eBook Packages: EngineeringEngineering (R0)