Efficient FPGA implementation of Recursive Least Square adaptive filter using non-restoring division algorithm
Abstract
In this paper, Recursive Least Square (RLS) and Affine Projection (AP) adaptive filters are designed using Xilinx System Generator and implemented on the Spartan6 xc6slx16-2csg324 FPGA platform. FPGA platform utilizes the non-restoring division algorithm and the COordinate Rotation DIgital Computer (CORDIC) division algorithm to perform the division task of the RLS and AP adaptive filters. The Non-restoring division algorithm demonstrates efficient performance in terms of convergence speed and signal-to-noise ratio. In contrast, the CORDIC division algorithm requires 31 cycles for division initialization, whereas the non-restoring algorithm initializes division in just one cycle. To validate the effectiveness of the proposed filters, a set of ten ECG records from the BIT-MIT database is used to test their ability to remove Power Line Interference (PLI) noise from the ECG signal. The proposed adaptive filters are compared with various adaptive algorithms in terms of Signal-to-Noise Ratio (SNR), convergence speed, residual noise, steady-state Mean Square Error (MSE), and complexity.
References
T. T. Hasan, M. H. Jasim, I. A. Hashim. FPGA Design and Hardware Implementation of Heart Disease Diagnosis System Based on NVG-RAM Classifier, 2018 Third Scientific Conference of Electrical Engineering (SCEE), 2018, pp. 33-38, doi: 10.1109/SCEE.2018.8684125.
A. Z. Khan, I. Shafi . Removing Artifacts from Raw Electrocardiogram Signals Using Adaptive Filter in State Space. Circuits Syst Signal Process, 1713 (2020). doi:10.1007/s00034-019-01149-3.
T. M. Jamel, K. K.Al-Magazachi KK, Simple variable step size LMS algorithm for adaptive identification of IIR filtering system, The 5th International Conference on Communications, Computers and Applications (MIC-CCA2012), 2012, pp. 23-28.
M. Kazemi, M. M. Arefi. A fast iterative recursive least squares algorithm for Wiener model identification of highly nonlinear systems, ISA Transactions, Volume 67, 2017, Pages 382-388, doi: 10.1016/j.isatra.2016.12.002.
A. O. Abid Noor. Adaptive Noise Cancellation Using Noise Dependent Affine Projection Algorithm, Engineering and Technology Journal, Vol. 35, Part A, No. 6, 2017.
G. Swaminathan, G. Murugesan, S. Sasikala, L. Murali. A novel implementation of combined systolic and folded architectures for adaptive filters in FPGA, Microprocessors and Microsystems, Volume 74, 2020, doi: 10.1016/j.micpro.2020.103018.
M. Jayapravintha, S. Gomathi, G. Murugesan. Design of Systolic architecture for various adaptive filters for noise cancellation, 2015 3rd International Conference on Signal Processing, Communication and Networking (ICSCN), Chennai, India, 2015, pp. 1-6, doi: 10.1109/ICSCN.2015.7219907.
V. Kavitha, P. K. Priya, Tha.Sugapriyaa. Efficient Implementation of Adaptive Filter Architecture Using Gate Level Modification for ECG Denoising," Proceedings of 2018 the 8th International Workshop on Computer Science and Engineering, pp. 171-177, Bangkok, 28-30 June, 2018, doi:10.18178/wcse.2018.06.031.
M. Chandra, P. Goel, A. Anand, A. Kar. Design and analysis of improved high-speed adaptive filter architectures for ECG signal denoising, Biomedical Signal Processing and Control, Volume 63, 2021, doi:10.1016/j.bspc.2020.102221.
S. C., S. S., M.G. Denoising ECG signal using combination of ENSLMS and ZA-LMS algorithms, 3rd International Conference on Signal Processing, Communication and Networking (ICSCN), 2015, pp. 1-6.
S. Veni, “Real Time Implementation of SIGN LMS Adaptive Filters using Xilinx System Generator,” International Journal of Mathematics and Computers in Simulation, vol. 14, 2020.
S. Jayapoorani, D. Pandey, N. S. Sasirekha, et al, “Systolic optimized adaptive filter architecture designs for ECG noise cancellation by Vertex-5. AS 6,” 163–173 (2023). doi:10.1007/s42401-022-00177-3
F. Salehi, E. Farshidi, H. Kaabi. Novel design for a low-latency CORDIC algorithm for sine-cosine computation and its Implementation on FPGA, Microprocessors and Microsystems,Volume 77, 2020, 103197, ISSN 0141-9331, https://doi.org/10.1016/j.micpro.2020.103197.
R. S. Hongal, D. J. Anita. Comparative Study of Different Division Algorithms for Fixed and Floating Point Arithmetic Unit for Embedded Applications, 2016.
F. Ding, Y. Wang, J. Ding. Recursive least squares parameter identification algorithms for systems with colored noise using the filtering technique and the auxilary model, Digital Signal Processing, Volume 37, 2015, Pages 100-108, doi:10.1016/j.dsp.2014.10.005.
Y. Hu. Iterative and recursive least squares estimation algorithms for moving average systems, Simulation Modelling Practice and Theory, Volume 34, 2013, Pages 12-19, doi: 10.1016/j.simpat.2012.12.009
D. Liu, H. Zhao.Affine Projection Sign Subband Adaptive Filter Algorithm With Unbiased Estimation Under System Identification, in IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 70, no. 3, pp. 1209-1213, March 2023, doi: 10.1109/TCSII.2022.3216807
Y. Ren, Y. Zhi, J. Zhang. Geometric-algebra affine projection adaptive filter, EURASIP J. Adv. Signal Process. 2021, 82 (2021). doi:10.1186/s13634-021-00790-y
Downloads
Published
Issue
Section
License
Copyright (c) 2023 International Journal of Electronics and Telecommunications
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
1. License
The non-commercial use of the article will be governed by the Creative Commons Attribution license as currently displayed on https://creativecommons.org/licenses/by/4.0/.
2. Author’s Warranties
The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s. The undersigned also warrants that the manuscript (or its essential substance) has not been published other than as an abstract or doctorate thesis and has not been submitted for consideration elsewhere, for print, electronic or digital publication.
3. User Rights
Under the Creative Commons Attribution license, the author(s) and users are free to share (copy, distribute and transmit the contribution) under the following conditions: 1. they must attribute the contribution in the manner specified by the author or licensor, 2. they may alter, transform, or build upon this work, 3. they may use this contribution for commercial purposes.
4. Rights of Authors
Authors retain the following rights:
- copyright, and other proprietary rights relating to the article, such as patent rights,
- the right to use the substance of the article in own future works, including lectures and books,
- the right to reproduce the article for own purposes, provided the copies are not offered for sale,
- the right to self-archive the article
- the right to supervision over the integrity of the content of the work and its fair use.
5. Co-Authorship
If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.
6. Termination
This agreement can be terminated by the author or the Journal Owner upon two months’ notice where the other party has materially breached this agreement and failed to remedy such breach within a month of being given the terminating party’s notice requesting such breach to be remedied. No breach or violation of this agreement will cause this agreement or any license granted in it to terminate automatically or affect the definition of the Journal Owner. The author and the Journal Owner may agree to terminate this agreement at any time. This agreement or any license granted in it cannot be terminated otherwise than in accordance with this section 6. This License shall remain in effect throughout the term of copyright in the Work and may not be revoked without the express written consent of both parties.
7. Royalties
This agreement entitles the author to no royalties or other fees. To such extent as legally permissible, the author waives his or her right to collect royalties relative to the article in respect of any use of the article by the Journal Owner or its sublicensee.
8. Miscellaneous
The Journal Owner will publish the article (or have it published) in the Journal if the article’s editorial process is successfully completed and the Journal Owner or its sublicensee has become obligated to have the article published. Where such obligation depends on the payment of a fee, it shall not be deemed to exist until such time as that fee is paid. The Journal Owner may conform the article to a style of punctuation, spelling, capitalization and usage that it deems appropriate. The Journal Owner will be allowed to sublicense the rights that are licensed to it under this agreement. This agreement will be governed by the laws of Poland.
By signing this License, Author(s) warrant(s) that they have the full power to enter into this agreement. This License shall remain in effect throughout the term of copyright in the Work and may not be revoked without the express written consent of both parties.
