Analysis of Normalized Orthogonal Gradient Adaptive Algorithm Based on Spline Adaptive Filtering for Smart Communication Technology
Keywords:Spline adaptive filtering (SAF), normalized orthogonal gradient adaptive (NOGA) algorithm, nonlinear systems
This paper presents a general theoretical framework of spline adaptive filtering based on a normalized version of orthogonal gradient adaptive algorithm. A nonlinear spline adaptive filter normally consists of a linear combination with a memory-less function and a spline function for adaptive approach. We explain how the adaptive linear filter and spline control points are derived in a straightforward iterative gradient-based method. In order to improve the convergence characteristics, the normalized version of orthogonal gradient adaptive algorithm is introduced by the orthogonal projection along with the gradient adaptive algorithm. In addition, a simple form of adaptation algorithm is introduced how to obtain a lower bound on the excess mean square error (MSE) in a theoretical basis. Convergence and stability analysis based on the MSE criterion are proven in terms of the excess MSE. Simulation results reveal that the proposed algorithm achieves more robustness compared with the conventional spline adaptive filtering algorithm.
L. Ljung. System Identification- Theory for the user. Upper Saddle River, NJ. 1999.
M. Scarpiniti, D. Comminiello, R. Parisi and A. Uncini. Nonlinear Spline Adaptive Filtering. Signal Processing, 93(4): 772–783, 2013.
M. Scarpiniti, D. Comminiello, R. Parisi and A. Uncini. Novel Cascade Spline Architectures for the Identification of Nonlinear Systems. IEEE Transactions on Circuits and Systems I: Regular Papers, 62(7): 1825–1835, 2015.
M. Scarpiniti, D. Comminiello, R. Parisi and A. Uncini. Hammerstein Uniform Cubic Spline Adaptive Filtering: Learning and Convergence Properties. Signal Processing, 100: 112–123, 2014.
M. Scarpiniti, D. Comminiello, R. Parisi and A. Uncini. Spline Adaptive Filters: Theory and Applications, Adaptive Learning Methods for Nonlinear System Modeling, ELSEVIER, 47–69, 2018.
S. Guan and Z. Li. Normalised Spline Adaptive Filtering Algorithm for Nonlinear System Identification. Neural Processing Letter, 46(2), 595–607, 2017.
M. Scarpiniti, D. Comminiello, R. Parisi and A. Uncini. Nonlinear System Identification using IIR Spline Adaptive Filters. Signal Processing, 108, 30–35, 2015.
C. Liu and Z. Zhang. Set-membership Normalised Least M-estimate Spline Adaptive Filtering Algorithm in Impulsive Noise. Electronics Letters, 54(6), 393–395, 2018.
P.S.R. Diniz. Adaptive Filtering: Algorithms and Practical Implementation. Springer, 2008.
S. Sitjongsataporn. Convergence Analysis of Greedy Normalised Orthogonal Gradient Adaptive Algorithm. In Proceedings of IEEE International Symposium on Communications and Information Technologies, Bangkok, Thailand, pp. 345–348, 2018.
S. Guarnieri, F. Piazza and A. Uncini. Multilayer Feedforward Networks with Adaptive Spline Activation Function. IEEE Transactions on Neural Network, 10(3): 672–683, 1999.
S. Kalluri, G.R. Arce. General Class of Nonlinear Normalized Adaptive Filtering Algorithms. IEEE Transactions on Signal Processing, 48(8): 2262–2272, 1999.
S. Sitjongsataporn and T. Wiangtong. Spline Adaptive Filtering based on Normalised Orthogonal Gradient Adaptive Algorithm. In Proceedings of IEEE International Conference on Engineering, Applied Sciences and Technology, pp. 575–578, 2019.
S. Prongnuch and S. Sitjongsataporn. Performance Analysis and Enhancement of Spline Adaptive Filtering based on Adaptive Step-size Variable Leaky Least Mean Square Algorithm. Advances in Science, Technology and Engineering Systems Journal, 5(6): 642–651, 2020.