Analysis of Normalized Orthogonal Gradient Adaptive Algorithm Based on Spline Adaptive Filtering for Smart Communication Technology

Abstract

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.

Diffusion Hammerstein Spline Adaptive Filtering Based on Orthogonal Gradient Adaptive Algorithm

“…Following [5], the forgetting factor λ q places on the orthogonal projection of gradient vector g qn and the previous directional vector d qn−1 as…”

“…N ONLINEAR spline-based adaptive filtering (SAF) has been interested for nonlinear system identification and modelling [1]- [5]. SAF structure consists of the adaptive linear finite impulse response (FIR) and the adaptive look-up table (LUT) by spline interpolation based on the least mean square (LMS) algorithm [1] and normalised LMS (NLMS) [2] in the nonlinear structure.…”

“…In [4], the authors have studied the SAF based on infinite impulse response (IIR) against the impulsive noise with the low computational complexity. As concerned with the fast convergence, an orthogonal gradient adaptive algorithm based on SAF framework has been revealed with the low disadjustment [5].…”

“…For the simulation following [28], a series of the DHSAF-based algorithms are compared with the non-cooperative HSAF-NOGA and based on HSAF-LMS [13] algorithms. The choice of used parameters are of the proposed HSAF-based algorithm are followed in [13], [36] with the learning rate set to µ q = µ w = 10 −3 , while these parameters of NOGA-based algorithm are referred to [5] with the learning rate set between µ q = µ w = 10 −4 and µ q = µ w = 10 −3 by randomly trial and error of learning rate to get the best solution for each algorithm.…”