scholarly journals The Generalized Complex Kernel Affine Projection Algorithms

2021 ◽  
Author(s):  
Xiaojian Wang ◽  
Ming Zhang ◽  
Jianxing Li ◽  
Wenchao Chen ◽  
Anxue Zhang
Keyword(s):  
Reproducing Kernel ◽  
Complete Solution ◽  
Nonlinear Problems ◽  
Statistical Characteristics ◽  
Gram Matrix ◽  
Least Mean Square ◽  
Performance Improvements ◽  
Affine Projection ◽  
Generalized Complex ◽  
Complex Valued

AbstractThe complex kernel adaptive filter (CKAF) has been widely applied to the complex-valued nonlinear problem in signal processing and machine learning. However, most of the CKAF applications involve the complex kernel least mean square (CKLMS) algorithms, which work in a pure complex or complexified reproducing kernel Hilbert space (RKHS). In this paper, we propose the generalized complex kernel affine projection (GCKAP) algorithms in the widely linear complex-valued RKHS (WL-RKHS). The proposed algorithms have two main notable features. One is that they provide a complete solution for both circular and non-circular complex nonlinear problems and show many performance improvements over the CKAP algorithms. The other is that the GCKAP algorithms inherit the simplicity of the CKLMS algorithm while reducing its gradient noise and boosting its convergence. The second-order statistical characteristics of WL-RKHS have also been developed. An augmented Gram matrix consists of a standard Gram matrix and a pseudo-Gram matrix. This decomposition provides more underlying information when the real and imaginary parts of the signal are correlated and learning is independent. In addition, some online sparsification criteria are compared comprehensively in the GCKAP algorithms, including the novelty criterion, the coherence criterion, and the angle criterion. Finally, two nonlinear channel equalization experiments with non-circular complex inputs are presented to illustrate the performance improvements of the proposed algorithms.

scholarly journals The Generalized Complex Kernel Least-Mean-Square Algorithm

2019 ◽  
Vol 67 (20) ◽  
pp. 5213-5222 ◽  
Author(s):  
Rafael Boloix-Tortosa ◽  
Juan Jose Murillo-Fuentes ◽  
Sotirios A. Tsaftaris
Keyword(s):  
Mean Square ◽  
Least Mean Square ◽  
Generalized Complex ◽  
Least Mean Square Algorithm ◽  
Kernel Least Mean Square

scholarly journals Memory-Dependent Forecasting of COVID-19: The Flexibility of Extrapolated Kernel Least Mean Square Algorithm

2021 ◽  
Author(s):  
Noor Ahmad ◽  
Mohd Hafiz Mohd
Keyword(s):  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Gradient Estimate ◽  
Situational Analysis ◽  
Mean Square ◽  
Least Mean Square ◽  
State Variables ◽  
Data Set ◽  
Least Mean Square Algorithm ◽  
Kernel Least Mean Square

The extrapolated kernel least mean square algorithm (extrap-KLMS) with memory is proposed for the forecasting of future trends of COVID-19. The extrap-KLMS is derived in the framework of data-driven modelling that attempts to describe the dynamics of infectious disease by reconstructing the phase-space of the state variables in a reproducing kernel Hilbert space (RKHS). Short-time forecasting is enabled via an extrapolation of the KLMS trained model using a forward euler step, along the direction of a memory-dependent gradient estimate. A user-defined memory averaging window allows users to incorporate prior knowledge of the history of the pandemic into the gradient estimate thus providing a spectrum of scenario-based estimates of futures trends. The performance of the extrap-KLMS method is validated using data set for Malaysia, Saudi Arabia and Italy in which we highlight the flexibility of the method in capturing persistent trends of the pandemic. A situational analysis of the Malaysian third wave further demonstrate the capabilities of our method

scholarly journals FIELD PROGRAMMABLE GATE ARRAY IMPLEMENTATION OF A VARIABLE LEAKY LEAST MEAN SQUARE ADAPTIVE ALGORITHM

2017 ◽  
Vol 10 (13) ◽  
pp. 69
Author(s):  
Purvika Kalkar ◽  
John Sahaya Rani Alex
Keyword(s):  
Field Programmable Gate Array ◽  
Noise Cancellation ◽  
Least Square ◽  
Lms Algorithm ◽  
Statistical Characteristics ◽  
Mean Square ◽  
Least Mean Square ◽  
Recursive Least Square ◽  
Field Programmable ◽  
Gate Array

Adaptive noise cancellation is an extensively researched area of signal processing. Many algorithms had been studied such as least mean square algorithm (LMS), recursive least square algorithm, and normalized LMS algorithm. The statistical characteristics of noise are fast in nature and the algorithms for noise cancellation should converge fast. Since LMS algorithm has slow convergence; in this paper, a variable leaky LMS (VLLMS) algorithm is explored. VLLMS is implemented using the concept of hardware-software cosimulation using Xilinx System Generator. The design is implemented on Virtex-6 ML605 field programmable gate array board. The implemented design is tested for sinusoidal signal added with an additivewhite Gaussian noise. The design summary and the utilization summary are presented. 

scholarly journals Multichannel Active Noise Control Based on Filtered-x Affine Projection-Like and LMS Algorithms with Switching Filter Selection

2019 ◽  
Vol 9 (21) ◽  
pp. 4669 ◽  
Author(s):  
Ángel A. Vázquez ◽  
Eduardo Pichardo ◽  
Juan G. Avalos ◽  
Giovanny Sánchez ◽  
Hugo M. Martínez ◽  
...  
Keyword(s):  
Steady State ◽  
Computational Cost ◽  
Lms Algorithm ◽  
Alternative Methods ◽  
Mean Square ◽  
Least Mean Square ◽  
Affine Projection ◽  
Mean Square Errors ◽  
Switching Filter ◽  
Filter Selection

Affine projection (AP) algorithms have been demonstrated to have faster convergence speeds than the conventional least mean square (LMS) algorithms. However, LMS algorithms exhibit smaller steady-state mean square errors (MSEs) when compared with affine projection (AP) algorithms. Recently, several authors have proposed alternative methods based on convex combinations to improve the steady-state MSE of AP algorithms, even with the increased computational cost from the simultaneous use of two filters. In this paper, we present an alternative method based on an affine projection-like (APL-I) algorithm and least mean square (LMS) algorithm to solve the ANC under stationary Gaussian noise environments. In particular, we propose a switching filter selection criteria to improve the steady-state MSE without increasing the computational cost when compared with existing models. Here, we validate the proposed strategy in a single and a multichannel system, with and without automatically adjusting the scaling factor of the APL-I algorithm. The results demonstrate that the proposed scheme exploits the best features of each filter (APL-I and LMS) to guarantee rapid convergence with a low steady-state MSE. Additionally, the proposed approach demands a low computational burden compared with existing convex combination approaches, which will potentially lead to the development of real-time ANC applications.

Investigation of Radial Basis Collocation Method for Incremental-Iterative Analysis

2016 ◽  
Vol 08 (01) ◽  
pp. 1650007 ◽  
Author(s):  
Judy P. Yang ◽  
Wan-Ting Su
Keyword(s):  
Nonlinear Analysis ◽  
Collocation Method ◽  
Reproducing Kernel ◽  
Nonlinear Problems ◽  
Quadrature Rule ◽  
Weak Form ◽  
Strong Form ◽  
Collocation Methods ◽  
Particle Methods ◽  
Radial Basis

We propose an incremental-iterative algorithm by using the strong form collocation method for solving geometric nonlinear problems. As nonlinear analyses concerning large deformation have been relied on the weak form-based methods such as the finite element methods and the reproducing kernel particle methods, the recently developed strong form collocation methods could be new research directions in that the mesh control and quadrature rule are abandoned in the collocation methods. In this work, the radial basis collocation method is adopted to perform the nonlinear analysis. The corresponding parameters affecting the deformation paths such as the increment of applied traction and shape parameter of the radial basis function are discussed. We also investigate the possibility of using the weighted collocation methods in the nonlinear analysis.

scholarly journals Adaptive Equalizer Using Selective Partial Update Algorithm and Selective Regressor Affine Projection Algorithm over Shallow Water Acoustic Channels

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Masoumeh Soflaei ◽  
Paeiz Azmi
Keyword(s):  
Shallow Water ◽  
Water Channel ◽  
Lms Algorithm ◽  
Projection Algorithm ◽  
Mean Square ◽  
Least Mean Square ◽  
Adaptive Equalizer ◽  
Affine Projection ◽  
The Family ◽  
Reliable Communications

One of the most important problems of reliable communications in shallow water channels is intersymbol interference (ISI) which is due to scattering from surface and reflecting from bottom. Using adaptive equalizers in receiver is one of the best suggested ways for overcoming this problem. In this paper, we apply the family of selective regressor affine projection algorithms (SR-APA) and the family of selective partial update APA (SPU-APA) which have low computational complexity that is one of the important factors that influences adaptive equalizer performance. We apply experimental data from Strait of Hormuz for examining the efficiency of the proposed methods over shallow water channel. We observe that the values of the steady-state mean square error (MSE) of SR-APA and SPU-APA decrease by 5.8 (dB) and 5.5 (dB), respectively, in comparison with least mean square (LMS) algorithm. Also the families of SPU-APA and SR-APA have better convergence speed than LMS type algorithm.

scholarly journals Memory-Dependent Forecasting of COVID-19: The Flexibility of Extrapolated Kernel Least Mean Square Algorithm

2021 ◽  
Author(s):  
Noor Ahmad ◽  
Mohd Hafiz Mohd
Keyword(s):  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Gradient Estimate ◽  
Situational Analysis ◽  
Mean Square ◽  
Least Mean Square ◽  
State Variables ◽  
Data Set ◽  
Least Mean Square Algorithm ◽  
Kernel Least Mean Square

The extrapolated kernel least mean square algorithm (extrap-KLMS) with memory is proposed for the forecasting of future trends of COVID-19. The extrap-KLMS is derived in the framework of data-driven modelling that attempts to describe the dynamics of infectious disease by reconstructing the phase-space of the state variables in a reproducing kernel Hilbert space (RKHS). Short-time forecasting is enabled via an extrapolation of the KLMS trained model using a forward euler step, along the direction of a memory-dependent gradient estimate. A user-defined memory averaging window allows users to incorporate prior knowledge of the history of the pandemic into the gradient estimate thus providing a spectrum of scenario-based estimates of futures trends. The performance of the extrap-KLMS method is validated using data set for Malaysia, Saudi Arabia and Italy in which we highlight the flexibility of the method in capturing persistent trends of the pandemic. A situational analysis of the Malaysian third wave further demonstrate the capabilities of our method

scholarly journals A NEW NUMERICAL METHOD TO SOLVE NONLINEAR VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 26 (3) ◽  
pp. 469-478
Author(s):  
Jinjiao Hou ◽  
Jing Niu ◽  
Welreach Ngolo
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Nonlinear Problems ◽  
Reproducing Kernel Method ◽  
Homotopy Perturbation ◽  
Linear Problems

In this paper, a new method combining the simplified reproducing kernel method (SRKM) and the homotopy perturbation method (HPM) to solve the nonlinear Volterra-Fredholm integro-differential equations (V-FIDE) is proposed. Firstly the HPM can convert nonlinear problems into linear problems. After that we use the SRKM to solve the linear problems. Secondly, we prove the uniform convergence of the approximate solution. Finally, some numerical calculations are proposed to verify the effectiveness of the approach.

Sign in / Sign up

Export Citation Format

Share Document