Study of Set-Membership Adaptive Kernel Algorithms

Abstract

In the last decade, a considerable research effort has been devoted to developing adaptive algorithms based on kernel functions. One of the main features of these algorithms is that they form a family of universal approximation techniques, solving problems with nonlinearities elegantly. In this paper, we present data-selective adaptive kernel normalized least-mean square (KNLMS) algorithms that can increase their learning rate and reduce their computational complexity. In fact, these methods deal with kernel expansions, creating a growing structure also known as the dictionary, whose size depends on the number of observations and their innovation. The algorithms described herein use an adaptive step-size to accelerate the learning and can offer an excellent tradeoff between convergence speed and steady state, which allows them to solve nonlinear filtering and estimation problems with a large number of parameters without requiring a large computational cost. The data-selective update scheme also limits the number of operations performed and the size of the dictionary created by the kernel expansion, saving computational resources and dealing with one of the major problems of kernel adaptive algorithms. A statistical analysis is carried out along with a computational complexity analysis of the proposed algorithms. Simulations show that the proposed KNLMS algorithms outperform existing algorithms in examples of nonlinear system identification and prediction of a time series originating from a nonlinear difference equation.

arXiv comment34 pages, 10 figures

References in corpus (8)

• Extension of Wirtinger's Calculus to Reproducing Kernel Hilbert Spaces and the Complex Kernel LMS
• Design of Robust Adaptive Beamforming Algorithms Based on Low-Rank and Cross-Correlation Techniques
• Multi-Branch Tomlinson-Harashima Precoding for MU-MIMO Systems: Theory and Algorithms
• Distributed Space-Time Coding Based on Adjustable Code Matrices for Cooperative MIMO Relaying Systems
• Sparsity-Aware Adaptive Algorithms Based on Alternating Optimization with Shrinkage
• Adaptive Reduced-Rank Minimum Symbol-Error-Rate Receive Processing for Large-Scale Multiple-Antenna Systems
• Direction Finding Algorithms with Joint Iterative Subspace Optimization
• Blind Adaptive Interference Suppression Based on Set-Membership Constrained Constant-Modulus Algorithms with Time-Varying Bounds