Square Root Extended Kernel Recursive Least Squares Algorithm for Nonlinear Channel Equalization

Abstract: This study presents a square root version of extended kernel recursive least square algorithm. Basically main idea is to overcome the divergence phenomena arise in the computation of weights of the extended kernel recursive least squares algorithm. Numerically stable givens orthogonal transformations are used to obtain the next iteration of the algorithm. The usefulness of the proposed algorithm is illustrated by discussing its application on the nonlinear multipath fading channel equalization based on Rayleigh distribution. Experiments are performed on slow fading Rayleigh channel with scattered signals

Kernel methods for short-term spatio-temporal wind prediction

Two nonlinear methods for producing short-term spatio-temporal wind speed forecast are presented. From the relatively new class of kernel methods, a kernel least mean squares algorithm and kernel recursive least squares algorithm are introduced and used to produce 1 to 6 hour-ahead predictions of wind speed at six locations in the Netherlands. The performance of the proposed methods are compared to their linear equivalents, as well as the autoregressive, vector autoregressive and persistence time series models. The kernel recursive least squares algorithm is shown to offer significant improvement over all benchmarks, particularly for longer forecast horizons. Both proposed algorithms exhibit desirable numerical properties and are ripe for further development

Distributed Adaptive Learning with Multiple Kernels in Diffusion Networks

We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion stage to achieve consensus on the estimates over the whole network. Multiple kernels are incorporated to enhance the approximation of functions with several high and low frequency components common in practical scenarios. We provide a thorough convergence analysis of the proposed scheme based on the metric of the Cartesian product of multiple reproducing kernel Hilbert spaces. To this end, we introduce a modified consensus matrix considering this specific metric and prove its equivalence to the ordinary consensus matrix. Besides, the use of hyperslabs enables a significant reduction of the computational demand with only a minor loss in the performance. Numerical evaluations with synthetic and real data are conducted showing the efficacy of the proposed algorithm compared to the state of the art schemes.Comment: Double-column 15 pages, 10 figures, submitted to IEEE Trans. Signal Processin