Complex-Valued Kernel Methods for Regression
In this paper, we propose a widely linear reproducing kernel Hilbert space (WL-RKHS) for nonlinear regression with complex-valued signals. Our approach is a nonlinear extension of WL signal processing that has been proven to be more versatile than linear systems for dealing with complex-value signal...
| Autores: | , , , |
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| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2017 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/162763 |
| Acesso em linha: | https://hdl.handle.net/11441/162763 https://doi.org/10.1109/TSP.2017.2726991 |
| Access Level: | acceso abierto |
| Palavra-chave: | Complex-valued RKHS Kernel methods Regression Non-linear channel equalization |
| Resumo: | In this paper, we propose a widely linear reproducing kernel Hilbert space (WL-RKHS) for nonlinear regression with complex-valued signals. Our approach is a nonlinear extension of WL signal processing that has been proven to be more versatile than linear systems for dealing with complex-value signals. To be able to use the WL concept in kernel methods, we need to introduce a pseudo-kernel to complement the standard kernel in RKHS, which is not defined in previous RKHS approaches in the existing literature. In this paper, we present WL-RKHS, its properties, and the kernel and pseudo-kernel designs. We illustrate the need of the pseudo-kernel with simply verifiable examples that allow understanding the intuitions behind this kernel. We conclude this paper, showing that in the all-relevant nonlinear equalization problem the pseudo-kernel plays a significant role and previous approaches that do not rely on this kernel clearly underperform. |
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