Gaussian Processes for Nonlinear Signal Processing

TL;DR

This paper introduces Gaussian processes as a powerful nonlinear extension to traditional signal processing methods, highlighting their applications, extensions, and advantages in various wireless communication scenarios.

Contribution

It presents GPs for regression in signal processing, discusses extensions like recursive algorithms, low-complexity solutions, and non-Gaussian noise handling, and applies them to wireless communications.

Findings

GPs effectively model nonlinear estimation problems

Recursive and adaptive algorithms improve non-stationarity handling

Applications demonstrate benefits in wireless digital communications

Abstract

Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning, but that are rarely used in signal processing. In this tutorial, we present GPs for regression as a natural nonlinear extension to optimal Wiener filtering. After establishing their basic formulation, we discuss several important aspects and extensions, including recursive and adaptive algorithms for dealing with non-stationarity, low-complexity solutions, non-Gaussian noise models and classification scenarios. Furthermore, we provide a selection of relevant applications to wireless digital communications.