Digital Communication Receivers Using Gaussian Processes for Machine Learning

Abstract

We propose Gaussian processes (GPs) as a novel nonlinear receiver for digital communication systems. The GPs framework can be used to solve both classification (GPC) and regression (GPR) problems. The minimum mean squared error solution is the expectation of the transmitted symbol given the information at the receiver, which is a nonlinear function of the received symbols for discrete inputs. GPR can be presented as a nonlinear MMSE estimator and thus capable of achieving optimal performance from MMSE viewpoint. Also, the design of digital communication receivers can be viewed as a detection problem, for which GPC is specially suited as it assigns posterior probabilities to each transmitted symbol. We explore the suitability of GPs as nonlinear digital communication receivers. GPs are Bayesian machine learning tools that formulates a likelihood function for its hyperparameters, which can then be set optimally. GPs outperform state-of-the-art nonlinear machine learning approaches that prespecify their hyperparameters or rely on cross validation. We illustrate the advantages of GPs as digital communication receivers for linear and nonlinear channel models for short training sequences and compare them to state-of-the-art nonlinear machine learning tools, such as support vector machines.