Gaussian processes regressors for complex proper signals in digital communications

In this paper we develop the complex-valued version of the Gaussian processes for regression (GPR) for proper complex signals. This tool has proved to be useful in the nonlinear detection in digital communications in real valued models. GPRs can be cast as nonlinear MMSE where hyperparameters can be tuned optimizing a marginal likelihood (ML). This feature allows for a flexible kernel that can easily adapt either to a linear or nonlinear solution. We introduce the complex-valued form of the GPR, and develop it for the proper complex case. We also deal with the optimization of the ML. Some experiments included illustrate the good performance of the proposal.