An empirical likelihood method for data aided channel identification in unknown noise field

In this work we propose a different approach to the problem of estimating a transfer matrix with data aided, which can be applied to SISO and SIMO channels, either baud-rate or fractionally sampled signals. The approach is based on the Empirical Likelihood method [1, 2], a flexible semi-parametric estimation method, which can easily integrate in the estimation procedure some prior informations on the structure of the parameter of interest. Moreover, this improved estimation method does not assume any model for the data distribution. The contributions of this paper is twofold: first, we introduce the Empirical Likelihood method in a general context, i.e. without any prior informations and then, we derive closed-form expressions of estimators for the transfer matrix. All results are presented under Gaussian assumptions and under a mixture of Gaussian and Student-t distributions. This allows to show the robustness of the proposed method.