Message Passing for a Bayesian Semi-Blind Approach to Cell-Free Massive MIMO

In this paper, we consider cell-free (CF) massive MIMO systems employing a massive number of access points (APs) geographically distributed over a wide area to jointly serve a smaller number of users over the same time-frequency resources. We consider semi-blind methods for channel estimation in the presence of Gaussian i.i.d. data to resolve the pilot contamination. This task is further aided by exploiting prior channel information in a Bayesian formulation. We propose a variable level expectation propagation (VL-EP) algorithm for message passing (MP) style semi-blind channel estimation which provides an approximate minimum mean square error (MMSE) channel estimator (which itself can not be found analytically). Numerical simulations verify the analytical derivations and the proposed algorithm.