Tackling Pilot Contamination in Cell-Free Massive MIMO by Joint Channel Estimation and Linear Multi-User Detection

In this paper we consider cell-free (CF) massive MIMO (MaMIMO) systems, which comprise a very large number of geographically distributed access points (APs) serving a much smaller number of users. We exploit channel sparsity to tackle pilot contamination, which originates from the reuse of pilot sequences. Specifically, we consider semi-blind methods for joint channel estimation and data detection. Under the challenging assumption of deterministic parameters, we determine sufficient conditions and necessary conditions for semi-blind identifiability, which guarantee the non-singularity of the Fisher Information Matrix (FIM) and the existence of the Cramer-Rao bound (CRB). We propose a message passing (MP) algorithm which determines the exact channel coefficients in the case of semi-blind identifiability. We show that the system is identifiable if the Karp-Sipser algorithm yields an empty core. Additionally, we propose a Bayesian semi-blind approach which results in an effective algorithm for joint channel estimation and multi-user detection. This algorithm alternates between channel estimation and linear multi-user detection. Numerical simulations verify the analytical derivations.