Semi-Blind Sparse Channel Learning in Cell-Free Massive MIMO - a CRB Analysis

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 channel estimation in the presence of unknown 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 develop Bayesian Maximum a Posteriori (MAP) channel estimators and we also provide various Cramer-Rao Bounds to characterize performance limits. The main contribution is the derivation of an original type of Bayesian CRB for the semi-blind problem at hand, in which a certain expectation operation is facilitated by the asymptotics of the large system dimensions considered here. Whereas Bayesian CRBs lead to fairly useless lose bounds, corresponding to unrealistic genie-aided scenarios, the proposed variation turns out to be quite tight as illustrated by performance comparisons with various estimation algorithms.