  Knowledge of second-order statistics of channels (e.g. in the form of
covariance matrices) is crucial for the acquisition of downlink channel state
information (CSI) in massive MIMO systems operating in the frequency division
duplexing (FDD) mode. Current MIMO systems usually obtain downlink covariance
information via feedback of the estimated covariance matrix from the user
equipment (UE), but in the massive MIMO regime this approach is infeasible
because of the unacceptably high training overhead. This paper considers
instead the problem of estimating the downlink channel covariance from uplink
measurements. We propose two variants of an algorithm based on projection
methods in an infinite-dimensional Hilbert space that exploit channel
reciprocity properties in the angular domain. The proposed schemes are
evaluated via Monte Carlo simulations, and they are shown to outperform current
state-of-the art solutions in terms of accuracy and complexity, for typical
array geometries and duplex gaps.
