  In this paper, we study the beamforming design problem in frequency-division
duplexing (FDD) downlink massive MIMO systems, where instantaneous channel
state information (CSI) is assumed to be unavailable at the base station (BS).
We propose to extract the information of the angle-of-departures (AoDs) and the
corresponding large-scale fading coefficients (a.k.a. spatial information) of
the downlink channel from the uplink channel estimation procedure, based on
which a novel downlink beamforming design is presented. By separating the
subpaths for different users based on the spatial information and the hidden
sparsity of the physical channel, we construct near-orthogonal virtual channels
in the beamforming design. Furthermore, we derive a sum-rate expression and its
approximations for the proposed system. Based on these closed-form rate
expressions, we develop two low-complexity beam selection schemes and carry out
asymptotic analysis to provide valuable insights on the system design.
Numerical results demonstrate a significant performance improvement of our
proposed algorithm over the state-of-the-art beamforming approach.
