  In order to unlock the full advantages of massive multiple input multiple
output (MIMO) in the downlink, channel state information (CSI) is required at
the base station (BS) to optimize the beamforming matrices. In frequency
division duplex (FDD) systems, full channel reciprocity does not hold, and CSI
acquisition generally requires downlink pilot transmission followed by uplink
feedback. Prior work proposed the end-to-end design of pilot transmission,
feedback, and CSI estimation via deep learning. In this work, we introduce an
enhanced end-to-end design that leverages partial uplink-downlink reciprocity
and temporal correlation of the fading processes by utilizing jointly downlink
and uplink pilots. The proposed method is based on a novel deep learning
architecture -- HyperRNN -- that combines hypernetworks and recurrent neural
networks (RNNs) to optimize the transfer of long-term channel features from
uplink to downlink. Simulation results demonstrate that the HyperRNN achieves a
lower normalized mean square error (NMSE) performance, and that it reduces
requirements in terms of pilot lengths.
