  Accurate downlink channel information is crucial to the beamforming design,
but it is difficult to obtain in practice. This paper investigates a deep
learning-based optimization approach of the downlink beamforming to maximize
the system sum rate, when only the uplink channel information is available. Our
main contribution is to propose a model-driven learning technique that exploits
the structure of the optimal downlink beamforming to design an effective hybrid
learning strategy with the aim to maximize the sum rate performance. This is
achieved by jointly considering the learning performance of the downlink
channel, the power and the sum rate in the training stage. The proposed
approach applies to generic cases in which the uplink channel information is
available, but its relation to the downlink channel is unknown and does not
require an explicit downlink channel estimation. We further extend the
developed technique to massive multiple-input multiple-output scenarios and
achieve a distributed learning strategy for multicell systems without an
inter-cell signalling overhead. Simulation results verify that our proposed
method provides the performance close to the state of the art numerical
algorithms with perfect downlink channel information and significantly
outperforms existing data-driven methods in terms of the sum rate.
