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.
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