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Beamforming techniques play an important role in multi-antenna communication systems and this work focuses on the downlink power minimization problem under a set of quality of service constraints. Conventional iterative algorithms can obtain optimal solutions but at the cost of high computational delay. Fast beamforming can be achieved by leveraging the powerful deep learning techniques. In this work, we propose a beamforming neural network (BNN), based on convolutional neural networks and exploitation of expert knowledge, for the power minimization problem. Instead of estimating beamforming matrix directly, we predict key features using the BNN which takes complex channel as input. Then the beamforming matrix is recovered from the predictions according to the uplink-downlink duality. The BNN adopts the supervised learning method with a loss function based on the mean-squared error metric to …