  Beamforming is an effective means to improve the quality of the received
signals in multiuser multiple-input-single-output (MISO) systems.
Traditionally, finding the optimal beamforming solution relies on iterative
algorithms, which introduces high computational delay and is thus not suitable
for real-time implementation. In this paper, we propose a deep learning
framework for the optimization of downlink beamforming. In particular, the
solution is obtained based on convolutional neural networks and exploitation of
expert knowledge, such as the uplink-downlink duality and the known structure
of optimal solutions. Using this framework, we construct three beamforming
neural networks (BNNs) for three typical optimization problems, i.e., the
signal-to-interference-plus-noise ratio (SINR) balancing problem, the power
minimization problem, and the sum rate maximization problem. For the former two
problems the BNNs adopt the supervised learning approach, while for the sum
rate maximization problem a hybrid method of supervised and unsupervised
learning is employed. Simulation results show that the BNNs can achieve
near-optimal solutions to the SINR balancing and power minimization problems,
and a performance close to that of the weighted minimum mean squared error
algorithm for the sum rate maximization problem, while in all cases enjoy
significantly reduced computational complexity. In summary, this work paves the
way for fast realization of optimal beamforming in multiuser MISO systems.
