  Multi-user multiple-input multiple-output (MU-MIMO) beamforming design is
typically formulated as a non-convex weighted sum rate (WSR) maximization
problem that is known to be NP-hard. This problem is solved either by iterative
algorithms, which suffer from slow convergence, or more recently by using deep
learning tools, which require time-consuming pre-training process. In this
paper, we propose a low-complexity meta-learning based gradient descent
algorithm. A meta network with lightweight architecture is applied to learn an
adaptive gradient descent update rule to directly optimize the beamformer. This
lightweight network is trained during the iterative optimization process, which
we refer to as \emph{training while solving}, which removes both the training
process and the data-dependency of existing deep learning based
solutions.Extensive simulations show that the proposed method achieves superior
WSR performance compared to existing learning-based approaches as well as the
conventional WMMSE algorithm, while enjoying much lower computational load.
