A Meta-Learning Based Gradient Descent Algorithm for MU-MIMO Beamforming

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.