  Downlink beamforming is an essential technology for wireless cellular
networks; however, the design of beamforming vectors that maximize the weighted
sum rate (WSR) is an NP-hard problem and iterative algorithms are typically
applied to solve it. The weighted minimum mean square error (WMMSE) algorithm
is the most widely used one, which iteratively minimizes the WSR and converges
to a local optimal. Motivated by the recent developments in meta-learning
techniques to solve non-convex optimization problems, we propose a
meta-learning based iterative algorithm for WSR maximization in a MISO downlink
channel. A long-short-term-memory (LSTM) network-based meta-learning model is
built to learn a dynamic optimization strategy to update the variables
iteratively. The learned strategy aims to optimize each variable in a less
greedy manner compared to WMMSE, which updates variables by computing their
first-order stationary points at each iteration step. The proposed algorithm
outperforms WMMSE significantly in the high signal to noise ratio(SNR) regime
and shows the comparable performance when the SNR is low.
