Deep learning (DL) techniques have been intensively studied for the optimization of multi-user multiple-input single-output (MU-MISO) downlink systems owing to the capability of handling nonconvex formulations. However, the fixed computation structure of existing deep neural networks (DNNs) lacks flexibility with respect to the system size, i.e., the number of antennas or users. This paper develops a bipartite graph neural network (BGNN) framework, a scalable DL solution designed for multi-antenna beamforming optimization. The MU-MISO system is first characterized by a bipartite graph where two disjoint vertex sets, each of which consists of transmit antennas and users, are connected via pairwise edges. These vertex interconnection states are modeled by channel fading coefficients. Thus, a generic beamforming optimization process is interpreted as a computation task over a weight bipartite graph. This approach partitions the beamforming optimization procedure into multiple suboperations dedicated to individual antenna vertices and user vertices. Separated vertex operations lead to scalable beamforming calculations that are invariant to the system size. The vertex operations are realized by a group of DNN modules that collectively form the BGNN architecture. Identical DNNs are reused at all antennas and users so that the resultant learning structure becomes flexible to the network size. Component DNNs of the BGNN are trained jointly over numerous MU-MISO configurations with randomly varying network sizes. As a result, the trained BGNN can be universally applied to arbitrary MU-MISO systems. Numerical results validate the advantages of the BGNN framework over conventional methods.

翻译：深度学习( DL) 技术已经深入研究, 优化多用户多输入单输出( MU- MISO) 的下链接系统。 但是, 现有的深神经网络( DNN) 的固定计算结构在系统大小( 即天线或用户的数量) 上缺乏灵活性。 本文开发了一个双部分图形神经网络( BGNN) 框架, 一种可缩放的 DL 解决方案, 用于多天线成型优化。 MU- MISO 系统首先使用双部分图形, 其中两个由传输天线和用户组成的双连接顶端结构。 这些顶端网络的固定计算结构( 由双部分图) 。 通用波形优化进程被解释为一个计算任务, 双面图。 这个方法将灵活的优化程序转换成多个子操作, 用于单个天线的双向和用户的双向结构。 由双向网络传输的双向网络的双端结构, 自动计算结果的内置的内向内流操作系统, 将自动的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置系统, 将自动结构变成为双向的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置的内置结构。 。