A Bipartite Graph Neural Network Approach for Scalable Beamforming Optimization

Abstract
Deep learning (DL) techniques have been intensively studied for the optimization of multi-user multiple
systems owing to the capability of handling nonconvex formulations. However, the fixed computation structure of e
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 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 chan  beamforming optimization process is interpreted as a computation task over a
weighted bipartite graph. This approach partitions the beamforming multiple-input single-output (MU-MISO) downlink
existing deep neural networks (DNNs) lacks multi-antenna beamformi  channel fading coefficients. Thus, a generic
xisting beamforming nel 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 MUMISO 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.