  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.
