  In order to achieve high data rate and ubiquitous connectivity in future
wireless networks, a key task is to efficiently manage the radio resource by
judicious beamforming and power allocation. Unfortunately, the iterative nature
of the commonly applied optimization-based algorithms cannot meet the low
latency requirements due to the high computational complexity. For real-time
implementations, deep learning-based approaches, especially the graph neural
networks (GNNs), have been demonstrated with good scalability and
generalization performance due to the permutation equivariance (PE) property.
However, the current architectures are only equipped with the node-update
mechanism, which prohibits the applications to a more general setup, where the
unknown variables are also defined on the graph edges. To fill this gap, we
propose an edge-update mechanism, which enables GNNs to handle both node and
edge variables and prove its PE property with respect to both transmitters and
receivers. Simulation results on typical radio resource management problems
demonstrate that the proposed method achieves higher sum rate but with much
shorter computation time than state-of-the-art methods and generalizes well on
different numbers of base stations and users, different noise variances,
interference levels, and transmit power budgets.
