  Deep neural networks have recently emerged as a disruptive technology to
solve NP-hard wireless resource allocation problems in a real-time manner.
However, the adopted neural network structures, e.g., multi-layer perceptron
(MLP) and convolutional neural network (CNN), are inherited from deep learning
for image processing tasks, and thus are not tailored to problems in wireless
networks. In particular, the performance of these methods deteriorates
dramatically when the wireless network size becomes large. In this paper, we
propose to utilize graph neural networks (GNNs) to develop scalable methods for
solving the power control problem in $K$-user interference channels.
Specifically, a $K$-user interference channel is first modeled as a complete
graph, where the quantitative information of wireless channels is incorporated
as the features of the graph. We then propose an interference graph
convolutional neural network (IGCNet) to learn the optimal power control in an
unsupervised manner. It is shown that one-layer IGCNet is a universal
approximator to continuous set functions, which well matches the permutation
invariance property of interference channels and it is robust to imperfect
channel state information (CSI). Extensive simulations will show that the
proposed IGCNet outperforms existing methods and achieves significant speedup
over the classic algorithm for power control, namely, WMMSE. The code is
available on https://github.com/yshenaw/Globecom2019.
