Learning Power Allocation for Multi-Cell-Multi-User Systems With Heterogeneous Graph Neural Networks

A well-trained deep neural network (DNN) enables real-time resource allocation by learning the relationship between a policy and its impacting parameters. When wireless systems operate in dynamic environments, the DNN has to be re-trained frequently and hence training complexity should be low. A promising approach to deal with this issue is to construct DNNs with prior knowledge. In this paper, we show that the power allocation policy in multi-cell-multi-user systems exhibits a combination of permutation equivariance properties, which can be harnessed by graph neural networks (GNNs). In particular, we construct a heterogeneous graph and resort to heterogeneous GNN for learning the policy, whose outputs are only equivariant to some permutations of vertexes rather than arbitrary permutations as homogeneous GNNs. We prove that the properties of the functions learned by existing heterogeneous GNN for the formulated graph are inconsistent with the properties of the policy. To avoid the performance degradation by embedding wrong priors, we design a parameter sharing scheme for heterogeneous GNN such that the learned relationship satisfies the desired properties. Simulation results show that the sample and computational complexities for training the constructed GNN are much lower than existing DNNs to achieve the same sum rate.