Learning Wireless Power Allocation Through Graph Convolutional Regression Networks Over Riemannian Manifolds

Optimum power allocation is a key enabler for maximizing data rate in wireless networks. Recently, various deep neural network models have been introduced for predicting power allocation in device-to-device (D2D) networks. However, they require large training samples (i.e., network layouts). On the contrary in this paper, we aim to develop a learning model for power allocation with fewer training samples, which is vital in dynamic networks (e.g., vehicular networks) with the need for fast learning of power allocation. The proposed model transforms Euclidean-based network layouts and power allocation problems into Riemannian (i.e., non-Euclidean) manifolds, which is shown to require fewer learning parameters and hence shorter learning time. Such transformation is possible thanks to the symmetric positive definite (SPD) property of spectral representation (i.e., Laplacian matrix) of network layouts. In particular, we propose a graph convolutional regression network (GCRN) for predicting power allocation over Riemannian manifolds in an unsupervised manner. Simulation results demonstrate that the proposed GCRN model approaches the maximum network rate in large-scale networks, with only 300 training samples as opposed to 10,000 in Euclidean-based learning models.