Graph Neural Networks for Distributed Power Allocation in Wireless Networks: Aggregation Over-the-Air

TL;DR

This paper introduces scalable graph neural network frameworks for distributed power allocation in wireless networks, leveraging over-the-air computation to reduce signaling overhead and improve sum-rate performance.

Contribution

It proposes the Air-MPNN and Air-MPRNN frameworks that significantly reduce signaling overhead and are compatible with existing systems, advancing distributed power control methods.

Findings

Air-MPNN reduces signaling overhead from quadratic to linear growth.

Proposed frameworks outperform existing algorithms in sum-rate performance.

Air-MPRNN can be integrated into current communication standards.

Abstract

Distributed power allocation is important for interference-limited wireless networks with dense transceiver pairs. In this paper, we aim to design low signaling overhead distributed power allocation schemes by using graph neural networks (GNNs), which are scalable to the number of wireless links. We first apply the message passing neural network (MPNN), a unified framework of GNN, to solve the problem. We show that the signaling overhead grows quadratically as the network size increases. Inspired from the over-the-air computation (AirComp), we then propose an Air-MPNN framework, where the messages from neighboring nodes are represented by the transmit power of pilots and can be aggregated efficiently by evaluating the total interference power. The signaling overhead of Air-MPNN grows linearly as the network size increases, and we prove that Air-MPNN is permutation invariant. To further reduce the signaling overhead, we propose the Air message passing recurrent neural network (Air-MPRNN), where each node utilizes the graph embedding and local state in the previous frame to update the graph embedding in the current frame. Since existing communication systems send a pilot during each frame, Air-MPRNN can be integrated into the existing standards by adjusting pilot power. Simulation results validate the scalability of the proposed frameworks, and show that they outperform the existing power allocation algorithms in terms of sum-rate for various system parameters.