Stability Analysis of Unfolded WMMSE for Power Allocation

TL;DR

This paper investigates the stability of the unfolded WMMSE algorithm, which uses graph neural networks for power allocation in wireless networks, demonstrating its robustness to input perturbations through theory and experiments.

Contribution

It provides the first stability analysis of UWMMSE, combining theoretical proofs with empirical validation to ensure reliable power allocation under input disturbances.

Findings

UWMMSE is stable to bounded additive input perturbations.

Theoretical analysis confirms bounded output variations.

Empirical results support the stability claims.

Abstract

Power allocation is one of the fundamental problems in wireless networks and a wide variety of algorithms address this problem from different perspectives. A common element among these algorithms is that they rely on an estimation of the channel state, which may be inaccurate on account of hardware defects, noisy feedback systems, and environmental and adversarial disturbances. Therefore, it is essential that the output power allocation of these algorithms is stable with respect to input perturbations, to the extent that the variations in the output are bounded for bounded variations in the input. In this paper, we focus on UWMMSE -- a modern algorithm leveraging graph neural networks --, and illustrate its stability to additive input perturbations of bounded energy through both theoretical analysis and empirical validation.