Attentional Graph Neural Network Is All You Need for Robust Massive Network Localization

TL;DR

This work tackles robust, scalable network localization in massive wireless networks under LOS/NLOS conditions by introducing an Attentional Graph Neural Network (AGNN). AGNN combines an Adjacency Learning Module (ALM) that learns distance-aware, edge-specific thresholds with a MGAL stack that uses dynamic attention to learn edge- and neighbor-specific aggregation weights, addressing threshold sensitivity and limited expressiveness of prior GCNs. Theoretical analyses establish the dynamic-attention properties and computational efficiency of AGNN, while extensive experiments show substantial reductions in localization error (approximately 37%–53% over vanilla GCN) and near-CRB performance, even for networks with up to 10,000 nodes. The approach yields robust performance against NLOS noise, scales to massive networks, and achieves competitive training times, offering a practical solution for real-world large-scale localization tasks.

Abstract

In this paper, we design Graph Neural Networks (GNNs) with attention mechanisms to tackle an important yet challenging nonlinear regression problem: massive network localization. We first review our previous network localization method based on Graph Convolutional Network (GCN), which can exhibit state-of-the-art localization accuracy, even under severe Non-Line-of-Sight (NLOS) conditions, by carefully preselecting a constant threshold for determining adjacency. As an extension, we propose a specially designed Attentional GNN (AGNN) model to resolve the sensitive thresholding issue of the GCN-based method and enhance the underlying model capacity. The AGNN comprises an Adjacency Learning Module (ALM) and Multiple Graph Attention Layers (MGAL), employing distinct attention architectures to systematically address the demerits of the GCN-based method, rendering it more practical for real-world applications. Comprehensive analyses are conducted to explain the superior performance of these methods, including a theoretical analysis of the AGNN's dynamic attention property and computational complexity, along with a systematic discussion of their robust characteristic against NLOS measurements. Extensive experimental results demonstrate the effectiveness of the GCN-based and AGNN-based network localization methods. Notably, integrating attention mechanisms into the AGNN yields substantial improvements in localization accuracy, approaching the fundamental lower bound and showing approximately 37\% to 53\% reduction in localization error compared to the vanilla GCN-based method across various NLOS noise configurations. Both methods outperform all competing approaches by far in terms of localization accuracy, robustness, and computational time, especially for considerably large network sizes.

Figures (16)

• Figure 1: Network localization scenario. The shaded area represents the region of interest for the $10$-th node after threshold selection which will be introduced in Sec. \ref{['sec: static_GCN_reg']}.
• Figure 2: The averaged loss (RMSE) v.s. threshold under different noise conditions in the GCN model.
• Figure 3: Spectral components of the $10$-th column vector (similar for other columns) of the noise, ${\mathbf n}_{10}$, and the true distance, ${\mathbf d}_{10}$, in dataset $(\sigma^2=0.1,p_B=30\%)$.
• Figure 4: Framework of AGNN.
• Figure 5: Visualization of AGNN localization performance with $(\sigma^2=0.1, p_B=0\%)$ and $N_l = 50$.

Theorems & Definitions (5)

• Theorem 1
• Theorem 2
• Theorem 3
• Theorem 4
• Theorem 5