Rethinking Channel Charting: A Graph Perspective
Channel charting is a self-supervised framework that learns low-dimensional spatial representations from high-dimensional channel state information. We revisit channel charting from a graph-theoretic perspective, and show that the position-diffusion objective is equivalent to a graph Laplacian smoothness functional. We propose a Graph Neural Network (GNN) formulation that replaces the Siamese network's global geodesic dissimilarity objective with a graph smoothness objective. We consider the reformulated objective to be the position diffusion objective. Without diverging from the original optimization objective, the GNN replaces the quadratic-cost self-correlation encoding with linear-cost message passing over an Angle-Delay Profile (ADP)-similarity graph, achieving comparable positioning accuracy with 512 times fewer parameters. Using Laplacian spectral analysis, we demonstrate that obstacles compress the ADP graph spectrum, while the GNN acts as a spectral decompressor against obstacles and other environmental semantics, but as a compressor against excessive ADP embedding space. Beyond this, the second eigenvector of the learned embedding encodes the line-of-sight/non-line-of-sight boundary rather than spatial coordinates.