Uncertainty-Aware Dimensionality Reduction for Channel Charting with Geodesic Loss

TL;DR

This paper tackles channel charting by introducing an uncertainty-aware dimensionality-reduction framework for dissimilarity-metric-based CC. It combines a batch-wise training scheme with three key improvements: (i) an acceleration constraint to enforce plausible latent-space dynamics, (ii) a geodesic loss that aligns latent-space path lengths with geodesic distances on nonconvex manifolds, and (iii) an uncertainty modeling approach using conditional distributions $p(d|\Delta)$ to capture distance variability and fuse multiple dissimilarities. The proposed methods—folded-normal acceleration modeling, sub-sampled geodesic paths, and Gaussian approximations for distance distributions—lead to substantial localization accuracy gains on the DICHASUS industrial dataset, achieving MAE as low as $0.330$ m and improving global-shape preservation (CT/TW ≈ $0.998$). While they introduce additional hyperparameters and complexity, these contribute to more physically consistent channel charts and potentially better network optimization and localization performance in challenging LOS/NLOS scenarios.

Abstract

Channel Charting is a dimensionality reduction technique that learns to reconstruct a low-dimensional, physically interpretable map of the radio environment by taking advantage of similarity relationships found in high-dimensional channel state information. One particular family of Channel Charting methods relies on pseudo-distances between measured CSI datapoints, computed using dissimilarity metrics. We suggest several techniques to improve the performance of dissimilarity metric-based Channel Charting. For one, we address an issue related to a discrepancy between Euclidean distances and geodesic distances that occurs when applying dissimilarity metric-based Channel Charting to datasets with nonconvex low-dimensional structure. Furthermore, we incorporate the uncertainty of dissimilarities into the learning process by modeling dissimilarities not as deterministic quantities, but as probability distributions. Our framework facilitates the combination of multiple dissimilarity metrics in a consistent manner. Additionally, latent space dynamics like constrained acceleration due to physical inertia are easily taken into account thanks to changes in the training procedure. We demonstrate the achieved performance improvements for localization applications on a measured channel dataset

Figures (9)

• Figure 1: Information about dataset and environment: Top view map with antenna arrays drawn to scale, their orientation indicated by the green sectors (left) and scatter plot of colorized "ground truth" positions in $\mathcal{S}$ (right).
• Figure 2: State of the art: Siamese neural network
• Figure 3: Proposed batch-wise loss training architecture
• Figure 4: Illustration of locations of datapoints (gray dots) in nonconvex two-dimensional arrangement (in channel chart / physical space). The red line is the Euclidean distance between the two green datapoints, the blue line is one potential geodesic distance between the two datapoints.
• Figure 5: Illustration of $q^{(i, j)}_m$ path notation: Shortest path of length $M^{(i, j)} = 3$ from datapoint $i = 5$ to datapoint $j = 8$ is via datapoints $l=9$ and $l=7$.