A Signature Based Approach Towards Global Channel Charting with Ultra Low Complexity

TL;DR

This paper tackles global channel charting with ultra-low complexity by mapping high-dimensional channel information into a compact signature map through the path signature transform $\mathbf{S}(X)$, enabling simultaneous preservation of local and global geometry. It introduces two scalable DR approaches: SPCA, a kernel-PCA-like reduction on signature features, and SSN, a Siamese network trained with a novel distance $\rho(\boldsymbol{\Lambda}_i,\boldsymbol{\Lambda}_j)=\|\boldsymbol{s}_i-\boldsymbol{s}_j\|_1$ and loss $\mathcal{L}(\boldsymbol{o}_i,\boldsymbol{o}_j)$ that aligns learned embeddings with signature-based dissimilarities, without geodesic or neighborhood graph computations, see $\mathcal{L}(\boldsymbol{o}_i, \boldsymbol{o}_j)=\sqrt{\sum_{(i,j)\in\mathcal{P}_{batch}}(\rho(\boldsymbol{\Lambda}_i,\boldsymbol{\Lambda}_j)-\|\boldsymbol{o}_i-\boldsymbol{o}_j\|_2)^2}$. The method builds a signature map $\boldsymbol{\Lambda}_i$ from each CIR using a cumulative energy path with time and basepoint augmentations and shows reduced feature dimensionality (e.g., from thousands to a small $L$) and large FLOPs savings. Evaluations on InF-DH, 5G, and UWB datasets demonstrate improved global similarity (MAE, CE90) while maintaining competitive or superior local similarity (CT, TW).

Abstract

Channel charting, an unsupervised learning method that learns a low-dimensional representation from channel information to preserve geometrical property of physical space of user equipments (UEs), has drawn many attentions from both academic and industrial communities, because it can facilitate many downstream tasks, such as indoor localization, UE handover, beam management, and so on. However, many previous works mainly focus on charting that only preserves local geometry and use raw channel information to learn the chart, which do not consider the global geometry and are often computationally intensive and very time-consuming. Therefore, in this paper, a novel signature based approach for global channel charting with ultra low complexity is proposed. By using an iterated-integral based method called signature transform, a compact feature map and a novel distance metric are proposed, which enable channel charting with ultra low complexity and preserving both local and global geometry. We demonstrate the efficacy of our method using synthetic and open-source real-field datasets.

Figures (6)

• Figure 1: An illustration of the signature map generation.
• Figure 2: An illustration of SSN based CC.
• Figure 3: Heatmaps for pairwise distance matrices.
• Figure 4: Ground-truth UE locations and CC results after affine transformation for InF-DH dataset.
• Figure 5: Ground-truth UE locations and CC results after affine transformation for 5G dataset.