Three-Dimensional Radio Localization: A Channel Charting-Based Approach

Channel charting creates a low-dimensional representation of the radio environment in a self-supervised manner using manifold learning. Preserving relative spatial distances in the latent space, channel charting is well suited to support user localization. While prior work on channel charting has mainly focused on two-dimensional scenarios, real-world environments are inherently three-dimensional. In this work, we investigate two distinct three-dimensional indoor localization scenarios using simulated, but realistic ray tracing-based datasets: a factory hall with a three-dimensional spatial distribution of datapoints, and a multistory building where each floor exhibits a two-dimensional datapoint distribution. For the first scenario, we apply the concept of augmented channel charting, which combines classical localization and channel charting, to a three-dimensional setting. For the second scenario, we introduce multistory channel charting, a two-stage approach consisting of floor classification via clustering followed by the training of a dedicated expert neural network for channel charting on each individual floor, thereby enhancing the channel charting performance. In addition, we propose a novel feature engineering method designed to extract sparse features from the beamspace channel state information that are suitable for localization.

💡 Research Summary

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This paper addresses the problem of indoor three‑dimensional (3‑D) localization by leveraging channel charting, a self‑supervised manifold learning technique that extracts a low‑dimensional representation of the radio environment directly from channel state information (CSI). While most prior work on channel charting has been confined to two‑dimensional (2‑D) scenarios, real‑world environments are inherently 3‑D, and accurate height estimation is crucial for applications such as UAV navigation, asset tracking in multistory buildings, and indoor positioning of devices on different floors.

System Model and Datasets
The authors consider a single‑antenna user equipment (UE) communicating with a base station (BS) equipped with multiple distributed uniform planar arrays (UPAs). The system operates at 3.438 GHz with a 50 MHz bandwidth and 64 OFDM sub‑carriers. CSI is collected as a four‑dimensional tensor H ∈ ℂ^{B × M_row × M_col × N_sub}. Two realistic ray‑tracing datasets are generated using Sionna:

1. Factory Hall – 8 distributed 8 × 8 UPAs placed around a large metallic cube. UE positions span a 16 m × 16 m area and heights from 2 m to 8 m, yielding 5 000 samples.

2. Multistory Building – A hypothetical five‑floor building. 20 distributed 2 × 4 UPAs are located outside the building. On each floor, 1 000 UE positions are uniformly spread over a 16 m × 16 m plane, with floor‑specific heights ranging from 1.5 m to 18.5 m (total 5 000 samples).

Baseline Classical Localization
An AoA‑based triangulation method is implemented as a reference. For each array, azimuth and elevation covariance matrices are formed, and the root‑MUSIC algorithm extracts AoA estimates. A von Mises‑Fisher likelihood model is then maximized to obtain a 3‑D position estimate. Because the system lacks time synchronization, TOA‑based multilateration is not used.

Conventional Channel Charting Pipeline
The standard approach consists of (i) computing a pairwise dissimilarity matrix using the geodesic angle‑delay profile (a cosine‑similarity metric applied per array and per delay tap) and applying a shortest‑path algorithm to obtain globally consistent “pseudo‑distances”, and (ii) training a Siamese neural network that maps engineered CSI features f(ℓ) to chart coordinates z(ℓ) ∈ ℝ³. The forward charting function C_θ is realized by a fully connected DNN (layers: 1024‑512‑256‑128‑64‑3). The Siamese loss enforces ‖z_i − z_j‖ ≈ d_ij, with an additional regularization term β.

Novel Beamspace Feature Engineering
To reduce redundancy and highlight spatial information, the authors propose a two‑step feature extraction: (1) zero‑pad the spatial dimensions of H, apply a 2‑D FFT to obtain a beamspace tensor (\bar{H}) ∈ ℂ^{B × U_el × U_az × N_sub}, where U_el = 2 M_row and U_az = 2 M_col, and (2) compute (a) mean power per beam P(b,u_el,u_az) = Σ_n | (\bar{H})_{b,u_el,u_az,n} |² and (b) a coarse time‑of‑arrival estimate D(b,u_el,u_az) by averaging phase across sub‑carriers. These two scalar fields per array constitute a sparse, physically meaningful feature vector that feeds the Siamese network.

Augmented Channel Charting (3‑D)
To obtain absolute positions directly from the chart, the authors extend their previous “augmented channel charting” concept to three dimensions. The pseudo‑distance matrix is first scaled using the Euclidean distances derived from AoA‑triangulation, thereby aligning chart distances with physical distances. The loss function becomes

L_aug = Σ_{i,j} (1‑λ)·(d_{ij} − ‖z_i − z_j‖)² − λ·