Channel Charting

Channel charting operates without labeled position data, learning a forward charting function that maps CSI vectors to a low-dimensional latent space (typically 2D or 3D). The core principle is that physically proximate transmitters experience similar propagation environments, causing their CSI to cluster in the learned manifold. Algorithms like Isomap, t-SNE, UMAP, and autoencoders enforce this neighborhood preservation by minimizing the discrepancy between pairwise distances in the original CSI space and the chart coordinates. This enables the network to construct a relative geometry map of users, even when absolute GPS coordinates are unavailable or denied.

The quality of a channel chart depends critically on the dissimilarity metric used to compare CSI vectors. Raw Euclidean distance in the angular or delay domain is often suboptimal due to phase wrapping and multipath complexity. Advanced approaches learn a pseudo-distance using:

• Cosine similarity between channel covariance matrices
• Frobenius norm of CSI differences
• Geodesic distances on the Grassmannian manifold of channel subspaces
• Triplet loss with Siamese networks to directly optimize for spatial proximity The learned metric must be robust to small-scale fading while capturing the large-scale spatial structure imposed by the environment's geometry.

Channel charting exploits the fact that each location in a rich scattering environment has a unique multipath signature. The angles of arrival (AoA), angles of departure (AoD), and delay spreads of dominant propagation paths act as a radio fingerprint for that position. By processing CSI matrices in the angular-delay domain via a 2D Discrete Fourier Transform, the charting algorithm isolates sparse multipath components. This sparsity is key: only a few dominant paths define a location, making the mapping robust to noise. The technique is particularly effective in massive MIMO systems, where the large antenna array provides high angular resolution for distinguishing closely spaced users.

Channel charting requires coherent CSI snapshots collected over time to capture the spatial structure of the environment. The base station accumulates CSI from uplink Sounding Reference Signals (SRS) or Demodulation Reference Signals (DMRS) across multiple time slots. A critical assumption is channel quasi-stationarity over the observation window—the physical geometry of scatterers must remain relatively static. For mobile users, the charting function must be updated continuously to track movement. Recurrent neural networks and Kalman filtering can be integrated to model temporal dynamics and smooth the chart coordinates, preventing jitter in the pseudo-map.

While channel charting provides a relative position map, its utility extends far beyond localization:

• Predictive handover: Anticipate cell transitions by tracking user trajectory on the chart before signal degradation occurs
• User grouping: Cluster users with similar spatial signatures for efficient multicast beamforming and Non-Orthogonal Multiple Access (NOMA) scheduling
• Anomaly detection: Identify unauthorized transmitters or environmental changes when a CSI vector maps to an unexpected chart region
• Rate prediction: Infer achievable spectral efficiency from a user's chart position relative to known coverage boundaries
• Digital twin alignment: Register the channel chart to a building floorplan for augmented reality and industrial IoT asset tracking

Several neural network architectures have been proposed for the forward charting function:

• Autoencoder-based: A bottleneck encoder compresses CSI to 2D latent coordinates; the decoder reconstructs CSI to enforce information preservation
• Siamese networks: Trained with contrastive loss to pull CSI from nearby locations together and push distant CSI apart
• Triplet networks: Use anchor-positive-negative triplets to learn a metric embedding where distance correlates with physical proximity
• Variational autoencoders (VAEs): Produce a probabilistic chart with uncertainty estimates for each coordinate
• Self-supervised contrastive learning: Leverages SimCLR or MoCo frameworks to learn representations from augmented CSI views without explicit distance labels

The raw material for Channel Charting. CSI describes how a signal propagates from transmitter to receiver, capturing the combined effects of scattering, fading, and power decay. In massive MIMO systems, the high-dimensional CSI matrix encodes rich spatial information that the charting manifold exploits.

• Represents the channel's complex gain per antenna pair
• Captured via pilot signals like CSI-RS in 5G NR
• Dimensionality scales with antennas × subcarriers

The property that makes Channel Charting geometrically meaningful. In massive MIMO, multipath components concentrate in a small number of distinct angles of arrival and departure. Transforming CSI into the angular domain via a Discrete Fourier Transform reveals a sparse representation where non-zero elements correspond to physical scatterers, enabling the manifold to learn a pseudo-map that preserves spatial proximity.

• Channel matrix becomes sparse in the DFT domain
• Each non-zero element maps to a physical path
• Fundamental to compressed sensing-based CSI acquisition

The unsupervised machine learning backbone of Channel Charting. Algorithms like t-SNE, UMAP, and autoencoders learn the low-dimensional structure embedded in high-dimensional CSI data. The core assumption is that geographically close transmitters produce similar channel fingerprints, so the learned latent space naturally forms a pseudo-map.

• Preserves local neighborhood relationships
• No explicit position labels required during training
• Dimensionality reduction from thousands of features to 2D or 3D

Defines the temporal validity window for Channel Charting. The coherence time is the duration over which the channel impulse response remains approximately invariant. Charting systems must sample CSI within this window to maintain a consistent pseudo-map; otherwise, channel aging causes decorrelation and degrades the spatial mapping.

• Inversely proportional to Doppler spread
• Dictates the maximum CSI sampling interval
• Critical for tracking mobile users on the chart

The standard metric for evaluating Channel Charting quality, inherited from channel estimation. NMSE measures the squared Frobenius norm of the error between original and reconstructed CSI, normalized by the true channel's norm. In charting, NMSE evaluates how well the learned manifold preserves channel similarity, though it does not directly measure spatial accuracy.

• Lower NMSE indicates better reconstruction fidelity
• Expressed in decibels (dB) for comparison
• Complements qualitative visual inspection of the chart