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Simplicity is Key: An Unsupervised Pretraining Approach for Sparse Radio Channels

Jonathan Ott, Maximilian Stahlke, Tobias Feigl, Bjoern M. Eskofier, Christopher Mutschler

TL;DR

SpaRTran tackles the challenge of learning effective radio-channel representations with limited labeled data by injecting a physics-informed prior into unsupervised pretraining. By combining a Transformer encoder with a sparse reconstruction head and a CS-inspired dictionary, SpaRTran preconditions latent representations toward sparse decompositions, improving localization accuracy and beamforming codebook selection under both standard and domain-shift conditions. Theoretical analysis in RKHS bounds and an extensive empirical evaluation across multiple datasets demonstrate improved generalization and robustness, particularly when some labeled data are available for fine-tuning. This approach advances wireless foundation-model development by decoupling representations from specific system topologies and leveraging domain knowledge to guide unsupervised learning.

Abstract

Unsupervised representation learning for wireless channel state information (CSI)reduces reliance on labeled data, thereby lowering annotation costs, and often improves performance on downstream tasks. However, state-of-the-art approaches take little or no account of domain-specific knowledge, forcing the model to learn well-known concepts solely from data. We introduce Sparse pretrained Radio Transformer (SpaRTran), a hybrid method based on the concept of compressed sensing for wireless channels. In contrast to existing work, SpaRTran builds around a wireless channel model that constrains the optimization procedure to physically meaningful solutions and induces a strong inductive bias. Compared to the state of the art, SpaRTran cuts positioning error by up to 28% and increases top-1 codebook selection accuracy for beamforming by 26 percentage points. Our results show that capturing the sparse nature of radio propagation as an unsupervised learning objective improves performance for network optimization and radio-localization tasks.

Simplicity is Key: An Unsupervised Pretraining Approach for Sparse Radio Channels

TL;DR

SpaRTran tackles the challenge of learning effective radio-channel representations with limited labeled data by injecting a physics-informed prior into unsupervised pretraining. By combining a Transformer encoder with a sparse reconstruction head and a CS-inspired dictionary, SpaRTran preconditions latent representations toward sparse decompositions, improving localization accuracy and beamforming codebook selection under both standard and domain-shift conditions. Theoretical analysis in RKHS bounds and an extensive empirical evaluation across multiple datasets demonstrate improved generalization and robustness, particularly when some labeled data are available for fine-tuning. This approach advances wireless foundation-model development by decoupling representations from specific system topologies and leveraging domain knowledge to guide unsupervised learning.

Abstract

Unsupervised representation learning for wireless channel state information (CSI)reduces reliance on labeled data, thereby lowering annotation costs, and often improves performance on downstream tasks. However, state-of-the-art approaches take little or no account of domain-specific knowledge, forcing the model to learn well-known concepts solely from data. We introduce Sparse pretrained Radio Transformer (SpaRTran), a hybrid method based on the concept of compressed sensing for wireless channels. In contrast to existing work, SpaRTran builds around a wireless channel model that constrains the optimization procedure to physically meaningful solutions and induces a strong inductive bias. Compared to the state of the art, SpaRTran cuts positioning error by up to 28% and increases top-1 codebook selection accuracy for beamforming by 26 percentage points. Our results show that capturing the sparse nature of radio propagation as an unsupervised learning objective improves performance for network optimization and radio-localization tasks.
Paper Structure (22 sections, 3 theorems, 37 equations, 3 figures, 6 tables)

This paper contains 22 sections, 3 theorems, 37 equations, 3 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Description
  4. SpaRTran Training Pipeline
  5. Sparse Reconstruction Head
  6. Dictionary Composition
  7. Finetuning
  8. Theoretical Analysis
  9. Evaluation
  10. Localization in small data regime
  11. Localization under domain shift
  12. Beamforming
  13. Ablations
  14. Conclusion
  15. Impact Statement
  16. ...and 7 more sections

Key Result

Theorem 4.1

Let $\mathcal{H}$ be a reproducing kernel Hilbert space, equipped with a basis $\{\psi_i\}^N_{i=0}$. For any $h\in\mathcal{H}$ let the best n-term approximator be Also define the 1-atomic norm as Assume that there exists an exact recovery condition (ERC) tropp_greed_2004 such that the $O(n^{1/2})$ rate is optimal klusowski_sharp_2025This is equivalent to asserting a generalised Jackson-type ineq

Figures (3)

  • Figure 1: Example of learned sparse CSI decomposition, our unsupervised objective. The input signal (blue) is decomposed into a linear combination of basis functions (black) and subsequently recovered (orange).
  • Figure 2: Overview of our unsupervised pretraining method - SpaRTran.
  • Figure 3: (a) shows the cumulative density of the wireless localization error under ablations, (b) shows the localization accuracy depending on the dictionary size $N$ and the sparsity coefficient $\lambda$ and (c) shows the distribution of number of activations on 10000 data points.

Theorems & Definitions (8)

  • Theorem 4.1
  • Theorem 4.2
  • Remark 4.3
  • Corollary 4.4
  • Remark 4.5
  • proof : Proof of Theorem \ref{['thm:OperatorBound']}
  • proof : Proof of Theorem \ref{['thm:DiagonalImprovement']}
  • proof : Proof of Corollary \ref{['cor:LowRankImprovement']}