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Model-based learning for multi-antenna multi-frequency location-to-channel mapping

Baptiste Chatelier, Vincent Corlay, Matthieu Crussière, Luc Le Magoarou

TL;DR

This work tackles the challenge of learning a continuous, location-to-channel mapping for multi-antenna, multi-frequency wireless systems where channel variation occurs on wavelength-scale spatial coordinates. It develops a model-based neural architecture that derives from a physics-based propagation model, using Taylor expansions to separate slow low-frequency content from fast high-frequency planar wavefronts, and aggregates local approximations into a global dictionary of planar wavefronts, steering vectors, and frequency responses. The architecture leverages Fourier-feature embeddings and hypernetworks to learn the dictionary components and complex activation weights, enabling efficient, scalable learning across antennas and frequencies while mitigating spectral bias. Empirical results on synthetic ray-traced channels show that the proposed MB approaches outperform INR baselines, generalize to unseen frequencies, and support radio-environment compression with substantial bandwidth savings, while maintaining explainability through its physics-driven structure.

Abstract

Years of study of the propagation channel showed a close relation between a location and the associated communication channel response. The use of a neural network to learn the location-to-channel mapping can therefore be envisioned. The Implicit Neural Representation (INR) literature showed that classical neural architecture are biased towards learning low-frequency content, making the location-to-channel mapping learning a non-trivial problem. Indeed, it is well known that this mapping is a function rapidly varying with the location, on the order of the wavelength. This paper leverages the model-based machine learning paradigm to derive a problem-specific neural architecture from a propagation channel model. The resulting architecture efficiently overcomes the spectral-bias issue. It only learns low-frequency sparse correction terms activating a dictionary of high-frequency components. The proposed architecture is evaluated against classical INR architectures on realistic synthetic data, showing much better accuracy. Its mapping learning performance is explained based on the approximated channel model, highlighting the explainability of the model-based machine learning paradigm.

Model-based learning for multi-antenna multi-frequency location-to-channel mapping

TL;DR

This work tackles the challenge of learning a continuous, location-to-channel mapping for multi-antenna, multi-frequency wireless systems where channel variation occurs on wavelength-scale spatial coordinates. It develops a model-based neural architecture that derives from a physics-based propagation model, using Taylor expansions to separate slow low-frequency content from fast high-frequency planar wavefronts, and aggregates local approximations into a global dictionary of planar wavefronts, steering vectors, and frequency responses. The architecture leverages Fourier-feature embeddings and hypernetworks to learn the dictionary components and complex activation weights, enabling efficient, scalable learning across antennas and frequencies while mitigating spectral bias. Empirical results on synthetic ray-traced channels show that the proposed MB approaches outperform INR baselines, generalize to unseen frequencies, and support radio-environment compression with substantial bandwidth savings, while maintaining explainability through its physics-driven structure.

Abstract

Years of study of the propagation channel showed a close relation between a location and the associated communication channel response. The use of a neural network to learn the location-to-channel mapping can therefore be envisioned. The Implicit Neural Representation (INR) literature showed that classical neural architecture are biased towards learning low-frequency content, making the location-to-channel mapping learning a non-trivial problem. Indeed, it is well known that this mapping is a function rapidly varying with the location, on the order of the wavelength. This paper leverages the model-based machine learning paradigm to derive a problem-specific neural architecture from a propagation channel model. The resulting architecture efficiently overcomes the spectral-bias issue. It only learns low-frequency sparse correction terms activating a dictionary of high-frequency components. The proposed architecture is evaluated against classical INR architectures on realistic synthetic data, showing much better accuracy. Its mapping learning performance is explained based on the approximated channel model, highlighting the explainability of the model-based machine learning paradigm.
Paper Structure (21 sections, 5 theorems, 35 equations, 14 figures, 1 table)

This paper contains 21 sections, 5 theorems, 35 equations, 14 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Towards a model-based approach for the location-to-channel mapping learning problem
  4. Model-based approach
  5. Discussion: a sparse recovery approach
  6. Model-based neural architecture
  7. Planar wavefront dictionary
  8. FRV dictionary
  9. SV dictionary
  10. Complex weights learning
  11. Global architecture
  12. Experiments
  13. Learning framework
  14. Baselines
  15. Experimental results
  16. ...and 6 more sections

Key Result

Lemma 1

Let $\mathbf{x}_r \in \mathbb{R}^3$ be a reference location and $\mathcal{D}_{\mathbf{x}} \subset \mathbb{R}^3$ be a local validity domain such that $\forall \mathbf{x} \in \mathcal{D}_{\mathbf{x}}, \left\lVert \mathbf{x}-\mathbf{x}_r \right\rVert_2 \leq \epsilon_{\mathbf{x}}$. Let $\mathbf{a}_{l,r} with $\mathbf{u}_{l,j}\left(\mathbf{x}_r\right) = \left(\mathbf{x}_r - \mathbf{a}_{l,j}\right)/\lef

Figures (14)

  • Figure 1: Virtual source theory used to model: (a) reflection, (b) diffraction.
  • Figure 2: Taylor expansion on locations only: $(a)$ location $\mathbf{x}$ far from reference $\mathbf{x}_r$, $(b)$ location $\mathbf{x}$ close to reference $\mathbf{x}_r$.
  • Figure 3: Proposed model-based neural architecture.
  • Figure 4: Ray-tracing scenes in Sionna: the red plane represents the possible train/test locations and the blue dot represents the BS. $(a)$: scene used for $\texttt{D}_1$ and $\texttt{D}_2$. $(b)$: scene used for $\texttt{D}_3$.
  • Figure 5: Baselines: 1. MLP, 2. and 3. RFFs.
  • ...and 9 more figures

Theorems & Definitions (18)

  • Remark 2.1
  • Remark 2.2
  • Lemma 1
  • proof
  • Corollary 1
  • proof
  • Proposition 1
  • proof
  • Remark 3.1
  • Proposition 2
  • ...and 8 more