Physics-Informed Transformer for Multi-Band Channel Frequency Response Reconstruction

2026-04-02

AI Summary

This work addresses the challenge of accurately reconstructing wideband channel frequency responses (CFRs) in multiband wireless systems, where co-channel interference causes missing subband signals. To this end, the paper proposes the first physics-informed complex-valued Transformer architecture, which efficiently processes fragmented spectral snapshots through joint time–frequency modeling, factorized self-attention, and complex holomorphic linear layers. The model uniquely embeds physical priors—including spectral fidelity, power delay profile (PDP) structure, channel sparsity, and temporal smoothness—and incorporates a velocity-randomized training strategy to enhance generalization across diverse mobility scenarios. Experimental results demonstrate that, under interference occupancy as high as 50%, the proposed method significantly outperforms state-of-the-art baselines in PDP similarity (ρ ≥ 0.82 versus ρ ≥ 0.62) and maintains consistently superior performance across the full range of user velocities.

Abstract

Wideband channel frequency response (CFR) estimation is challenging in multi-band wireless systems, especially when one or more sub-bands are temporarily blocked by co-channel interference. We present a physics-informed complex Transformer that reconstructs the full wideband CFR from such fragmented, partially observed spectrum snapshots. The interference pattern in each sub-band is modeled as an independent two-state discrete-time Markov chain, capturing realistic bursty occupancy behavior. Our model operates on the joint time-frequency grid of $T$ snapshots and $F$ frequency bins and uses a factored self-attention mechanism that separately attends along both axes, reducing the computational complexity to $O(TF^2 + FT^2)$. Complex-valued inputs and outputs are processed through a holomorphic linear layer that preserves phase relationships. Training uses a composite physics-informed loss combining spectral fidelity, power delay profile (PDP) reconstruction, channel impulse response (CIR) sparsity, and temporal smoothness. Mobility effects are incorporated through per-sample velocity randomization, enabling generalization across different mobility regimes. Evaluation against three classical baselines, namely, last-observation-carry-forward, zero-fill, and cubic-spline interpolation, shows that our approach achieves the highest PDP similarity with respect to the ground truth, reaching $ρ\geq 0.82$ compared to $ρ\geq 0.62$ for the best baseline at interference occupancy levels up to 50%. Furthermore, the model degrades smoothly across the full velocity range, consistently outperforming all other baselines.

Problem

• channel frequency response
• multi-band wireless systems
• co-channel interference
• spectrum reconstruction
• wideband CFR estimation

Innovation

• Physics-Informed Transformer
• Channel Frequency Response Reconstruction
• Complex-Valued Self-Attention
• Markovian Interference Modeling
• Holomorphic Neural Networks