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

TL;DR

This paper introduces a physics-informed complex Transformer model that reconstructs wideband channel frequency responses from fragmented spectra in multi-band wireless systems, effectively handling interference and mobility.

Contribution

The proposed model uniquely combines physics-informed loss, factored self-attention, and complex-valued processing to improve CFR reconstruction under interference and mobility conditions.

Findings

Achieves higher PDP similarity (ρ ≥ 0.82) than classical baselines up to 50% interference.

Outperforms baselines across various mobility regimes with smooth degradation.

Effectively models bursty interference using Markov chains and incorporates mobility via velocity randomization.

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 $\rho \geq 0.82$ compared to $\rho \geq 0.62$ 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.