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

arXiv: https://arxiv.org/abs/2604.01944 · HTML: https://mlsanity.com/paper/2604.01944/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 18 references that are in the map.
- First posted on arXiv 2 Apr 2026.

## Builds on (most cited first, 7 of 7)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Axial Attention in Multidimensional Transformers](https://mlsanity.com/paper/1912.12180/) (2019)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Deep Learning-Based Channel Estimation](https://mlsanity.com/paper/1810.05893/) (2018)
- [Physics-informed deep learning for incompressible laminar flows](https://mlsanity.com/paper/2002.10558/) (2020)
- [Channelformer: Attention based Neural Solution for Wireless Channel Estimation and Effective Online Training](https://mlsanity.com/paper/2302.04368/) (2023)
- [Towards Multi-Functional 6G Wireless Networks: Integrating Sensing, Communication and Security](https://mlsanity.com/paper/2107.07735/) (2021)

## Built on by (most cited first, 1 of 1)

- [PilotWiMAE: Pilot-Native Representation Learning for Wireless Channels](https://mlsanity.com/paper/2605.22856/) (2026)

## Abstract (arXiv)

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(TF2 + FT2). 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 ≥ 0.82 compared to ρ ≥ 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.