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This paper introduces a physics-informed complex Transformer network to reconstruct wideband channel frequency responses (CFR) from partially observed spectrum snapshots in multi-band wireless systems. The model uses a factored self-attention mechanism to reduce computational complexity and a holomorphic linear layer to preserve phase relationships. Training incorporates a composite loss function enforcing spectral fidelity, power delay profile (PDP) reconstruction, channel impulse response (CIR) sparsity, and temporal smoothness, achieving superior PDP similarity compared to classical baselines under various interference conditions and mobility regimes.
Reconstructing blocked wireless channels with a physics-informed Transformer beats traditional methods by 32% in PDP similarity, even with high interference and mobility.
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.