Deep-Learning Denoising of Radio Observations for Ultra-High-Energy Cosmic-Ray Detection

Ultra-high-energy cosmic rays (UHECRs) can be detected via the broadband radio pulses produced by their extensive air showers. The Giant Radio Array for Neutrino Detection (GRAND) is a planned radio observatory that aims to deploy autonomous antenna arrays over areas of order $\sim 10^5,\mathrm{km}^2$ to detect this emission. However, Galactic and instrumental radio backgrounds make the identification of low signal-to-noise ratio (SNR) pulses a central challenge. Here, we present a deep convolutional denoiser model that jointly processes each GRAND antenna trace in the time and frequency domains, allowing the network to learn transient pulse morphology and broadband spectral features while suppressing background noise. By training the model on $4.1\times 10^5$ simulated traces that include detailed UHECR radio emission and realistic detector response and noise, we find a median output-SNR improvement of $\sim 15-23,\mathrm{dB}$ in the $50-200~\mathrm{MHz}$ band and a reduction of the normalized mean squared error of the waveform by about an order of magnitude relative to a Hilbert-envelope denoiser baseline. We also verify that applying the denoiser to noise-only windows does not produce spurious pulse candidates. Near the detection threshold, the denoiser increases the number of antennas contributing reliable pulse timing by a factor of $\sim 2-3$, which correspondingly tightens direction reconstruction uncertainties. When we additionally require accurate recovery of the waveform shape, the denoiser yields a median gain of $\sim 3-4$ antennas usable for energy reconstruction at SNR$\simeq 5-6$, strengthening event-level direction and energy estimates in sparse radio arrays.

💡 Research Summary

The paper addresses the fundamental challenge of detecting ultra‑high‑energy cosmic‑ray (UHECR) radio pulses in the presence of overwhelming Galactic and instrumental noise, a problem that will be central to the planned Giant Radio Array for Neutrino Detection (GRAND). The authors develop a deep‑learning denoising auto‑encoder that processes each antenna trace simultaneously in the time domain and in the frequency domain (via real‑FFT magnitude and phase). By providing both representations, the network can learn the characteristic nanosecond‑scale pulse morphology together with its broadband spectral signature, while learning to suppress various noise patterns, including non‑Gaussian radio‑frequency interference (RFI).

Data generation: The clean signal set is produced with ZHAireS simulations of extensive air showers (proton and iron primaries, 0.4–4 EeV, zenith angles 37°–87°, full azimuthal coverage) using the GRAND‑Proto300 site configuration for geomagnetic and atmospheric conditions. The simulated electric‑field waveforms are passed through a simplified “toy” RF chain that mimics the low‑noise amplifier, cable, variable‑gain amplifier, analog band‑pass filter, and ADC response of a GRAND antenna. A small random GPS timing jitter (few ns) and broadband Gaussian noise at a level comparable to the Galactic background are added, yielding realistic noisy traces. Each trace consists of three polarization channels (X, Y, Z) sampled at 0.5 ns intervals over 1 024 bins. The final dataset contains 410 673 traces, split 80 %/10 %/10 % for training, validation, and testing, with the test set deliberately dominated by low‑SNR examples (SNR ≈ 0–6).

Network architecture: The model is a dual‑branch auto‑encoder. The time‑domain branch consists of an initial 1‑D convolution, two residual blocks, and max‑pooling stages that progressively compress the temporal axis. The frequency‑domain branch first applies a Hann window, computes a real FFT, and splits the result into magnitude and phase streams, each processed by an analogous convolution‑residual‑pooling pipeline. After three down‑sampling steps, the two branches are concatenated (fusion layer) to form a shared latent code that mixes transient and spectral information. The decoder uses three transposed‑convolution stages to up‑sample back to the original shape, outputting denoised waveforms for all three polarizations. Hyper‑parameter optimization via Ray Tune selected channel widths of 128→256 (time) and 64→256 (magnitude/phase), with decoder channels 32, 16, 8, 3. The loss combines an L1 term on the time‑domain waveform and weighted L1 terms on magnitude and phase, with the magnitude weight (≈0.85) larger than the phase weight (≈0.44).

Performance metrics and results:

• SNR improvement: Median output‑SNR gains of 15–23 dB across the 50–200 MHz band.
• Waveform fidelity: Normalized mean‑squared error (NMSE) reduced by roughly an order of magnitude compared with a Hilbert‑envelope denoiser baseline.
• False‑positive control: When fed pure noise windows, the network produces negligible spurious pulses, confirming that it does not hallucinate signals.
• Impact on reconstruction: Near the detection threshold (SNR ≈ 5–6), the number of antennas providing reliable pulse timing increases by a factor of 2–3, tightening direction‑reconstruction uncertainties. When requiring accurate waveform shape (important for energy estimation), the denoiser yields a median gain of 3–4 additional usable antennas per event. This translates into significantly better angular resolution and lower energy‑reconstruction bias, especially in the sparse antenna regime of GRAND.

Discussion and outlook: The joint time‑frequency approach proves robust against non‑stationary noise and RFI, outperforming traditional matched‑filter or wavelet methods that assume Gaussian statistics. The authors note that their toy RF chain and Gaussian noise model, while sufficient for training, do not capture the full sidereal‑time dependence and spectral coloring of the real Galactic background; future work should validate the model on measured GRAND data and explore domain‑adaptation techniques. Real‑time implementation considerations (e.g., FPGA/GPU acceleration) are mentioned as necessary for deployment in a large‑scale array. The code and trained models are publicly released on Zenodo (DOI: 10.5281/zenodo.18233878), facilitating reproducibility and adaptation to other radio‑astronomy experiments.

In summary, the study demonstrates that a deep‑learning denoiser leveraging both temporal and spectral information can dramatically enhance the detectability of low‑SNR UHECR radio pulses, increase the number of antennas contributing to event‑level reconstruction, and thereby lower the effective detection threshold of GRAND. This represents a significant step forward in the application of modern AI techniques to ultra‑high‑energy astrophysics.