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

TL;DR

The paper tackles detecting ultra-high-energy cosmic-ray (UHECR) radio pulses with the GRAND array under dominant Galactic and instrumental backgrounds. It introduces a dual-branch time-frequency denoising approach—a convolutional autoencoder that jointly processes time-domain traces and their FFT content—trained on realistic GRAND-like simulations. The method achieves median output SNR gains of about $15$--$23$ dB in the $50$--$200$ MHz band and reduces the waveform NMSE by approximately an order of magnitude compared with a Hilbert-envelope baseline, while near-threshold antennas see a $2$--$3$× increase in usability and additional gains for energy-reconstruction when waveform fidelity is required. These improvements translate into more reliable direction and energy estimates in sparse radio arrays, with potential integration into an end-to-end GRAND reconstruction pipeline.

Abstract

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.

Figures (13)

• Figure 1: Overview of the mock noisy signal generation. An UHECR air shower produces a short radio pulse that is measured by the GRAND HORIZON antennas GRAND:2018iaj, whose response we model with a toy model. The incident field is converted to an open-circuit voltage at the antenna, then passed through the analog front end (Low-Noise Amplifier, balun, filter, balun) before digitization by the analog-to-digital counts (ADC) converter. This yields the observed ADC traces which are already embedded in Galactic and instrumental noise. We use these simulated noisy traces to train and validate our ML denoiser model.
• Figure 2: Signal-to-Noise Ratio (SNR) distribution of the held-out test sample. Histogram of the simulated UHECR radio signals as measured by GRAND-like antennas in the three polarization channels (X, Y, Z).
• Figure 3: Encoder decoder denoiser architecture. The input consists of three channels sampled in time (with 1,024 bins per channel). The encoder has a time domain branch (orange blocks) and a frequency domain branch that splits into magnitude (dark blue) and phase (purple). Each branch starts with a one dimensional convolution followed by two residual blocks. Their outputs are combined in a fusion module (cyan) that provides a shared latent representation of the time, magnitude, and phase features and uses two additional convolutional layers. The decoder (red blocks) maps this latent representation back to waveform space and returns denoised traces with the same dimensions as the noisy input.
• Figure 4: Evolution of training diagnostics for the best performing hyperparameter configurations. The training and validation losses decline and then level off as the denoising network converges.
• Figure 5: Representative denoising reconstructions across channels in the time and frequency domains. Example three-channel traces (X, Y, Z) for different antenna traces, illustrating a high-SNR case (X; top), an intermediate-SNR case (Y; middle), and a lower-SNR case (Z; bottom). Left panels show the time-domain waveforms: the clean target waveform is shown in red (dotted), the noisy input in orange (dashed), and the denoised reconstruction in blue (continuous). Right panels show the corresponding frequency-domain amplitude spectra (magnitude of the Fourier transform) for the same traces. The per-channel SNR (and PSNR) values are annotated in each time-domain panel.