A high-precision interpolation method for pulsed radio signals from cosmic-ray air showers

TL;DR

This paper introduces a high-precision interpolation method for reconstructing radio pulse signals from cosmic-ray air showers, reducing simulation costs while maintaining accuracy for large antenna arrays like SKA.

Contribution

The paper presents a novel interpolation algorithm using Fourier series and cubic splines that accurately reconstructs radio signals from a limited set of simulated antennas, enabling efficient large-scale air shower analysis.

Findings

Interpolation achieves high accuracy with only ~200 antennas.

Significantly reduces computational time for large antenna arrays.

Enables precise pulse shape and timing analysis for SKA-scale studies.

Abstract

Analysis of radio signals from cosmic-ray induced air showers has been shown to be a reliable method to extract shower parameters such as primary energy and depth of shower maximum. The required detailed air shower simulations take 1 to 3 days of CPU time per shower for a few hundred antennas. With nearly $60,000$ antennas envisioned to be used for air shower studies at the Square Kilometre Array (SKA), simulating all of these would come at unreasonable costs. We present an interpolation algorithm to reconstruct the full pulse time series at any position in the radio footprint, from a set of antennas simulated on a polar grid. Relying on Fourier series representations and cubic splines, it significantly improves on existing linear methods. We show that simulating about 200 antennas is sufficient for high-precision analysis in the SKA era, including e.g. interferometry which relies on accurate pulse shapes and timings. We therefore propose the interpolation algorithm and its implementation as a useful extension of radio simulation codes, to limit computational effort while retaining accuracy.