A measurement-based approach to EPFD calculation, to quantify the impact of satellite mega-constellations on low-frequency radio astronomy

Context: Satellite mega-constellations generate Unintended Electro-Magnetic Radiation (UEMR) impacting low frequency radio astronomy. The Radio Regulations of the International Telecommunications Union Radiocommunication Sector (ITU-R) contain the basis for addressing UEMR, but enforcement mechanisms are absent. Aims: To adapt compatibility study methods based on satellite constellation simulations, in particular the Equivalent Power Flux-Density (EPFD) framework, to radio telescope measurements. Methods: We adapt the ITU-R EPFD calculation framework to measurement data obtained from all-sky interferometric imaging. We address the conceptual differences between forward-model EPFD calculations and measurement-based approaches. In particular, we consider low frequency systems, which are typically wide field-of-view and interferometric instruments. Results: For the first time, we demonstrate that all-sky interferometric observations enable a direct adaptation of the EPFD formalism to measurement data. We thus confirm previous estimations (Di Vruno et al. 2023) that the resulting measurement-based EPFD distributions exceed the radio astronomy interference threshold levels defined in Recommendation ITU-R RA.769-2 in 50-70% of samples. These exceedance fractions are well above the 2% single-system data-loss criterion in Recommendation ITU-R RA.1513-2. Expressed using the conventional 2% compatibility margin, the corresponding margins are negative, ranging from -18.6 to -16.3 dB, equivalent to a required uniform attenuation of 16.3-18.6 dB. Conclusions: Measurement-based implementations provide a practical pathway toward verification and long-term monitoring at low radio frequencies, which could form an important component of enforceability. We suggest instrumentation approaches to support measurement.