Identifiability Limits of Low-Rank RFI Mitigation Under Single-Epoch Constraints: A Controlled Failure-Mode Study

TL;DR

This work addresses the identifiability limits of low-rank RFI mitigation under single-epoch data, showing that when RFI and astrophysical signals overlap in subspace structure, no rank cutoff can simultaneously suppress leakage and preserve signal. It analyzes a baseline truncated SVD and a frequency-weighted SVD, using two-bias diagnostics and Pareto fronts to quantify the trade-off between RFI leakage and science loss. A key finding is an irreducible Pareto floor under single-epoch constraints, indicating fundamental limits to low-rank mitigation in this regime, even with weighting. The study provides diagnostic plots and actionable guidelines to inform single-epoch mitigation strategies for next-generation radio observations.

Abstract

The rapid proliferation of low Earth orbit (LEO) satellite constellations has introduced a new class of radio frequency interference (RFI) that poses a fundamental challenge to modern radio astronomy. In particular, unintended electromagnetic radiation emitted by satellite electronics exhibits strong temporal variability and weak spectral regularity, limiting the effectiveness of conventional mitigation techniques that rely on long term averaging or multi epoch observations. In this work, we investigate the fundamental limits of low rank interference mitigation in the single epoch regime, where only a single time frequency snapshot is available. We formulate satellite induced interference as a structured but non stationary component superposed on astrophysical signals and thermal noise, and analyze the conditions under which low rank decomposition can successfully suppress interference while preserving underlying astronomical information. Through controlled simulations and empirical analysis, we demonstrate that aggressive rank truncation can lead to substantial signal distortion, particularly for diffuse or low signal to noise astrophysical features. We quantify this trade off using preservation and suppression metrics, and show that beyond a critical interference strength, low rank methods inevitably induce irreversible information loss. Our results clarify the operational boundaries of low rank approaches for next generation radio observations and highlight the need for interference aware, data driven mitigation strategies tailored to the single epoch regime.

Figures (5)

• Figure 1: Core diagnostics for the single-epoch failure mode. Top: leading singular modes can be visibly mixed (science + RFI). Bottom left: rank-sweep showing the two complementary biases: under-cleaning (RFI leakage, $\mathrm{Bias}_{+}$) and over-cleaning (signal loss, $\mathrm{Bias}_{-}$). Bottom right: Pareto view illustrating an irreducible error floor---the curve does not reach the origin under single-epoch mixing.
• Figure 2: Bias magnitude vs. rank cutoff $k$ for the baseline truncated SVD cleaning. The monotone, opposing trends formalize the mitigation trade-off.
• Figure 3: Pareto front of $(\mathrm{Bias}_{-},\mathrm{Bias}_{+})$ over a rank sweep. A nonzero floor implies that perfection is impossible for this dataset under single-epoch constraints.
• Figure 4: Distributional view of bias (example). Broad tails are consistent with intermittent but substantial science loss or residual leakage when modes are mixed.
• Figure 5: Example frequency-weighting sweep for FWSVD. Weighting may shift the knee but does not eliminate the irreducible error floor under strong science--RFI subspace overlap.