Downlink Co-Frequency Interference Analysis for Beam-Hopping Multi-Layer LEO Constellations Based on Stochastic Geometry

Abstract

With the rapid deployment of multi-layer low Earth orbit (LEO) constellations, spectrum scarcity has led to severe downlink co-frequency interference. While beam-hopping offers a flexible solution for resource allocation in these systems, its inherent spatio-temporal dynamics introduce significant complexity for interference modeling. Existing interference analytical models rely on static transmit gain assumptions and fail to capture these dynamics, leaving a critical research gap in inter-layer co-frequency interference assessment. To address this issue, this paper proposes a stochastic geometry-based analytical framework that jointly characterizes the temporal beam activation and spatial three-dimensional off-axis angle distribution to model beam-hopping induced co-frequency interference in multi-layer LEO constellations. We further derive the receive off-axis angle distribution to characterize the receive antenna gain and free-space path loss, and obtain a closed-form expression for the expected interference power. On this basis, a systematic analysis of the interference-to-noise (I/N) ratio is enabled across various elevation angles and latitudes. Monte Carlo simulations demonstrate that the proposed method achieves a relative mean absolute error (RMAE) of ${1. 6 2} \%$, and reduces computational time by over 99.6%. This work enables efficient and reliable interference evaluation for the design and interference mitigation of beam-hopping multi-layer LEO constellations.