Accelerated LCMV Beamforming for Collinear Interference Mitigation in Beam-Hopping LEO Mega-Constellations

Abstract

The rapid proliferation of large-scale Low Earth Orbit (LEO) mega-constellations has intensified co-frequency coexistence challenges, particularly collinear interference, where a victim user is simultaneously illuminated by the high-gain beams of serving and interfering satellites. High satellite mobility and millisecond-level beam-hopping updates make such interference highly dynamic and spatially coupled. To address this issue, we propose a low-complexity accelerated Linearly Constrained Minimum Variance (LCMV) transmit beamforming algorithm. By constructing a tractable equality-constrained surrogate for the original non-convex problem and exploiting the Woodbury identity, the method replaces full-array matrix inversion with low-dimensional operations, enabling sub-millisecond weight updates. System-level simulations using realistic Project Kuiper and Starlink parameters show over 54 dB average interference suppression, up to 20 dB worst-case SINR improvement, and an 8× speedup over conventional LCMV, meeting real-time beamhopping requirements.