arXiv:2610.41248v1 Announce Type: new Abstract: Direct-to-device connectivity from low Earth orbit (LEO) satellites is commercially available, but its throughput is limited by the satellite antenna size and by payloads that separate users only by beams and frequency reuse. This article shows that a single LEO satellite with a meter-scale array can serve hundreds of users on the same time-frequency resource through multi-user multiple-input multiple-output precoding. The number of users it can separate with a single stream each, i.e., its spatial degrees of freedom (DoF), follows from the aperture in wavelengths, the orbit altitude, and the minimum elevation angle. With minimum mean-square error (MMSE) precoding, the throughput of these users grows with the signal-to-noise ratio (SNR), whereas maximum-ratio transmission becomes interference-limited. The precoder can be computed from the user positions and the satellite ephemeris and attitude, with a throughput loss of less than 0.5\% at 20~dB SNR compared with perfect channel knowledge under the 3GPP non-terrestrial channel models. The DoF also set the number of digital chains of a hybrid payload, and the functional split among satellites and ground trades inter-satellite-link and feeder-link load against on-board processing. As the satellite moves, the precoder can be updated from the known geometry every radio frame, i.e., 10~ms, while the computationally intensive user pairing can be kept for a few seconds with a throughput loss below 1\%. Finally, we keep the cell-specific signals on fixed beams while precoding the user data jointly across all cells of the satellite. For a $50\times50$ array at 600~km and a minimum elevation angle of $60^\circ$, one satellite serves 410 users at 6.1~bps/Hz on average, more than four times the throughput of fixed beams with four-color frequency reuse.