  Space AI has become increasingly important and sometimes even necessary for
government, businesses, and society. An active research topic under this
mission is integrating federated learning (FL) with satellite communications
(SatCom) so that numerous low Earth orbit (LEO) satellites can collaboratively
train a machine learning model. However, the special communication environment
of SatCom leads to a very slow FL training process up to days and weeks. This
paper proposes NomaFedHAP, a novel FL-SatCom approach tailored to LEO
satellites, that (1) utilizes high-altitude platforms (HAPs) as distributed
parameter servers (PS) to enhance satellite visibility, and (2) introduces
non-orthogonal multiple access (NOMA) into LEO to enable fast and
bandwidth-efficient model transmissions. In addition, NomaFedHAP includes (3) a
new communication topology that exploits HAPs to bridge satellites among
different orbits to mitigate the Doppler shift, and (4) a new FL model
aggregation scheme that optimally balances models between different orbits and
shells. Moreover, we (5) derive a closed-form expression of the outage
probability for satellites in near and far shells, as well as for the entire
system. Our extensive simulations have validated the mathematical analysis and
demonstrated the superior performance of NomaFedHAP in achieving fast and
efficient FL model convergence with high accuracy as compared to the
state-of-the-art.
