  This paper proposes, and evaluates the benefit of, one particular hybrid
satellite-HAPS-ground network, where one high-altitude-platform-station (HAPS)
connected to one geo-satellite assists the ground base-stations (BSs) at
serving ground-level users. The paper assumes that the geo-satellite is
connected to the HAPS using free-space-optical backhaul link. The HAPS,
equipped with multiple antennas, aims at transmitting the geo-satellite data to
the users via radio-frequency (RF) links using spatial-multiplexing. Each
ground BS, on the other hand, is equipped with multiple antennas, but directly
serves the users through the RF links. The paper then focuses on maximizing the
network-wide throughput, subject to HAPS payload connectivity constraint, HAPS
and BSs power constraints, and backhaul constraints, so as to jointly determine
the user association strategy of each user (i.e., user to geo-satellite via
HAPS, or user to BS), and their associated beamforming vectors. We tackle such
a mixed discrete-continuous optimization problem using an iterative approach,
where the user association is determined using a combination of integer linear
programming and generalized assignment problems, and where the beamforming
strategy is found using a weighted-minimum-mean-squared-error approach. The
simulations illustrate the appreciable gain of our proposed algorithm, and
highlight the prospects of augmenting the ground networks with beamforming
empowered HAPS for connecting the unconnected, and super-connecting the
connected.
