  This paper studies the scalability of a wireless backhaul network modeled as
a random extended network with multi-antenna base stations (BSs), where the
number of antennas per BS is allowed to scale as a function of the network
size. The antenna scaling is justified by the current trend towards the use of
higher carrier frequencies, which allows to pack large number of antennas in
small form factors. The main goal is to study the per-BS antenna requirement
that ensures scalability of this network, i.e., its ability to deliver
non-vanishing rate to each source-destination pair. We first derive an
information theoretic upper bound on the capacity of this network under a
general propagation model, which provides a lower bound on the per-BS antenna
requirement. Then, we characterize the scalability requirements for two
competing strategies of interest: (i) long hop: each source-destination pair
minimizes the number of hops by sacrificing multiplexing gain while achieving
full beamforming (power) gain over each hop, and (ii) short hop: each
source-destination pair communicates through a series of short hops, each
achieving full multiplexing gain. While long hop may seem more intuitive in the
context of massive multiple-input multiple-output (MIMO) transmission, we show
that the short hop strategy is significantly more efficient in terms of per-BS
antenna requirement for throughput scalability. As a part of the proof, we
construct a scalable short hop strategy and show that it does not violate any
fundamental limits on the spatial degrees of freedom (DoFs).
