  We consider the problem of covert communication over wireless adhoc networks
in which (roughly) $n$ legitimate nodes (LNs) and $n^{\kappa}$ for $0<\kappa<1$
non-communicating warden nodes (WNs) are randomly distributed in a square of
unit area. Each legitimate source wants to communicate with its intended
destination node while ensuring that every WN is unable to detect the presence
of the communication. In this scenario, we study the throughput scaling law.
Due the covert communication constraint, the transmit powers are necessarily
limited. Under this condition, we introduce a preservation region around each
WN. This region serves to prevent transmission from the LNs and to increase the
transmit power of the LNs outside the preservation regions. For the
achievability results, multi-hop (MH), hierarchical cooperation (HC), and
hybrid HC-MH schemes are utilized with some appropriate modifications. In the
proposed MH and hybrid schemes, because the preservation regions may impede
communication along direct data paths, the data paths are suitably modified by
taking a detour around each preservation region. To avoid the concentration of
detours resulting extra relaying burdens, we distribute the detours evenly over
a wide region. In the proposed HC scheme, we control the symbol power and the
scheduling of distributed multiple-input multiple-output transmission. We also
present matching upper bounds on the throughput scaling under the assumption
that every active LN consumes the same average transmit power over the time
period in which the WNs observe the channel outputs.
