  We conduct novel coverage probability analysis of downlink transmission in a
three-dimensional (3D) terahertz (THz) communication (THzCom) system. In this
system, we address the unique propagation properties in THz band, e.g.,
absorption loss, super-narrow directional beams, and high vulnerability towards
blockage, which are fundamentally different from those at lower frequencies.
Different from existing studies, we characterize the performance while
considering the effect of 3D directional antennas at both access points (APs)
and user equipments (UEs), and the joint impact of the blockage caused by the
user itself, moving humans, and wall blockers in a 3D environment. Under such
consideration, we develop a tractable analytical framework to derive a new
expression for the coverage probability by examining the regions where dominant
interferers (i.e., those can cause outage by themselves) can exist, and the
average number of interferers existing in these regions. Aided by numerical
results, we validate our analysis and reveal that ignoring the impact of the
vertical heights of THz devices in the analysis leads to a substantial
underestimation of the coverage probability. We also show that it is more
worthwhile to increase the antenna directivity at the APs than at the UEs, to
produce a more reliable THzCom system.
