  In this paper, we investigate covert communication over millimeter-wave
(mmWave) frequencies. In particular, a dual-beam mmWave transmitter, comprised
of two independent antenna arrays, attempts to reliably communicate to a
receiver Bob when hiding the existence of transmission from a warden Willie. In
this regard, operating over mmWave bands not only increases the covertness
thanks to directional beams, but also increases the transmission data rates
given much more available bandwidths and enables ultra-low form factor
transceivers due to the lower wavelengths used compared to the conventional
radio frequency (RF) counterpart. We assume that the transmitter Alice employs
one of its antenna arrays to form a directive beam for transmission to Bob. The
other antenna array is used by Alice to generate another beam toward Willie as
a jamming signal with its transmit power changing independently from a
transmission block to another block. We characterize Willie's detection
performance with the optimal detector and the closed-form of its expected value
from Alice's perspective. We further derive the closed-form expression for the
outage probability of the Alice-Bob link, which enables characterizing the
optimal covert rate that can be achieved using the proposed setup. Our results
demonstrate the superiority of mmWave covert communication, in terms of
covertness and rate, compared to the RF counterpart.
