  We study the maximum achievable rate of a two-hop amplified-and-forward (AF)
relaying millimeter-wave (mm-wave) system, where two AF relaying schemes, i.e.,
half-duplex (HD) and full-duplex (FD) are discussed. By considering the two-ray
mm-wave channel and the Gaussian-type directional antenna, jointly, the impacts
of the beamwidth and the self-interference coefficient on maximum achievable
rates are investigated. Results show that, under a sum-power constraint, the
rate of FD-AF mm-wave relaying outperforms its HD counterpart only when
antennas with narrower beamwidth and smaller self-interference coefficient are
applied. However, when the sum-power budget is sufficiently high or the
beamwidth of directional antenna is sufficiently small, direct transmission
becomes the best strategy, rather than the AF relaying schemes. For both
relaying schemes, we show that the rates of both AF relaying schemes scale as $
\mathcal{O}\left(\min\left\lbrace\theta_m^{-1},\theta_m^{-2}\right\rbrace\right)
$ with respect to beamwidth $ \theta_ m $, and the rate of FD-AF relaying
scales as $ \mathcal{O}\left(\mu^{-\frac{1}{2}}\right) $ with respect to
self-interference coefficient $ \mu $. Besides, we show that, ground
reflections may significantly affect the performance of mm-wave communications,
constructively or destructively. Thus, the impact of ground reflections
deserves careful considerations for analyzing or designing future mm-wave
wireless networks.
