  The emerging millimeter-wave (mm-wave) unmanned aerial vehicle (UAV)
air-to-ground (A2G) communications are facing the Doppler effect problem that
arises from the inevitable wobbling of the UAV. The fast time-varying channel
for UAV A2G communications may lead to the outdated channel state information
(CSI) from the channel estimation. In this paper, we introduce two detectors to
demodulate the received signal and get the instantaneous bit error probability
(BEP) of a mm-wave UAV A2G link under imperfect CSI. Based on the designed
detectors, we propose an adaptive modulation scheme to maximize the average
transmission rate under imperfect CSI by optimizing the data transmission time
subject to the maximum tolerable BEP. A power control policy is in conjunction
with adaptive modulation to minimize the transmission power while maintaining
both the BEP under the threshold and the maximized average transmission rate.
Numerical results show that the proposed adaptive modulation scheme in
conjunction with the power control policy could maximize the temporally
averaged transmission rate, while saves as much as 50\% energy.
