  Recently, intelligent reflecting surface (IRS) and unmanned aerial vehicle
(UAV) have been introduced into wireless communication systems to enhance the
performance of air-ground transmission. To make a good balance between
performance, cost, and power consumption, a hybrid-IRS-and-UAV-assisted
directional modulation (DM) network is investigated in this paper, where the
hybrid IRS consists of passive and active reflecting elements. To maximize the
achievable rate, three optimization algorithms, called maximum signal-to-noise
ratio (SNR)-fractional programming (FP) (Max-SNR-FP), maximum SNR-equal
amplitude reflecting (EAR) (Max-SNR-EAR), and maximum
SNR-majorization-minimization (MM) (Max-SNR-MM), are proposed to jointly design
the beamforming vector and phase shift matrix (PSM) of hybrid IRS by
alternately optimizing one and giving another. The Max-SNR-FP method employs
the successive convex approximation and FP methods to derive the beamforming
vector and hybrid IRS PSM. The Max-SNR-EAR method adopts the maximum
signal-to-leakage-noise ratio method and the criteria of phase alignment and
EAR to design them. In addition, the Max-SNR-MM method utilizes the MM
criterion to derive the IRS PSM. Simulation results show that the rates
harvested by the proposed three methods are slightly lower than those of active
IRS with higher power consumption, which are 35 percent higher than those of no
IRS and random phase IRS, while passive IRS achieves only about 17 percent rate
gain over the latter. Moreover, compared to Max-SNR-FP, the proposed
Max-SNR-EAR and Max-SNR-MM methods make an obvious complexity degradation at
the price of a slight performance loss.
