  To make a good balance between performance, cost, and power consumption, a
hybrid intelligent reflecting surface (IRS)-aided 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, two
optimization algorithms, called maximum signal-to-noise ratio (SNR)-fractional
programming (FP) (Max-SNR-FP) and maximum SNR-equal amplitude reflecting (EAR)
(Max-SNR-EAR), are proposed to jointly design the beamforming vector and phase
shift matrix (PSM) of hybrid IRS by alternately optimizing one and giving
another. The former employs the successive convex approximation and FP methods
to derive the beamforming vector and hybrid IRS PSM, while the latter adopts
the maximum signal-to-leakage-noise ratio method and the criteria of phase
alignment and EAR to design them. Simulation results show that the rates
harvested by the proposed two 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 method makes an obvious complexity degradation at the price of a
slight performance loss.
