  To boost the secrecy rate (SR) of the conventional directional modulation
(DM) network and overcome the double fading effect of the cascaded channels of
passive intelligent reflecting surface (IRS), a novel active IRS-assisted DM
system with a power adjusting strategy between transmitter and active IRS is
proposed in this paper. Then, a joint optimization of maximizing the SR is cast
by alternately optimizing the power allocation (PA) factors, transmit
beamforming, receive beamforming, and reflect beamforming at IRS, subject to
the power constraint at IRS. To tackle the formulated non-convex optimization
problem, a high-performance scheme of maximizing SR based on successive convex
approximation (SCA) and Schur complement (Max-SR-SS) is proposed, where the
derivative operation are employed to optimize the PA factors, the generalized
Rayleigh-Rize theorem is adopted to derive the receive beamforming, and the SCA
strategy is utilized to design the transmit beamforming and phase shift matrix
of IRS. To reduce the high complexity, a low-complexity scheme, named
maximizing SR based on equal amplitude reflecting (EAR) and
majorization-minimization (MM) (Max-SR-EM), is developed, where the EAR and MM
methods are adopted to derive the amplitude and phase of the IRS phase shift
matrix, respectively. In particular, when the receivers are single antenna, a
scheme of maximizing SR based on alternating optimization (Max-SR-AO) is
proposed, where the PA factors, transmit and reflect beamforming are derived by
the fractional programming (FP) and SCA algorithms. Simulation results show
that with the same power constraint, the SR gains achieved by the proposed
schemes outperform those of the fixed PA and passive IRS schemes.
