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.

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