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.

翻译：为提升传统方向调制（DM）网络的安全速率（SR），并克服无源智能反射面（IRS）级联信道的双重衰落效应，本文提出一种在发射机与有源IRS之间采用功率调整策略的新型有源IRS辅助DM系统。在此基础上，通过交替优化IRS处的功率分配（PA）因子、发射波束成形、接收波束成形及反射波束成形，在满足IRS功率约束的条件下，构建了最大化SR的联合优化问题。为解决所提出的非凸优化问题，本文提出一种基于逐次凸近似（SCA）与舒尔补（Schur complement）的高性能最大化SR方案（Max-SR-SS），其中采用导数运算优化PA因子，利用广义瑞利-里兹定理推导接收波束成形，并运用SCA策略设计发射波束成形及IRS的相移矩阵。为降低高计算复杂度，本文进一步开发了一种低复杂度方案，即基于等幅反射（EAR）与主化最小化（MM）的最大化SR方案（Max-SR-EM），分别采用EAR和MM方法推导IRS相移矩阵的幅度与相位。特别地，当接收机为单天线时，提出一种基于交替优化的最大化SR方案（Max-SR-AO），其中PA因子、发射波束成形及反射波束成形通过分数规划（FP）和SCA算法联合推导。仿真结果表明，在相同功率约束条件下，所提方案实现的SR增益优于固定PA方案及无源IRS方案。