Intelligent reflecting surface (IRS) is a promising solution to build a programmable wireless environment for future communication systems, in which the reflector elements steer the incident signal in fully customizable ways by passive beamforming. In this paper, an IRS-aided secure spatial modulation (SM) is proposed, where the IRS perform passive beamforming and information transfer simultaneously by adjusting the on-off states of the reflecting elements. We formulate an optimization problem to maximize the average secrecy rate (SR) by jointly optimizing the passive beamforming at IRS and the transmit power at transmitter under the consideration that the direct pathes channels from transmitter to receivers are obstructed by obstacles. As the expression of SR is complex, we derive a newly fitting expression (NASR) for the expression of traditional approximate SR (TASR), which has simpler closed-form and more convenient for subsequent optimization. Based on the above two fitting expressions, three beamforming methods, called maximizing NASR via successive convex approximation (Max-NASR-SCA), maximizing NASR via dual ascent (Max-NASR-DA) and maximizing TASR via semi-definite relaxation (Max-TASR-SDR) are proposed to improve the SR performance. Additionally, two transmit power design (TPD) methods are proposed based on the above two approximate SR expressions, called Max-NASR-TPD and Max-TASR-TPD. Simulation results show that the proposed Max-NASR-DA and Max-NASR-SCA IRS beamformers harvest substantial SR performance gains over Max-TASR-SDR. For TPD, the proposed Max-NASR-TPD performs better than Max-TASR-TPD. Particularly, the Max-NASR-TPD has a closed-form solution.

中文翻译：

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用于智能可重构表面辅助安全空间调制的波束成形和发射功率设计

智能反射面 (IRS) 是为未来通信系统构建可编程无线环境的一种很有前途的解决方案，其中反射器元件通过无源波束成形以完全可定制的方式引导入射信号。在本文中，提出了一种 IRS 辅助的安全空间调制 (SM)，其中 IRS 通过调整反射元件的开关状态同时执行无源波束成形和信息传输。在考虑到从发射机到接收机的直接路径信道被障碍物阻塞的情况下，我们通过联合优化 IRS 的无源波束成形和发射机的发射功率，制定了一个优化问题，以最大化平均保密率 (SR)。由于SR的表达很复杂，我们为传统近似SR（TASR）的表达式推导出一个新的拟合表达式（NASR），它具有更简单的封闭形式，更便于后续优化。基于以上两个拟合表达式，三种波束形成方法，称为通过逐次凸逼近最大化NASR（Max-NASR-SCA），通过双上升最大化NASR（Max-NASR-DA）和通过半定松弛最大化TASR（Max- TASR-SDR) 被提出来提高 SR 性能。此外，基于上述两个近似SR表达式，提出了两种发射功率设计（TPD）方法，称为Max-NASR-TPD和Max-TASR-TPD。仿真结果表明，与 Max-TASR-SDR 相比，所提出的 Max-NASR-DA 和 Max-NASR-SCA IRS 波束形成器获得了显着的 SR 性能提升。对于 TPD，建议的 Max-NASR-TPD 比 Max-TASR-TPD 表现更好。