In this paper, we propose a robust secure transmission scheme for an active reconfigurable intelligent surface (RIS) enabled symbiotic radio (SR) system in the presence of multiple eavesdroppers (Eves). In the considered system, the active RIS is adopted to enable the secure transmission of primary signals from the primary transmitter to multiple primary users in a multicasting manner, and simultaneously achieve its own information delivery to the secondary user by riding over the primary signals. Taking into account the imperfect channel state information (CSI) related with Eves, we formulate the system power consumption minimization problem by optimizing the transmit beamforming and reflection beamforming for the bounded and statistical CSI error models, taking the worst-case SNR constraints and the SNR outage probability constraints at the Eves into considerations, respectively. Specifically, the S-Procedure and the Bernstein-Type Inequality are implemented to approximately transform the worst-case SNR and the SNR outage probability constraints into tractable forms, respectively. After that, the formulated problems can be solved by the proposed alternating optimization (AO) algorithm with the semi-definite relaxation and sequential rank-one constraint relaxation techniques. Numerical results show that the proposed active RIS scheme can reduce up to 27.0% system power consumption compared to the passive RIS.

翻译：本文针对存在多个窃听者的主动可重构智能表面（RIS）赋能共生无线电（SR）系统，提出一种鲁棒安全传输方案。在所考虑系统中，采用主动RIS以多播方式实现主发射机到多个主用户的主信号安全传输，同时通过将自身信息搭载于主信号上完成向次用户的信息传递。考虑与窃听者相关的不完美信道状态信息（CSI），分别针对有界CSI误差模型和统计CSI误差模型，通过优化发射波束成形与反射波束成形，在考虑窃听者处最差信噪比约束与信噪比中断概率约束的条件下，构建系统功耗最小化问题。具体而言，采用S-过程与伯恩斯坦型不等式分别将最差信噪比约束和信噪比中断概率约束近似转化为易处理形式。进而，通过结合半定松弛与逐次秩一约束松弛技术的交替优化（AO）算法求解所构建问题。数值结果表明，与被动RIS方案相比，所提主动RIS方案可降低高达27.0%的系统功耗。