Robust Resource Allocation Algorithm for Active Reconfigurable Intelligent Surface-Assisted Symbiotic Secure Communication Systems
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摘要: 针对有源可重构智能表面(RIS)辅助共生安全通信的系统总功耗问题，该文提出一种基于惩罚的鲁棒资源分配算法。考虑不完美的串行干扰消除，在主系统安全性、次系统可靠性，以及有源RIS的相移与功率约束下，通过联合优化发射机波束赋形向量与有源RIS反射系数矩阵，建立了一个基于线性函数模型的鲁棒系统总功耗最小化资源分配问题。利用交替优化方法将上述变量与约束高度耦合的非凸问题解耦，通过变量替换、等价转换与基于惩罚的连续凸逼近将子问题转换成凸优化问题，最后利用CVX对子问题进行求解。仿真结果表明，所提算法具有良好的收敛性，且相比经典的无源RIS，系统总功耗降低89%。Abstract:
Objective The existing research on Reconfigurable Intelligent Surface (RIS)-assisted symbiotic radio systems has primarily focused on passive RIS. However, due to the severe double-fading effect, it is difficult to achieve significant capacity gains using passive RIS in communication scenarios with strong direct paths. The assistance of the active RIS can effectively solve this problem. Moreover, the signal amplification capability of active RIS enhances the signal-to-noise ratio of the secondary signal and improves the security of the primary signal. Additionally, by considering imperfect Successive Interference Cancellation (SIC), a penalized-based Successive Convex Approximation (SCA) algorithm utilizing alternating optimization is investigated. Methods The original optimization problem is challenging to solve directly due to its complex and non-convex constraints. Thus, the alternating optimization method is adopted to decouple the original optimization problem into two subproblems. These subproblems pertain to designing the transmit beamforming vector at the primary transmitter and the reflection coefficient matrix at the active RIS. Then, the variable substitution, the equivalent transformation, and the penalty-based SCA methods are utilized for alternating iterative solutions. Specifically, for the beamforming design, the rank-one constraint is first equivalently transformed. The penalty-based SCA method is then applied to recover the rank-one optimal solution, and iterative optimization is finally employed to obtain the result. For the reflection coefficient matrix design, the problem is first reformulated. Auxiliary variables are then introduced to avoid feasibility check issues, after which a penalty-based SCA approach is used to handle the rank-one constraint. The solution is ultimately obtained using the CVX toolbox. Based on the above procedures, a robust resource allocation algorithm based on penalty is proposed using alternating optimization. Results and Discussions The convergence curves of the proposed algorithm under different numbers of primary transmitter antennas (K) and RIS reflecting elements (N) is shown ( Fig.3 ). The results indicate that the total power consumption of the system gradually decreases with the increase of iterations and converges within a finite number of steps. The relationship between the total power consumption of the system and the Signal-to-Interference-and-Noise Ratio (SINR) threshold of the secondary signal is depicted (Fig.4 ). As the SINR threshold increases, the system requires more power to maintain the lowest service quality of the secondary signal, leading to a rise in the total power consumption. Besides, with the imperfect interference cancellation factor decreases, the total power consumption of the system diminishes. To compare performance, three baseline algorithms are introduced (Fig.5 ), namely: the passive RIS, the active RIS with random phase shift, and the non-robust algorithm. The total system power consumption under the proposed algorithm is consistently lower than that of the passive RIS and active RIS with random phase shift. Although additional power is consumed by the active RIS itself, the savings in transmit power outweigh this consumption, resulting in higher overall energy efficiency. When random phase shifts are applied, the active beamforming and amplification capabilities of the RIS are underutilized. This forces the primary transmitter to solely compensate for meeting the performance constraints, thereby increasing its power consumption. Besides, due to the consideration of imperfect SIC in the proposed algorithm, a higher transmit power is required to compensate for residual interference to satisfy the secondary system’s minimum SINR constraint. As a result, the total power consumption remains higher than that of the non-robust algorithm. The influence of the primary signal’s secrecy rate threshold on the secure energy efficiency of the primary system under different N has been revealed (Fig.6 ). The results indicate that there exists an optimal secrecy rate threshold, which maximizes the secure energy efficiency of the main system. To investigate the impact of the active RIS deployment on the total power consumption of the system, the positions of each node are rearranged (Fig.7 ). The fading effect experienced is weakened as the active RIS is placed closer to the receiver, thus the total system power consumption is reduced.Conclusions This paper investigates the total power consumption of an active RIS-assisted symbiotic secure communication system under imperfect SIC. To improve the energy efficiency of the system, a system-wide total power minimization problem is formulated, subject to multiple constraints including the quality of service for both primary and secondary signals, as well as the power and phase shift constraints of the active RIS. To address this non-convex problem with uncertain disturbance parameters, techniques such as the variable substitution, the equivalent transformation and the penalty-based SCA method are employed to convert the original problem into a convex optimization form. Simulation results validate the effectiveness of the proposed algorithm, demonstrating a significant reduction in the total system power consumption compared to benchmark schemes. -
表 1 算法1 基于惩罚的鲁棒资源分配算法
初始化参数：$ {P_I} $，K，N, L，$ {C_0} $，$ R_s^{\min } $，$ \gamma _c^{\min } $，$ \mu $，$ \sigma _i^2 $，
$ \sigma _e^2 $，$ \sigma _A^2 $，$ \eta $，$ {{\boldsymbol{w}}^{(0)}} $，$ {{\boldsymbol{Q}}^{(0)}} $；设置收敛精度$ \varepsilon = {\varepsilon _1} = {\varepsilon _2} \ge 0 $，
内外层最大迭代次数${I_{\max }}$，初始化外层迭代次数$ I = 0 $，内层迭
代次数$ {I_1} = {I_2} = 0 $；(1) While $ \Gamma ({{\boldsymbol{w}}^{(I + 1)}},{{\boldsymbol{Q}}^{(I + 1)}}) - \Gamma ({{\boldsymbol{w}}^{(I)}},{{\boldsymbol{Q}}^{(I)}}) \ge \varepsilon $或$I \le {I_{\max }}$
do(2) While $ |tr{({\boldsymbol{W}})^{({I_1})}} - {\kappa _{max}}{({\boldsymbol{W}})^{({I_1} - 1)}}| \ge {\varepsilon _1} $或${I_1} \le {I_{\max }}$ do (3) 给定$ {{\boldsymbol{w}}^{(I)}} $，$ {{\boldsymbol{Q}}^{(I)}} $，求解问题式(10)获得$ {{\boldsymbol{W}}^{({I_1})}} $，
$ {I_1} = {I_1} + 1 $；(4) End While (5) $ {{\boldsymbol{W}}^{({I_1})}} = {{\boldsymbol{W}}^{({I_1} + 1)}} $； (6) While $ |tr({\boldsymbol{F}}{{\boldsymbol{U}}^{({I_2})}}) - tr({\boldsymbol{F}}{{\boldsymbol{U}}^{({I_2} - 1)}})| \ge {\varepsilon _2} $或${I_2} \le {I_{\max }}$ do (7) 给定$ {{\boldsymbol{W}}^{({I_1})}} $，求解问题式(15)获得$ {{\boldsymbol{Q}}^{({I_2})}} $，$ {I_2} = {I_2} + 1 $； (8) End While (9) $ {{\boldsymbol{Q}}^{({I_2})}} = {{\boldsymbol{Q}}^{({I_2} + 1)}} $； (10) 计算$ \Gamma ({{\boldsymbol{w}}^{(I)}},{{\boldsymbol{Q}}^{(I)}}) $； (11) 设置迭代次数$ I = I + 1 $； (12) End While 
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