Secure and Robust Beamforming Algorithm for RIS Assisted MISO Systems
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摘要: 为解决无线信道开放性导致的信息传输安全及信道估计误差等不确定性带来的系统传输性能恶化问题，该文提出一种存在用户窃听的可重构智能超表面(RIS)辅助多输入单输出(MISO)系统的Charnes-Cooper鲁棒波束赋形算法。针对窃听用户建立有界信道不确定性模型，并通过约束最大发射功率以及RIS相移，联合优化基站波束和RIS相移来最大化用户保密率。为求解该非凸问题，首先通过变量替换、Charnes-Cooper方法和S-procedure方法将其转换为凸优化问题，进而采用间接交替优化耦合变量来获得鲁棒波束赋形矩阵和RIS相移。仿真结果表明，该文提出的基于RIS的联合优化算法具有更好的用户保密率和鲁棒性。Abstract: To solve the problem of information transmission security caused by wireless channel openness and system transmission performance deterioration caused by channel estimation error, a Charnes-Cooper robust beamforming algorithm is proposed for Reconfigurable Intelligent Surface (RIS) assisted Multiple-Input Single-Output (MISO) systems with eavesdroppers. A bounded channel uncertainty model is established for the eavesdropper, and the base station beamforming and RIS phase shift are jointly optimized to maximize user secrecy rate based on the constraints of maximum transmit power and RIS phase shifts. To solve the non-convex problem, it is first converted to a convex optimization problem by variable substitution, Charnes-Cooper method and S-procedure method, and then the coupling variables are indirectly and alternately optimized to obtain robust beamforming matrix and RIS phase shifts. Simulation results show that the proposed RIS-based joint optimization algorithm has better user confidentiality and robustness.
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算法1 具体步骤 初始化$N$, $M$, $ {P^{\max }} $, ${\boldsymbol{Z}}$、信道参数、信道不确定度和位置，设
置最大迭代次数和收敛精度；1: for iter=1, 2,···, iter(max)： 2: 求解问题式(18)得到Charnes-Cooper转化后的半正定矩阵${\boldsymbol{U}}$和
辅助变量$ \eta $；3: 根据特征值分解以及高斯随机化得到${\boldsymbol{\varphi }}$和$\overline {\boldsymbol{U}} $； 4: 根据公式$ \overline {\boldsymbol{V}} = \overline {\boldsymbol{U}} /\varsigma $得到RIS的相移矩阵${\boldsymbol{\psi }}$； 5: 求解问题式(26)得到Charnes-Cooper转化后的半正定矩阵${\boldsymbol{Z}}$和
辅助变量$ \varepsilon $；6: 依据公式${\boldsymbol{W}} = {\boldsymbol{Z}}/\vartheta $得到基站的波束矩阵${\boldsymbol{W}}$; 7: 根据式(28)计算用户保密率； 8: if $\left| { {R^{({\rm{iter}} + 1)} } - {R^{({\rm{iter}})} } } \right| \le { { {\varepsilon } }_{\text{p} } }$ break else iter=iter+1； end 9: end 
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