Wireless Covert Communications Based on Intelligent Reflecting Surface Aided and Artificial Noise Enhanced
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摘要: 该文考虑一种智能反射面(IRS)辅助及人工噪声(AN)增强的无线隐蔽通信以提升隐蔽传输性能。首先，分析了Willie的探测性能并给出了总的最小探测错误概率下界表达式。 在此基础之上，构建以最大化有效吞吐量为目标函数，以隐蔽需求和最大AN发射功率为约束的优化问题。该优化问题为非凸的，通常很难直接求解。该文提出基于Dinkelbach方法的交替迭代算法联合设计IRS的反射系数和Alice的发射功率及Bob的AN发射功率。为了降低计算复杂度，进一步提出一种低复杂度算法以获取相应优化变量的解析表达式。仿真结果表明：与无IRS及无AN方案相比，所提方案可以显著提升隐蔽传输性能。Abstract: In this work, an Intelligent Reflecting Surface (IRS) aided and Artificial Noise (AN) enhanced covert wireless communications is considered to improve the covert transmission performance. Firstly, the detection performance at Willie is analyzed and a lower bound on Willie’s minimum total detection error probability is presented. On this basis, an optimization problem that maximizes the effective throughput subject to the covertness constraint and the maximum AN transmit power constraint is formulated. The optimization problem is non-convex, which is generally difficult to tackle directly. Then, an alternating iterative algorithm based on Dinkelbach method is proposed to jointly design the IRS reflection beamforming and Alice’s transmit power together with Bob’s AN transmit power. In order to reduce the computational complexity, a low-complexity algorithm is further proposed to obtain analytical expressions for the corresponding optimization variables. Simulation results show that the proposed scheme improves significantly the covert transmission performance compared with the schemes without IRS and without AN.
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表 1 基于Dinkelbach理论的迭代算法
初始化参数$P_{\rm{b}}^{\max }$, $ K $, $ N $, $ \rho $, $ {\sigma _{\rm{b}}} $, $ {\sigma _{\rm{w}}} $, $ \beta $, $ {P_{\rm{a}}} $和$ {P_{\rm{b}}} $；设置收敛精
度$ \varepsilon \ge 0 $； 设置$ {V_M} = 1 $和$ {V_D} = 1 $；(1) While $ |{V_M} - \beta | \ge \varepsilon $ do (2) 求解优化问题式(19)获得$ M $并计算目标函数值记为$ {V_M} $； (3) While $ |{V_D}| \ge \varepsilon $ do 将步骤(3)所求最优的$ M $代入优化问题式(20)，求解
优化问题式(20)得到$ {P_{\rm{a}}} $和$ {P_{\rm{b}}} $；
更新$ \beta = \dfrac{{{P_{\rm{a}}}{\rm{Tr}}({\boldsymbol{BM}})}}{{\rho {P_{\rm{b}}} + \sigma _{\text{b}}^2}} $；计算$ {V_D} = {P_{\rm{a}}}{\rm{Tr}}({\boldsymbol{BM}}) - \beta (\rho {P_{\rm{b}}} + \sigma _{\text{b}}^2) $； End While (4) 更新$ {P_{\rm{a}}} $和$ {P_{\rm{b}}} $ (5) End While 
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表 2 低复杂度算法
初始化：设置系统参数$ P_{\rm b}^{\max } $, $ K $, $ N $, $ \rho $,$ {\sigma _{\rm b}} $和${\sigma _{\rm{w}}}$； (1) 根据式(23)计算IRS反射系数$ u $；
(2) if $\sigma _{\rm b}^2 \ge \dfrac{ {\rho \sigma _{\rm{w}}^2} }{ {|{ {\boldsymbol{u} }^{\rm{H} } }{\boldsymbol{c} } + {h_{ {\rm{bw} } } }{|^2} } }$ then；$ P_{\rm b}^* = P_{\rm b}^{\max } $ Else $ P_{\rm b}^* = 0 $； End if (3) 计算目标函数值； (4) End
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