Cognitive Radio Multiple-Input Multiple-Output Wireless Secure Transmission with Reconfigurable Intelligent Surface
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摘要: 考虑一个可重构智能反射面(RIS)辅助的频谱共享认知无线电(CR)多输入多输出(MIMO)安全通信系统。在存在窃听者的情况下，配备有多根天线的次级发送机与次级用户进行通信。首先，利用统计信道状态信息，得到了系统遍历安全速率的确定性等价表达式。然后，在满足总发送功率约束和干扰功率约束的条件下，提出一种结合泰勒级数展开法和拉格朗日乘子法的交替优化算法，联合优化了发送协方差矩阵和RIS相移矩阵。最后，仿真结果验证了所提算法的有效性。Abstract: A Reconfigurable Intelligent Surface (RIS)-assisted spectrum sharing Cognitive Radio (CR) Multiple-Input Multiple-Output (MIMO) wireless secure communication system is considered. In the case of eavesdropper, the secondary transmitter equippes with multiple antennas communicates with the secondary user. Firstly, by using the statistical channel state information, the deterministic equivalent expression of the ergodic security rate is derived. Then, on the premise of meeting the constraints of total transmission power and interference power, an alternating optimization algorithm combining Taylor series expansion method and Lagrange multiplier method is proposed to optimize jointly the transmission covariance matrix and phase shift matrix. Finally, simulation results verify the effectiveness of the proposed algorithm.
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算法1 AO算法 初始化：
$ {{\boldsymbol{Q}}^{\left( 0 \right)}} = {{\boldsymbol{I}}_M} $, $ {{\boldsymbol{\varPhi }}^{\left( 0 \right)}} = {{\boldsymbol{\varPhi }}^0} $, $ b_i^{\left( 0 \right)}{\text{ = }}\tilde b_i^{\left( 0 \right)} = e_i^{\left( 0 \right)} = \tilde e_i^{\left( 0 \right)} = $$1\;\left( {i = 1,2} \right) $,
$ {\bar C_{\text{s}}}^{\left( 1 \right)} = 0 $, $ \varepsilon = {10^{{{ - 4}}}} $(1) 循环 (2) 过程1：给定$ {\boldsymbol{\varPhi }} $，注水算法求解最优解$ {{\boldsymbol{Q}}^{{\text{opt}}}} $ (3) 根据式(11a)和式(16)，计算$ {{\boldsymbol{F}}_{\text{u}}}^{\left( {t + 1} \right)} $,$ {{\boldsymbol{F}}_{\text{e}}}^{\left( {t + 1} \right)} $和$ {{\boldsymbol{K}}^{\left( {t + 1} \right)}} $； (4) 根据式(15)计算$ {{\boldsymbol{Q}}^{\left( {t + 1} \right)}} $，并且根据干扰功率约束
$ {\text{E}}\{ {\text{tr}}({{\boldsymbol{H}}_{\text{P}}}{\boldsymbol{\varPhi }}{{\boldsymbol{H}}_{\text{a}}}{\boldsymbol{Q}}{({{\boldsymbol{H}}_{\text{P}}}{\boldsymbol{\varPhi }}{{\boldsymbol{H}}_{\text{a}}})^{\text{H}}})\} \le M{P_{\text{I}}} $和发送功率约束
$ {\text{ tr(}}{\boldsymbol{Q}}) \le M{P_{\text{T}}} $确定合适的$ {\lambda ^{\left( {t + 1} \right)}} $,$ {\nu ^{\left( {t + 1} \right)}} $；(5) 根据式(9)、式(10)计算$b_i^{\left( {t + 1} \right)},\tilde b_i^{\left( {t + 1} \right)},e_i^{\left( {t + 1} \right)},\tilde e_i^{\left( {t + 1} \right)} $
$\left( {i = 1,2} \right)$，更新$ {{\boldsymbol{\tilde Q}}^{\left( {t + 1} \right)}} = {{\boldsymbol{Q}}^{\left( {t + 1} \right)}} $；(6) 根据式(8)计算$ {\bar C_{\text{s}}}\left( {{{\boldsymbol{Q}}^{\left( {t + 1} \right)}},{\boldsymbol{\varPhi }}} \right) $； (7) 更新$ t: = t + 1 $，直到$ \left| {{{\bar C}_{\text{s}}}({{\boldsymbol{Q}}^{\left( {t + 1} \right)}},{\boldsymbol{\varPhi }}) - {{\bar C}_{\text{s}}}({{\boldsymbol{Q}}^{\left( t \right)}},{\boldsymbol{\varPhi }})} \right| \le \varepsilon $； (8) 获得$ {{\boldsymbol{Q}}^{{\text{opt}}}} = {{\boldsymbol{Q}}^{\left( {t + 1} \right)}} $； (9) 过程2：给定$ {\boldsymbol{Q}} $，投影梯度上升法求解最优解$ {{\boldsymbol{\varPhi }}^{{\text{opt}}}} $ (10) 根据式(30)更新$ {\mu ^{\left( {t + 1} \right)}} $； (11) 基于给定$ {{\boldsymbol{\varPhi }}^{\left( t \right)}} $，根据式(9)、式(10)计算
$ b_i^{\left( {t + 1} \right)},\tilde b_i^{\left( {t + 1} \right)},e_i^{\left( {t + 1} \right)},\tilde e_i^{\left( {t + 1} \right)} $ $ \left( {i = 1,2} \right) $；(12) 根据式(28)计算$ {{\boldsymbol{\theta }}^{\left( {n + 1} \right)}} $,${ {\boldsymbol{\varPhi } }^{\left( {t + 1} \right)} } = {\rm{diag}}({ {\boldsymbol{\theta } }^{\left( {t + 1} \right)} })$； (13) 根据式(8)计算$ {\bar C_{\text{s}}}\left( {{\boldsymbol{Q}},{{\boldsymbol{\varPhi }}^{\left( {t + 1} \right)}}} \right) $； (14) 更新$ t: = t + 1 $，直到$ \left| {{{\bar C}_{\text{s}}}{\text{(}}{\boldsymbol{Q}},{{\boldsymbol{\varPhi }}^{\left( {t + 1} \right)}}{\text{)}} - {{\bar C}_{\text{s}}}({\boldsymbol{Q}},{{\boldsymbol{\varPhi }}^{\left( t \right)}})} \right| \le \varepsilon $ (15) 获得$ {{\boldsymbol{\varPhi }}^{{\text{opt}}}} = {{\boldsymbol{\varPhi }}^{\left( {t + 1} \right)}} $； (16) 直到 $ \left| {{{\bar C}_{\text{s}}}\left( {{{\boldsymbol{Q}}^{{\text{opt}}}},{{\boldsymbol{\varPhi }}^{{\text{opt}}}}} \right) - {{\bar C}_{\text{s}}}\left( {{{\boldsymbol{Q}}^{\left( t \right)}},{{\boldsymbol{\varPhi }}^{\left( t \right)}}} \right)} \right| \le \varepsilon $，结束循环。 
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