Robust Beamforming Algorithm for Terahertz Communication Systems Aided by Reconfigurable Intelligent Surfaces
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摘要: 太赫兹通信作为6G的关键技术之一，被认为是能够解决频谱资源短缺、提升系统容量的有效手段。然而，由于路径损耗极高和分子的吸收作用，太赫兹容易被障碍物阻挡导致通信中断。为了解决该问题，该文将可重构智能反射面(RIS)引入到太赫兹通信系统中，且考虑信道不确定性对传输稳定性的影响，基于用户服务质量约束、基站发射功率约束及RIS离散相移约束，建立多用户能效最大化波束赋形模型。利用丁克尔巴赫、连续凸近似、S-程序、半正定松弛、相位映射和块坐标下降将原非凸优化问题转化为凸优化问题进行求解。仿真结果表明，与传统非鲁棒波束赋形对比，所提算法能效提升了15.4%，中断概率减小了15.48%。Abstract: Terahertz communication, as one of the key technologies for 6G, is considered an effective means of addressing the scarcity of spectrum resources and improving system capacity. However, due to high path loss and the molecule absorption, terahertz is easily blocked by obstacles leading to communication interruptions. To address this problem, Reconfigurable Intelligent Surface (RIS) is introduced into terahertz communication systems and the impact of channel uncertainty on transmission stability is considered to establish a multi-user energy-efficiency maximization beamforming model based on user quality of service constraints, base station transmit power constraints and RIS discrete phase shift constraints. The original nonconvex optimization problem is solved by transforming it into a convex optimization problem using Dinkelbach, continuous convex approximation, S-procedure, semi-positive definite relaxation, phase mapping and block coordinate descent. Simulation results show that the proposed algorithm improves the energy efficiency by 15.4% and reduces the outage probability by 15.48% compared with the traditional non-robust beamforming algorithm.
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算法1 基于BCD的鲁棒波束赋形算法 初始化系统参数：$M,N,K,\sigma _k^2,{P^{\max } },{P_{ {\text{BS} } } },{P_{ {\text{RIS} } } },R_k^{\min },\bar x_k^{(2)}$,
$\bar x_k^{(3)},\bar \eta ,{\varepsilon _k},\mu $;设置$ \mu $的上界和下界使之满足$ {\mu ^{\min }} < = {\mu ^ * } < = {\mu ^{\max }} $; 设置最大迭代次数$ {L_{\max }} $，收敛精度$ \varpi $，迭代索引$ l = 0 $; (1) While $ l < = {L_{\max }} $do (2) $ \mu (l) = ({\mu ^{\min }} + {\mu ^{\max }})/2 $; (3) 初始化$ {{\boldsymbol{V}}_k} $,$ {\boldsymbol{\tilde \varTheta }} $; (4) 重复 (5) 给定$ {\boldsymbol{\tilde \varTheta }} $，求解问题式(32)得到$ {{\boldsymbol{V}}_k}^{} $; (6) 更新$ {{\boldsymbol{V}}_k}^{} $; (7) 直到 收敛 (8) 重复 (9) 给定$ {{\boldsymbol{V}}_k}^{} $，求解问题式(34)得到$ {\boldsymbol{\tilde \varTheta }} $; (10) 更新$ {\boldsymbol{\tilde \varTheta }} $; (11) 直到 收敛 (12) if $f(\mu (l)) \le \varpi$ then (13) $ {{\boldsymbol{V}}_k}^ * = {{\boldsymbol{V}}_k}(l) $, $ {{\boldsymbol{\tilde \varTheta }}^{\boldsymbol{*}}} = {\boldsymbol{\tilde \varTheta }}(l) $，通过式(35)、式(16)分别得
到$ {{\boldsymbol{\hat \varTheta }}^{\boldsymbol{*}}} $, $ \mu (l) $;(14) break (15) else (16) if $ f(\mu (l)) < 0 $ then (17) $ {\mu ^{\max }} = \mu (l); $ (18) else (19) $ {\mu ^{\min }} = \mu (l); $ (20) end if (21) end if (22) 设置迭代次数$ l = l + 1 $; (23) end while 
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表 1 仿真参数
参数 值 参数 值 $ f $ 340 GHz ${P^{\max } }$ 10 W ${G_{\rm{t}}}$ 1 $\sigma _{}^2$ 10–8 W ${G_{\rm{r}}}$ $ 4 + 20\lg \sqrt M $ c $ 3 \times {10^8} \;({\text{m/s)}}$ $ \varpi $ 10–3 $ {L_{\max }} $ 20 $ \tau (f) $ 0.0033 m $ K $ 2
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