Task Offloading for Simultaneously Transmitting And Reflecting Reconfigurable Intelligent Surface-assisted Mobile Edge Computing
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摘要: 为弥补可重构智能表面(RIS)半空间覆盖和“乘性衰落”等不足，该文提出一种有源同时透射和反射可重构智能表面(aSTAR-RIS)技术用于提升移动边缘计算(MEC)卸载性能增益。首先，考虑MEC服务器计算资源、aSTAR-RIS能耗以及相移耦合约束，联合设计任务卸载比例、计算资源配置、多用户检测矩阵(MUD)、aSTAR-RIS相移以及用户上传功率，建立一个多变量耦合的加权总时延最小化问题。然后，借助块坐标下降法(BCD)将原问题分解为两个子问题，使用拉格朗日乘子法和罚项对偶分解法(PDD)交替优化子问题。仿真结果表明，相较于无源STAR-RIS方案，所提aSTAR-RIS辅助MEC方案加权总时延降低了12.66%。
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关键词:
- 有源同时透射和反射可重构智能表面 /
- 移动边缘计算 /
- 计算卸载 /
- 资源分配
Abstract:Objective Mobile Edge Computing (MEC) is a distributed computing paradigm that brings computational resources closer to users, alleviating issues such as high latency and interference found in cloud computing. To enhance the offloading performance of MEC systems and promote green communication, Reconfigurable Intelligent Surface (RIS), a low-cost and easily deployable technology, offers a promising solution. RIS consists of numerous low-cost reflecting elements that can adjust phase shifts to alter the amplitude and phase of incident signals, thereby reconstructing the electromagnetic environment. This transforms traditional passive adaptation into active control. However, the signal reflected by RIS must pass through a two-stage cascaded channel, which is susceptible to multiplicative fading, leading to limited performance gains when direct links are unobstructed. To mitigate this, the concept of active RIS has been proposed, integrating signal amplification circuits into RIS elements, which not only reflect but also amplify signals, effectively overcoming this issue. Additionally, RIS can only transmit or reflect incident signals, limiting coverage to half-space: either the user and base station must be on the same side (reflecting RIS) or on opposite sides (transmitting RIS). This constraint limits deployment flexibility. To address this, Simultaneously Transmitting And Reflecting Reconfigurable Intelligent Surface (STAR-RIS) is proposed, combining both transmission and reflection functions, where part of the signal is reflected to the same side, and the rest is transmitted to the opposite side. To address the challenges in practical RIS-assisted MEC systems, the active Simultaneously Transmitting And Reflecting Reconfigurable Intelligent Surface (aSTAR-RIS) is integrated into the MEC system to overcome geographic deployment constraints and effectively mitigate the effects of multiplicative fading. Methods Considering the computational resources available at the MEC server, the energy consumption of the aSTAR-RIS, and the phase shift coupling constraints, the task offloading ratio, computational resource allocation, Multi-User Detection (MUD) matrix, aSTAR-RIS phase shift, and transmission power are jointly optimized, resulting in a multivariable coupled weighted total latency minimization problem. To solve this problem, an iterative algorithm combining Block Coordinate Descent (BCD) and Penalty Dual Decomposition (PDD) algorithms is proposed. In each iteration, the original problem is decomposed into two subproblems: one for optimizing computational resource allocation and task offloading ratio, and the other for designing the aSTAR-RIS phase shift, MUD matrix, and transmission power. For the first subproblem, the Lagrange multiplier method is used to incorporate constraints into the objective function and enable efficient optimization. The optimal Lagrange multiplier and resource allocation are found using the bisection method. The second subproblem involves handling the fractional objective function using the weighted minimum mean square error algorithm. From the first-order conditions, the optimal MUD matrix is derived. For the aSTAR-RIS phase shift optimization, a non-convex phase shift coupling constraint is decoupled using the PDD algorithm. Results And discussions as shown in ( Fig. 2 ), with increasing iterations, the weighted total latency steadily decreases and stabilizes, validating the effectiveness of the proposed algorithm. A comparison with three benchmark schemes reveals that, although the proposed scheme converges more slowly, it achieves the lowest weighted total latency upon convergence, with a 12.66% reduction compared to the passive STAR-RIS scheme. This improvement is mainly due to the power amplification effect, which reduces the impact of multiplicative fading, thereby enhancing the received signal at the base station and reducing latency. As illustrated in (Fig. 3 ), the weighted total latency decreases as the number of aSTAR-RIS elements increases, allowing for more reflection paths and higher channel gain. For fewer elements, aSTAR-RIS shows a significant performance gain over STAR-RIS, but as the number of elements grows, the performance of both aSTAR-RIS and passive STAR-RIS converges, primarily due to thermal noise and power constraints. Moreover, compared to the benchmark scheme that optimizes for maximum rate, the proposed scheme shows significant advantages in reducing latency. As shown in (Fig. 4 ), when the aSTAR-RIS power overhead increases, the weighted total latency decreases, further showing the potential of aSTAR-RIS in improving communication performance via active amplification.Conclusions This paper investigates a task offloading scheme for an aSTAR-RIS-assisted MEC system, which optimizes the task offloading ratio, computational resource allocation, MUD matrix, aSTAR-RIS phase shift, and transmission power to minimize total user delay. The optimization problem is solved using an iterative approach, decomposing the problem into two subproblems and applying the Lagrange multiplier method, PDD, and BCD algorithms. Simulation results demonstrate that the proposed algorithm significantly outperforms benchmark schemes in terms of weighted total latency. The findings validate the effectiveness of aSTAR-RIS in MEC systems, highlighting its advantages over passive STAR-RIS in task offloading, resource optimization, and communication performance. -
1 求解最优任务卸载比和MEC计算资源分配算法
初始化优化变量，${n_1} = 0$，收敛阈值$ {\varepsilon }_{1}={10}^{-4} $ 步骤1 利用式(3)计算${R_{\tau ,i}}$，根据式(9)对${{\boldsymbol{\alpha}} ^{({n_1})}}$进行更新； 步骤2 利用二分法求得${\mu ^{({n_1})}}$，根据式(12)计算${{\boldsymbol{f}}^{\text{e}}}^{({n_1})}$； 步骤3 计算$ {\varepsilon }^{({n}_{1})} $，若$ {\varepsilon }^{({n}_{1})}\ge {\varepsilon }_{1} $且${n_1} \le n_1^{\max }$，令${n_1} = {n_1} + 1$，
回到步骤1；步骤4 输出$({{\boldsymbol{\alpha}} ^*},{{\boldsymbol{f}}^{\text{e}}}^*)$ 
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2 MUD矩阵、aSTAR-RIS相移和用户上传功率交替优化算法
初始化优化变量，${n_2} = 0$，收敛阈值$ \zeta ={\varepsilon }_{2}={\varepsilon }_{3}={10}^{-4} $,
$\rho = 10$步骤1 根据式(20)更新$ {{\boldsymbol{W}}^{({n_2})}} $； 步骤2 解决问题式P2.5更新$\{ {{\boldsymbol{\theta}} _{\text{t}}}^{({n_2})},{{\boldsymbol{\theta}} _{\text{r}}}^{({n_2})}\} $； 步骤3 更新$\left\{ {\tilde {\boldsymbol{\psi}} _{\text{t}}^{({n_2})},\tilde{\boldsymbol{ \psi}} _{\text{r}}^{({n_2})}} \right\}$和$\left\{ {{{\tilde {\boldsymbol{\beta}} }_{\text{t}}}^{({n_2})},{{\tilde {\boldsymbol{\beta }}}_{\text{r}}}^{({n_2})}} \right\}$； 步骤4 解决问题式P2.8更新$ {{\boldsymbol{p}}^{({n_2})}} $； 步骤5 更新辅助变量${{\boldsymbol{\varphi}} ^{({n_2})}}$； 步骤6 计算$ {\varepsilon }^{\left({n}_{2}\right)} $，若$ {\varepsilon }^{\left({n}_{2}\right)} \gt {\varepsilon }_{2} $，且${n_2} \le n_2^{{\text{max}}}$，令
${n_2} = {n_2} + 1$，回到步骤1；步骤7 更新$ {{\boldsymbol{\lambda}} ^{({n_2})}} $, $ {{\boldsymbol{\xi}} ^{({n_2})}} $，若$ \left|{\lambda }_{k}^{({n}_{2})}{R}_{k}^{({n}_{2})}-1\right| \gt {\varepsilon }_{2} $或
$ \left|{\xi }_{k}^{({n}_{2})}{R}_{k}^{({n}_{2})}-{\varpi }_{k}{\alpha }_{k}{L}_{k}\right| \gt {\varepsilon }_{2} $，令${n_2} = {n_2} + 1$，回到步骤1；步骤8 若$ \upsilon \le \zeta $, $ {{\boldsymbol{\eta}} _{\,\tau }} = {{\boldsymbol{\eta}} _{\,\tau }} + \dfrac{1}{\rho }({\tilde {\boldsymbol{\theta}} _\tau } - {{\boldsymbol{\theta}} _\tau }) $，否则设置$ \rho = c\rho $； 步骤9 $ \zeta = 0.9\upsilon $，若$ \upsilon \gt {\varepsilon }_{3} $，令${n_2} = 0$，回到步骤1； 输出 $ \left( {{{\boldsymbol{W}}^*},{{\boldsymbol{\theta}} _{\text{t}}}^*,{{\boldsymbol{\theta}} _{\text{r}}}^*,{{\boldsymbol{p}}^*}} \right) $
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3 整体算法
初始化优化变量，${n_3} = 0$，收敛阈值$ \varepsilon ={10}^{-4} $ 步骤1 根据算法1，给定$ {{\boldsymbol{W}}^{({n_3} - 1)}} $, ${{\boldsymbol{\theta}} _{\text{t}}}^{({n_3} - 1)}$, ${{\boldsymbol{\theta}} _{\text{r}}}^{({n_3} - 1)}$,
$ {{\boldsymbol{p}}^{({n_3} - 1)}} $优化${{\boldsymbol{\alpha}} ^{({n_3})}}$, ${{\boldsymbol{f}}^{\text{e}}}^{({n_3})}$；步骤2 根据算法2，给定${{\boldsymbol{\alpha}} ^{({n_3})}}$, ${{\boldsymbol{f}}^{\text{e}}}^{({n_3})}$优化$ {{\boldsymbol{W}}^{({n_3})}} $, ${{\boldsymbol{\theta }}_{\text{t}}}^{({n_3})}$,
${{\boldsymbol{\theta}} _{\text{r}}}^{({n_3})}$, ${{\boldsymbol{p}}^{({n_3})}}$；步骤3 计算$ {\varepsilon }^{\left({n}_{3}\right)} $，若$ {\varepsilon }^{\left({n}_{3}\right)} \gt \varepsilon $且$ {n_3} \le n_3^{\max } $，令${n_3} = {n_3} + 1$，
回到步骤1；输出：$\left( {{{\boldsymbol{\alpha}} ^*},{{\boldsymbol{f}}^{\text{e}}}^*,{{\boldsymbol{W}}^*},{{\boldsymbol{\theta}} _{\text{t}}}^*,{{\boldsymbol{\theta}} _{\text{r}}}^*,{{\boldsymbol{p}}^*}} \right)$
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