In this paper, simultaneously transmitting and reflecting (STAR) reconfigurable intelligent surface (RIS) is investigated in the multi-user mobile edge computing (MEC) system to improve the computation rate. Compared with traditional RIS-aided MEC, STAR-RIS extends the service coverage from half-space to full-space and provides new flexibility for improving the computation rate for end users. However, the STAR-RIS-aided MEC system design is a challenging problem due to the non-smooth and non-convex binary amplitude coefficients with coupled phase shifters. To fill this gap, this paper formulates a computation rate maximization problem via the joint design of the STAR-RIS phase shifts, reflection and transmission amplitude coefficients, the receive beamforming vectors, and energy partition strategies for local computing and offloading. To tackle the discontinuity caused by binary variables, we propose an efficient smoothing-based method to decrease convergence error, in contrast to the conventional penalty-based method, which brings many undesired stationary points and local optima. Furthermore, a fast iterative algorithm is proposed to obtain a stationary point for the joint optimization problem, with each subproblem solved by a low-complexity algorithm, making the proposed design scalable to a massive number of users and STAR-RIS elements. Simulation results validate the strength of the proposed smoothing-based method and show that the proposed fast iterative algorithm achieves a higher computation rate than the conventional method while saving the computation time by at least an order of magnitude. Moreover, the resultant STAR-RIS-aided MEC system significantly improves the computation rate compared to other baseline schemes with conventional reflect-only/transmit-only RIS.

翻译：本文研究了同时发射与反射（STAR）可重构智能表面（RIS）在多用户移动边缘计算（MEC）系统中的应用，旨在提升计算速率。与传统RIS辅助MEC相比，STAR-RIS将服务覆盖范围从半空间扩展至全空间，并为提升终端用户计算速率提供了新灵活性。然而，由于存在非光滑、非凸且具有耦合移相器的二元幅度系数，STAR-RIS辅助MEC系统设计极具挑战性。为填补这一空白，本文通过联合设计STAR-RIS相位偏移、反射与透射幅度系数、接收波束赋形向量以及本地计算与卸载的能耗分配策略，提出了计算速率最大化问题。为处理二元变量导致的非连续性，我们提出一种基于平滑的高效方法以降低收敛误差，区别于传统基于惩罚的方法——后者会引入大量非期望驻点与局部最优解。此外，本文提出一种快速迭代算法来获取联合优化问题的驻点，其中每个子问题均通过低复杂度算法求解，使所提设计可扩展至海量用户与STAR-RIS单元。仿真结果验证了所提平滑方法的优势，并表明所提快速迭代算法在实现更高计算速率的同时，将计算时间至少降低一个数量级。此外，所构建的STAR-RIS辅助MEC系统相较于其他采用传统仅反射/仅透射RIS的基线方案，显著提升了计算速率。