Latency Minimization in Phase-Coupled STAR-RIS Assisted Multi-MEC Server Systems

In this paper, we consider a simultaneous transmitting and reflecting (STAR)-reconfigurable intelligent surface (RIS)-assisted multi mobile-edge-computing (MEC) system, where servers can be placed on both sides of the STAR-RIS and each device offloads a part of its computational tasks to the MEC servers. Specifically, we formulate a weighted-sum computing and communication latency minimization problem to jointly optimize the offloading data volume, edge computing resource of servers, multi-user detection (MUD) matrices, as well as energy splitting coefficients and phase-shifts of the STAR-RIS in the presence of coupling between transmission and reflection phase shifts. Using block coordinate descent (BCD), we decompose the computing and communication problems and solve them in an iterative manner through alternating optimization. We show that the optimal offloading volume can be given by establishing the equivalence of the local computing latency and edge computing latency of servers. Also, we proved that the edge resource allocation problem is jointly convex in both the transmit and reflect MEC resources. Therefore, the optimal MEC resources can be found using KKT conditions and the bisection search method. Numerical results demonstrate the effectiveness of the proposed STAR-RIS-enabled multi-MEC system in terms of obtained latency and convergence compared to the conventional benchmarks.