LAUSR

This paper investigates the task offloading problem in a hybrid intelligent reflecting surface (IRS) and massive multiple-input multiple-output (MIMO) relay assisted fog computing system, where multiple task nodes (TNs) offload their computational tasks to computing nodes (CNs) nearby massive MIMO relay node (MRN) and fog access node (FAN) via the IRS for execution. By considering the practical imperfect channel state information (CSI) model, we formulate a joint task offloading, IRS phase shift optimization, and power allocation problem to minimize the total energy consumption. We solve the resultant non-convex optimization problem in three steps. First, we solve the IRS phase shift optimization problem with the sequential rank-one constraint relaxation (SROCR) algorithm and semidefinite relaxation (SDR) algorithm for a given power- and computational resource allocation. Then, we exploit a differential convex (DC) optimization framework to determine the power allocation decision that minimizes the total energy consumption. Given the IRS phase shifts, the computational resources, and the power allocation, we propose an alternating optimization algorithm for finding the jointly optimized results. The simulation results demonstrate the effectiveness of the proposed scheme as compared with other benchmark schemes, and the energy efficient offloading strategy for the proposed fog computing system can be chosen according to the asymptotic form of the effective signal-to-interference-plus-noise ratio (SINR).