Min-Max Fairness Based Joint Optimal Design for IRS-Assisted MEC Systems

In this paper, we study a joint computation offloading and resource allocation optimization problem for the intelligent reflecting surface (IRS)-assisted mobile edge computing (MEC) system. Specifically, we consider an IRS-assisted multi-device MEC system, where mobile devices (MDs) can either execute the computation-intensive tasks locally or offload their tasks to the MEC server. With the aim of minimizing the maximum weighted consumed energy, the offloading decisions, the transmit power at the MDs, the central processing unit (CPU) clock frequencies at the MDs and the MEC server, the receive beamforming vectors at the base station (BS), and the reflecting coefficient matrix at the IRS are jointly optimized. To handle the underlying mixed integer non-linear programming (MINLP) problem, we propose a bisection search based alternate feasibility verification suboptimal algorithm. In particular, we use the bisection search method to optimize the offloading decision threshold and which determines the offloading MDs' set. Subsequently, the alternate optimization (AO) method is employed to solve the feasibility verification problem by decomposing it into four feasibility-checking subproblems and then separately tackling each of them. In specific, by fixing the three other parameters, the Rayleigh entropy property is leveraged to handle the BS's receive beamforming optimization subproblem for each MD. Then, the successive convex approximation (SCA) method is adopted to solve the MDs' transmit power control subproblem. Moreover, the difference of convex functions (DC) programming and the semidefinite relaxation (SDR) method are employed to address the IRS phase shift design subproblem. As such, we are able to obtain the closed-form solution of the computing resource allocation for the MEC. Finally, we use simulations to validate the advantages of deploying IRS and optimizing its reflecting phase shift for the considered system, and also confirm the effectiveness of the proposed algorithm and its performance gain over the benchmark schemes.