Energy efficient collaborative computation for double-RIS assisted mobile edge networks

Computation offloading in mobile edge computing (MEC) systems emerges as a novel paradigm of supporting various resource-intensive applications. However, the potential capabilities of MEC cannot be fully unleashed when the communication links are blocked by obstacles. This paper investigates a double-reconfigurable-intelligent-surfaces (RISs) assisted MEC system. To efficiently utilize the limited frequency resource, the users can partially offload their computational tasks to the MEC server deployed at base station (BS) by adopting non-orthogonal multiple access (NOMA) protocol. We aim to minimize the energy consumption of users with limited resource by jointly optimizing the transmit power of users, the offloading fraction of users and the phase-shifts of RISs. Since the problem is non-convex with highly coupled variables, the block coordinate descent (BCD) method is leveraged to alternatively optimize the decomposed four subproblems. Specifically, we invoke successive convex approximation for low complexity (SCALE) and Dinkelbach technique to tackle the fractional programming of power optimization. Then the offloading fraction is obtained by closed-form solution. Further, we leverage semidefinite relaxation (SDR) and bisection method to address the phase-shifts design of double RISs. Finally, numerical results illustrate that the proposed double-RIS assisted NOMA scheme is capable of efficiently reducing the energy consumption and achieves significant performance gain over the benchmark schemes.