On performance of multi-RIS assisted multi-user nonorthogonal multiple access system over Nakagami-m fading channels

In practice, multiple reconfigurable intelligent surfaces (RISs) may be deployed to assist wireless systems. Unfortunately, the mathematical analysis of multiple RISs aided wireless systems is challenging. In this paper, multiple RISs are utilized in a multi-user nonorthogonal multiple access (NOMA) system. Particularly, multiple users combine signals traveling on the transmitter–user direct paths and the reflected paths from the RISs. We successfully derive the closed-form expressions of the outage probability (OP) and ergodic capacity (EC) of this multi-RIS aided multi-user NOMA (RIS-NOMA) system. We also obtain the OP and EC expressions of the RIS-NOMA system in the case that there are only two NOMA users, where the specific derived forms depend on the exact values of power allocation coefficients and threshold. We validate all derived expressions through Monte-Carlo simulations. Numerical results show that compared with the case without RISs, the performance in terms of OP and EC of the NOMA system with RISs are significantly improved. In particular, the OP in the case with RISs is greatly lower than that in the case without RISs for the considered range of transmission power. However, the EC in the case with RISs is only significantly higher than that in the case without RISs in the low transmission power regime. In the high transmission power regime, they are similar. Consequently, depending on the certain requirements in practical scenarios where the RIS-NOMA system is deployed, we can use a suitable transmission power to achieve the OP and EC performance target and save the power consumption.