NOMA for Multi-Cell RIS Networks: A Stochastic Geometry Model

This paper investigates reconfigurable intelligent surface (RIS) aided multi-cell non-orthogonal multiple access (NOMA) networks with stochastic geometry methods. Under Rayleigh and Nakagami-m fading channels, we provide two types of approximate channel models to depict RIS channels, i.e., the N-fold convolution model and the curve fitting model. The analysis reveals that the N-fold convolution model is accurate and tractable when ignoring inter-cell interference, while the curve fitting model can evaluate the impact of inter-cell interference with a small error. The N-fold convolution model provides accurate diversity orders compared to other existing approaches such as the central limit model. Based on these channel models, we derive the closed-form analytical and asymptotic expressions of coverage probabilities and ergodic rates for two paired NOMA users. The analytical results demonstrate that: i) When we ignore inter-cell interference, the diversity order of the typical user is equal to the number of Rayleigh fading channels; and ii) For Nakagami-m fading channels with coefficient m , the diversity order is equal to m times of the channel number. Numerical results show that: i) RISs are capable of enhancing the coverage performance and ergodic rates of the proposed network; and ii) RISs provide extra flexibility for NOMA decoding orders.