Multi-RIS-aided Wireless Systems: Statistical Characterization and Performance Analysis

In this paper, we study the statistical characterization and modeling of distributed multi-reconfigurable intelligent surface (RIS)-aided wireless systems. Specifically, we consider a practical system model where the RISs with different geometric sizes are distributively deployed, and wireless channels associated to different RISs are assumed to be independent but not identically distributed (i.n.i.d.). We propose two purpose-oriented multi-RIS-aided schemes, namely, the exhaustive RIS-aided (ERA) and opportunistic RIS-aided (ORA) schemes. In the ERA scheme, all RISs participate in assisting the communication of a pair of transceivers, whereas in the ORA scheme, only the most appropriate RIS participates and the remaining RISs are utilized for other purposes. A mathematical framework, which relies on the method of moments, is proposed to statistically characterize the end-to-end (e2e) channels of these schemes. It is shown that either a Gamma distribution or a LogNormal distribution can be used to approximate the distribution of the magnitude of the e2e channel coefficients in both schemes. With these findings, we evaluate the performance of the two schemes in terms of outage probability (OP) and ergodic capacity (EC), where tight approximate closed-form expressions for the OP and EC are derived. Representative results show that the ERA scheme outperforms the ORA scheme in terms of OP and EC. Nevertheless, the ORA scheme gives a better energy efficiency (EE) in a specific range of the target spectral efficiency (SE). In addition, under i.n.i.d. fading channels, the reflecting element setting and location setting of RISs have a significant impact on the overall system performance of both the ERA or ORA schemes. A centralized large-RIS-aided scheme might achieve higher EC than the distributed ERA scheme when the large-RIS is located near a transmitter or a receiver, and vise-versa.