  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.
