Asymptotic Insights Into Outage Probability of Multi-Cascaded RISs Over Doubly-Correlated MIMO Fading Channels

Cascaded reconfigurable intelligent surfaces (RISs) greatly improve network coverage and reliability. This paper examines the outage probability (OP) of multi-cascaded RISs (MCRISs)-aided systems over doubly-correlated Rayleigh multiple-input multiple-output (MIMO) channels. The moment-generating function is invoked to convert the OP into a numerical inversion of Laplace integral. To capture profound insights, we conduct an in-depth asymptotic investigation into the outage behavior of MCRIS-aided MIMO communications by leveraging random matrix theory in the high-SNR regime. The asymptotic results reveal that the first h RISs with the smallest number of reflective elements primarily dictate the bottleneck of reliability performance, where h is influenced by the variation in the number of reflective elements across the RISs. Specifically, smaller variations result in a larger h, while greater disparities reduce it. Additionally, we identify an “unsaturation effect” that occurs when the performance margin, or residual spatial degree of freedom (DoF), after propagation through the first h RISs cannot be evenly distributed between the transmitter and the RISs. This effect slows down the decline of the OP with increasing SNR. More cascaded RISs impair the spatial DoF of wireless communications, resulting in the loss of half of the independent fading channels compared to the system without the support of RIS as the cascaded number of RISs increases. Majorization theory is subsequently applied to unveil the negative effect of doubly-spatial correlation on system reliability. Finally, Monte Carlo simulations are carried out for validations.