A simulation framework for cooperative reconfigurable intelligent surface based systems

We present a simulation framework for evaluating the performance of cooperative reconfigurable intelligent surface (RIS) based systems, which may ultimately deploy an arbitrary number of RISs to overcome adverse propagation-related effects, such as cascaded fading. The physical model underlying the proposed framework considers the (optional) presence of a dominant signal path between the source and RIS, and then between each subsequent stage of the communication link to the destination. Accompanying the dominant signal component is a non-isotropic scattered signal contribution, which accounts for angular selectivity within the cascaded RIS stages between the source and destination. The simulation of the time-correlated scattered signal, reflected by the illuminated reflective elements, is achieved using autoregressive modelling. As a by-product of our analysis, significant insights are drawn which enable us to characterize the amplitude and phase properties of the received signal, and the associated complex autocorrelation functions (ACFs) for the product of multiple Rician channels. For both single and cooperative RIS systems, the outage probability (OP), and important second-order statistics, such as the level crossing rate (LCR) and average outage duration (AOD), are analyzed for a variety of system configurations, accounting for practical limitations, such as phase errors. It is shown that by using multiple RISs cooperatively, the AOD is reduced at a lower signal-to-noise-ratio (SNR) compared to single RIS-assisted transmission under the same operating conditions. Lastly, increased channel variations (i.e., higher maximum Doppler frequencies) are shown to decrease the AOD in the case of absent phase errors; yet, this improvement is not observed when phase errors are present.