Cascaded Composite Turbulence and Misalignment: Statistical Characterization and Applications to Reconfigurable Intelligent Surface-Empowered Wireless Systems

Reconfigurable intelligent surfaces (RISs) empowered high-frequency wireless systems are expected to become the supporting pillar for several reliability and data rate hungry applications. Such systems are, however, sensitive to misalignment and atmospheric phenomena including turbulence. Most of the existing studies on the performance assessment of RIS-empowered wireless systems ignore the impact of the aforementioned phenomena. Motivated by this, the current contribution presents a theoretical framework for statistically characterizing cascaded composite turbulence and misalignment channels. More specifically, we present the probability density and cumulative distribution functions for the cascaded composite turbulence and misalignment channels. Building upon the derived analytical expressions and in order to demonstrate the applicability and importance of the extracted framework in different use cases of interest, we present novel closed-form formulas that quantify the joint impact of turbulence and misalignment on the outage performance for two scenarios, namely cascaded multi-RIS-empowered free space optics (FSO) and terahertz (THz) wireless systems. For the aforementioned scenarios, the diversity order is extracted. In addition, we provide an insightful outage probability upper-bound for a third scenario that considers parallel multi-RIS-empowered FSO systems. The obtained results highlight the importance of accurately modeling both turbulence and misalignment when assessing the system performance.