Impact of Inter-Hop Correlation on Reconfigurable Intelligent Surfaces

Reconfigurable Intelligent Surfaces (RISs) are commonly analyzed under the assumption that the base-station-RIS and RIS-user-equipment hops are statistically independent. This assumption can be inaccurate when the two hops interact with common scatterers or clusters, producing inter-hop correlation in the RIS-side angular support. This paper investigates the impact of such inter-hop power correlation on a phase optimized RIS-assisted single-input-single-output channel. We propose a geometry-based shared-scatterer model in which the two hops have common scatterer angles and power weights, while the small-scale fading amplitudes are correlated through a tunable parameter. The results show that inter-hop correlation increases the average phase-aligned cascaded gain but can degrade outage performance by increasing the probability of jointly weak cascaded channel realizations. These results indicate that independent-hop models may overestimate RIS reliability, even when average gain predictions appear favorable.