Theoretical modeling and analysis of Uplink performance for Three-dimension spatial RISs-aided Wireless communication systems

Reconfigurable intelligent surface (RIS) has emerged as a crucial technology capable of improving the performance of future wireless communication (WC) systems. Although a significant body of studies has investigated into the performance analysis of RIS-aided WC systems, most of them fail to consider the impact of multiple RISs on WC systems. Particularly, the influence of RISs randomly distributed in 3-D (three dimension) space is still an open issue. Furthermore, how phase shift error and ARQ (automatic repeat request) scheme affect the transmission behavior of RIS-aided WC systems should also be taken into account. In light of the above limitations, we propose a novel theoretical model to analyze the uplink transmission performance of 3-D spatial RISs-aided WC systems. In the modeling process, we firstly provide an end-to-end (E2E) channel model using a single RIS, where the RIS enables optimal phase shift control. Next we construct a 3-D spatial uplink transmission model, where the multiple RISs are spatially distributed as a homogeneous 3-D PPP (Poisson point process). The impacts of multiple factors including the selection of RISs, buffer size of user, traffic rate and ARQ scheme are comprehensively considered. With this, we derive the closed-form expressions of uplink transmission metrics. Moreover, we further extend the proposed theoretical model under imperfect phase shift control. Finally, we evaluate the uplink transmission performance of 3-D spatial RIS-aided WC systems, and validate the proposed theoretical model.