Coverage Characterization and Number Configuration for RIS-Aided Systems With Phase Delivery: How Far Is the Coverage Distance?

Reconfigurable intelligent surface (RIS) has garnered escalating attention in recent years. However, existing works overlook the phase delivery and typically analyze the coverage performance of the RIS under a given location of the RIS, which may limit the coverage improvement of the RIS-aided systems. In this letter, our aim is to investigate how far the coverage distance is by maximizing the sum of the coverage radius for RIS-aided systems with phase delivery. The resulting optimization problem can be solved by reformulating it as a convex problem via variable transformation and block coordinate descent. To get more insight into the coverage range, we obtain the closed-form solutions of the coverage radii and investigate number configuration for the case of deterministic coverage. Furthermore, we relax the deterministic coverage to the probabilistic coverage and analyze how many reflecting elements are needed to achieve a coverage probability close to 1. The results can provide design guidelines for RIS deployment/location and user distribution areas. Numerical simulations demonstrate the benefit of the proposed algorithm compared with existing ones in terms of the coverage radius.