Optimal RIS Placement in a Multi-User MISO System with User Randomness

It is well established that the performance of reconfigurable intelligent surface (RIS)-assisted systems critically depends on the optimal placement of the RIS. Previous works consider either simple coverage maximization or simultaneous optimization of the placement of the RIS along with the beamforming and reflection coefficients, most of which assume that the location of the RIS, base station (BS), and users are known. However, in practice, only the spatial variation of user density and obstacle configuration are likely to be known prior to deployment of the system. Thus, we formulate a non-convex problem that optimizes the position of the RIS over the expected minimum signal-to-interference-plus-noise ratio (SINR) of the system with user randomness, assuming that the system employs joint beamforming after deployment. To solve this problem, we propose a recursive coarse-to-fine methodology that constructs a set of candidate locations for RIS placement based on the obstacle configuration and evaluates them over multiple instantiations from the user distribution. The search is recursively refined within the optimal region identified in each stage to determine the final optimal region for RIS deployment. Numerical results are presented to corroborate our findings.