Hierarchical Passive Beamforming for Reconfigurable Intelligent Surface Aided Communications

This letter considers a multiple-input single-output (MISO) downlink communication assisted by dense deployment of reconfigurable intelligent surfaces (RISs), where traditional passive beamforming (PB) design may be too complicated to implement due to a massive number of reflecting elements. To overcome this difficulty, we propose a hierarchical passive beamforming (HPB) design by fully exploiting the reflection property of a RIS, in which the dimension of the variable space involved in optimization is significantly reduced by adopting the generalized Snell's law. We develop efficient HPB algorithms to maximize the achievable rate of the target user. Simulation results demonstrate the appealing performance and low complexity of the proposed HPB design.