Beamforming on Reconfigurable Intelligent Surface: A Codebook Design for Spatial Coverage with Beam Squint Effect

In this paper, we propose a novel reconfigurable intelligent surface (RIS) codebook design by leveraging beam squint with the help of half-power beamwidth (HPBW) concept. In particular, the beam squint effect incurs the array responses' direction change of RIS under different frequencies. We aim to design the RIS phase shifts such that the beams with squint generated by different RIS weights could tile over the entire spatial domain of the RIS without overlapping. To quantify the spatial coverage performance in wideband systems, a new term - wideband-HPBW (W-HPBW), is introduced based on the definition of HPBW. The closed-form expression of the angular information of W-HPBW is derived. To further reduce RIS weights switching and realize lower pilot overhead in channel estimation, a beam broadening technique is then investigated. This design largely reduces the times of RIS phase adjustments and the requirement for accurate channel estimation. Simulation results show that the designed codebook can effectively realize spatial coverage under the W-HBPW criterion.