Energy-efficient Beamforming Design with Partial CSI Feedback for RIS-assisted Systems

This paper investigates beamforming design with partial channel state information (CSI) feedback aimed at maximizing the energy efficiency (EE) of a reconfigurable intelligent surface (RIS)-assisted millimeter-wave (mmWave) multi-user system. By leveraging the spatial reciprocity, which means that the path angle information (PAI) and power angular spectrum (PAS) of sparse paths are similar in the uplink and downlink channels, we can acquire the downlink PAI and PAS at the base station (BS) via uplink estimation. Subsequently, we select several paths that contribute to EE maximization from all the cascaded paths and define them as dominant paths. Consequently, only the small-scale fading coefficients (i.e., the normalized path gain information, NPGI) of these selected dominant paths need to be fed back from the user equipments (UEs), thereby significantly reducing the feedback overhead. Moreover, we update the active BS beamformer and passive RIS beamformer by using the feedback of partial NPGI to further improve the EE. Numerical results demonstrate the superiority of our proposed algorithms over conventional schemes.