Rate-Overhead Tradeoff in Beam Training for RRS-Assisted Multi-User Communications

Holographic multiple-input multiple-output (HMIMO) with a spatially continuous aperture is a promising solution for future radio access to handle the explosively increasing data demands. As a key enabler of HMIMO, the reconfigurable refractive surface (RRS) can serve as an antenna array with numerous programmable radiation elements. In this paper, we consider a multi-user system with an RRS-aided base station (BS) where the transmit signal is refracted by the RRS towards the users. A beamforming scheme is developed via codebook design and beam training. A larger codebook size implies more codewords, each corresponding to a directional beam. When the codebook size increases, the directivity of the refracted beam is enhanced, bringing a higher data rate. However, it also leads to an exponential growth of the training overhead. To achieve the critical tradeoff between the data rate and overhead, we evaluate the system throughput and model the relation between the codebook size of the RRS and the throughput mathematically. The optimal codebook size is then derived given different user distributions. Simulation results verify our theoretical analysis and show the influence of both codebook size and RRS size on the throughput.