  This work focuses on the synergy of rate-splitting multiple access (RSMA) and
beyond diagonal reconfigurable intelligent surface (BD-RIS) to enlarge the
coverage, improve the performance, and save on antennas. Specifically, we
employ a multi-sector BD-RIS modeled as a prism, which can achieve highly
directional full-space coverage, in a multiuser multiple input single output
communication system. With the multi-sector BD-RIS aided RSMA model, we jointly
design the transmit precoder and BD-RIS matrix under the imperfect channel
state information (CSI) conditions. The robust design is performed by solving a
stochastic average sum-rate maximization problem. With sample average
approximation and weighted minimum mean square error-rate relationship, the
stochastic problem is transformed into a deterministic one with multiple
blocks, each of which is iteratively designed. Simulation results show that
multi-sector BD-RIS aided RSMA outperforms space division multiple access
schemes. More importantly, synergizing multi-sector BD-RIS with RSMA is an
efficient strategy to reduce the number of active antennas at the transmitter
and the number of passive antennas in BD-RIS.
