  The sixth-generation (6G) wireless technology recognizes the potential of
reconfigurable intelligent surfaces (RIS) as an effective technique for
intelligently manipulating channel paths through reflection to serve desired
users. Full-duplex (FD) systems, enabling simultaneous transmission and
reception from a base station (BS), offer the theoretical advantage of doubled
spectrum efficiency. However, the presence of strong self-interference (SI) in
FD systems significantly degrades performance, which can be mitigated by
leveraging the capabilities of RIS. Moreover, accurately obtaining channel
state information (CSI) from RIS poses a critical challenge. Our objective is
to maximize downlink (DL) user data rates while ensuring quality-of-service
(QoS) for uplink (UL) users under imperfect CSI from reflected channels. To
address this, we propose a robust active BS and passive RIS beamforming (RAPB)
scheme for RIS-FD, accounting for both SI and imperfect CSI. RAPB incorporates
distributionally robust design, conditional value-at-risk (CVaR), and penalty
convex-concave programming (PCCP) techniques. Simulation results demonstrate
the UL/DL rate improvement are achieved by considering different levels of
imperfect CSI. The proposed RAPB schemes validate their effectiveness across
different RIS deployments and RIS/BS configurations. Benefited from robust
beamforming, RAPB outperforms the existing methods in terms of non-robustness,
deployment without RIS, conventional approximation, and half-duplex systems.
