  As a critical technology for next-generation communication networks,
integrated sensing and communication (ISAC) aims to achieve the harmonious
coexistence of communication and sensing. The degrees-of-freedom (DoF) of ISAC
is limited due to multiple performance metrics used for communication and
sensing. Reconfigurable Intelligent Surfaces (RIS) composed of metamaterials
can enhance the DoF in the spatial domain of ISAC systems. However, the
availability of perfect Channel State Information (CSI) is a prerequisite for
the gain brought by RIS, which is not realistic in practical environments.
Therefore, under the imperfect CSI condition, we propose a decomposition-based
large deviation inequality approach to eliminate the impact of CSI error on
communication rate and sensing Cram\'er-Rao bound (CRB). Then, an alternating
optimization (AO) algorithm based on semi-definite relaxation (SDR) and
gradient extrapolated majorization-maximization (GEMM) is proposed to solve the
transmit beamforming and discrete RIS beamforming problems. We also analyze the
complexity and convergence of the proposed algorithm. Simulation results show
that the proposed algorithms can effectively eliminate the influence of CSI
error and have good convergence performance. Notably, when CSI error exists,
the gain brought by RIS will decrease with the increase of the number of RIS
elements. Finally, we summarize and outline future research directions.
