Abstract
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 Cramér-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.