Enhancing Performance of Integrated Sensing and Communication via Joint Optimization of Hybrid and Passive Reconfigurable Intelligent Surfaces

Recent years have witnessed an increasing interest in leveraging reconfigurable intelligent surfaces (RISs) to enhance the capabilities of integrated sensing and communication (ISAC) systems. RISs are advantageous in improving detection and communication performance, especially in challenging environments characterized by non-line-of-sight (NLOS) conditions and dense urban settings. In this paper, a hybrid RIS, comprising passive reflecting elements and active sensors, and multiple fully passive RISs are deployed to enhance an ISAC system, where the direct paths between the base station (BS) and users/targets are blocked. The signal sent from the BS and reflected by RISs is received by the communication user, and simultaneously scattered by the target towards the sensors of the hybrid RIS. A joint optimization of the transmit covariance matrix at the BS and phase-shifting matrices at RISs is formulated, which considers the trade-off between the communication and sensing performance. The optimization is based on the derived closed-form communication achievable rate by leveraging the free probability theory and positioning error bound (PEB) via Cramér-Rao lower bound (CRLB) analysis. The block coordinate descend (BCD) algorithm is utilized to tackle the non-convex problem, where the transmit covariance matrix and phase-shifting matrices are optimized iteratively. Therein, the Riemannian gradient descent algorithm is exploited for optimizing phase-shifting matrices. Numerical results verify the effectiveness of the proposed algorithm, and both communication and sensing performance gains increase with the number of RIS panels and RIS elements.