Reconfigurable Intelligent Surfaces for ISAC: CRB Analysis and Optimization for Joint Angle and Radial Velocity Estimation

In conventional sensing systems, the performance of sensing is highly dependent on the line-of-sight (LoS) link, which is often obstructed by obstacles. To address this, reconfigurable intelligent surfaces (RIS) are introduced to enhance sensing capability. In this paper, we first propose a passive RIS-enabled integrated sensing and communications (ISAC) framework for mobile target. By considering general transmit waveforms, the Fisher information matrix (FIM) corresponding to the unknown target related parameter is derived, which facilitates the closed-form derivation of the Cramer-Rao bound (CRB) for estimating the joint 2D coordinates and radial velocity. Then, semidefinite relaxation and successive convex approximation approach are leveraged to minimizing the CRB under constraints of maximum transmit power and unit-modulus. Furthermore, we propose semi-passive RIS-assisted systems, where additional active elements are employed to receive sensing echoes. The resulting CRB minimization challenge is transformed into a FIM optimization problem, which is subsequently solved using an alternating optimization method. Finally, numerical results verify that the proposed frameworks effectively reduce the CRB compared to other benchmarks, while the semi-passive RIS scheme achieving higher sensing accuracy than the fully passive RIS. Moreover, the enhanced sensing accuracy significantly improves communication quality.