Semi-Passive RIS Aided Near-Field ISAC: CRB Analysis and Optimization

A semi-passive reconfigurable intelligent surface (RIS) enables integrated sensing and communications (ISAC) framework is proposed, where the passive elements is used for communication in the RIS-user links and the active elements are used for sensing in the RIS-target links. By considering general transmit waveforms, the Fisher information matrix (FIM) corresponding to the unknown parameters in the three-dimensional (3D) coordinates is derived. According to the FIM, the Cramér-Rao bound (CRB) for estimating the 3D coordinates can be obtained. Furthermore, by introducing the priori information into the ISAC system, the corresponding FIM and CRB can be derived. Both CRB without the priori information and CRB with the priori information are investigated: 1) For the CRB without prior information, to optimize the objective function, the CRB is converted to an closed-form expression. Since the optimization problem of CRB is non-convex, a semidefinite relaxation based method is proposed to deal with it; 2) For the CRB with prior information, a more trackable modified FIM optimization problem is proposed to transform the complicated CRB minimization problem. Finally, the numerical results demonstrate that: 1) The proposed scheme can effectively improve the sensing performance compared with benchmark schemes; 2) The additional prior angle information can effectively improve the sensing accuracy. 3) As the minimum communication rate increases, the system with prior information has better performance and is more robust than that without prior information.