Cramér-Rao Bound Analysis for Cell-Free ISAC Systems with Fluid Intelligent Metasurfaces
Fluid intelligent metasurfaces (FIMs) reshape antenna geometry to improve angular sensitivity. This paper studies their role in cell-free integrated sensing and communication, where distributed access points provide distinct observation directions. Under calibrated path gains, we derive the conditional angular Fisher information matrix, retain cross-AP coupling, and map it to a position-domain Cramér--Rao bound (CRB). A diagonal-information specialization exposes the dependence on angular diversity, while a multi-target extension quantifies the loss from jointly estimating other target positions. We use CRB-driven coordinate search to design transmit and receive shapes and evaluate sensing performance, equal-resource AP scaling, and MRT-based communication--sensing allocation. In the considered four-Tx/four-Rx configuration, shape design reduces the position root CRB from 0.300 to 0.227 m at 10 dB reference SNR. Two-target results further illustrate how cross-target coupling increases the joint localization bound at small separations.