Cramér-Rao Bound Analysis for Cell-Free ISAC Systems with Fluid Intelligent Metasurfaces

Abstract

Fluid intelligent metasurface (FIM) is an emerging antenna architecture that continuously reshapes its physical geometry to optimize wireless performance. While existing studies on FIM-aided integrated sensing and communication (ISAC) rely on co-located single-base-station (BS) deployments, they fundamentally underutilize FIM's morphological flexibility due to restricted observation angles. In this paper, we investigate a FIM-augmented cell-free ISAC architecture, where distributed access points (APs) collaboratively observe a target from diverse angles. We derive the complete Fisher information matrix for target angle estimation and obtain a closed-form localization CRB that explicitly quantifies the angular diversity gain. By analyzing the block structure of the Fisher information matrix, we uncover three cell-free-specific phenomena: (i) cross-AP information coupling, (ii) multiplicative Tx--Rx FIM coupling, and (iii) angular diversity amplification. Under a 28\,GHz configuration with four APs and eight FIM elements per AP, our analysis shows that distributed angular diversity amplifies the FIM morphing gain to 15.8\,dB, compared to only 0.4\,dB in a single-AP pair deployment with the same total antenna count. We further propose an alternating optimization algorithm for joint beamforming and FIM shape design via semidefinite relaxation whose tightness is formally proved. Numerical results confirm that the proposed cell-free FIM-ISAC architecture achieves a 4.5\,dB localization CRB reduction over the single-AP fixed-array baseline at 10\,dB sensing SNR while maintaining communication quality-of-service constraints across the entire Pareto frontier.