Integrated sensing and communication (ISAC) have been widely recognized as a key enabler for future wireless networks, where the Cramér-Rao bound (CRB) plays a central role in quantifying sensing accuracy.In this paper, we present the first study on CRB minimization in flexible intelligent metasurface (FIM)-enabled ISAC systems.Specifically, we first derive an average CRB expression that explicitly depends on FIM surface shape and demonstrate that array reconfigurability can substantially reduce the CRB, thereby significantly enhancing sensing performance.Moreover, to tackle the challenging CRB minimization problem, we adopt average Fisher information maximization as a surrogate objective and use the Gauss-Hermite quadrature method to obtain an explicit approximation of the objective function.The resulting problem is then decoupled into three subproblem, i.e., beamforming optimization and transmit/receive FIM surface shape optimization.For beamforming optimization, we employ the Schur complement and penalty-based semi-definite relaxation (SDR) technique to solve it.Furthermore, we propose a fixed-point equation method and a projected gradient algorithm to optimize the surface shapes of the receive and transmit FIMs, respectively.Simulation results demonstrate that, compared to rigid arrays, surface shaping of both transmit and receive FIMs can significantly reduce the average sensing CRB while maintaining communication quality, and remains effective even in multi-target scenarios.

翻译：集成感知与通信（ISAC）已被广泛认为是未来无线网络的关键使能技术，其中克拉美-罗下界（CRB）在量化感知精度方面起着核心作用。本文首次研究了基于柔性智能超表面（FIM）的ISAC系统中的CRB最小化问题。具体而言，我们首先推导了显式依赖于FIM表面形状的平均CRB表达式，并证明阵列可重构性能够显著降低CRB，从而大幅提升感知性能。此外，为应对具有挑战性的CRB最小化问题，我们采用平均费希尔信息最大化作为替代目标，并利用高斯-埃尔米特求积法获得目标函数的显式近似。随后将原问题解耦为三个子问题，即波束成形优化以及发射/接收FIM表面形状优化。针对波束成形优化，我们采用舒尔补与基于惩罚的半定松弛（SDR）技术进行求解。进一步地，我们提出不动点方程法与投影梯度算法分别优化接收与发射FIM的表面形状。仿真结果表明，与刚性阵列相比，通过对发射与接收FIM进行表面形貌优化，在保证通信质量的同时能显著降低平均感知CRB，且该方案在多目标场景中依然保持有效性。