Cram´ er-Rao Bound Minimization for Flexible Intelligent Metasurface-Enabled ISAC Systems

Integrated sensing and communication (ISAC) have been widely recognized as a key enabler for future wireless networks, where the Cram´ er-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 subproblems, i.e., beamforming optimization and transmit/receive FIM surface shape optimization. For beam forming 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.