Cramér-Rao Bound Minimization for Flexible Intelligent Metasurface-Enabled ISAC Systems

TL;DR

This work tackles the problem of enhancing sensing accuracy in ISAC by leveraging flexible intelligent metasurfaces (FIM) that enable dynamic surface-shape reconfiguration. By deriving an average CRB expression that depends on the FIM geometry and adopting Bayesian average information maximization as a surrogate objective, the authors develop an alternating-optimization framework to jointly design beamforming and FIM surface shapes. They formulate and solve three interlinked subproblems using Schur-complement based SDR for beamforming, a fixed-point duality approach for receive-shape optimization, and a projected gradient with IPDD for transmit-shape optimization, all under QoS constraints. Simulation results show that joint transmit–receive FIM surface shaping significantly reduces the average CRB compared with rigid-array designs while maintaining user QoS, and the approach remains effective in multi-target scenarios. The work thus demonstrates the practical value of surface reconfigurability in boosting sensing performance in ISAC systems.

Abstract

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.

Figures (6)

• Figure 1: The model for FIM-enabled ISAC systems.
• Figure 2: Average CRB values under different achievable rate threshold $R_{\rm th}$ with morphing range $\lambda$.
• Figure 3: Average CRB values under different transmit power budgets $P_{\rm max}$ with morphing range $\lambda$, $R_{\rm th}=4\,$bps/Hz.
• Figure 4: Average CRB values under different number of users with morphing range $\lambda$, $R_{\rm th}=4\,$bps/Hz.
• Figure 5: Average CRB values obtained when the morphing range is between $0$ and $3\lambda$, $R_{\rm th}=4\,$bps/Hz.