Low-Complexity CRB Minimization for ISAC With a Generalized Target Response Matrix

This paper presents a beamforming design for integrated sensing and communication (ISAC) systems using Riemannian manifold optimization to minimize the Cramér-Rao bound (CRB) of a generic target response matrix (TRM) for improving target estimation. CRB optimization is a challenging non-convex problem involving matrix inversion and its complex dependence on system parameters (e.g., beamforming, number of antennas, and number of targets), resulting in high dimensionality and the need to balance sensing accuracy and communication quality. Traditional solutions to these challenges, such as relaxed semidefinite programming (RSDP) and sequential convex cone optimization (SCCO), are computationally complex and have slow convergence. Thus, we propose a Riemannian conjugate iterative augmented Lagrangian manifold (RC-IALM) algorithm to minimize the TRM’s CRB while ensuring communication quality. Numerical results demonstrate its superior computational efficiency and reduced running time. For instance, it is 33 and 12 times, respectively, faster than RSDP and SCCO benchmarks when there are 24 transmit/receiver antennas at the base station.