Cramér-Rao Bound Analysis and Beamforming Design for 3D Extended Target in ISAC

This paper considers an integrated sensing and communication system where a multi-antenna base station transmits a common signal for joint multi-user communication and extend target (ET) sensing. We first propose a second-order truncated Fourier series surface model for an arbitrarily-shaped three-dimensional (3D) ET, characterized by center range, center elevation, center azimuth, orientation, and surface coefficients. Based on this model, we consider the backscattering effects of the visible elements along the ET surface, and derive novel closed-form Cramér-Rao bounds (CRBs) for the ET characteristic parameter estimation. Further, we formulate a CRB minimization problem by optimizing the transmit beamformers, under the constraints of transmit power budget, communication-specific signal-to-interference-plus-noise requirements, and ET-specific beam coverage requirement. The non-convex optimization problem can be efficiently solved by the semidefinite relaxation technique. Numerical results demonstrate that the proposed beamforming design is superior to existing baselines with significantly lower CRBs and a more appropriate beampattern for sensing a 3D ET.