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

TL;DR

The paper extends ISAC design to 3D extended targets by representing ET surfaces with a second-order truncated Fourier series and deriving a closed-form CRB for ET kinematic parameters $d_o$, ${\theta}_o$, ${\phi}_o$, and ${\varphi}$. It then develops two optimization-based beamforming schemes, one minimizing the sensing CRB under SINR and beam-coverage constraints via SDR, and another balancing CRB with sum-rate via SCA; to reduce complexity, a learning-based ISACBeam-GNN is proposed, with separate sensing and communication modules feeding a final integration stage. Numerical results show that shape-aware beamforming significantly improves joint sensing and communication performance, and that ISACBeam-GNN provides comparable performance with much lower complexity and better adaptability to varying numbers of CUs and ET scatterers. The work demonstrates substantial gains over PT-centric designs and offers a scalable, practical path toward accurate 3D ET parameter estimation in ISAC systems.

Abstract

This paper investigates an integrated sensing and communication (ISAC) system where the sensing target is a three-dimensional (3D) extended target, for which multiple scatterers from the target surface can be resolved. We first introduce a second-order truncated Fourier series surface model for an arbitrarily-shaped 3D ET. Utilizing this model, we derive tractable Cramer-Rao bounds (CRBs) for estimating the ET kinematic parameters, including the center range, azimuth, elevation, and orientation. These CRBs depend explicitly on the transmit covariance matrix and ET shape. Then we formulate two transmit beamforming optimization problems for the base station (BS) to simultaneously support communication with multiple users and sensing of the 3D ET. The first minimizes the sensing CRB while ensuring a minimum signal-to-interference-plus-noise ratio (SINR) for each user, and it is solved using semidefinite relaxation. The second balances minimizing the CRB and maximizing communication rates through a weight factor, and is solved via successive convex approximation. To reduce the computational complexity, we further propose ISACBeam-GNN, a novel graph neural network-based beamforming method that employs a separate-then-integrate structure, learning communication and sensing (C&S) objectives independently before integrating them to balance C&S trade-offs. Simulation results show that the proposed beamforming designs that account for ET shapes significantly outperform existing baselines, offering better communication-sensing performance trade-offs as well as an improved beampattern for sensing. Results also demonstrate that ISACBeam-GNN is an efficient alternative to the optimization-based methods, with remarkable adaptability and scalability.

Figures (9)

• Figure 1: The global and local coordinates in the ISAC system.
• Figure 2: The proposed ISACBeam-GNN.
• Figure 3: The update of the scatterer node $\bar{s}_k^l$, the ET center node $\bar{s}_0^l$, and the CU node $\bar{w}_n^l$ in the $l$-th layer.
• Figure 4: Normalized CRBs of vehicle-shaped ET, drone-shaped ET, and PT kinematic parameters versus distance $d_o$.
• Figure 5: Normalized beampatterns of different design methods of the vehicle-shaped ET for (a)-(c) The CRB-min problem $\mathcal{P}1.1$, the preset SINR threshold is $\Gamma=4\ \mathrm{dB}$; (d)-(e) The WIM problem $\mathcal{P}2.1$, the path loss for the CU at ($0^\circ,30^\circ$) is $3\ \mathrm{dB}$ greater than that of the CU at ($0^\circ,-30^\circ$). The red solid triangle and blue hollow rhombus refer to the directions of the ET center and CUs, respectively. The black dotted line defines the boundary of the visible ET surface.