Extended Target Adaptive Beamforming for ISAC: A Perspective of Predictive Error Ellipse

Utilizing communication signals to extract motion parameters has emerged as a key direction in Vehicle-to-Everything (V2X) networks. Accurately modeling the relationship between communication signals and sensing performance is critical for the advancement of such systems. Unlike prior work that relies primarily on qualitative analysis, this paper derives the Cramér-Rao Bound (CRB) for radar parameter estimation in the context of Orthogonal Frequency Division Multiplexing (OFDM) waveforms and Uniform Planar Array (UPA) configurations. Recognizing that vehicles may act as extended targets, we propose two New Radio (NR)-V2X-compatible beamforming schemes tailored to different phases of the communication process. During the initial beam establishment phase, we develop a beamforming approach based on the union of predictive error ellipses, which enhances scatterer localization through temporally assisted beam training. In the beam adjustment phase, we introduce an adaptive narrowest-beam strategy that leverages the positions of scatterers and the communication receiver (CR), enabling effective tracking with reduced complexity. The beam design problem is addressed using the minimum enclosing ellipse algorithm and tailored antenna control methods. Simulation results validate the proposed approach, showing up to a 32.4% improvement in achievable rate with a 32×32 transmit antenna array and a 5.2% gain with an 8×8 array, compared to conventional beam sweeping under identical SNR conditions.