  This paper investigates robust beamforming for system-centric energy
efficiency (EE) optimization in the vehicular integrated sensing and
communication (ISAC) system, where the mobility of vehicles poses significant
challenges to channel estimation. To obtain the optimal beamforming under
channel uncertainty, we first formulate an optimization problem for maximizing
the system EE under bounded channel estimation errors. Next, fractional
programming and semidefinite relaxation (SDR) are utilized to relax the rank-1
constraints. We further use Schur complement and S-Procedure to transform
Cramer-Rao bound (CRB) and channel estimation error constraints into convex
forms, respectively. Based on the Lagrangian dual function and
Karush-Kuhn-Tucker (KKT) conditions, it is proved that the optimal beamforming
solution is rank-1. Finally, we present comprehensive simulation results to
demonstrate two key findings: 1) the proposed algorithm exhibits a favorable
convergence rate, and 2) the approach effectively mitigates the impact of
channel estimation errors.
