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.

翻译：本文研究了车辆集成感知与通信系统中以系统为中心的能效鲁棒波束赋形问题，其中车辆移动性对信道估计提出了显著挑战。为在信道不确定性条件下获得最优波束赋形，我们首先构建了一个在信道估计误差有界约束下最大化系统能效的优化问题。随后，利用分式规划与半定松弛松弛了秩1约束，并通过Schur补与S-Procedure分别将克拉美-罗界与信道估计误差约束转化为凸形式。基于拉格朗日对偶函数与Karush-Kuhn-Tucker条件，证明了最优波束赋形解满足秩1性质。最后，综合仿真结果揭示两个关键发现：1) 所提算法具有优异的收敛速度；2) 该方法能有效抑制信道估计误差的影响。