Energy Efficient Robust Beamforming for Vehicular ISAC with Imperfect Channel Estimation

TL;DR

This paper develops a robust beamforming method to enhance energy efficiency in vehicular ISAC systems despite imperfect channel estimation, using advanced optimization techniques and convex transformations.

Contribution

It introduces a novel energy-efficient beamforming design that accounts for channel uncertainties in vehicular ISAC, employing fractional programming, SDR, and convex optimization.

Findings

The proposed algorithm converges rapidly.

It effectively mitigates channel estimation errors.

The method improves energy efficiency in vehicular ISAC.

Abstract

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.