Robust Beamforming for STAR-RIS Aided Hybrid-Field ISAC Systems

This paper proposes a joint beamforming design for optimizing integrated sensing and communication (ISAC) systems under imperfect channel state information (CSI), leveraging a simultaneous transmission and reflection reconfigurable intelligent surface (STAR-RIS). Owing to the deployment of large-scale antenna arrays and high carrier frequencies, the Rayleigh distance can extend to tens or even hundreds of meters. This expansion leads to a fundamental paradigm shift in electromagnetic field characteristics, transitioning from the conventional far-field regime to the emerging near-field regime. As a result, the propagation characteristics experienced by users and the target may differ. Accordingly, we consider a practical scenario in which users and the target are situated in distinct fields. However, this hybrid-field model increases the system’s sensitivity to channel estimation errors (CEE). To this end, we propose a robust design that jointly optimizes beamforming for base station (BS) and STAR-RIS, aiming to maximize the achievable sum-rate of the nodes while satisfying the constraint of sensing requirements. Under a statistical CEE model, we derive the interference covariance matrix and reformulate the maximization problem as an equivalent weighted mean square error (MSE) minimization problem. Subsequently, the transformed problem is decoupled into multiple sub-problems using a block coordinate descent (BCD)-based algorithm. The algorithm capitalizes on semidefinite relaxation and Gaussian randomization to obtain an effective solution. Finally, simulation results validate the effectiveness of the proposed robust design. Compared with the baseline schemes, the proposed algorithm achieves a higher communication sum-rate and illustrates how various parameters affect the performance.