Robust Design for STAR-RIS Assisted Over-the-Air Computation Systems With Imperfect CSI

Over-the-air computation (AirComp) is a technology that exploits the superposition properties of wireless channels to integrate communication and computation. To improve the performance of AirComp, simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) is employed to provide a full-plane coverage. However, the CSI estimation is challenging, while the imperfect CSI degrades the performance of AirComp. Then, to address this issue, in this paper we investigate the robust beamforming design for STAR-RIS assisted AirComp system. Specifically, both the imperfect CSI of cascaded channels and direct channels are considered with a bounded CSI-error-uncertainty. In this work, we aim at optimizing the computation accuracy in the worst case of CSI error. To solve this intractable max-min problem, we propose an alternating optimization algorithm based on the Lagrange multiplier method and the binary property of transmit/reflect coefficient vectors at the STAR-RIS. Simulation results show that the our algorithm approaches the lower bound where the perfect CSI is assumed.