Worst-Case Design for RIS-Aided Over-the-Air Computation With Imperfect CSI

Over-the-air computation (AirComp) enables fast wireless data aggregation at the receiver through concurrent transmission by sensors in the application of Internet-of-Things (IoT). To further improve the performance of AirComp under unfavorable propagation channel conditions, we consider the problem of computation distortion minimization in a reconfigurable intelligent surface (RIS)-aided AirComp system. In particular, we take into account an additive bounded uncertainty of the channel state information (CSI) and the total power constraint, and jointly optimize the transceiver (Tx-Rx) and the RIS phase design from the perspective of worst-case robustness by minimizing the mean squared error (MSE) of the computation. To solve this intractable nonconvex problem, we develop an efficient alternating algorithm where both solutions to the robust sub-problem and to the joint design of Tx-Rx and RIS are obtained in closed forms. Simulation results demonstrate the effectiveness of the proposed method.