Joint Beamforming Design for Multi-Functional RIS-Aided Over-the-Air Computation

To facilitate fast data aggregation in Internet of Things, over-the-air computation (AirComp) is a communication-efficient enabler by virtue of its high spectrum efficiency and low transmission latency. However, traditional AirComp faces challenges such as signal misalignment, imperfect channel state information (CSI), and noisy fading channels. In this paper, we employ a multi-functional reconfigurable intelligent surface (MF-RIS) to alleviate mean square error (MSE) of AirComp through a joint design of transceiver beamforming and MF-RIS coefficients, but it necessitates solving a mixed-integer nonlinear programming problem. To tackle this issue, we propose an alternating optimization algorithm based on the semidefinite relaxation approach and difference-of-convex programming. Numerical results underscore the performance gains achieved by the proposed algorithm, as well as the remarkable proficiency of the MF-RIS in suppressing MSE under imperfect CSI.