Double-RIS Assisted Over-the-Air Computation

Over-the-air computation (AirComp) is a promising multiple-access scheme that seamlessly integrates the computation and communication by leveraging the waveform superposition properly of a multiple access channel. To unleash the full potential of AirComp, in this paper, we present a double-RIS assisted multiple-input multiple-output AirComp system, where two RISs are deployed to extend the effective coverage area and enhance the channel quality of randomly distributed sensors. We consider the cooperative passive beamforming design at RISs to further improve the performance. Our objective is to minimize the mean-squared error of AirComp by jointly optimizing the receive beamforming, denoising factor, transmit power control, cooperative passive beamforming design. The formulated problem is challenging to be optimally solved due to the coupled cooperative passive beamforming and transceiver variables. To this end, we propose an efficient algorithm based on the block coordinate descent method and semidefinite relaxation to obtain the receive beamforming at the AP and the cooperative passive beamforming at RISs after deriving the closed-form solutions for denoising factor and transmit power control. The numerical results validate that the double-RIS assisted AirComp system achieves a better performance compared to the single-RIS baseline in various system settings.