Joint Beamforming Aided Over-the-Air Computation Systems Relying on Both BS-Side and User-Side Reconfigurable Intelligent Surfaces

Over-the-air computation (AirComp) has received substantial attention, given its ability to aggregate massive amounts of data from distributed wireless devices (WDs). However, the accuracy at fusion center (FC) may be severely affected by receiving corrupted poor channel conditions. To mitigate this issue, we consider employment reconfigurable intelligent surfaces (RISs) in AirComp system considered for improving quality data, and hence improve accuracy. most previous contributions on RIS-assisted systems only employ a single RIS resultant single-RIS-assisted (SRIS-assisted) systems. We develop concept further mitigating deleterious effects conceiving double-RIS-assisted (DRIS-assisted) system, where one RISs is located near WDs other vicinity FC. theoretically prove that DRIS-assisted outperforms SRIS-assisted counterpart terms mean-squared-error (MSE). Furthermore, propose pair algorithms jointly optimizing transmit power WDs, receive beamforming vector FC, passive matrices minimizing computational MSE. Specifically, updated exploiting Lagrange duality method, while optimized utilizing first-order optimality condition. techniques are developed based semidefinite relaxation (SDR) penalty-duality-decomposition (PDD), respectively. Both complexity convergence proposed analyzed. Finally, simulation results provided quantifying overall performance system.