Reconfigurable Intelligent Surface Assisted Over-the-Air Computation in Multi-Cell Networks

Over-the-air computation (AirComp) becomes a promising technology for fast wireless data aggregation which supports the requirement of ultra-fast wireless data transmission. However, current works mainly focus on the single-cell systems, ignoring the inter-cell interference caused by multiple-cell task coexisting. To unleash the potential of AirComp in multi-cell networks, in this paper we consider the reconfigurable intelligent surface (RIS) to overcome the unfavorable signal condition by adjusting the phase shift at the RIS. Our goal is to minimize the mean-square error for AirComp by jointly optimizing the receive beamforming vectors at the base station and the phase-shift ma-trix at the RIS. However, due to the highly coupled optimization variables, the resulting problem is non-convex and challenging. We thus present an alternating optimization framework to decompose the problem into several quadratic sum-of-ratios problems (QSRP) with nonconvex quadratic constraints. Then, we apply successive convex approximation method to transform each QSRP into several convex sub-problems. Simulation results demonstrate the convergence of proposed algorithm and validate the ability of an RIS in enlarging the channel-gain difference under multiple-cell network systems.