  Over-the-air computation (AirComp) is a disruptive technique for fast
wireless data aggregation in Internet of Things (IoT) networks via exploiting
the waveform superposition property of multiple-access channels. However, the
performance of AirComp is bottlenecked by the worst channel condition among all
links between the IoT devices and the access point. In this paper, a
reconfigurable intelligent surface (RIS) assisted AirComp system is proposed to
boost the received signal power and thus mitigate the performance bottleneck by
reconfiguring the propagation channels. With an objective to minimize the
AirComp distortion, we propose a joint design of AirComp transceivers and RIS
phase-shifts, which however turns out to be a highly intractable non-convex
programming problem. To this end, we develop a novel alternating minimization
framework in conjunction with the successive convex approximation technique,
which is proved to converge monotonically. To reduce the computational
complexity, we transform the subproblem in each alternation as a smooth
convex-concave saddle point problem, which is then tackled by proposing a
Mirror-Prox method that only involves a sequence of closed-form updates.
Simulations show that the computation time of the proposed algorithm can be two
orders of magnitude smaller than that of the state-of-the-art algorithms, while
achieving a similar distortion performance.
