Optimal Power Control and CSI Acquisition for Over-the-Air Computation in OFDM System

Over-the-air computation (AirComp) is a novel technology that utilizes the superposition characteristic of the wireless multiple-access channel to accomplish communication and computation tasks simultaneously, which can be used to achieve efficient data fusion in wireless networks. However, the performance of AirComp can be compromised due to non-ideal conditions in practical systems, such as limited transmitting power budget, receiving noise, etc. In this paper, we first propose a joint transmitting-receiving power control scheme for over-the-air computation in the OFDM-based multicarrier wireless system, which can minimize the mean square error (MSE) of the received signal by taking into account of limited transmitting power budget and receiving noise. Based on the special structure of the problem, which depends on the set of users that either use up their power budget or not, we decompose the problem into two sub-problems, one deals with the power allocation at the transmitters, the other deals with the power scaling at the receiver. The optimal results are obtained by searching the set of users with used up power budget and solving these two sub-problems accordingly. We then propose an efficient channel state information (CSI) acquisition and feedback scheme for the AirComp power control scheme, and the effect of imperfect CSI is also considered accordingly. We provide extensive simulation results to demonstrate the performance of the proposed scheme under different network conditions.