Over-the-Air Computation for IoT Networks: Computing Multiple Functions With Antenna Arrays

Over-the-air computation combines communication and computation efficiently by utilizing the superposition property of wireless channels, when Internet of Things (IoT) networks focus more on the computed functions than the individual messages. In this paper, we study the computation of multiple linear functions of Gaussian sources over-the-air using antenna arrays at both the IoT devices and the IoT access point (AP). The key challenges in this paper are the intranode interference of multiple functions, the nonuniform fading between different IoT devices and the massive channel state information (CSI) required at the IoT AP. We propose a novel transmitter design at the IoT devices with zero-forcing beamforming to cancel the intranode interference and uniform-forcing power control to compensate the nonuniform fading. In order to avoid massive CSI requirement, receive antenna selection is adopted at the IoT AP and a corresponding signaling procedure is proposed utilizing the OR property of the wireless channel. The performance of the proposed transceiver design is analyzed. The closed-form expression for the mean squared function error (MSFE) outage is derived. Due to the complexity of the expression, an asymptotic analysis of the MSFE outage is further provided to demonstrate the diversity order in terms of the transmit power constraint and the number of IoT devices. Simulation results are presented to show the performance of the proposed design.