Integrated Sensing and Over-the-Air Computation: Dual-Functional MIMO Beamforming Design

Abstract

To support the unprecedented growth of the Internet-of-Things (IoT) applications and the radio access of tremendous IoT devices, two new technologies have emerged recently to overcome the shortage of spectrum resources. The first one, known as integrated sensing and communication (ISAC), aims to share the spectrum between radar sensing and data communication. The second one, called over-the-air computation (AirComp), enables simultaneous transmission and computation of data from multiple IoT devices at the same frequencies. The promising performance of ISAC and AirComp motivates the current work on developing a framework that combines the merits of both called integrated sensing and AirComp (ISAA). In the framework, a dual-functional beamforming scheme is designed to support multiple-input-multiple-output (MIMO) ISAA simultaneously. The performance metrics of radar sensing and AirComp are evaluated by the mean squared errors of the estimated target response matrix and the received computation results, respectively. The design challenge of MIMO ISAA lies in the joint optimization of transmit beamformers at the IoT devices, and aggregation beamformer at the server, which results in a non-convex problem. To solve this problem, an algorithmic solution based on the technique of semidefinite relaxation is proposed. The results reveal that the transmit beamformer tries to balance the performance of sensing and AirComp, while the aggregation beamformer aims at reducing the AirComp error via channel equalization. Simulations are offered to confirm the efficiency of the proposed design.