MIMO Over-the-Air Computation for High-Mobility Multimodal Sensing

In future Internet-of-Things networks, sensors or even access points can be mounted on ground/aerial vehicles for smart-city surveillance or environment monitoring. For such high-mobility sensing, it is impractical to collect data from a large population of sensors using any traditional orthogonal multi-access scheme due to the excessive latency. To tackle the challenge, a technique called over-the-air computation (AirComp) was recently developed to enable a data-fusion center to receive a desired function of sensing data from concurrent sensor transmissions, by exploiting the superposition property of a multi-access channel. This paper aims at further developing multiple-input-multiple output (MIMO) AirComp for enabling high-mobility multimodal sensing. Specifically, we design MIMO-AirComp equalization and channel feedback techniques for spatially multiplexing multifunction computation. Given the objective of minimizing the computation error, a close-to-optimal equalizer is derived in closed-form using differential geometry. The solution can be computed as the weighted centroid of points on a Grassmann manifold, where each point represents the sub-space spanned by the channel matrix of a sensor. As a by-product, the problem of MIMO-AirComp equalization is proved to have the same form as the classic problem of multicast beamforming, establishing the AirComp-multicasting duality. Its significance lies in making the said Grassmannian-centroid solution transferable to the latter problem which otherwise is solved using the computation-intensive semidefinite relaxation method. Last, building on the AirComp architecture, an efficient channel-feedback technique is designed for direct acquisition of the equalizer at the access point from simultaneous feedback by all sensors. This over-comes the difficulty of provisioning orthogonal feedback channels for many sensors.