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 subspace 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 overcomes the difficulty of provisioning orthogonal feedback channels for many sensors.