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. To support the high-mobility sensing with low network latency, a
technique called over-the-air-computation (AirComp) was recently developed
which enables an access-point to receive a desired function of sensing-data
from concurrent-transmissions by exploiting the superposition property of a
multi-access-channel. This work aims at further developing AirComp for
next-generation multi-antenna multi-modal sensor networks. Specifically, we
design beamforming and channel-feedback techniques for multi-function AirComp.
Given the objective of minimizing sum-mean-squared-error of computed functions,
the optimization of receive-beamforming for multi-function AirComp is a NP-hard
problem. The approximate problem based on tightening transmission-power
constraints, however, is shown to be solvable using differential-geometry. The
solution is proved to be 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 beamforming problem is found
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-technique. Last, building on the AirComp-beamforming
solution, an efficient channel-feedback technique is designed for an
access-point to receive the beamformer from distributed sensor transmissions of
designed signals that are functions of local channel-state-information.

该研究论文探讨了将 over-the-air-computation 技术用于下一代多天线多模传感器网络，特别是设计用于多功能 AirComp 的波束成形和信道反馈技术，其中接收波束成形的优化是通过紧缩传输功率约束的近似问题使用微分几何来求解的。