Reduced-Dimension Design of MIMO Over-the-Air Computing for Data Aggregation in Clustered IoT Networks

One basic operation of Internet-of-Things (IoT) networks is to acquire a function of distributed data collected from sensors over wireless channels, called wireless data aggregation (WDA). In the presence of dense sensors, low-latency WDA poses a design challenge for high-mobility or mission critical IoT applications. A promising solution is a low-latency multi-access scheme, called over-the-air computing (AirComp), that supports simultaneous transmission such that an access point (AP) can estimate and receive a summation-form function of the distributed sensing data by exploiting the waveform-superposition property of a multi-access channel. In this work, we propose a multiple-input-multiple-output (MIMO) AirComp framework for an IoT network with clustered multi-antenna sensors and an AP with large receive arrays. The framework supports low-complexity and low-latency AirComp of a vector-valued function. The contributions of this work are two-fold. Define the AirComp error as the error in the functional value received at AP due to channel noise. First, under the criterion of minimum error, the optimal receive beamformer at the AP, called decomposed aggregation beamformer (DAB), is shown to have a decomposed architecture: the inner component focuses on channel-dimension reduction and the outer component focuses on joint equalization of the resultant low-dimensional small-scale fading channels. In addition, an algorithm is designed to adjust the ranks of individual components of the DAB for a further performance improvement. Second, to provision DAB with the required channel state information (CSI), a low-latency channel feedback scheme is proposed by intelligently leveraging the AirComp principle to support simultaneous channel feedback by sensors. The proposed framework is shown by simulation to substantially reduce AirComp error compared with the existing design without considering channel structures.