Over-the-Air Computation in Massive MIMO Systems with Hybrid Beamforming

In future Internet-of-Things (IoT) networks, there are a myriad of distributed sensors for various intelligent applications. Over-the-air computation (AirComp) can achieve fast wireless data aggregation by exploiting the waveform superposition property of multiple-access channels. However, the mean-square error (MSE) performance of AirComp deteriorates rapidly with the proliferation of IoT devices. To circumstance this issue, integrating AirComp with massive multiple-input multiple-output (MIMO) serves as an energyefficient method. In this work, we investigate the deployment of cost-effective hybrid beamforming architecture in the AirComp system, which is still in the early exploration. We propose to minimize the MSE of system based on the manner of alternating optimization. Specifically, the transmit beamforming at each device is independently tackled with an optimal solution, and the receive beamforming is transformed into a matrix factorization problem which aims to minimize the weighted Euclidean distance between the hybrid beamforming combiner and optimal unconstrained fully-digital (FD) combiner. Importantly, we consider both the finite-resolution and infinite-resolution phase shifters. The proposed algorithms are capable of realizing near performance as the FD scheme with low computational complexity. Simulation results well exhibit the efficiency of our proposed algorithms.