Over-the-Air Computation with Quantized CSI and Discrete Power Control Levels

In this paper, an Over-the-Air Computation (AirComp) scheme for fast data aggregation is considered. Multisource data are simultaneously transmitted by single-antenna mobile devices to a single-antenna fusion center (FC) through a wireless multiple-access channel. The optimal power levels at the devices and a postprocessing scaling function at the FC are jointly derived such that mean square error of the computation is minimized. Different than the existing approaches that rely on perfect channel state information (CSI) at the FC and assume that the devices’ optimal power levels can be selected from an infinite solution set, in the present paper, it is assumed that only quantized CSI is available at the FC and that the aforementioned optimal power levels lie in a finite discrete set of solutions. To derive the optimal power levels and FC’s scaling factor, a difficult nonconvex constrained optimization problem is formulated. An efficient and robust solution to quantization errors is developed via the deep reinforcement learning framework. Numerical results verify the good performance of the proposed approach while it exhibits a significant reduction in the required feedback.