Distributionally Robust Over-the-Air Computation in Presence of Channel Uncertainties

Over-the-air computation (AirComp) emerges as a promising method to integrate computation and communication in 5G and beyond network architecture. Nevertheless, the performance of AirComp, measured by mean-square error (MSE), can be severely bottlenecked by the availability of channel information. In this paper, we investigate the AirComp design in presence of channel uncertainties. Particularly, we consider the case that only the first and second moments of the channel, which can be easily obtained through actual measurement, are available, without the exact statistical information. Then, we establish the chance-constrained AirComp with a thresholded MSE under a given outage probability. Correspondingly, we address the distributionally robust AirComp design to guarantee the intended threshold regardless of the channel distribution. By leveraging conditional value-at-risk (CVaR), we reformulate the probabilistic-form constraint into its deterministic counterpart to facilitate the analysis. Then, the reformulated problem is decomposed to optimize the transmit and receive scaling factors alternatively. Simulation results demonstrate that our proposal rigorously ensures robustness amid uncertainties and effectively reduces computation distortion when compared to the baseline methods.