Optimal Power Control for Over-The-Air Federated Edge Learning Using Statistical Channel Knowledge

Over-the-air federated edge learning (OTA-FEEL) is an efficient distributed machine learning framework in terms of radio resource requirements. Delicate power control is needed to combat the distortion of the local models caused by channel fading. This paper develops the optimal power control policy under fading channels, to minimize the optimality gap of OTA-FEEL by exploiting the statistical channel state information (CSI), i.e., the mean and variance of the fading. We reveal that the optimal power control policy takes a form where the variance of the effective channel between the server and devices should be minimized when its mean is given. Based on this structure, we propose to iteratively minimize the variance using the Lagrange-duality method and then optimize the mean of the effective channels using a one-dimensional search. A closed-form expression for the optimal power control is derived. Simulations confirm the benefit of the use of the statistical CSI, and the superiority of the proposed optimal power control policy to the existing approaches in the convergence of OTA-FEEL.