Energy-efficient Optimization for Over-the-Air Federated Learning in Cell-free Massive MIMO

Federated Learning (FL) is a distributed learning framework in wireless edge networks, intended to bolster in-telligent application capabilities. This paper considers an over-the-air FL scheme in cell-free massive MIMO (CF-mMIMO) system. In order to address the FL performance degradation issue caused by aggregation error, we establish a joint optimization problem of device scheduling and power scaling factor under the energy consumption constraint to minimize the optimality gap on the basis of convergence analysis. Besides, we introduce the Lyapunov method to transform the long-term issue into a short-term one, and then propose an alternating optimization to address the mixed integer nonlinear programming problem. Simulations results validate that the proposed FL scheme is energy-efficient with satisfying learning performance.