Theoretical Analysis of Federated Learning Supported by Cell-Free Massive MIMO Networks With Enhanced Power Allocation

In this letter, we explore the process of transmitting model parameters for federated learning (FL) across cell-free massive multiple-input multiple-output (CFmMIMO) networks. We conduct a theoretical analysis to examine the impact of wireless transmission errors on the parameter updating process of the FL model within the framework of CFmMIMO networks. In particular, we ingeniously reformulate the optimization problem of minimizing the loss function in FL by substituting the loss function with the packet error rate function and eventually approximating it as a tractable closed-form expression. Taking the impact of wireless resource allocation on the efficacy of FL into account, we specialize in the optimization of uplink transmission power to minimize the packet error rate function. The fractional programming (FP) algorithm is employed to perform a quadratic transformation of the objective function, facilitating the transformation of the initial non-convex problem into a convex problem. The results derived from the simulation demonstrate that the implementation of the power control strategy yields a significant reduction of 84.3% in the equivalent loss function.