Federated learning (FL) is a distributed learning paradigm wherein users exchange FL models with a server instead of raw datasets, thereby preserving data privacy and reducing communication overhead. However, the increased number of FL users may hinder completing large-scale FL over wireless networks due to high imposed latency. Cell-free massive multiple-input multiple-output~(CFmMIMO) is a promising architecture for implementing FL because it serves many users on the same time/frequency resources. While CFmMIMO enhances energy efficiency through spatial multiplexing and collaborative beamforming, it remains crucial to meticulously allocate uplink transmission powers to the FL users. In this paper, we propose an uplink power allocation scheme in FL over CFmMIMO by considering the effect of each user's power on the energy and latency of other users to jointly minimize the users' uplink energy and the latency of FL training. The proposed solution algorithm is based on the coordinate gradient descent method. Numerical results show that our proposed method outperforms the well-known max-sum rate by increasing up to~$27$\% and max-min energy efficiency of the Dinkelbach method by increasing up to~$21$\% in terms of test accuracy while having limited uplink energy and latency budget for FL over CFmMIMO.

翻译：联邦学习（FL）是一种分布式学习范式，用户与服务器交换FL模型而非原始数据集，从而保护数据隐私并降低通信开销。然而，FL用户数量的增加可能因高延迟而阻碍无线网络上的大规模FL部署。无蜂窝大规模多输入多输出（CFmMIMO）是一种实现FL的有前景架构，因为它能在相同时间/频率资源上服务众多用户。尽管CFmMIMO通过空间复用和协作波束成形提升了能量效率，但精确分配FL用户的上行传输功率仍至关重要。本文针对CFmMIMO上的FL，提出了一种上行功率分配方案，该方案考虑每个用户功率对其他用户能量与延迟的影响，旨在联合最小化用户上行能量与FL训练延迟。所提出的求解算法基于坐标梯度下降法。数值结果表明，在CFmMIMO上FL的有限上行能量与延迟预算约束下，我们提出的方法在测试精度方面，比著名的最大化总速率方法提升高达27%，比Dinkelbach方法的最大最小能量效率提升高达21%。