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.

在本文中，我们提出了一种基于协调梯度下降法的在 CFmMIMO 上进行 FL 的上行功率分配方案，通过考虑每个用户的功率对其他用户的能量和延迟的影响，共同最小化用户的上行能量和 FL 训练的延迟。数值结果显示，我们提出的方法在限定的上行能量和延迟预算下，在测试准确性方面将最大和最小求和速率的已知方法分别提高了最多 27% 和 Dinkelbach 方法的最大最小能量效率提高了最多 21%。