In this paper, we quantitatively compare these two effective communication
schemes, i.e., digital and analog ones, for wireless federated learning (FL)
over resource-constrained networks, highlighting their essential differences as
well as their respective application scenarios. We first examine both digital
and analog transmission methods, together with a unified and fair comparison
scheme under practical constraints. A universal convergence analysis under
various imperfections is established for FL performance evaluation in wireless
networks. These analytical results reveal that the fundamental difference
between the two paradigms lies in whether communication and computation are
jointly designed or not. The digital schemes decouple the communication design
from specific FL tasks, making it difficult to support simultaneous uplink
transmission of massive devices with limited bandwidth. In contrast, the analog
communication allows over-the-air computation (AirComp), thus achieving
efficient spectrum utilization. However, computation-oriented analog
transmission reduces power efficiency, and its performance is sensitive to
computational errors. Finally, numerical simulations are conducted to verify
these theoretical observations.

比较无线联合学习中的数字和模拟通信方案，在资源受限网络中量化比较了它们的主要区别和应用场景，研究发现两种方案的基本区别在于是否联合设计了通信和计算，其中数字方案难以支持带宽有限的大量设备的同时上行传输，而模拟通信允许空中计算，实现了高效的频谱利用，但计算导向的模拟传输会降低功率效率，并且对计算误差敏感。通过数值模拟验证了这些理论观察结果。

无线网络上联合学习的数字与模拟传输对比

Digital versus Analog Transmissions for Federated Learning over Wireless  Networks

This paper studies a federated edge learning system, in which an edge server
coordinates a set of edge devices to train a shared machine learning model
based on their locally distributed data samples. During the distributed
training, we exploit the joint communication and computation design for
improving the system energy efficiency, in which both the communication
resource allocation for global ML parameters aggregation and the computation
resource allocation for locally updating MLparameters are jointly optimized. In
particular, we consider two transmission protocols for edge devices to upload
ML parameters to edge server, based on the non orthogonal multiple access and
time division multiple access, respectively. Under both protocols, we minimize
the total energy consumption at all edge devices over a particular finite
training duration subject to a given training accuracy, by jointly optimizing
the transmission power and rates at edge devices for uploading MLparameters and
their central processing unit frequencies for local update. We propose
efficient algorithms to optimally solve the formulated energy minimization
problems by using the techniques from convex optimization. Numerical results
show that as compared to other benchmark schemes, our proposed joint
communication and computation design significantly improves the energy
efficiency of the federated edge learning system, by properly balancing the
energy tradeoff between communication and computation.

本文研究了联邦边缘学习系统，旨在通过协调边缘设备共同训练机器学习模型，以提高系统能效。同时，利用联合通信和计算设计优化边缘设备传输协议，通过最小化边缘设备上传机器学习模型参数时的总能耗，提高系统能效。作者提出了一种有效的算法来优化能量下降问题。数值结果显示，相对于其他基准方案，作者提出的联合通信和计算设计可以显著提高联邦边缘学习系统的能效。