To enable wireless federated learning (FL) in communication resource-constrained networks, two communication schemes, i.e., digital and analog ones, are effective solutions. In this paper, we quantitatively compare these two techniques, highlighting their essential differences as well as respectively suitable scenarios. We first examine both digital and analog transmission schemes, together with a unified and fair comparison framework under imbalanced device sampling, strict latency targets, and transmit power constraints. A universal convergence analysis under various imperfections is established for evaluating the performance of FL over wireless networks. These analytical results reveal that the fundamental difference between the digital and analog communications lies in whether communication and computation are jointly designed or not. The digital scheme decouples the communication design from FL computing tasks, making it difficult to support uplink transmission from massive devices with limited bandwidth and hence the performance is mainly communication-limited. In contrast, the analog communication allows over-the-air computation (AirComp) and achieves better spectrum utilization. However, the computation-oriented analog transmission reduces power efficiency, and its performance is sensitive to computation errors from imperfect channel state information (CSI). Furthermore, device sampling for both schemes are optimized and differences in sampling optimization are analyzed. Numerical results verify the theoretical analysis and affirm the superior performance of the sampling optimization.

翻译：为在通信资源受限网络中实现无线联邦学习（FL），数字与模拟两种通信方案均为有效解决方案。本文定量比较这两种技术，阐明其本质差异及各自适用场景。我们首先在设备采样不均衡、严格延迟目标及发射功率约束下，考察数字与模拟传输方案，并建立统一公平的比较框架。通过建立多种非理想条件下的通用收敛性分析，评估无线网络中联邦学习的性能。分析结果表明，数字与模拟通信的根本差异在于通信与计算是否联合设计。数字方案将通信设计与FL计算任务解耦，难以在有限带宽下支持海量设备的上行传输，因此其性能主要受通信限制。相比之下，模拟通信支持空中计算（AirComp），能实现更优的频谱利用率。然而，面向计算的模拟传输会降低功率效率，且其性能对非完美信道状态信息（CSI）引起的计算误差较为敏感。此外，本文优化了两种方案的设备采样策略，并分析了采样优化的差异。数值结果验证了理论分析，并证实了采样优化的优越性能。