Wireless Federated Learning over Resource-Constrained Networks: Digital versus Analog Transmissions

TL;DR

This paper provides a comprehensive, quantitative comparison of digital and analog uplink transmissions for wireless Federated Learning under resource constraints. It introduces a unified framework and derives convergence bounds that separate the effects of quantization in digital schemes and CSI-induced computation errors in analog AirComp, enabling fair performance evaluation under fixed latency and power budgets. The analysis reveals fundamental differences: digital FL is limited by the number of reliably transmit-able bits and becomes more sensitive to device sampling and channel outages, while analog AirComp benefits from massive device participation but hinges on CSI accuracy and computational distortion. The work further optimizes device inclusion probabilities via convex and fractional programming (KKT and Dinkelbach) to enhance convergence, and validates findings through numerical simulations on MNIST and CIFAR-10 datasets, highlighting when each transmission paradigm is preferable in practice.

Abstract

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.

Figures (8)

• Figure 1: The architecture of a typical wireless FL system.
• Figure 2: Convergence performance under digital transmission: (a) MNIST dataset, (b) CIFAR-10 dataset.
• Figure 3: Convergence performance under analog transmission: (a) MNIST dataset, (b) CIFAR-10 dataset.
• Figure 4: Test accuracy versus transmit power budget.
• Figure 5: Test accuracy versus the number of participating devices.