To address the limitations of traditional over-the-air federated learning (OA-FL) such as limited server coverage and low resource utilization, we propose an OA-FL in MIMO cloud radio access network (MIMO Cloud-RAN) framework, where edge devices upload (or download) model parameters to the cloud server (CS) through access points (APs). Specifically, in every training round, there are three stages: edge aggregation; global aggregation; and model updating and broadcasting. To better utilize the correlation among APs, called inter-AP correlation, we propose modeling the global aggregation stage as a lossy distributed source coding (L-DSC) problem to make analysis from the perspective of rate-distortion theory. We further analyze the performance of the proposed OA-FL in MIMO Cloud-RAN framework. Based on the analysis, we formulate a communication-learning optimization problem to improve the system performance by considering the inter-AP correlation. To solve this problem, we develop an algorithm by using alternating optimization (AO) and majorization-minimization (MM), which effectively improves the FL learning performance. Furthermore, we propose a practical design that demonstrates the utilization of inter-AP correlation. The numerical results show that the proposed practical design effectively leverages inter-AP correlation, and outperforms other baseline schemes.

翻译：为克服传统空中联邦学习（OA-FL）在服务器覆盖范围有限及资源利用率低等方面的局限性，我们提出了基于MIMO云接入网（MIMO Cloud-RAN）的OA-FL框架。在该框架中，边缘设备通过接入点（AP）向云服务器（CS）上传（或下载）模型参数。具体而言，每轮训练包含三个阶段：边缘聚合、全局聚合以及模型更新与广播。为更好地利用接入点间的关联性（称为AP间相关性），我们将全局聚合阶段建模为有损分布式信源编码（L-DSC）问题，从而从率失真理论视角进行分析。我们进一步分析了所提MIMO Cloud-RAN框架下OA-FL的性能，并基于分析结果，通过考虑AP间相关性构建了一个通信-学习联合优化问题以提升系统性能。为解决该问题，我们提出了一种交替优化（AO）与最小化-最大化（MM）相结合的高效算法，有效改善了联邦学习（FL）性能。此外，我们还提出了一项实践设计方案，展示了AP间相关性的利用方式。数值结果表明，该实践设计方案能有效利用AP间相关性，性能优于其他基线方案。