We study federated learning (FL), where power-limited wireless devices
utilize their local datasets to collaboratively train a global model with the
help of a remote parameter server (PS). The PS has access to the global model
and shares it with the devices for local training, and the devices return the
result of their local updates to the PS to update the global model. This
framework requires downlink transmission from the PS to the devices and uplink
transmission from the devices to the PS. The goal of this study is to
investigate the impact of the bandwidth-limited shared wireless medium in both
the downlink and uplink on the performance of FL with a focus on the downlink.
To this end, the downlink and uplink channels are modeled as fading broadcast
and multiple access channels, respectively, both with limited bandwidth. For
downlink transmission, we first introduce a digital approach, where a
quantization technique is employed at the PS to broadcast the global model
update at a common rate such that all the devices can decode it. Next, we
propose analog downlink transmission, where the global model is broadcast by
the PS in an uncoded manner. We consider analog transmission over the uplink in
both cases. We further analyze the convergence behavior of the proposed analog
approach assuming that the uplink transmission is error-free. Numerical
experiments show that the analog downlink approach provides significant
improvement over the digital one, despite a significantly lower transmit power
at the PS. The experimental results corroborate the convergence results, and
show that a smaller number of local iterations should be used when the data
distribution is more biased, and also when the devices have a better estimate
of the global model in the analog downlink approach.

本文研究了联合学习中带宽受限的广播通道对性能的影响，提出了数字和模拟两种下行传输方法，并证明了模拟方法的收敛性更好，尤其在数据分布不均和设备能够更好地估计全局模型时性能更优。

嘈杂下行联邦学习的收敛性

Convergence of Federated Learning over a Noisy Downlink

We propose a generalized feedback model and compressive sensing based
opportunistic feedback schemes for feedback resource reduction in MIMO
Broadcast Channels under the assumption that both uplink and downlink channels
undergo block Rayleigh fading. Feedback resources are shared and are
opportunistically accessed by users who are strong, i.e. users whose channel
quality information is above a certain fixed threshold. Strong users send same
feedback information on all shared channels. They are identified by the base
station via compressive sensing. Both analog and digital feedbacks are
considered. The proposed analog & digital opportunistic feedback schemes are
shown to achieve the same sum-rate throughput as that achieved by dedicated
feedback schemes, but with feedback channels growing only logarithmically with
number of users. Moreover, there is also a reduction in the feedback load. In
the analog feedback case, we show that the propose scheme reduces the feedback
noise which eventually results in better throughput, whereas in the digital
feedback case the proposed scheme in a noisy scenario achieves almost the
throughput obtained in a noiseless dedicated feedback scenario. We also show
that for a fixed given budget of feedback bits, there exist a trade-off between
the number of shared channels and thresholds accuracy of the feedback SINR.

本文提出通用反馈模型和基于压缩感知的机会反馈方案，用于在 MIMO 广播通道中减少反馈资源的使用，并研究了模拟和数字方案。该方案通过压缩感知技术识别强用户，从而有效降低反馈信道的数量和反馈负荷，同时达到相同的总速率吞吐量。同时，研究表明，在固定的反馈比特预算下，存在着反馈 SINR 准确性和共享通道数量之间的折衷。