Vertical federated learning (FL) is a collaborative machine learning
framework that enables devices to learn a global model from the
feature-partition datasets without sharing local raw data. However, as the
number of the local intermediate outputs is proportional to the training
samples, it is critical to develop communication-efficient techniques for
wireless vertical FL to support high-dimensional model aggregation with full
device participation. In this paper, we propose a novel cloud radio access
network (Cloud-RAN) based vertical FL system to enable fast and accurate model
aggregation by leveraging over-the-air computation (AirComp) and alleviating
communication straggler issue with cooperative model aggregation among
geographically distributed edge servers. However, the model aggregation error
caused by AirComp and quantization errors caused by the limited fronthaul
capacity degrade the learning performance for vertical FL. To address these
issues, we characterize the convergence behavior of the vertical FL algorithm
considering both uplink and downlink transmissions. To improve the learning
performance, we establish a system optimization framework by joint transceiver
and fronthaul quantization design, for which successive convex approximation
and alternate convex search based system optimization algorithms are developed.
We conduct extensive simulations to demonstrate the effectiveness of the
proposed system architecture and optimization framework for vertical FL.

本文提出了一种基于云无线接入网络 (Cloud-RAN) 的竖直联合学习系统，利用空中计算 (AirComp) 和协作模型聚合技术减少地理分布的边缘服务器之间的通信延迟，结合传输优化模型和前传量化设计优化模型，提高竖直联合学习的模型聚合准确性。

云 RAN 上的竖直联邦学习：收敛分析与系统优化

Vertical Federated Learning over Cloud-RAN: Convergence Analysis and  System Optimization

The heterogeneous cloud radio access network (Cloud-RAN) provides a
revolutionary way to densify radio access networks. It enables centralized
coordination and signal processing for efficient interference management and
flexible network adaptation. Thus, it can resolve the main challenges for
next-generation wireless networks, including higher energy efficiency and
spectral efficiency, higher cost efficiency, scalable connectivity, and low
latency. In this article, we shall provide an algorithmic thinking on the new
design challenges for the dense heterogeneous Cloud-RAN based on convex
optimization. As problem sizes scale up with the network size, we will
demonstrate that it is critical to take unique structures of design problems
and inherent characteristics of wireless channels into consideration, while
convex optimization will serve as a powerful tool for such purposes. Network
power minimization and channel state information acquisition will be used as
two typical examples to demonstrate the effectiveness of convex optimization
methods. We will then present a two-stage framework to solve general
large-scale convex optimization problems, which is amenable to parallel
implementation in the cloud data center.

本文基于凸优化对密集异构云 RAN 设计挑战提出了算法思路，强调考虑无线信道固有特征和设计问题的独特结构，以实现网络能量、信道状态信息的最小化和最大化，提出了一个适用于云数据中心的并行实现的两阶段框架。

超密集云无线接入网络的大规模凸优化

Large-Scale Convex Optimization for Ultra-Dense Cloud-RAN

A cloud radio access network (Cloud-RAN) is a network architecture that holds
the promise of meeting the explosive growth of mobile data traffic. In this
architecture, all the baseband signal processing is shifted to a single
baseband unit (BBU) pool, which enables efficient resource allocation and
interference management. Meanwhile, conventional powerful base stations can be
replaced by low-cost low-power remote radio heads (RRHs), producing a green and
low-cost infrastructure. However, as all the RRHs need to be connected to the
BBU pool through optical transport links, the transport network power
consumption becomes significant. In this paper, we propose a new framework to
design a green Cloud-RAN, which is formulated as a joint RRH selection and
power minimization beamforming problem. To efficiently solve this problem, we
first propose a greedy selection algorithm, which is shown to provide near-
optimal performance. To further reduce the complexity, a novel group sparse
beamforming method is proposed by inducing the group-sparsity of beamformers
using the weighted $\ell_1/\ell_2$-norm minimization, where the group sparsity
pattern indicates those RRHs that can be switched off. Simulation results will
show that the proposed algorithms significantly reduce the network power
consumption and demonstrate the importance of considering the transport link
power consumption.

该研究提出了一种新的框架来设计绿色 Cloud-RAN，包括 RRH 选择和功率最小化波束成形问题，通过引入群组稀疏性和加权的 l1/l2 范数最小化来解决这个问题，结果显示，该算法显着降低了网络功耗并减少了传输链接的功耗。