Federated learning is a privacy-preserving approach to train a global model
at a central server by collaborating with wireless devices, each with its own
local training data set. In this paper, we present a compressive sensing
approach for federated learning over massive multiple-input multiple-output
communication systems in which the central server equipped with a massive
antenna array communicates with the wireless devices. One major challenge in
system design is to reconstruct local gradient vectors accurately at the
central server, which are computed-and-sent from the wireless devices. To
overcome this challenge, we first establish a transmission strategy to
construct sparse transmitted signals from the local gradient vectors at the
devices. We then propose a compressive sensing algorithm enabling the server to
iteratively find the linear minimum-mean-square-error (LMMSE) estimate of the
transmitted signal by exploiting its sparsity. We also derive an analytical
threshold for the residual error at each iteration, to design the stopping
criterion of the proposed algorithm. We show that for a sparse transmitted
signal, the proposed algorithm requires less computationally complexity than
LMMSE. Simulation results demonstrate that the presented approach outperforms
conventional linear beamforming approaches and reduces the performance gap
between federated learning and centralized learning with perfect
reconstruction.

本文提出了一种基于压缩感知的联邦学习算法，通过传输策略构造稀疏的梯度向量信号，利用压缩感知算法迭代地求解线性最小均方误差 (LMMSE) 估计量。通过仿真实验，证明了该方法在无线设备通信系统中具有比传统线性波束赋形方法更好的性能，并减小了联邦学习和中央学习的性能差距。