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.

中文翻译：

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一种在大规模 MIMO 通信系统上进行联合学习的压缩感知方法

联合学习是一种隐私保护方法，通过与无线设备协作在中央服务器上训练全局模型，每个无线设备都有自己的本地训练数据集。在本文中，我们提出了一种压缩感知方法，用于在大规模多输入多输出通信系统上进行联合学习，其中配备了大量天线阵列的中央服务器与无线设备进行通信。系统设计中的一项主要挑战是在中央服务器准确重建本地梯度向量，这些向量是从无线设备计算和发送的。为了克服这一挑战，我们首先建立了一种传输策略，以从设备的局部梯度向量构建稀疏传输信号。然后，我们提出了一种压缩感知算法，使服务器能够通过利用其稀疏性来迭代地找到传输信号的线性最小均方误差 (LMMSE) 估计。我们还为每次迭代的残差导出了一个分析阈值，以设计所提出算法的停止标准。我们表明，对于稀疏传输信号，所提出的算法需要的计算复杂度低于 LMMSE。仿真结果表明，所提出的方法优于传统的线性波束成形方法，并通过完美的重建缩小了联邦学习和集中学习之间的性能差距。我们还为每次迭代的残差导出了一个分析阈值，以设计所提出算法的停止标准。我们表明，对于稀疏传输信号，所提出的算法需要的计算复杂度低于 LMMSE。仿真结果表明，所提出的方法优于传统的线性波束成形方法，并通过完美的重建缩小了联邦学习和集中学习之间的性能差距。我们还为每次迭代的残差导出了一个分析阈值，以设计所提出算法的停止标准。我们表明，对于稀疏传输信号，所提出的算法需要的计算复杂度低于 LMMSE。仿真结果表明，所提出的方法优于传统的线性波束成形方法，并通过完美的重建缩小了联邦学习和集中学习之间的性能差距。