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Federated learning is a privacy-preserving approach to train a global modelat a central server by collaborating with wireless devices, each with its ownlocal training data set. In this paper, we present a compressive sensingapproach for federated learning over massive multiple-input multiple-outputcommunication systems in which the central server equipped with a massiveantenna array communicates with the wireless devices. One major challenge insystem design is to reconstruct local gradient vectors accurately at thecentral server, which are computed-and-sent from the wireless devices. Toovercome this challenge, we first establish a transmission strategy toconstruct sparse transmitted signals from the local gradient vectors at thedevices. We then propose a compressive sensing algorithm enabling the server toiteratively find the linear minimum-mean-square-error (LMMSE) estimate of thetransmitted signal by exploiting its sparsity. We also derive an analyticalthreshold for the residual error at each iteration, to design the stoppingcriterion of the proposed algorithm. We show that for a sparse transmittedsignal, the proposed algorithm requires less computationally complexity thanLMMSE. Simulation results demonstrate that the presented approach outperformsconventional linear beamforming approaches and reduces the performance gapbetween federated learning and centralized learning with perfectreconstruction.

A Compressive Sensing Approach for Federated Learning over Massive MIMO Communication Systems