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Cell-free communication has the potential to significantly improve grant-freetransmission in massive machine-type communication, wherein multiple accesspoints jointly serve a large number of user equipments to improve coverage andspectral efficiency. In this paper, we propose a novel framework for jointactive user detection (AUD), channel estimation (CE), and data detection (DD)for massive grant-free transmission in cell-free systems. We formulate anoptimization problem for joint AUD, CE, and DD by considering both the sparsityof the data matrix, which arises from intermittent user activity, and thesparsity of the effective channel matrix, which arises from intermittent useractivity and large-scale fading. We approximately solve this optimizationproblem with a box-constrained forward-backward splitting algorithm, whichsignificantly improves AUD, CE, and DD performance. We demonstrate theeffectiveness of the proposed framework through simulation experiments.

Joint Active User Detection, Channel Estimation, and Data Detection for Massive Grant-Free Transmission in Cell-Free Systems