Massive grant-free transmission and cell-free wireless communication systems have emerged as pivotal enablers for massive machine-type communication. This paper proposes a deep-unfolding-based joint activity and data detection (DU-JAD) algorithm for massive grant-free transmission in cell-free systems. We first formulate a joint activity and data detection optimization problem, which we solve approximately using forward-backward splitting (FBS). We then apply deep unfolding to FBS to optimize algorithm parameters using machine learning. In order to improve data detection (DD) performance, reduce algorithm complexity, and enhance active user detection (AUD), we employ a momentum strategy, an approximate posterior mean estimator, and a novel soft-output AUD module, respectively. Simulation results confirm the efficacy of DU-JAD for AUD and DD.
Cell-free communication has the potential to significantly improve grant-free transmission in massive machine-type communication, wherein multiple access points jointly serve a large number of user equipments to improve coverage and spectral efficiency. In this paper, we propose a novel framework for joint active user detection (AUD), channel estimation (CE), and data detection (DD) for massive grant-free transmission in cell-free systems. We formulate an optimization problem for joint AUD, CE, and DD by considering both the sparsity of the data matrix, which arises from intermittent user activity, and the sparsity of the effective channel matrix, which arises from intermittent user activity and large-scale fading. We approximately solve this optimization problem with a box-constrained forward-backward splitting algorithm, which significantly improves AUD, CE, and DD performance. We demonstrate the effectiveness of the proposed framework through simulation experiments.