  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.
