  In this work, we study the multiuser detection (MUD) problem for a grant-free
massive-device multiple access (MaDMA) system, where a large number of
single-antenna user devices transmit sporadic data to a multi-antenna base
station (BS). Specifically, we put forth two MUD schemes, termed random
sparsity learning multiuser detection (RSL-MUD) and structured sparsity
learning multiuser detection (SSL-MUD) for the time-slotted and
non-time-slotted grant-free MaDMA systems, respectively. In the time-slotted
RSL-MUD scheme, active users generate and transmit data packets with random
sparsity. In the non-time-slotted SSL-MUD scheme, we introduce a
sliding-window-based detection framework, and the user signals in each
observation window naturally exhibit structured sparsity. We show that by
exploiting the sparsity embedded in the user signals, we can recover the user
activity state, the channel, and the user data in a single phase, without using
pilot signals for channel estimation and/or active user identification. To this
end, we develop a message-passing based statistical inference framework for the
BS to blindly detect the user data without any prior knowledge of the
identities and the channel state information (CSI) of the active users.
Simulation results show that our RSL-MUD and SSL-MUD schemes significantly
outperform their counterpart schemes in both reducing the transmission overhead
and improving the error behavior of the system.
