  Massive Machine-Type Communications (mMTC) features a massive number of
low-cost user equipments (UEs) with sparse activity. Tailor-made for these
features, grant-free random access (GF-RA) serves as an efficient access
solution for mMTC. However, most existing GF-RA schemes rely on strict
synchronization, which incurs excessive coordination burden for the low-cost
UEs. In this work, we propose a receiver design for asynchronous GF-RA, and
address the joint user activity detection (UAD) and channel estimation (CE)
problem in the presence of asynchronization-induced inter-symbol interference.
Specifically, the delay profile is exploited at the receiver to distinguish
different UEs. However, a sample correlation problem in this receiver design
impedes the factorization of the joint likelihood function, which complicates
the UAD and CE problem. To address this correlation problem, we design a
partially uni-directional (PUD) factor graph representation for the joint
likelihood function. Building on this PUD factor graph, we further propose a
PUD message passing based sparse Bayesian learning (SBL) algorithm for
asynchronous UAD and CE (PUDMP-SBL-aUADCE). Our theoretical analysis shows that
the PUDMP-SBL-aUADCE algorithm exhibits higher signal-to-interference-and-noise
ratio (SINR) in the asynchronous case than in the synchronous case, i.e., the
proposed receiver design can exploit asynchronization to suppress multi-user
interference. In addition, considering potential timing error from the low-cost
UEs, we investigate the impacts of imperfect delay profile, and reveal the
advantages of adopting the SBL method in this case. Finally, extensive
simulation results are provided to demonstrate the performance of the
PUDMP-SBL-aUADCE algorithm.
