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Massive Machine-Type Communications (mMTC) features a massive number oflow-cost user equipments (UEs) with sparse activity. Tailor-made for thesefeatures, grant-free random access (GF-RA) serves as an efficient accesssolution for mMTC. However, most existing GF-RA schemes rely on strictsynchronization, which incurs excessive coordination burden for the low-costUEs. In this work, we propose a receiver design for asynchronous GF-RA, andaddress 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 distinguishdifferent UEs. However, a sample correlation problem in this receiver designimpedes the factorization of the joint likelihood function, which complicatesthe UAD and CE problem. To address this correlation problem, we design apartially uni-directional (PUD) factor graph representation for the jointlikelihood function. Building on this PUD factor graph, we further propose aPUD message passing based sparse Bayesian learning (SBL) algorithm forasynchronous UAD and CE (PUDMP-SBL-aUADCE). Our theoretical analysis shows thatthe PUDMP-SBL-aUADCE algorithm exhibits higher signal-to-interference-and-noiseratio (SINR) in the asynchronous case than in the synchronous case, i.e., theproposed receiver design can exploit asynchronization to suppress multi-userinterference. In addition, considering potential timing error from the low-costUEs, we investigate the impacts of imperfect delay profile, and reveal theadvantages of adopting the SBL method in this case. Finally, extensivesimulation results are provided to demonstrate the performance of thePUDMP-SBL-aUADCE algorithm.

Asynchronous Grant-Free Random Access: Receiver Design with Partially Uni-Directional Message Passing and Interference Suppression Analysis