Not yet reviewed by Pith; the record is open.

Grant-free access is considered as a key enabler to massive machine-type communications (mMTC) as it promotes energy-efficiency and small signalling overhead. Due to the sporadic user activity in mMTC, joint user identification and channel estimation (JUICE) is a main challenge. This paper addresses the JUICE in single-cell mMTC with single-antenna users and a multi-antenna base station (BS) under spatially correlated fading channels. In particular, by leveraging the sporadic user activity, we solve the JUICE in a multi measurement vector compressed sensing (CS) framework under two different cases, with and without the knowledge of prior channel distribution information (CDI) at the BS. First, for the case without prior information, we formulate the JUICE as an iterative reweighted $\ell_{2,1}$-norm minimization problem. Second, when the CDI is known to the BS, we exploit the available information and formulate the JUICE from a Bayesian estimation perspective as a maximum \emph{a posteriori} probability (MAP) estimation problem. For both JUICE formulations, we derive efficient iterative solutions based on the alternating direction method of multipliers (ADMM). The numerical experiments show that the proposed solutions achieve higher channel estimation quality and activity detection accuracy with shorter pilot sequences compared to existing algorithms.