  Joint user identification and channel estimation (JUICE) is a main challenge
in grant-free massive machine-type communications (mMTC). The sparse pattern in
users' activity allows to solve the JUICE as a compressed sensing problem in a
multiple measurement vector (MMV) setup. This paper addresses the JUICE under
the practical spatially correlated fading channel. We formulate the JUICE as an
iterative reweighted $\ell_{2,1}$-norm optimization. We develop a
computationally efficient alternating direction method of multipliers (ADMM)
approach to solve it. In particular, by leveraging the second-order statistics
of the channels, we reformulate the JUICE problem to exploit the covariance
information and we derive its ADMM-based solution. The simulation results
highlight the significant improvements brought by the proposed approach in
terms of channel estimation and activity detection performances.
