  This paper addresses the problem of joint user identification and channel
estimation (JUICE) for grant-free access in massive machine-type communications
(mMTC). We consider the JUICE under a spatially correlated fading channel model
as that reflects the main characteristics of the practical multiple-input
multiple-output channels. We formulate the JUICE as a sparse recovery problem
in a multiple measurement vector setup and present a solution based on the
approximate message passing (AMP) algorithm that takes into account the channel
spatial correlation. Using the state evolution, we provide a detailed
theoretical analysis on the activity detection performance of AMP-based JUICE
by deriving closed-from expressions for the probabilities of miss detection and
false alarm. The simulation experiments show that the performance predicted by
the theoretical analysis matches the one obtained by the numerical results.
