  This paper investigates the massive random access for a huge amount of user
devices served by a base station (BS) equipped with a massive number of
antennas. We consider a grant-free unsourced random access (U-RA) scheme where
all users possess the same codebook and the BS aims at declaring a list of
transmitted codewords and recovering the messages sent by active users. Most of
the existing works concentrate on applying U-RA in the oversimplified
independent and identically distributed (i.i.d.) channels. In this paper, we
consider a fairly general joint-correlated MIMO channel model with
line-of-sight components for the realistic outdoor wireless propagation
environments. We conduct the activity detection for the emitted codewords by
performing an improved coordinate descent approach with Bayesian learning
automaton to solve a covariance-based maximum likelihood estimation problem.
The proposed algorithm exhibits a faster convergence rate than traditional
descent approaches. We further employ a coupled coding scheme to resolve the
issue that the dimensions of the common codebook expand exponentially with user
payload size in the practical massive machine-type communications scenario. Our
simulations reveal that to achieve an error probability of 0.05 for reliable
communications in correlated channels, one must pay a 0.9 to 1.3 dB penalty
comparing to the minimum signal to noise ratio needed in i.i.d. channels on
condition that a sufficient number of receiving antennas is equipped at the BS.
