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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.