  In this paper, we design a novel two-phase unsourced random access (URA)
scheme in massive multiple input multiple output (MIMO). In the first phase, we
collect a sequence of information bits to jointly acquire the user channel
state information (CSI) and the associated information bits. In the second
phase, the residual information bits of all the users are partitioned into
sub-blocks with a very short length to exhibit a higher spectral efficiency and
a lower computational complexity than the existing transmission schemes in
massive MIMO URA. By using the acquired CSI in the first phase, the sub-block
recovery in the second phase is cast as a compressed sensing (CS) problem. From
the perspective of the statistical physics, we provide a theoretical framework
for our proposed URA scheme to analyze the induced problem based on the replica
method.
  The analytical results show that the performance metrics of our URA scheme
can be linked to the system parameters by a single-valued free entropy
function. An AMP-based recovery algorithm is designed to achieve the
performance indicated by the proposed theoretical framework. Simulations verify
that our scheme outperforms the most recent counterparts.
