In this paper, we propose a novel fully Bayesian approach for the massive
multiple-input multiple-output (MIMO) massive unsourced random access (URA).
The payload of each user device is coded by the sparse regression codes
(SPARCs) without redundant parity bits. A Bayesian model is established to
capture the probabilistic characteristics of the overall system. Particularly,
we adopt the core idea of the model-based learning approach to establish a
flexible Bayesian channel model to adapt the complex environments. Different
from the traditional divide-and-conquer or pilot-based massive MIMO URA
strategies, we propose a three-layer message passing (TLMP) algorithm to
jointly decode all the information blocks, as well as acquire the massive MIMO
channel, which adopts the core idea of the variational message passing and
approximate message passing. We verify that our proposed TLMP significantly
enhances the spectral efficiency compared with the state-of-the-arts baselines,
and is more robust to the possible codeword collisions