  This paper considers a low-complexity Gaussian Message Passing (GMP) scheme
for a coded massive Multiple-Input Multiple-Output (MIMO) systems with
Non-Orthogonal Multiple Access (massive MIMO-NOMA), in which a base station
with $N_s$ antennas serves $N_u$ sources simultaneously in the same frequency.
Both $N_u$ and $N_s$ are large numbers, and we consider the overloaded cases
with $N_u>N_s$. The GMP for MIMO-NOMA is a message passing algorithm operating
on a fully-connected loopy factor graph, which is well understood to fail to
converge due to the correlation problem. In this paper, we utilize the
large-scale property of the system to simplify the convergence analysis of the
GMP under the overloaded condition. First, we prove that the \emph{variances}
of the GMP definitely converge to the mean square error (MSE) of Linear Minimum
Mean Square Error (LMMSE) multi-user detection. Secondly, the \emph{means} of
the traditional GMP will fail to converge when $ N_u/N_s<
(\sqrt{2}-1)^{-2}\approx5.83$. Therefore, we propose and derive a new
convergent GMP called scale-and-add GMP (SA-GMP), which always converges to the
LMMSE multi-user detection performance for any $N_u/N_s>1$, and show that it
has a faster convergence speed than the traditional GMP with the same
complexity. Finally, numerical results are provided to verify the validity and
accuracy of the theoretical results presented.
