  Soft demodulation of received symbols into bit log-likelihood ratios (LLRs)
is at the very heart of multiple-input-multiple-output (MIMO) detection.
However, the optimal maximum a posteriori (MAP) detector is complicated and
infeasible to be used in a practical system. In this paper, we propose a soft
MIMO detection algorithm based on marginal posterior probability statistics
(MPPS). With the help of optimal transport theory and order statistics theory,
we transform the posteriori probability distribution of each layer into a
Gaussian distribution. Then the full sampling paths can be implicitly restored
from the first- and second-order moment statistics of the transformed
distribution. A lightweight network is designed to learn to recovery the
log-MAP LLRs from the moment statistics with low complexity. Simulation results
show that the proposed algorithm can improve the performance significantly with
reduced samples under fading and correlated channels.
