  Solving the optimal symbol detection problem in multiple-input
multiple-output (MIMO) systems is known to be NP-hard. Hence, the objective of
any detector of practical relevance is to get reasonably close to the optimal
solution while keeping the computational complexity in check. In this work, we
propose a MIMO detector based on an annealed version of Langevin (stochastic)
dynamics. More precisely, we define a stochastic dynamical process whose
stationary distribution coincides with the posterior distribution of the
symbols given our observations. In essence, this allows us to approximate the
maximum a posteriori estimator of the transmitted symbols by sampling from the
proposed Langevin dynamic. Furthermore, we carefully craft this stochastic
dynamic by gradually adding a sequence of noise with decreasing variance to the
trajectories, which ensures that the estimated symbols belong to a
pre-specified discrete constellation. Based on the proposed MIMO detector, we
also design a robust version of the method by unfolding and parameterizing one
term -- the score of the likelihood -- by a neural network. Through numerical
experiments in both synthetic and real-world data, we show that our proposed
detector yields state-of-the-art symbol error rate performance and the robust
version becomes noise-variance agnostic.
