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Optimal symbol detection in multiple-input multiple-output (MIMO) systems isknown to be an NP-hard problem. Hence, the objective of any detector ofpractical relevance is to get reasonably close to the optimal solution whilekeeping the computational complexity in check. In this work, we propose a MIMOdetector based on an annealed version of Langevin (stochastic) dynamics. Moreprecisely, we define a stochastic dynamical process whose stationarydistribution coincides with the posterior distribution of the symbols given ourobservations. In essence, this allows us to approximate the maximum aposteriori estimator of the transmitted symbols by sampling from the proposedLangevin dynamic. Furthermore, we carefully craft this stochastic dynamic bygradually adding a sequence of noise with decreasing variance to thetrajectories, which ensures that the estimated symbols belong to apre-specified discrete constellation. Through numerical experiments, we showthat our proposed detector yields state-of-the-art symbol error rateperformance.

Detection by Sampling: Massive MIMO Detector based on Langevin Dynamics