Annealed Langevin Dynamics for Massive MIMO Detection

Nicolas Zilberstein, Chris Dick, Rahman Doost-Mohammady, Ashutosh Sabharwal, Santiago Segarra

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)3762-3776
Number of pages15
JournalIEEE Transactions on Wireless Communications
Issue number6
StatePublished - Jun 1 2023


  • deep algorithm unfolding
  • langevin dynamics
  • Markov chain Monte Carlo
  • Massive MIMO detection
  • score-based methods

ASJC Scopus subject areas

  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Applied Mathematics


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