# Annealed Langevin Dynamics for Massive MIMO Detection

arXiv: https://arxiv.org/abs/2205.05776 · HTML: https://mlsanity.com/paper/2205.05776/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 May 2022.

## Built on by (most cited first, 16 of 16)

- [Solving Inverse Problems with Score-Based Generative Priors learned from Noisy Data](https://mlsanity.com/paper/2305.01166/) (2023)
- [Provable Benefit of Annealed Langevin Monte Carlo for Non-log-concave Sampling](https://mlsanity.com/paper/2407.16936/) (2024)
- [Repulsive Latent Score Distillation for Solving Inverse Problems](https://mlsanity.com/paper/2406.16683/) (2024)
- [Robust Bayesian Learning for Reliable Wireless AI: Framework and Applications](https://mlsanity.com/paper/2207.00300/) (2022)
- [Score-based Source Separation with Applications to Digital Communication Signals](https://mlsanity.com/paper/2306.14411/) (2023)
- [Deep Graph Unfolding for Beamforming in MU-MIMO Interference Networks](https://mlsanity.com/paper/2304.00446/) (2023)
- [Solving Linear Inverse Problems using Higher-Order Annealed Langevin Diffusion](https://mlsanity.com/paper/2305.05014/) (2023)
- [A Massive MIMO Sampling Detection Strategy Based on Denoising Diffusion Model](https://mlsanity.com/paper/2404.13281/) (2024)
- [Dimension-Free Multimodal Sampling via Preconditioned Annealed Langevin Dynamics](https://mlsanity.com/paper/2602.01449/) (2026)
- [The Radio-Frequency Transformer for Signal Separation](https://mlsanity.com/paper/2603.09201/) (2026)
- [To Trust or Not to Trust: On Calibration in ML-based Resource Allocation for Wireless Networks](https://mlsanity.com/paper/2507.17494/) (2025)
- [Calibrating AI Models for Wireless Communications via Conformal Prediction](https://mlsanity.com/paper/2212.07775/) (2022)
- [Generative Diffusion Model Driven Massive Random Access in Massive MIMO Systems](https://mlsanity.com/paper/2505.12382/) (2025)
- [Sampling with Shielded Langevin Monte Carlo Using Navigation Potentials](https://mlsanity.com/paper/2512.22153/) (2025)
- [GD4: Graph-based Discrete Denoising Diffusion for MIMO Detection](https://mlsanity.com/paper/2605.00423/) (2026)
- [Dimension-Uniform Discretization Analysis of Preconditioned Annealed Langevin Dynamics for Multimodal Gaussian Mixtures](https://mlsanity.com/paper/2605.16473/) (2026)

## Abstract (arXiv)

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.