The discrete nature of transmitted symbols poses challenges for achieving optimal detection in multiple-input multiple-output (MIMO) systems associated with a large number of antennas. Recently, the combination of two powerful machine learning methods, Markov chain Monte Carlo (MCMC) sampling and gradient descent, has emerged as a highly efficient solution to address this issue. However, existing gradient-based MCMC detectors are heuristically designed and thus are theoretically untenable. To bridge this gap, we introduce a novel sampling algorithm tailored for discrete spaces. This algorithm leverages gradients from the underlying continuous spaces for acceleration while maintaining the validity of probabilistic sampling. We prove the convergence of this method and also analyze its convergence rate using both MCMC theory and empirical diagnostics. On this basis, we develop a MIMO detector that precisely samples from the target discrete distribution and generates posterior Bayesian estimates using these samples, whose performance is thereby theoretically guaranteed. Furthermore, our proposed detector is highly parallelizable and scalable to large MIMO dimensions, positioning it as a compelling candidate for next-generation wireless networks. Simulation results show that our detector achieves near-optimal performance, significantly outperforms state-of-the-art baselines, and showcases resilience to various system setups.

翻译：在多输入多输出（MIMO）系统中，由于发射符号的离散特性，在涉及大规模天线配置时实现最优检测面临挑战。近年来，结合马尔可夫链蒙特卡洛（MCMC）采样与梯度下降这两种强大的机器学习方法，已成为解决该问题的高效方案。然而，现有的基于梯度的MCMC检测器均采用启发式设计，因而在理论上缺乏严谨性。为弥补这一缺陷，我们提出一种专为离散空间设计的新型采样算法。该算法利用底层连续空间的梯度进行加速，同时保持概率采样的有效性。我们证明了该方法的收敛性，并综合运用MCMC理论与实证诊断分析了其收敛速率。在此基础上，我们开发了一种MIMO检测器，该检测器能够从目标离散分布中精确采样，并利用这些样本生成后验贝叶斯估计，从而使其性能在理论上得到保证。此外，所提出的检测器具备高度并行化特性，可扩展至大规模MIMO维度，使其成为下一代无线网络的有力候选方案。仿真结果表明，我们的检测器实现了近最优性能，显著优于现有先进基线方法，并在不同系统配置下展现出良好的鲁棒性。