  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.
