Hamiltonian Monte Carlo-Based Near-Optimal MIMO Signal Detection

TL;DR

The authors address the challenge of achieving near-optimal MIMO signal detection while keeping computational complexity manageable by recasting the discrete detection problem as a continuous Bayesian inference task solvable via Hamiltonian Monte Carlo. They introduce a mixture of $t$-distribution priors for symbol positions and treat the likelihood temperature as a random variable, yielding a horseshoe-like likelihood that enhances exploration around constellation points and into multimodal posteriors. In the uncoded setting, HMC with the $t$-mixture prior outperforms linear MMSE and rivals other stochastic methods, with especially strong gains for higher-order modulations; in the coded setting, LDPC decoding with LLR feedback and the horseshoe likelihood achieves near-SISO AWGN performance across modulations and channel conditions. The results indicate a practical, scalable detector suitable for next-generation wireless systems, while acknowledging limitations to 96×96 antenna configurations and Gaussian-noise assumptions and outlining clear avenues for extension.

Abstract

Multiple-input multiple-output (MIMO) technology is essential for the optimal functioning of next-generation wireless networks; however, enhancing its signal-detection performance for improved spectral efficiency is challenging. Here, we propose an approach that transforms the discrete MIMO detection problem into a continuous problem while leveraging the efficient Hamiltonian Monte Carlo algorithm. For this continuous framework, we employ a mixture of t-distributions as the prior distribution. To improve the performance in the coded case further, we treat the likelihood's temperature parameter as a random variable and address its optimization. This treatment leads to the adoption of a horseshoe density for the likelihood. Theoretical analysis and extensive simulations demonstrate that our method achieves near-optimal detection performance while maintaining polynomial computational complexity. This MIMO detection technique can accelerate the development of 6G mobile communication systems.

Figures (11)

• Figure 1: Two examples of priors for binary phase-shift keying (BPSK).
• Figure 2: Criteria for selecting a single one from soft-value symbol candidates.
• Figure 3: System diagram for the uncoded and coded cases.
• Figure 4: Uncoded QPSK ($\rho = 0$): trace plots and autocorrelation plots.
• Figure 5: Uncoded QPSK ($\rho = 0$): ESS/chain (top left), $\hat{R}$ (bottom left), $1-r$ (top right), and SER (bottom right).