GD4: Graph-based Discrete Denoising Diffusion for MIMO Detection

TL;DR

GD4 is a graph-based discrete denoising diffusion method for MIMO detection that achieves high-quality solutions with fewer inference steps, outperforming existing diffusion and classical detectors in various system configurations.

Contribution

GD4 introduces a novel discrete denoising diffusion approach operating directly in symbol space, enabling fast inference and improved detection performance in MIMO systems.

Findings

GD4 outperforms existing diffusion-based detectors in quality under similar compute budgets.

GD4 surpasses classical methods like Babai and Klein-Babai points in both under- and over-determined systems.

GD4 achieves high-quality solutions with only one or a few denoising evaluations.

Abstract

In wireless communications, recovering the optimal solution to the multiple-input multiple-output (MIMO) detection problem is NP-hard. Obtaining high-quality suboptimal solutions with a favorable performance-complexity trade-off is particularly challenging in under-determined systems with $N_t$ transmit antennas and $N_r < N_t$ receive antennas. Recent diffusion-based MIMO detectors have shown promise, but they require extensive sampling iterations at inference time, and their performance degrades in under-determined scenarios. We propose GD4, a graph-based discrete denoising diffusion method for MIMO detection. Unlike existing diffusion-based detectors that operate in a continuous relaxed space, GD4 performs denoising directly in the discrete symbol space and enables fast inference with one or a few denoising evaluations. Numerical results show that, under a similar inference-time compute budget, GD4 produces higher-quality suboptimal solutions than existing diffusion-based detectors and some widely used classical baseline including box-constrained Babai point and the $K$-best box-constrained randomized Klein-Babai point in both under-determined and overdetermined settings.