# Hubbard-Stratonovich Detector for Simple Trainable MIMO Signal Detection

arXiv: https://arxiv.org/abs/2302.04461 · HTML: https://mlsanity.com/paper/2302.04461/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 24 references that are in the map.
- First posted on arXiv 9 Feb 2023.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Unfolding: Model-Based Inspiration of Novel Deep Architectures](https://mlsanity.com/paper/1409.2574/) (2014)
- [Learning to Detect](https://mlsanity.com/paper/1805.07631/) (2018)
- [Deep Unfolding for Communications Systems: A Survey and Some New Directions](https://mlsanity.com/paper/1906.05774/) (2019)
- [Redefining Wireless Communication for 6G: Signal Processing Meets Deep Learning with Deep Unfolding](https://mlsanity.com/paper/2004.10715/) (2020)
- [Sampling Approximately Low-Rank Ising Models: MCMC meets Variational Methods](https://mlsanity.com/paper/2202.08907/) (2022)
- [Trainable Projected Gradient Detector for Massive Overloaded MIMO Channels: Data-driven Tuning Approach](https://mlsanity.com/paper/1812.10044/) (2018)
- [Convergence Acceleration via Chebyshev Step: Plausible Interpretation of Deep-Unfolded Gradient Descent](https://mlsanity.com/paper/2010.13335/) (2020)
- [Deep Learning-Aided Projected Gradient Detector for Massive Overloaded MIMO Channels](https://mlsanity.com/paper/1806.10827/) (2018)
- [Chebyshev Inertial Iteration for Accelerating Fixed-Point Iterations](https://mlsanity.com/paper/2001.03280/) (2020)

## Abstract (arXiv)

Massive multiple-input multiple-output (MIMO) is a key technology used in fifth-generation wireless communication networks and beyond. Recently, various MIMO signal detectors based on deep learning have been proposed. Especially, deep unfolding (DU), which involves unrolling of an existing iterative algorithm and embedding of trainable parameters, has been applied with remarkable detection performance. Although DU has a lesser number of trainable parameters than conventional deep neural networks, the computational complexities related to training and execution have been problematic because DU-based MIMO detectors usually utilize matrix inversion to improve their detection performance. In this study, we attempted to construct a DU-based trainable MIMO detector with the simplest structure. The proposed detector based on the Hubbard--Stratonovich (HS) transformation and DU is called the trainable HS (THS) detector. It requires only O(1) trainable parameters and its training and execution cost is O(n2) per iteration, where n is the number of transmitting antennas. Numerical results show that the detection performance of the THS detector is better than that of existing algorithms of the same complexity and close to that of a DU-based detector, which has higher training and execution costs than the THS detector.