Hubbard-Stratonovich Detector for Simple Trainable MIMO Signal Detection

TL;DR

The paper tackles the problem of detecting signals in overloaded MIMO systems under URLLC constraints by introducing a low-complexity trainable detector. It fuses the Hubbard--Stratonovich transformation with deep unfolding to create the THS detector, which maintains only $O(1)$ trainable parameters per layer and requires $O(n^2)$ computations per iteration, avoiding matrix inversions. Empirical results show THS outperforms low-cost baselines and approaches the performance of more expensive DU-based detectors, with greater stability across varying antenna configurations. This approach offers a practical, scalable solution for real-time MIMO detection in high-dimensional wireless systems, enabling efficient online adaptation to channel variations.

Abstract

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 $O(n^2)$ 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.

Figures (5)

• Figure 1: BER performance for $(n,m)=(50,32)$. The number of iterations of (T)HS and (scalable) TPG detectors is $T=30$ and that of ERTS is $K=500$.
• Figure 2: BER performance for $(n,m)=(100,64)$.
• Figure 3: BER performance for $(n,m)=(150,96)$.
• Figure 4: Average amplitude of gradient $G$ of the THS and scalable TPG detectors over $10^4$ signals for a noiseless MIMO system with $(n,m)=(50,32)$. The BER performances of the THS and scalable TPG detectors are $1.1\times 10^{-3}$ and $4.8\times 10^{-3}$, respectively.
• Figure 5: Average bit-flip ratio of the THS and scalable TPG detectors over $10^4$ signals for a noiseless MIMO system with $(n,m)=(50,32)$.