# Trainable Projected Gradient Detector for Massive Overloaded MIMO Channels: Data-driven Tuning Approach

arXiv: https://arxiv.org/abs/1812.10044 · HTML: https://mlsanity.com/paper/1812.10044/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Dec 2018.

## Built on by (most cited first, 7 of 7)

- [LoRD-Net: Unfolded Deep Detection Network with Low-Resolution Receivers](https://mlsanity.com/paper/2102.02993/) (2021)
- [ISAC-NET: Model-driven Deep Learning for Integrated Passive Sensing and Communication](https://mlsanity.com/paper/2307.15074/) (2023)
- [Unsupervised Deep Unfolded PGD for Transmit Power Allocation in Wireless Systems](https://mlsanity.com/paper/2306.11865/) (2023)
- [Hubbard-Stratonovich Detector for Simple Trainable MIMO Signal Detection](https://mlsanity.com/paper/2302.04461/) (2023)
- [Deep Unfolded Simulated Bifurcation for Massive MIMO Signal Detection](https://mlsanity.com/paper/2306.16264/) (2023)
- [Accelerating Convergence of Stein Variational Gradient Descent via Deep Unfolding](https://mlsanity.com/paper/2402.15125/) (2024)
- [Deep Unfolding for MIMO Signal Detection](https://mlsanity.com/paper/2507.21152/) (2025)

## Abstract (arXiv)

This paper presents a deep learning-aided iterative detection algorithm for massive overloaded multiple-input multiple-output (MIMO) systems where the number of transmit antennas n is larger than that of receive antennas m. Since the proposed algorithm is based on the projected gradient descent method with trainable parameters, it is named the trainable projected gradient-detector (TPG-detector). The trainable internal parameters, such as the step-size parameter, can be optimized with standard deep learning techniques, i.e., the back propagation and stochastic gradient descent algorithms. This approach is referred to as data-driven tuning, and ensures fast convergence during parameter estimation in the proposed scheme. The TPG-detector mainly consists of matrix-vector product operations whose computational cost is proportional to m n for each iteration. In addition, the number of trainable parameters in the TPG-detector is independent of the number of antennas. These features of the TPG-detector result in a fast and stable training process and reasonable scalability for large systems. Numerical simulations show that the proposed detector achieves a comparable detection performance to those of existing algorithms for massive overloaded MIMO channels, e.g., the state-of-the-art IW-SOAV detector, with a lower computation cost.