# Learning to Quantize and Precode in Massive MIMO Systems for Energy Reduction: a Graph Neural Network Approach

arXiv: https://arxiv.org/abs/2507.10634 · HTML: https://mlsanity.com/paper/2507.10634/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 52 references that are in the map.
- First posted on arXiv 14 Jul 2025.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [A Review of the Gumbel-max Trick and its Extensions for Discrete Stochasticity in Machine Learning](https://mlsanity.com/paper/2110.01515/) (2021)
- [Massive MIMO is a Reality -- What is Next? Five Promising Research Directions for Antenna Arrays](https://mlsanity.com/paper/1902.07678/) (2019)
- [1-bit Massive MU-MIMO Precoding in VLSI](https://mlsanity.com/paper/1702.03449/) (2017)
- [Neural Combinatorial Optimization: a New Player in the Field](https://mlsanity.com/paper/2205.01356/) (2022)
- [Energy Efficiency Maximization Precoding for Quantized Massive MIMO Systems](https://mlsanity.com/paper/2108.03048/) (2021)
- [Neural-Network Optimized 1-bit Precoding for Massive MU-MIMO](https://mlsanity.com/paper/1903.03718/) (2019)
- [Terahertz Communications for 6G and Beyond Wireless Networks: Challenges, Key Advancements, and Opportunities](https://mlsanity.com/paper/2207.11021/) (2022)
- [Model-Driven Beamforming Neural Networks](https://mlsanity.com/paper/2001.05277/) (2020)
- [Self-Supervised Learning of Linear Precoders under Non-Linear PA Distortion for Energy-Efficient Massive MIMO Systems](https://mlsanity.com/paper/2210.07037/) (2022)
- [Toward Energy-Efficient Massive MIMO: Graph Neural Network Precoding for Mitigating Non-Linear PA Distortion](https://mlsanity.com/paper/2312.04591/) (2023)
- [Deep Unfolding for Fast Linear Massive MIMO Precoders under a PA Consumption Model](https://mlsanity.com/paper/2304.12745/) (2023)
- [GNN-based Precoder Design and Fine-tuning for Cell-free Massive MIMO with Real-world CSI](https://mlsanity.com/paper/2505.08788/) (2025)

## Abstract (arXiv)

Massive MIMO systems are moving toward increased numbers of radio frequency chains, higher carrier frequencies and larger bandwidths. As such, digital-to-analog converters (DACs) are becoming a bottleneck in terms of hardware complexity and power consumption. In this work, non-linear precoding for coarsely quantized downlink massive MIMO is studied. Given the NP-hard nature of this problem, a graph neural network (GNN) is proposed that directly outputs the precoded quantized vector based on the channel matrix and the intended transmit symbols. The model is trained in a self-supervised manner, by directly maximizing the achievable rate. To overcome the non-differentiability of the objective function, introduced due to the non-differentiable DAC functions, a straight-through Gumbel-softmax estimation of the gradient is proposed. The proposed method achieves a significant increase in achievable sum rate under coarse quantization. For instance, in the single-user case, the proposed method can achieve the same sum rate as maximum ratio transmission (MRT) by using one-bit DAC's as compared to 3 bits for MRT. This reduces the DAC's power consumption by a factor 4-7 and 3 for baseband and RF DACs respectively. This, however, comes at the cost of increased digital signal processing power consumption. When accounting for this, the reduction in overall power consumption holds for a system bandwidth up to 3.5 MHz for baseband DACs, while the RF DACs can maintain a power reduction of 2.9 for higher bandwidths. Notably, indirect effects, which further reduce the power consumption, such as a reduced fronthaul consumption and reduction in other components, are not considered in this analysis.