# Toward Energy-Efficient Massive MIMO: Graph Neural Network Precoding for Mitigating Non-Linear PA Distortion

arXiv: https://arxiv.org/abs/2312.04591 · HTML: https://mlsanity.com/paper/2312.04591/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 58 references that are in the map.
- First posted on arXiv 5 Dec 2023.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [A Survey on Deep Learning Hardware Accelerators for Heterogeneous HPC Platforms](https://mlsanity.com/paper/2306.15552/) (2023)
- [Learning on Hardware: A Tutorial on Neural Network Accelerators and Co-Processors](https://mlsanity.com/paper/2104.09252/) (2021)
- [Manticore: A 4096-core RISC-V Chiplet Architecture for Ultra-efficient Floating-point Computing](https://mlsanity.com/paper/2008.06502/) (2020)
- [On Antenna Array Out-of-Band Emissions](https://mlsanity.com/paper/1908.02982/) (2019)
- [Distortion-Aware Linear Precoding for Massive MIMO Downlink Systems with Nonlinear Power Amplifiers](https://mlsanity.com/paper/2012.13337/) (2020)
- [Z3RO Precoder Canceling Nonlinear Power Amplifier Distortion in Large Array Systems](https://mlsanity.com/paper/2110.07891/) (2021)
- [Measurement-Based Validation of Z3RO Precoder to Prevent Nonlinear Amplifier Distortion in Massive MIMO Systems](https://mlsanity.com/paper/2202.00286/) (2022)
- [The Z3RO Family of Precoders Cancelling Nonlinear Power Amplification Distortion in Large Array Systems](https://mlsanity.com/paper/2206.05112/) (2022)
- [Self-Supervised Learning of Linear Precoders under Non-Linear PA Distortion for Energy-Efficient Massive MIMO Systems](https://mlsanity.com/paper/2210.07037/) (2022)
- [Distortion-Aware Linear Precoding for Millimeter-Wave Multiuser MISO Downlink](https://mlsanity.com/paper/1906.11611/) (2019)
- [Efficient Autoprecoder-based deep learning for massive MU-MIMO Downlink under PA Non-Linearities](https://mlsanity.com/paper/2202.03190/) (2022)
- [Understanding the Performance of Learning Precoding Policy with GNN and CNNs](https://mlsanity.com/paper/2211.14775/) (2022)

## Built on by (most cited first, 2 of 2)

- [Learning to Quantize and Precode in Massive MIMO Systems for Energy Reduction: a Graph Neural Network Approach](https://mlsanity.com/paper/2507.10634/) (2025)
- [A Low-Complexity Plug-and-Play Deep Learning Model for Generalizable Massive MIMO Precoding](https://mlsanity.com/paper/2601.21897/) (2026)

## Abstract (arXiv)

Massive MIMO systems are typically designed assuming linear power amplifiers (PAs). However, PAs are most energy efficient close to saturation, where non-linear distortion arises. For conventional precoders, this distortion can coherently combine at user locations, limiting performance. We propose a graph neural network (GNN) to learn a mapping between channel and precoding matrices, which maximizes the sum rate affected by non-linear distortion, using a high-order polynomial PA model. In the distortion-limited regime, this GNN-based precoder outperforms zero forcing (ZF), ZF plus digital pre-distortion (DPD) and the distortion-aware beamforming (DAB) precoder from the state-of-the-art. At an input back-off of -3 dB the proposed precoder compared to ZF increases the sum rate by 8.60 and 8.84 bits/channel use for two and four users respectively. Radiation patterns show that these gains are achieved by transmitting the non-linear distortion in non-user directions. In the four user-case, for a fixed sum rate, the total consumed power (PA and processing) of the GNN precoder is 3.24 and 1.44 times lower compared to ZF and ZF plus DPD respectively. A complexity analysis shows six orders of magnitude reduction compared to DAB precoding. This opens perspectives to operate PAs closer to saturation, which drastically increases their energy efficiency.