# Self-Supervised Learning of Linear Precoders under Non-Linear PA Distortion for Energy-Efficient Massive MIMO Systems

arXiv: https://arxiv.org/abs/2210.07037 · HTML: https://mlsanity.com/paper/2210.07037/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 22 references that are in the map.
- First posted on arXiv 13 Oct 2022.

## Builds on (most cited first, 8 of 8)

- [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)
- [The exploding gradient problem demystified - definition, prevalence, impact, origin, tradeoffs, and solutions](https://mlsanity.com/paper/1712.05577/) (2017)
- [The Bussgang Decomposition of Non-Linear Systems: Basic Theory and MIMO Extensions](https://mlsanity.com/paper/2005.01597/) (2020)
- [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)

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

- [Toward Energy-Efficient Massive MIMO: Graph Neural Network Precoding for Mitigating Non-Linear PA Distortion](https://mlsanity.com/paper/2312.04591/) (2023)
- [Learning to Quantize and Precode in Massive MIMO Systems for Energy Reduction: a Graph Neural Network Approach](https://mlsanity.com/paper/2507.10634/) (2025)

## Abstract (arXiv)

Massive multiple input multiple output (MIMO) systems are typically designed under the assumption of linear power amplifiers (PAs). However, PAs are typically most energy-efficient when operating close to their saturation point, where they cause non-linear distortion. Moreover, when using conventional precoders, this distortion coherently combines at the user locations, limiting performance. As such, when designing an energy-efficient massive MIMO system, this distortion has to be managed. In this work, we propose the use of a neural network (NN) to learn the mapping between the channel matrix and the precoding matrix, which maximizes the sum rate in the presence of this non-linear distortion. This is done for a third-order polynomial PA model for both the single and multi-user case. By learning this mapping a significant increase in energy efficiency is achieved as compared to conventional precoders and even as compared to perfect digital pre-distortion (DPD), in the saturation regime.