# The Bussgang Decomposition of Non-Linear Systems: Basic Theory and MIMO Extensions

arXiv: https://arxiv.org/abs/2005.01597 · HTML: https://mlsanity.com/paper/2005.01597/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2020.

## Built on by (most cited first, 6 of 6)

- [On the Mean Square Error Optimal Estimator in One-Bit Quantized Systems](https://mlsanity.com/paper/2212.04470/) (2022)
- [SignalNet: A Low Resolution Sinusoid Decomposition and Estimation Network](https://mlsanity.com/paper/2106.05490/) (2021)
- [Design and Analysis of Hardware-limited Non-uniform Task-based Quantizers](https://mlsanity.com/paper/2208.07525/) (2022)
- [Plug-in Channel Estimation with Dithered Quantized Signals in Spatially Non-Stationary Massive MIMO Systems](https://mlsanity.com/paper/2301.04641/) (2023)
- [Self-Supervised Learning of Linear Precoders under Non-Linear PA Distortion for Energy-Efficient Massive MIMO Systems](https://mlsanity.com/paper/2210.07037/) (2022)
- [Differential Deep Detection in Massive MIMO With One-Bit ADC](https://mlsanity.com/paper/2110.14534/) (2021)

## Abstract (arXiv)

Many of the systems that appear in various signal processing applications are non-linear, for example, due to hardware impairments such as non-linear amplifiers and finite-resolution quantization. The Bussgang decomposition is a popular tool for analyzing the performance of systems that involve such non-linear components. In a nutshell, the decomposition provides an exact probabilistic relationship between the output and the input of a non-linearity: the output is equal to a scaled version of the input plus uncorrelated distortion. The decomposition can either be used to compute exact performance results or lower bounds where the uncorrelated distortion is treated as independent noise. This lecture note explains the basic theory, provides key examples, extends the theory to complex-valued vector signals, and clarifies some potential misconceptions.