Behavioral LED model in MATLAB

This GitHub repository contains a ready-to-use implementation of a behavioral model for Light Emitting Diode (LED) nonlinearity in MATLAB. The model is based on two filters and was detailed in the paper:

Juliusz Bojarczuk, Michal Marzecki, Di Sun, Zuxin Jin, Pengfei Tian and Grzegorz Stepniak, "A Behavioral Model of the Light Emitting Diode Nonlinearity", IEEE Transactions on Communications, may 2025.

When using the behavioral LED model, please remember to support our work by citing the aforementioned paper in your article.

Sample MATLAB Scripts (on how to use behavioral model in your code)

This repository contains three MATLAB scripts that serve as examples: - TransmitThroughModel.m - EyediagramForSampleData.m - PlotKernels.m

TransmitThroughModel

(1) Suppose that you have measured LED 3dB bandwidth ($fB$,ledBandwidth3dB) and is equal to 45 MHz.\ (2) For the same frequency, you have generated sinusoidal signal with amplitude $Ia$ and measured fundamental harmonic power at the receiver as $P{h1}(2\pi fB)$. Electrical to optical conversion factor ($\eta$, eta) is equal to exactly $\frac{2\sqrt{P{h1}(2\pi fB)}}{Ia}$. For our case it will be 0.02.\ (3a) Next, you drive the LED again with harmonic signal with amplitude $Ia$ and frequency equal to $fB$. However you calculate the power ratio of the second harmonic ($2fB$) to fundamental one ($fB$) at the receiver and treat this ratio as $P{r1}$.\ (3b) We need the second measurement point for obtaining model parameters. Thus, you drive the LED with harmonic signal with amplitude $Ia$ and frequency equal to $\frac{1}{2} fB$. Obtained power ratio of the second harmonic ($fB$) to fundamental one ($frac{1}{2}fB$) at the receiver is $P{r2}$.\ (4) Nonlinearity factor $\Gamma$ is equal to exactly $\sqrt{\frac{160}{3 Ia^2 \eta^2} \left ( P{r2}-P{r1} \right)}$, while cutoff frequency of second filter $2\pi fA$ is equal to $\sqrt{4\omegaB^2\frac{P{r2}-P{r1}}{4P{r1}-P{r2}}}$.[^1].

[^1]: Each parameter is described in detail in the main paper, and a brief overview can be found in the ledbehavioral.m.

For this case, you can set LED model parameters as follows:

Matlab % Set parameters of LED model ledBandwidth3dB = 45e6; fA = 11e6; eta = 0.02; lengthOfLedResponse = 50; gamma = 10;

You can use our pre-generated PAM-4 signal, which will be put into LED transmission function:

Matlab % Load symbols xInput = readmatrix('Sample data\example_PAM4_UF4_Alfa1_FilterSpan20.txt');

Suppose that you want to send 100 MBaud/s signal with amplitude coefficient equal to 1.2.

Matlab % Signal parameters baudRate = 100e6; upsamplingFactor = 4; samplingFrequency = baudRate*upsamplingFactor; signalAmplitudeCoefficient = 1.2;

To pass the pregenerated PAM-4 signal through LED mode use this code:

Matlab xOutput = ledbehavioral(xInput*signalAmplitudeCoefficient, ledBandwidth3dB, fA, gamma, eta, samplingFrequency, lengthOfLedResponse);

EyediagramForSampleData

This script is used for plotting and comparing the output signal from the rate equation-based LED model with the proposed behavioral model.

PlotKernels

Script for plotting 2nd order Volterra kernels for OSRAM W5SN white LED for 50 and 200 mA bias estimated from 100 MBaud/s PAM-4 signal.

Measurement Data

Functions

System Requirements

The functions and scripts have been tested in MATLAB R2022b.

Contact

• E-mail: grzegorz.stepniak@pw.edu.pl or juliusz.bojarczuk@pw.edu.pl
• Institute of Telecommunications, Warsaw University of Technology

Acknowledgments

This work was supported by National Centre for Research and Development under grant USVEGAN no. WPC2/20/USVEGAN/2019.

License

Original source code assets present in this repository are licensed under the GNU LGPLv3.