Ultra-Reliable Communications in Two-Ray Ground Reflection Scenarios

This repository is accompanying the paper "An Efficient Frequency Diversity Scheme for Ultra-Reliable Communications in Two-Path Fading Channels" (K.-L. Besser, E. Jorswieck, J. Coon, Journal of Communications and Networks, 2024. arXiv:2206.13459).

The idea is to give an interactive version of the calculations and presented concepts to the reader. One can also change different parameters and explore different behaviors on their own.

File List

The following files are provided in this repository:

run.sh: Bash script that reproduces the figures presented in the paper.
Ultra-Reliability Two-Ray Ground Reflection.ipynb: Jupyter notebook that contains interactive plots of most of the results shown in the paper.
util.py: Python module that contains utility functions, e.g., for saving results.
model.py: Python module that contains utility functions around the two-ray ground reflection model.
single_frequency.py: Python module that contains the functions to calculate the receive power when a single frequency is used.
two_frequencies.py: Python module that contains the functions to calculate the receive power when two frequencies are used in parallel.
optimal_frequency_distance.py: Python module that contains the algorithm to calculate the optimal frequency spacing for worst-case design.
rate_comparison.py: Python module that contains the functions to calculate the achievable rates for the different scenarios.
outage_probability.py: Python module that contains the functions to estimate the outage probabilities.
uav_example.py: Python module that contains the UAV example.

Usage

Running it online

The easiest way is to use services like Binder to run the notebook online. Simply navigate to https://mybinder.org/v2/gh/klb2/two-ray-ultra-reliability/HEAD to run the notebooks in your browser without setting everything up locally.

Local Installation

If you want to run it locally on your machine, Python3 and Jupyter are needed. The present code was developed and tested with the following versions:

Python 3.10
Jupyter 1.0
numpy 1.22
scipy 1.8
sdeint 0.2.4

Make sure you have Python3 installed on your computer. You can then install the required packages (including Jupyter) by running

pip3 install -r requirements.txt
jupyter nbextension enable --py widgetsnbextension

This will install all the needed packages which are listed in the requirements file. The second line enables the interactive controls in the Jupyter notebooks.

Finally, you can run the Jupyter notebooks with

jupyter notebook

You can also recreate the figures from the paper by running

bash run.sh

Acknowledgements

This research was supported by the German Research Foundation (DFG) under grant BE 8098/1-1, by the Federal Ministry of Education and Research Germany (BMBF) through the Program of "Souverän. Digital. Vernetzt." Joint Project 6G-Research and Innovation Cluster (RIC) under grant 16KISK031, and by the EPSRC under grant number EP/T02612X/1.

License and Referencing

This program is licensed under the GPLv3 license. If you in any way use this code for research that results in publications, please cite our original article listed above.

You can use the following BibTeX entry

@article{Besser2024tworay,
  title = {An Efficient Frequency Diversity Scheme for Ultra-Reliable Communications in Two-Path Fading Channels},
  author = {Besser, Karl-Ludwig and Jorswieck, Eduard A. and Coon, Justin P.},
  year = {2024},
  journal = {Journal of Communications and Networks},
  archiveprefix = {arXiv},
  eprint = {2206.13459},
  primaryClass = {cs.IT},
}