GFGE: From Gaussian Fading to Gilbert-Elliott

Code and paper for "From Gaussian Fading to Gilbert-Elliott: Bridging Physical and Link-Layer Channel Models in Closed Form" by Bhaskar Krishnamachari and Victor Gutierrez, University of Southern California.

Paper: modeling_coherence_time_dynamic_wireless_channels.pdf

Summary

This paper provides an exact, closed-form bridge between two ubiquitous wireless channel models:

• Physical layer: correlated Gaussian fading process (e.g., log-normal shadow fading)
• Link layer: Gilbert-Elliott (GE) two-state Markov chain

By thresholding the Gaussian process at discrete slot boundaries, we derive GE transition probabilities via Owen's T-function for any threshold, reducing to an elementary arcsine identity when the threshold equals the mean. The bridge reveals that the GE persistence time grows linearly in the correlation length for smooth (squared-exponential) kernels but only as the square root for rough (exponential/Ornstein-Uhlenbeck) kernels.

Figures

The script generate_ge_figures.py produces all figures from the paper:

Figure	Description
fig_paths	Sample paths from squared-exponential and exponential kernels
fig_transition_probs	GE transition probability p01 vs. coherence time
fig_empirical_vs_theory	Exact theory vs. asymptotic approximations vs. Monte Carlo (symmetric threshold)
fig_empirical_vs_theory_multithreshold	Multi-threshold comparison (S/sigma in {0, 0.5, 1.0, 1.5})
fig_markov_gap	Markov gap and run-length TV distance diagnostics
fig_ge_vs_bernoulli	Run-length distributions: GE vs. second-order Markov vs. empirical
fig_asymmetric_dual_kernel	Asymmetric transition probabilities and dwell times for non-zero thresholds

Requirements

• Python 3.8+
• NumPy
• SciPy
• Matplotlib

Install dependencies:

pip install numpy scipy matplotlib

Usage

Generate all figures (PDF and PNG) and summary tables:

python generate_ge_figures.py

This produces 7 figure files (each as .pdf and .png), plus ge_empirical_vs_theory_summary.csv, summary_table.csv, and summary_table.tex.

Citation

If you use this code in your research, please cite:

B. Krishnamachari and V. Gutierrez, "From Gaussian Fading to Gilbert-Elliott:
Bridging Physical and Link-Layer Channel Models in Closed Form," 2026.

License

This project is licensed under the PolyForm Noncommercial License 1.0.0.