Simulating generalized fading channels

## Project description

## Simulation of generalized fading channels in Python

Let’s say you have a complicated density function for which there is no implementation in `Scipy`, e.g., Yacoub’s Kappa-Mu.
Don’t worry, **maoud** got you covered:

import numpy as np import scipy.special as sps def kappa_mu_pdf(x, kappa, mu): return (2.0 * mu * np.power(1.0 + kappa, (mu + 1.0) / 2.0) * np.power(x, mu) * np.exp(-mu * (1.0 + kappa) * x * x - mu * kappa + 2 * x * mu * np.sqrt(kappa * (1.0 + kappa))) * sps.ive(mu - 1, 2 * mu * x * np.sqrt(kappa * (1.0 + kappa))) / (np.power(kappa, (mu - 1.0) / 2.0)))

Then you want to do the following in order to draw samples:

from maoud.sampling import rejection_sampling n_samples = int(1e6) kappa = 0.75 mu = 0.87 low = 1e-6 high = 3 kappa_mu_samples, af = rejection_sampling(kappa_mu_pdf, low, high, n_samples, kappa, mu)

To verify that the samples are in accordance with Yacoub’s Kappa-Mu density, let’s plot the histogram of the samples:

import matplotlib.pyplot as plt x = np.linspace(1e-6, 3, 1000) y = kappa_mu_pdf(x, kappa, mu) plt.plot(x, y) plt.hist(kappa_mu_samples, bins=50, normed=True)

SHAZAM!!

## Citation

If you made use of the code available in this repository, please consider citing the following work:

@ARTICLE{7986939, author={J. V. M. Cardoso and W. J. L. Queiroz and H. Liu and M. S. Alencar}, journal={Tsinghua Science and Technology}, title={On the performance of the energy detector subject to impulsive noise in κ—μ, α—μ, and η—μ fading channels}, year={2017}, volume={22}, number={4}, pages={360-367}, doi={10.23919/TST.2017.7986939}, month={Aug},}

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