Novel Results for the $\kappa$– $\mu$ Extreme Fading Distribution: Generation of White Samples and Capacity Analysis

Abstract

We provide new analytical results for the κ-µ extreme (κ-µ-E) fading distribution, which is useful to model propagation conditions more severe than Rayleigh fading. First, we calculate a closed-form expression for the cumulative distribution function in terms of the first-order Marcum Q-function, which allows us to accurately generate κ-µ-E distributed random variables using the inversion method. Then, we investigate the ergodic capacity in this scenario. Strikingly, we observe that the capacity in the high-SNR regime scales differently than in all conventional fading models.

Pedestrian-to-Vehicle Communications in an Urban Environment: Channel Measurements and Modeling

“…Surprisingly, in some scenarios the often omitted wing mirror channels were found to suffer less fading than the roof mounted antennas, suggesting that adopting a wing mirror mounted antenna for use in P2V communications may also be valuable. Finally, it is worth remarking that using the simulation technique proposed in [50] for producing κµ Extreme random variables, along with the straightforward generation of the Gaussian large-scale fading and computation of the path loss, the results presented in this work can readily be reproduced for incorporation into ITS network simulations.…”

The Lomax Distribution for Wireless Channel Modeling: Theory and Applications

“…This only happens with the Nakagami-m distribution, if we include the numerical implementation of its ICDF available in MATLAB or Mathematica within the closed-form definition (that's why the corresponding entry in Table II is marked with an asterisk). Even in otherwise tractable distributions such as the Rician and Folded-Normal ones, the CDF inversion needs to be implemented numerically [47].…”

“…• Generation of white samples: The generation of random samples from a target distribution is key for empirically validating statistical results using Monte Carlo (MC) simulations, and a first step towards the generation of correlated random sequences [62]. The use of the inverse transformation method is reportedly more efficient than other alternatives based on acceptance-rejection methods [47,63], but it is only possible when the CDF is invertible. Hence, the closed-form expression for the ICDF in eq.…”