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The α-κ-μ Shadowed Fading Distribution: Statistical Characterization and Applications

Pablo Ramirez-Espinosa, Jules M. Moualeu, Daniel Benevides da Costa, F. Javier Lopez-Martinez

Abstract

We introduce the α-κ-μ shadowed (α-KMS) fading distribution as a natural generalization of the versatile α-κ-μ and α-η-μ distributions. The α-KMS fading distribution unifies a wide set of fading distributions, as it includes the α-κ-μ, α- η-μ, α-μ, Weibull, κ-μ shadowed, Rician shadowed, κ-μ and η- μ distributions as special cases, together with classical models like Rice, Nakagami-m, Hoyt, Rayleigh and one-sided Gaussian. Notably, the α-KMS distribution reduces to a finite mixture of α-μ distributions when the fading parameters μ and m take positive integer values, so that performance analysis over α-KMS fading channels can be tackled by leveraging previous (existing) results in the literature for the simpler α-μ case. As application examples, important performance metrics like the outage probability and average channel capacity are analyzed.

The α-κ-μ Shadowed Fading Distribution: Statistical Characterization and Applications

Abstract

We introduce the α-κ-μ shadowed (α-KMS) fading distribution as a natural generalization of the versatile α-κ-μ and α-η-μ distributions. The α-KMS fading distribution unifies a wide set of fading distributions, as it includes the α-κ-μ, α- η-μ, α-μ, Weibull, κ-μ shadowed, Rician shadowed, κ-μ and η- μ distributions as special cases, together with classical models like Rice, Nakagami-m, Hoyt, Rayleigh and one-sided Gaussian. Notably, the α-KMS distribution reduces to a finite mixture of α-μ distributions when the fading parameters μ and m take positive integer values, so that performance analysis over α-KMS fading channels can be tackled by leveraging previous (existing) results in the literature for the simpler α-μ case. As application examples, important performance metrics like the outage probability and average channel capacity are analyzed.

Paper Structure

This paper contains 13 sections, 4 theorems, 18 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Physical Model -- $\alpha$-KMS Fading Distribution
  3. Statistical Characterization
  4. Definitions
  5. Chief Probability Functions
  6. Integer values of $\mu$ and $m$
  7. Applications
  8. Outage probability
  9. Average channel capacity
  10. Numerical Results
  11. Effect of fading parameters
  12. Performance analysis
  13. Conclusion

Key Result

Lemma 1

Let $\gamma$ be a real RV characterizing the instantaneous SNR under $\alpha$-KMS fading, with $\overline\gamma=\mathbb{E}[\gamma]$ and non-negative real shape parameters $\alpha$, $\kappa$, $\mu$ and $m$, i.e. $\gamma\sim\mathcal{A}_{kms}\left(\overline{\gamma}; \alpha,\kappa,\mu,m\right)$. Then, i where $_1{F}_1(\cdot)$ is the confluent hypergeometric function Abra72 and with ${}_2F_1(\cdot)$ d

Figures (6)

  • Figure 1: Evaluation of the $\alpha$-KMS fading PDF for different values of $\alpha$, with $\overline\gamma=1$ (i.e., 0 dB). Parameter values are $\kappa=3$, $\mu=3.2$ and $m=7.3$.
  • Figure 2: Evaluation of the $\alpha$-KMS fading PDF for different values of $\kappa$. Solid lines correspond to the $m>\mu$ case, with $\overline\gamma=1$ (i.e., 0 dB) and parameter values $\alpha=2.3$, $\mu=1.8$ and $m=5.5$. Dashed lines correspond to the $m<\mu$ case, with $\overline\gamma=2$ (i.e., 3 dB) and parameter values $\alpha=2.3$, $\mu=5.5$ and $m=1.8$.
  • Figure 3: Evaluation of the $\alpha$-KMS fading PDF for different values of $\mu$, with $\overline\gamma=1$ (i.e., 0 dB). Parameter values are $\alpha=1.8$, $\kappa=4$ and $m=6$.
  • Figure 4: Evaluation of the $\alpha$-KMS fading PDF for different values of $m$, with $\overline\gamma=1$ (i.e., 0 dB). Parameter values are $\alpha=2.1$, $\kappa=5$ and $\mu=3$.
  • Figure 5: Outage probability vs. normalized $\overline{\gamma}$ for $\alpha$-KMS fading with $\kappa = 3.1$, $\mu = 3$, $m = 2$ and different values of $\alpha$.
  • ...and 1 more figures

Theorems & Definitions (5)

  • Definition 1: $\alpha$-$\mu$ distribution
  • Lemma 1: The $\alpha$-KMS distribution: PDF
  • Lemma 2: The $\alpha$-KMS distribution: CDF
  • Lemma 3: The $\alpha$-KMS distribution: Moments
  • Lemma 4: The $\alpha$-KMS distribution with integer $\mu$ and $m$