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The Second Order Scattering Fading Model with Fluctuating Line-of-Sight

Jesus Lopez-Fernandez, Gonzalo J. Anaya-Lopez, F. Javier Lopez-Martinez

Abstract

We present a generalization of the notoriously unwieldy second-order scattering fading model, which is helpful to alleviate its mathematical complexity while providing an additional degree of freedom. This is accomplished by allowing its dominant specular component associated to line-of-sight propagation to randomly fluctuate. The statistical characterization of the newly proposed model is carried out, providing closed-form expressions for its probability and cumulative distribution functions, as well as for its generalized Laplace-domain statistics and raw moments. We exemplify how performance analysis can be done in this scenario, and discuss the role of the fading model parameters on system performance.

The Second Order Scattering Fading Model with Fluctuating Line-of-Sight

Abstract

We present a generalization of the notoriously unwieldy second-order scattering fading model, which is helpful to alleviate its mathematical complexity while providing an additional degree of freedom. This is accomplished by allowing its dominant specular component associated to line-of-sight propagation to randomly fluctuate. The statistical characterization of the newly proposed model is carried out, providing closed-form expressions for its probability and cumulative distribution functions, as well as for its generalized Laplace-domain statistics and raw moments. We exemplify how performance analysis can be done in this scenario, and discuss the role of the fading model parameters on system performance.
Paper Structure (9 sections, 4 theorems, 32 equations, 3 figures)

This paper contains 9 sections, 4 theorems, 32 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Physical model
  3. Statistical Characterization
  4. Numerical results
  5. Conclusions
  6. Proof of Lemma \ref{['lemma1']}
  7. Proof of Lemma \ref{['lemma2']}
  8. Proof of Lemma \ref{['lemma3']}
  9. Proof of Lemma \ref{['lemma4']}

Key Result

Lemma 1

Let $\gamma$ be an fSOSF-distributed RV with shape parameters $\{\alpha,\beta,m\}$, i.e., $\gamma\sim\mathcal{F}_{\rm SOSF}\left(\alpha,\beta,m;\overline\gamma\right)$. Then, the PDF of $\gamma$ is given by for $m\in\mathbb{R}^+$ and $m\in\mathbb{Z}^+$, respectively, and where $_1F_{1}\left(\cdot;\cdot;\cdot\right)$ and $\Gamma(a,z,b)=\int_{z}^{\infty}t^{a-1} e^{-t}e^{\tfrac{-b}{t}}dt$ are Kummer

Figures (3)

  • Figure 1: PDF of fSOSF model for different values of $m$. Parameter values are $\alpha=0.1$, $\beta=0.7$ and $\overline{\gamma}_{\rm dB}=3$dB. Theoretical values (\ref{['Eq_PDF']}) are represented with lines. Markers correspond to MC simulations.
  • Figure 2: PDF comparison for different values of $\alpha$ and $\beta$. Solid/dashed lines obtained with (\ref{['Eq_PDF']}) correspond to ($m=1$, $\overline{\gamma}_{\rm dB}=5$dB) and ($m=20$, $\overline{\gamma}_{\rm dB}=1$dB), respectively. Markers correspond to MC simulations.
  • Figure 3: OP as a function of $\overline\gamma$, for different values of $m$. Parameter values are $\alpha=0.1$ and $\beta=0.7$. Solid/dashed lines correspond to $\gamma_{\rm th}=3$ and $\gamma_{\rm th}=1$ respectively. Theoretical values (\ref{['Eq_OP']}) are represented with lines. Markers correspond to MC simulations.

Theorems & Definitions (8)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof