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Outage performance of the $α$-Beaulieu-Xie Shadowed Fading Channel Model

Aleksey S. Gvozdarev

TL;DR

This work derives closed-form outage analysis for the α-modified Beaulieu-Xie shadowed fading channel, including the instantaneous SNR pdf and cdf (and their bounds), arbitrary-order SNR moments, amount of fading (AoF), and channel quality estimation indicator (CQEI). It further provides an explicit outage probability expression involving Appell functions and establishes high-SNR bounds to illuminate asymptotic behavior. A joint quality-reliability analysis is proposed to balance reliability and error performance, demonstrated with CQEI and outage metrics. Numerical simulations validate the analytical results and reveal how parameters such as the nonlinearity coefficient $\alpha$, fading parameters $m_X,m_Y$, and power terms $\Omega_X,\Omega_Y$ shape outage performance, offering practical insights for THz/FSO system design.

Abstract

The research presents the closed-form outage analysis of the newly presented $α$-modification of the shadowed Beaulieu-Xie fading model for wireless communications. For the considered channel, the closed-form analytical expressions for the outage probability (including its upper and lower bounds), raw moments, amount of fading, and channel quality estimation indicator are derived. The carried out thorough numerical simulation and analysis demonstrates strong agreement with the presented closed-form solutions and illustrates the relationship between the outage probability and channel parameters.

Outage performance of the $α$-Beaulieu-Xie Shadowed Fading Channel Model

TL;DR

This work derives closed-form outage analysis for the α-modified Beaulieu-Xie shadowed fading channel, including the instantaneous SNR pdf and cdf (and their bounds), arbitrary-order SNR moments, amount of fading (AoF), and channel quality estimation indicator (CQEI). It further provides an explicit outage probability expression involving Appell functions and establishes high-SNR bounds to illuminate asymptotic behavior. A joint quality-reliability analysis is proposed to balance reliability and error performance, demonstrated with CQEI and outage metrics. Numerical simulations validate the analytical results and reveal how parameters such as the nonlinearity coefficient , fading parameters , and power terms shape outage performance, offering practical insights for THz/FSO system design.

Abstract

The research presents the closed-form outage analysis of the newly presented -modification of the shadowed Beaulieu-Xie fading model for wireless communications. For the considered channel, the closed-form analytical expressions for the outage probability (including its upper and lower bounds), raw moments, amount of fading, and channel quality estimation indicator are derived. The carried out thorough numerical simulation and analysis demonstrates strong agreement with the presented closed-form solutions and illustrates the relationship between the outage probability and channel parameters.
Paper Structure (11 sections, 5 theorems, 3 equations, 6 figures)

This paper contains 11 sections, 5 theorems, 3 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Channel model
  3. Classical Beaulieu-Xie shadowed model
  4. $\alpha$-modification of the Beaulieu-Xie shadowed model: prior work
  5. $\alpha$-Beaulieu-Xie shadowed model: new derived results
  6. SNR raw moments
  7. Amount of fading and channel quality estimation index
  8. Outage probability
  9. Joint quality-reliability analysis
  10. Simulation and results
  11. Conclusion

Key Result

Lemma 1

The basic probabilistic description of the $\alpha$-BX-shadowed channel with arbitrary parameters ($m_X, m_Y, \Omega_X, \Omega_Y, \alpha \geq 0$), including pdf $f_{\gamma }(\gamma )$ and cdf $F_{\gamma }(\gamma )$ of the instantaneous SNR $\gamma$ are given in the following form: where $\bar{\gamma }$ is the expected value of the instantaneous SNR, $\Phi_2( \cdot )$ is the bivariate confluent

Figures (6)

  • Figure 1: Outage probability for various fading scenarios: solid lines - proposed analytical expression \ref{['eq:8']}, densely dashed - upper bound \ref{['eq:9']}, loosely dashed - lower bound \ref{['eq:9']}, markers - numeric simulation.
  • Figure 2: $\mathrm{P_{out}}$ versus $\alpha$ for $\gamma_{th}=3$ dB, $\bar{\gamma }=10$ dB, $\Omega_X=5$ dB, $\Omega_Y=-5$ dB: solid lines - $m_Y=2.5$, dashed lines - $m_Y=0.5$.
  • Figure 3: $\mathrm{P_{out}}$ versus $\Omega_X$ for $\gamma_{th}=3$ dB, $\bar{\gamma }=10$ dB, $\alpha=3.5$: solid lines - $m_X=0.2, m_Y=0.5$, dashed lines - $m_X=2.2, m_Y=0.5$.
  • Figure 4: $\mathrm{P_{out}}$ versus CQEI for $\gamma_{th}=10$ dB: solid lines - $\Omega_X=\Omega_Y=0$ dB and $m_X=m_Y=0.5$, dashed lines - $\Omega_X=\Omega_Y=5$ dB and $m_X=m_Y=3$.
  • Figure 5: Amount of fading contour map for various $m_X, m_Y$ with $\alpha=4$, $\Omega_X=\Omega_Y=5$ dB, yellow dashed line - AoF for Rayleigh channel.
  • ...and 1 more figures

Theorems & Definitions (5)

  • Lemma 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Corollary 4.1