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Statistical characterization of kappa-mu shadowed fading

J. F. Paris

TL;DR

It is shown that the sum and maximum distributions of independent but arbitrarily distributed κ - μ shadowed variates can be expressed in closed form and this set of new statistical results is finally applied to modeling and analysis of several wireless communication systems, e.g., the proposed distribution has applications to land mobile satellite (LMS) communications and underwater acoustic communications (UAC).

Abstract

This paper investigates a natural generalization of the kappa-mu fading channel in which the line-of-sight (LOS) component is subject to shadowing. This fading distribution has a clear physical interpretation, good analytical properties and unifies the one-side Gaussian, Rayleigh, Nakagami-m, Ricean, kappa-mu and Ricean shadowed fading distributions. The three basic statistical characterizations, i.e. probability density function (PDF), cumulative distribution function (CDF) and moment generating function (MGF), of the kappa-mu shadowed distribution are obtained in closed-form. Then, it is also shown that the sum and maximum distributions of independent but arbitrarily distributed kappa-mu shadowed variates can be expressed in closed-form. This set of new statistical results is finally applied to the performance analysis of several wireless communication systems.

Statistical characterization of kappa-mu shadowed fading

TL;DR

It is shown that the sum and maximum distributions of independent but arbitrarily distributed κ - μ shadowed variates can be expressed in closed form and this set of new statistical results is finally applied to modeling and analysis of several wireless communication systems, e.g., the proposed distribution has applications to land mobile satellite (LMS) communications and underwater acoustic communications (UAC).

Abstract

This paper investigates a natural generalization of the kappa-mu fading channel in which the line-of-sight (LOS) component is subject to shadowing. This fading distribution has a clear physical interpretation, good analytical properties and unifies the one-side Gaussian, Rayleigh, Nakagami-m, Ricean, kappa-mu and Ricean shadowed fading distributions. The three basic statistical characterizations, i.e. probability density function (PDF), cumulative distribution function (CDF) and moment generating function (MGF), of the kappa-mu shadowed distribution are obtained in closed-form. Then, it is also shown that the sum and maximum distributions of independent but arbitrarily distributed kappa-mu shadowed variates can be expressed in closed-form. This set of new statistical results is finally applied to the performance analysis of several wireless communication systems.

Paper Structure

This paper contains 15 sections, 7 theorems, 33 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Physical Model
  3. Fundamental Statistics
  4. Sum and Maximum Distributions
  5. Sum distribution
  6. Maximum distribution
  7. Performance Analysis of Wireless Communication Systems
  8. Selection combining with $\kappa$-$\mu$ shadowed fading
  9. Maximal ratio combining with $\kappa$-$\mu$ shadowed fading
  10. Conclusions
  11. Proof of Lemma I
  12. Proof of Lemma II
  13. Proof of Proposition I
  14. Proof of Lemma IV
  15. Numerical computation of the functions $\Phi_2$ and $F_D$

Key Result

Lemma 1

Let $\gamma\sim{\mathcal{S}}_{\kappa\mu}(\bar{\gamma};\kappa,\mu, m)$, then, its PDF is given by where $_1F_1(\cdot)$ is the confluent hypergeometric function Gradstein2007.

Figures (4)

  • Figure 1: PDF of the $\kappa$-$\mu$ shadowed distribution ($\bar{\gamma}=1$).
  • Figure 2: Outage probability versus average SNR per branch over $\kappa$-$\mu$ shadowed fading channels. A triple-branch SC scenario is considered, with parameters $\bar{\gamma}_1=\bar{\gamma}_2=\bar{\gamma}_3=\bar{\gamma}$, $\kappa_1=1.2$, $\kappa_2=2.7$, $\kappa_3=3.1$, $\mu_1=4$, $\mu_2=2$, $\mu=1$ and $m_1=m_2=m_3=m$.
  • Figure 3: Outage probability versus average SNR per branch in $\kappa$-$\mu$ shadowed fading channels. A triple-branch MRC scenario is considered, with parameters $\bar{\gamma}_1=\bar{\gamma}_2=\bar{\gamma}_3=\bar{\gamma}$, $\kappa_1=1.2$, $\kappa_2=2.7$, $\kappa_3=3.1$, $\mu_1=4$, $\mu_2=2$, $\mu=1$ and $m_1=m_2=m_3=m$.
  • Figure 4: Bit error rate versus average SNR per branch in $\kappa$-$\mu$ shadowed fading channels. In this plot BPSK modulation and triple-branch MRC are considered, with parameters $\bar{\gamma}_1=\bar{\gamma}_2=\bar{\gamma}_3=\bar{\gamma}$, $\kappa_1=1.2$, $\kappa_2=2.7$, $\kappa_3=3.1$, $\mu_1=4$, $\mu_2=2$, $\mu=1$ and $m_1=m_2=m_3=m$.

Theorems & Definitions (14)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Proposition 1
  • proof
  • Lemma 4
  • proof
  • ...and 4 more