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A Tractable Product Channel Model for Line-of-Sight Scenarios

Unai Fernandez-Plazaola, Laureano Moreno-Pozas, F. Javier Lopez-Martinez, José F. Paris, Eduardo Martos-Naya, Juan M. Romero-Jerez

TL;DR

The proposed model shows a higher flexibility when fitting field measurements with respect to conventional approaches based on product distributions with deterministic LOS, together with a more complete physical interpretation of the underlying propagation characteristics.

Abstract

We present a general and tractable fading model for line-of-sight (LOS) scenarios, which is based on the product of two independent and non-identically distributed $κ$-$μ$ shadowed random variables. Simple closed-form expressions for the probability density function, cumulative distribution function and moment-generating function are derived, which are as tractable as the corresponding expressions derived from a product of Nakagami-$m$ random variables. This model simplifies the challenging characterization of LOS product channels, as well as combinations of LOS channels with non-LOS ones. We leverage these results to analyze performance measures of interest in the contexts of wireless powered and backscatter communications, where both forward and reverse links are inherently of LOS nature, as well as in device-to-device communications subject to composite fading. In these contexts, the model shows a higher flexibility when fitting field measurements with respect to conventional approaches based on product distributions with deterministic LOS, together with a more complete physical interpretation of the underlying propagation characteristics.

A Tractable Product Channel Model for Line-of-Sight Scenarios

TL;DR

The proposed model shows a higher flexibility when fitting field measurements with respect to conventional approaches based on product distributions with deterministic LOS, together with a more complete physical interpretation of the underlying propagation characteristics.

Abstract

We present a general and tractable fading model for line-of-sight (LOS) scenarios, which is based on the product of two independent and non-identically distributed - shadowed random variables. Simple closed-form expressions for the probability density function, cumulative distribution function and moment-generating function are derived, which are as tractable as the corresponding expressions derived from a product of Nakagami- random variables. This model simplifies the challenging characterization of LOS product channels, as well as combinations of LOS channels with non-LOS ones. We leverage these results to analyze performance measures of interest in the contexts of wireless powered and backscatter communications, where both forward and reverse links are inherently of LOS nature, as well as in device-to-device communications subject to composite fading. In these contexts, the model shows a higher flexibility when fitting field measurements with respect to conventional approaches based on product distributions with deterministic LOS, together with a more complete physical interpretation of the underlying propagation characteristics.

Paper Structure

This paper contains 20 sections, 6 theorems, 34 equations, 15 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Statistical Characterization
  3. Preliminary results
  4. Main results
  5. Applications
  6. Wireless Powered Communications
  7. Backscatter Communications
  8. RF Modulated Backscatter Systems
  9. Dyadic Backscatter Systems
  10. D2D communications
  11. Numerical Results
  12. Wireless Powered Communications
  13. Backscatter Communications
  14. RF Modulated Backscatter Systems
  15. Dyadic Backscatter Systems
  16. ...and 5 more sections

Key Result

Lemma 1

Let $\gamma$ be a squared $\kappa$-$\mu$ shadowed random variable with mean $\bar{\gamma}$ and shape parameters $\kappa$, $\mu$ and $m$Paris2014. If the parameters $\mu$ and $m$ are restricted to be positive integers, then for any arbitrary non-negative real $\kappa$ the PDF and CDF of $\gamma$ are where $M$ and the set of parameters $\{C_j,m_j,\Omega_j\}_{j=1,...,M}$ are expressed in terms of $\

Figures (15)

  • Figure 1: Normalized power envelope $\mathcal{P}$-distribution for different values of $\kappa$ and $\hat{\kappa}$, with $\mu=1$, $\hat{\mu}=2$, $m=5$ and $\hat{m}=10$. Solid lines correspond to the exact PDF derived from eq. (5) in the paper, markers correspond to Monte Carlo simulations.
  • Figure 2: Normalized power envelope $\mathcal{P}$-distribution for different values of $\mu$ and $\hat{\mu}$, with $\kappa=4$, $\hat{\kappa}=2$, $m=5$, and $\hat{m}=10$. Solid lines correspond to the exact PDF derived from eq. (5) in the paper, markers correspond to Monte Carlo simulations.
  • Figure 3: Normalized power envelope $\mathcal{P}$-distribution for different values of $m$ and $\hat{m}$, with $\mu=1$, $\hat{\mu}=2$, $\kappa=10$ and $\hat{\kappa}=3$. Solid lines correspond to the exact PDF derived from eq. (5) in the paper, markers correspond to Monte Carlo simulations.
  • Figure 4: System Model for Wireless Powered Communications.
  • Figure 5: System Model for RFMB.
  • ...and 10 more figures

Theorems & Definitions (6)

  • Lemma 1: SNR distribution under $\kappa$-$\mu$ shadowed fading with integer parameters Lopez2017
  • Lemma 2: Product of Two Squared Nakagami-$m$ RVs
  • Proposition 1: The $\mathcal{P}$-distribution as a finite mixture of $\Gamma\Gamma$ distributions
  • Proposition 2: CDF of the $\mathcal{P}$-distribution as a finite mixture
  • Proposition 3: MGF of the $\mathcal{P}$-distribution as a finite mixture
  • Proposition 4: Central moments of the $\mathcal{P}$-distribution