Alternative Formulations for the Fluctuating Two-Ray Fading Model

TL;DR

This paper introduces two new formulations for the fluctuating two-ray (FTR) fading model, simplifying its statistical analysis and enabling easier performance evaluation through connections to Rician Shadowed and Nakagami-m distributions.

Contribution

It provides alternative expressions for the FTR distribution's PDF and CDF, linking it to simpler models for improved analytical tractability and performance analysis.

Findings

New PDF and CDF expressions for FTR model

Performance metrics expressed as finite-range integrals

Simplified analysis using Rician Shadowed and Nakagami-m models

Abstract

We present two alternative formulations for the distribution of the fluctuating two-ray (FTR) fading model, which simplify its statistical characterization and subsequent use for performance evaluation. New expressions for the probability density function (PDF) and cumulative distribution function of the FTR model are obtained based on the observation that the FTR fading distribution is described, for arbitrary $m$, as an underlying Rician Shadowed (RS) distribution with continuously varying parameter $K$, while for the special case of $m$ being an integer, the FTR fading model is described in terms of a finite number of underlying squared Nakagami-$m$ distributions. It is shown that the chief statistics and any performance metric that are computed by averaging over the PDF of the FTR fading model can be expressed in terms of a finite-range integral over the corresponding statistic or performance metric for the RS (for arbitrary $m$) or the Nakagami-$m$ (for integer $m$) fading models, which have a simpler analytical characterization than the FTR model and for which many results are available in closed-form. New expressions for some Laplace-domain statistics of interest are also obtained; these are used to exemplify the practical relevance of this new formulation for performance analysis.