The Multi-cluster Fluctuating Two-Ray Fading Model

TL;DR

This paper introduces the Multi-cluster Fluctuating Two-Ray (MFTR) fading model, a comprehensive channel model that generalizes existing models and provides closed-form expressions for key probability functions, facilitating performance analysis.

Contribution

The paper presents the MFTR fading model as a new, mathematically tractable generalization of FTR and $ppa$-$mu$ shadowed models, with derived probability functions and analytical formulations.

Findings

Closed-form PDFs, CDFs, and MGFs for MFTR model

Analytical expressions as mixtures of $ppa$-$mu$ shadowed and Gamma distributions

Performance analysis of wireless systems under MFTR fading

Abstract

We introduce a new class of fading channels, built as the superposition of two fluctuating specular components with random phases, plus a clustering of scattered waves: the Multi-cluster Fluctuating Two-Ray (MFTR) fading channel. The MFTR model emerges as a natural generalization of both the fluctuating two-ray (FTR) and the $\kappa$-$\mu$ shadowed fading models through a more general yet equally mathematically tractable model. This generalization enables the presence of additional multipath clusters in the purely ray-based FTR model, and the convenience of the new underlying fading channel model is discussed in depth. Then, we derive all the chief probability functions of the MFTR model (e.g., probability density function (PDF), cumulative density function (CDF), and moment generation function) in closed-form, having {a mathematical complexity similar to} other fading models in the state-of-the-art. We also provide two additional analytical formulations for the PDF and the CDF: (i) in terms of a continuous mixture of $\kappa$-$\mu$ shadowed distributions, and (ii) as an infinite discrete mixture of Gamma distributions. Such expressions enable to conduct performance analysis under MFTR fading by directly leveraging readily available results for the $\kappa$-$\mu$ shadowed or Nakagami-$m$ cases, respectively. The performance of wireless communications systems undergoing MFTR fading is exemplified in terms of a classical benchmarking metric like the outage probability, both in exact and asymptotic forms, and the amount of fading.