The Multi-Cluster Fluctuating Two-Ray Fading Model

Abstract

We introduce and characterize the Multi-cluster Fluctuating Two-Ray (MFTR) fading channel, generalizing both the fluctuating two-ray (FTR) and the κ-μ shadowed fading models through a more general yet equally mathematically tractable model. We derive all the chief probability functions of the MFTR model such as probability density function (PDF), cumulative distribution function (CDF), and moment generating function (MGF) 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 κ-μ 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 κ-μ shadowed or Nakagami-m cases, respectively. We demonstrate that the MFTR fading model provides a much better fit than FTR and κ-μ shadowed models for small-scale measurements of channel amplitude in outdoor Terahertz (THz) wireless links. Finally, the performance of wireless communications systems undergoing MFTR fading is exemplified in terms of classical benchmarking metrics like the outage probability, both in exact and asymptotic forms, and the amount of fading.