The Multi-Cluster Fluctuating Two-Ray Fading Model

• Published in: IEEE transactions on wireless communications Vol. 23; no. 5; pp. 4199 - 4213
• Main Authors: Sanchez, Jose David Vega, Lopez-Martinez, F. Javier, Paris, Jose F., Romero-Jerez, Juan M.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.05.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Analytical models; Channel models; Clusters; Distribution functions; Fading; Fading channels; fluctuating two-ray; Formulations; Generalized fading channels; Mathematical models; Mixtures; moment generating function; multipath propagation; Probability density function; Probability density functions; Rician channels; wireless channel modeling; Wireless communication; Wireless communication systems
• ISSN: 1536-1276; 1558-2248
• DOI: 10.1109/TWC.2023.3315732

We introduce and characterize the Multi-cluster Fluctuating Two-Ray (MFTR) fading channel, generalizing both the fluctuating two-ray (FTR) and the <inline-formula> <tex-math notation="LaTeX">\kappa </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">\mu </tex-math></inline-formula> 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: (<inline-formula> <tex-math notation="LaTeX">{i} </tex-math></inline-formula>) in terms of a continuous mixture of <inline-formula> <tex-math notation="LaTeX">\kappa </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">\mu </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">\kappa </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">\mu </tex-math></inline-formula> shadowed or Nakagami-<inline-formula> <tex-math notation="LaTeX">m </tex-math></inline-formula> cases, respectively. We demonstrate that the MFTR fading model provides a much better fit than FTR and <inline-formula> <tex-math notation="LaTeX">\kappa </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">\mu </tex-math></inline-formula> 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.