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The Multi-cluster Two-Wave Fading Model

Maryam Olyaee, Juan P. Pena-Martin, F. J. Lopez-Martinez, Juan M. Romero-Jerez

TL;DR

The newly proposed model, referred to as the Multi-cluster Two-Wave (MTW) fading model, generalizes both the TWDP and the kappa-mu models under a common umbrella, aimed to model harsh fading conditions reported in experimental measurements obtained in enclosed environments.

Abstract

We introduce and characterize the Multi-cluster Two-Wave (MTW) fading model, which generalizes \textit{both} the Durgin's Two-Wave with Diffuse Power (TWDP) and the $κ$-$μ$ models under a common umbrella. The MTW model consists of an arbitrary number of clusters of waves each of which may include one or two dominant (specular) components. The chief probability functions of the MTW fading model are obtained, including the probability density function, the cumulative distribution function and the generalized moment-generating function. \textcolor{black}{The proposed model is empirically validated using channel measurements in the sub-THz band and} a number of applications are exemplified, including the outage probability in noise-limited and interference-limited scenarios and the energy detection probability. %Exact expressions for the outage capacity are also obtained. A composite Inverse Gamma (IG)/MTW model is also investigated, thus extending the proposed propagation model to include shadowing.

The Multi-cluster Two-Wave Fading Model

TL;DR

The newly proposed model, referred to as the Multi-cluster Two-Wave (MTW) fading model, generalizes both the TWDP and the kappa-mu models under a common umbrella, aimed to model harsh fading conditions reported in experimental measurements obtained in enclosed environments.

Abstract

We introduce and characterize the Multi-cluster Two-Wave (MTW) fading model, which generalizes \textit{both} the Durgin's Two-Wave with Diffuse Power (TWDP) and the - models under a common umbrella. The MTW model consists of an arbitrary number of clusters of waves each of which may include one or two dominant (specular) components. The chief probability functions of the MTW fading model are obtained, including the probability density function, the cumulative distribution function and the generalized moment-generating function. \textcolor{black}{The proposed model is empirically validated using channel measurements in the sub-THz band and} a number of applications are exemplified, including the outage probability in noise-limited and interference-limited scenarios and the energy detection probability. %Exact expressions for the outage capacity are also obtained. A composite Inverse Gamma (IG)/MTW model is also investigated, thus extending the proposed propagation model to include shadowing.
Paper Structure (15 sections, 7 theorems, 50 equations, 9 figures, 1 table)

This paper contains 15 sections, 7 theorems, 50 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. MTW channel model
  3. Probability distribution (PDF and CDF)
  4. Generalized moment generating function
  5. Asymptotic CDF and diversity order
  6. Empirical Validation
  7. Applications to wireless communication systems
  8. Outage probability
  9. Outage probability in interference-limited scenarios
  10. Average energy detection probability
  11. Composite IG/MTW Fading Model
  12. Numerical results
  13. Conclusions
  14. Proof of Lemma 2
  15. Proof of Lemma 3

Key Result

Lemma 1

Let $\gamma$ represent the received SNR in an MTW fading channel. Then, the PDF of $\gamma$ is given by (eq:019).

Figures (9)

  • Figure 1: Empirical vs. theoretical PDFs for the scenarios listed in Table \ref{['Tablefit']}.
  • Figure 2: Analysis and simulation results for the PDF of SNR under the MTW fading model with parameters $K=1$, $\bar{\gamma} = 1$, $N=1$, $\Delta= 0.8$ and different values of $\mu = 2,5,10,50$.
  • Figure 3: Analysis and simulation results for the CDF of SNR under the MTW fading model with parameters $K=1$, $\bar{\gamma} = 1$, $N=1$, $\Delta= 0.8$ and different values of $\mu = 2,5,10,50$.
  • Figure 4: Analysis and simulation results for the PDF of SNR under the MTW fading model with parameters $K=15$, $\bar{\gamma} = 1$, $\mu= 10$ and different values of $N$ and $\Delta = \left[ {\Delta _1 , \ldots ,\Delta _N } \right]$.
  • Figure 5: Analysis and simulation results for the CDF of SNR under the MTW fading model with parameters $K=15$, $\bar{\gamma} = 1$, $\mu= 10$ and different values of $N$ and $\Delta = \left[ {\Delta _1 , \ldots ,\Delta _N } \right]$.
  • ...and 4 more figures

Theorems & Definitions (7)

  • Lemma 1
  • Corollary 1
  • Lemma 2
  • Lemma 3
  • Corollary 2
  • Corollary 3
  • Corollary 4