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A Tractable Statistical Representation of IFTR Fading with Applications

Maryam Olyaee, Hadi Hashemi, Juan M. Romero-Jerez

TL;DR

A new formulation of the IFTR model is presented as a countable mixture of Gamma distributions which greatly facilitates the performance evaluation for this model in terms of the metrics already known for the much simpler and widely used Nakagami-m fading, and is shown to provide a better fit to empirical measurements than the original formulation.

Abstract

The recently introduced independent fluctuating two-ray (IFTR) fading model, consisting of two specular components fluctuating independently plus a diffuse component, has proven to provide an excellent fit to different wireless environments, including the millimeter-wave band. However, the original formulations of the probability density function (PDF) and cumulative distribution function (CDF) of this model are not applicable to all possible values of its defining parameters, and are given in terms of multifold generalized hypergeometric functions, which prevents their widespread use for the derivation of performance metric expressions. In this paper we present a new formulation of the IFTR model as a countable mixture of Gamma distributions which greatly facilitates the performance evaluation for this model in terms of the metrics already known for the much simpler and widely used Nakagami-m fading. Additionally, a closed-form expression is presented for the generalized moment generating function (GMGF), which permits to readily obtain all the moments of the distribution of the model, as well as several relevant performance metrics. Based on these new derivations, the IFTR model is evaluated for the average channel capacity, the outage probability with and without co-channel interference, and the bit error rate (BER), which are verified by Monte Carlo simulations.

A Tractable Statistical Representation of IFTR Fading with Applications

TL;DR

A new formulation of the IFTR model is presented as a countable mixture of Gamma distributions which greatly facilitates the performance evaluation for this model in terms of the metrics already known for the much simpler and widely used Nakagami-m fading, and is shown to provide a better fit to empirical measurements than the original formulation.

Abstract

The recently introduced independent fluctuating two-ray (IFTR) fading model, consisting of two specular components fluctuating independently plus a diffuse component, has proven to provide an excellent fit to different wireless environments, including the millimeter-wave band. However, the original formulations of the probability density function (PDF) and cumulative distribution function (CDF) of this model are not applicable to all possible values of its defining parameters, and are given in terms of multifold generalized hypergeometric functions, which prevents their widespread use for the derivation of performance metric expressions. In this paper we present a new formulation of the IFTR model as a countable mixture of Gamma distributions which greatly facilitates the performance evaluation for this model in terms of the metrics already known for the much simpler and widely used Nakagami-m fading. Additionally, a closed-form expression is presented for the generalized moment generating function (GMGF), which permits to readily obtain all the moments of the distribution of the model, as well as several relevant performance metrics. Based on these new derivations, the IFTR model is evaluated for the average channel capacity, the outage probability with and without co-channel interference, and the bit error rate (BER), which are verified by Monte Carlo simulations.
Paper Structure (14 sections, 5 theorems, 54 equations, 8 figures, 1 table)

This paper contains 14 sections, 5 theorems, 54 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminary definitions and channel model
  3. New representation of the fading model
  4. and of IFTR fading
  5. Series convergence and Kolmogorov-Smirnov goodness-of-fit statistical test
  6. GMGF and moments of the IFTR model
  7. Performance analysis
  8. Average channel capacity
  9. Outage probability in interference-limited multi-antenna receiver
  10. Exact and approximated average BER
  11. Numerical and simulation results
  12. Conclusion
  13. Proof of Lemma I
  14. Proof of Lemma 2: Case (ii)

Key Result

Lemma 1

Let $\gamma \sim \mathcal{IFTR}(\overline{\gamma},m_1, m_2,K,\Delta)$, then, its PDF and CDF can be expressed, respectively, as where $f^{\mathcal{G}}$ and $F^{\mathcal{G}}$ are, respectively, the PDF and CDF of the Gamma distribution given in fg and FFg, and coefficients $A_j$ are given in eq3 in terms of the channel parameters and the regularized Gauss hypergeometric functionThe regularized Gau

Figures (8)

  • Figure 1: PDF of the SNR under IFTR fading for different channel parameters $m_1,m_2$ and $\Delta$. Simulation confirmation results are displayed as circular markers. $K=10$. $\bar{\gamma}=1$.
  • Figure 2: PDF of the SNR under IFTR fading for different channel parameters $m_1,m_2$ and $K$. Simulation confirmation results are displayed as circular markers. $\Delta=0.5$. $\bar{\gamma}=1$.
  • Figure 3: CDF of the SNR under IFTR fading for different channel parameters $m_1,m_2$, $K$, and $\Delta$. Simulation confirmation results are displayed as circular markers.
  • Figure 4: Numerical and simulation results for the average capacity vs. average SNR in dB for different channel parameters values and ($\bar{\gamma}=1$). Simulation confirmation results are displayed as circular markers.
  • Figure 5: Numerical and simulation results for the outage probability vs. $\bar{\gamma}$ with $\gamma_{th} = 0$ dB. Simulation confirmation results are displayed as circular markers.
  • ...and 3 more figures

Theorems & Definitions (10)

  • Definition 1
  • Remark 1
  • Definition 2
  • Lemma 1
  • Remark 2
  • Corollary 1
  • Definition 3
  • Lemma 2
  • Lemma 3
  • Corollary 2