# An Alternative Statistical Characterization of TWDP Fading Model

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## Abstract

**:**

## 1. Introduction

- 1
- Existing TWDP parameterization is not in accordance with the model’s underlying physical mechanisms,
- 2
- Analytical forms of the existing expressions for PDF and MGF disallow accurate evaluation of the effects of TWDP fading on system performance.

- 1
- We proposed alternative TWDP parameterization, which is in accordance with the model’s underlying physical mechanisms.
- 2
- 3
- We derived the alternative exact form of SNR MGF based on the adopted CDF expression and proposed parameterization, which is shown to be suitable for mathematical manipulations.
- 4
- Based on the obtained MGF, we derived M-ary PSK ASEP in exact infinite-series form, which is, to the best of our knowledge, the first such expression proposed to date.
- 5
- We also derived asymptotic M-ary PSK ASEP as a simple closed-form expression, which tightly follows the exact one for the practical range of SNR values, i.e., for SNR > 20 dB.

## 2. TWDP Fading Model

#### 2.1. The Revision of Parameter $\Delta $

#### 2.2. Envelope PDF and CDF Expressions

#### 2.2.1. Special Cases of a TWDP Model

#### 2.2.2. Convergence Analysis

#### 2.2.3. Graphical Results

## 3. Alternative form of TWDP SNR MGF Expression

## 4. Error Probability of M-ary PSK Receiver in TWDP Fading Channel

#### 4.1. The Exact M-ary PSK ASEP Expression

#### 4.2. Asymptotic Expression of M-ary PSK ASEP

#### 4.3. Numerical Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**TWDP normalized envelope (

**a**) PDF and (

**b**) CDF curves for various combinations of K and $\mathrm{\Gamma}$.

**Figure 5.**Exact (solid line) and asymptotic (dashed line) expressions of TWDP ASEP for (

**a**) 2-PSK, (

**b**) 4-PSK, (

**c**) 8-PSK and (

**d**) 16-PSK modulations compared with Monte Carlo simulation results (dots).

**Figure 6.**BPSK ASEP in TWDP channel for $K=6$ and different values of parameter (

**a**) $\Delta $ (

**b**) $\mathrm{\Gamma}$.

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Maric, A.; Kaljic, E.; Njemcevic, P.
An Alternative Statistical Characterization of TWDP Fading Model. *Sensors* **2021**, *21*, 7513.
https://doi.org/10.3390/s21227513

**AMA Style**

Maric A, Kaljic E, Njemcevic P.
An Alternative Statistical Characterization of TWDP Fading Model. *Sensors*. 2021; 21(22):7513.
https://doi.org/10.3390/s21227513

**Chicago/Turabian Style**

Maric, Almir, Enio Kaljic, and Pamela Njemcevic.
2021. "An Alternative Statistical Characterization of TWDP Fading Model" *Sensors* 21, no. 22: 7513.
https://doi.org/10.3390/s21227513