# Accurate Evaluation of the Average Probability of Error of Pulse Position Modulation in Amplified Optical Wireless Communications under Turbulence

^{*}

## Abstract

**:**

## 1. Introduction

## 2. PPM Reception

#### 2.1. Receiver Model

#### 2.2. PPM PER

#### 2.3. PER Results

## 3. Average PER in Turbulent Channels

#### 3.1. Channel Model

#### 3.2. Weak and Moderate Fading

#### 3.3. Strong Fading

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

EGC | Equal-gain combiner |

OSNR | Optical signal-to-noise-ratio |

OWC | Optical wireless communication |

PER | Probability of error |

PPM | Pulse position modulation |

RV | Random variable |

SER | Symbol error probability |

## References

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**Figure 2.**Probability of error (PER) vs. ${E}_{b}/{N}_{0}$ for $Q=2,16,256$. The plot lines and points correspond to the exact and approximated results, respectively.

**Figure 3.**Average PER vs $\overline{{E}_{b}}/{N}_{0}$ for $Q=2,16,256$ in weak (

**top row**) and moderate (

**bottom row**) $\gamma -\gamma $ fading. The plot lines and points correspond to the exact and approximated results, respectively. The optical noise modes are equal to $k=2$ (

**left column**) and $k=8$ (

**right column**).

**Figure 4.**Average PER vs $\overline{{E}_{b}}/{N}_{0}$ for $Q=2,16,256$ in strong fading. The plot lines and points correspond to the exact and approximated results, respectively. $k=2$ (

**a**) and $k=8$ (

**b**).

l (m) | ${\mathbf{m}}_{\mathbf{x}}$ | ${\mathbf{m}}_{\mathbf{y}}$ |
---|---|---|

100 | 16.53 | 14.91 |

500 | 4.04 | 1.53 |

l–100 m | l–500 m | |||||
---|---|---|---|---|---|---|

L-2 | L-5 | L-10 | L-2 | L-5 | L-10 | |

$\alpha $ | 0.49 | 0.48 | 0.47 | 0.51 | 0.46 | 0.43 |

$\mu $ | 64.76 | 167.71 | 339.61 | 7.72 | 23.09 | 50.45 |

$L\phantom{\rule{0.166667em}{0ex}}\widehat{y}$ | 1.97 | 4.97 | 9.97 | 1.78 | 4.73 | 9.71 |

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**MDPI and ACS Style**

Boucouvalas, A.C.; Sagias, N.C.; Yiannopoulos, K. Accurate Evaluation of the Average Probability of Error of Pulse Position Modulation in Amplified Optical Wireless Communications under Turbulence. *Appl. Sci.* **2019**, *9*, 749.
https://doi.org/10.3390/app9040749

**AMA Style**

Boucouvalas AC, Sagias NC, Yiannopoulos K. Accurate Evaluation of the Average Probability of Error of Pulse Position Modulation in Amplified Optical Wireless Communications under Turbulence. *Applied Sciences*. 2019; 9(4):749.
https://doi.org/10.3390/app9040749

**Chicago/Turabian Style**

Boucouvalas, Anthony C., Nikos C. Sagias, and Konstantinos Yiannopoulos. 2019. "Accurate Evaluation of the Average Probability of Error of Pulse Position Modulation in Amplified Optical Wireless Communications under Turbulence" *Applied Sciences* 9, no. 4: 749.
https://doi.org/10.3390/app9040749