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Performance Analysis of Optical Spatial Modulation in Atmospheric Turbulence Channel ^{†}

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^{†}

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## Abstract

**:**

## 1. Introduction

## 2. System and Channel Model

#### 2.1. The SPPM Scheme

#### 2.2. SPPM System Model

#### 2.3. FSO Channel Model

## 3. Performance Analysis of SPPM in FSO

#### 3.1. Probability of Correct TX Index Detection

#### 3.2. Probability of Correct Pulse Position Detection

## 4. Results and Discussions

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## Appendix B

## References

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**Figure 1.**Illustration of spatial pulse position modulation (SPPM) encoding using ${N}_{\mathrm{t}}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}4$, $L\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}4$.

**Figure 2.**Error performance of SPPM in weak and strong atmospheric turbulence (AT) conditions. ${N}_{\mathrm{t}}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}2$, ${N}_{\mathrm{r}}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}4$, and $L\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}[2,8]$. ST, strong AT; WT, weak AT; SER, symbol error rate.

**Figure 3.**Error performance of SPPM in weak and strong AT conditions. ${N}_{\mathrm{t}}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}4$, ${N}_{\mathrm{r}}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}4$, and $L\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}[2,8]$.

**Figure 4.**Performance under a varying AT regime. SNR required to achieve SER of ${10}^{-5}$ for the SPPM configuration: ${N}_{\mathrm{t}}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}4$, $L\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}8$.

**Figure 5.**SNR required to achieve SER $\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}{10}^{-5}$, using varying numbers of photodetectors (PDs). SPPM configuration: ${N}_{\mathrm{t}}=4$, $L=8$.

**Figure 6.**Spectral efficiency comparison of SPPM with space shift keying (SSK), repetition coding (RC)-PPM, and spatial multiplexing (SMX)-PPM for different values of L, using ${N}_{\mathrm{t}}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}4$, and under the strong AT condition.

**Figure 7.**Energy efficiency comparison of SPPM with SSK, RC-PPM, and SMX-PPM for different values of L, using ${N}_{\mathrm{t}}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}4$, ${N}_{\mathrm{r}}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}4$, and under the strong AT condition.

**Table 1.**Atmospheric turbulence parameters [1].

Turbulence Level | ${\mathit{\sigma}}_{\mathit{l}}^{2}$ | $\mathit{\alpha}$ | $\mathit{\beta}$ |
---|---|---|---|

Weak | 0.2 | 11.7 | 10.1 |

Moderate | 1.6 | 4.0 | 1.9 |

Strong | 3.5 | 4.2 | 1.4 |

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**MDPI and ACS Style**

Olanrewaju, H.G.; Thompson, J.; Popoola, W.O.
Performance Analysis of Optical Spatial Modulation in Atmospheric Turbulence Channel ^{†}. *Photonics* **2018**, *5*, 53.
https://doi.org/10.3390/photonics5040053

**AMA Style**

Olanrewaju HG, Thompson J, Popoola WO.
Performance Analysis of Optical Spatial Modulation in Atmospheric Turbulence Channel ^{†}. *Photonics*. 2018; 5(4):53.
https://doi.org/10.3390/photonics5040053

**Chicago/Turabian Style**

Olanrewaju, Hammed G., John Thompson, and Wasiu O. Popoola.
2018. "Performance Analysis of Optical Spatial Modulation in Atmospheric Turbulence Channel ^{†}" *Photonics* 5, no. 4: 53.
https://doi.org/10.3390/photonics5040053