# Effect of Link Misalignment in the Optical-Internet of Underwater Things

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## Abstract

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## 1. Introduction

- First, we investigate the misalignment between Tx and Rx for a single-input-single-output (SISO) O-IoUT system by considering various optical beams such as Plane, Gaussian, and Spherical.
- Then, we analyze the effect of divergence angle for all these beams in the presence of link misalignment.
- Furthermore, we derive the BER expression for the O-IoUT link when there is a misalignment between the Tx and the Rx.
- Lastly, the proposed approach for link misalignment in O-IoUT has been evaluated based on normalized received power, maximum acceptable literal offset (MALO), and BER performance.

## 2. Related Work

#### 2.1. Literature on O-IoUT

#### 2.2. O-IoUT: Requirements and Challenges

#### 2.2.1. Absorption and Scattering

#### 2.2.2. Multi-path fading and Time Jitter

#### 2.2.3. Pointing and Link Misalignment

## 3. Proposed System Modeling and Effect of Misalignment

- A well-known UWOC channel model is considered for the system evaluation, i.e., the radiative transfer equation (RTE) [13]. The best consideration of RTE is given by Beer Lambert’s law, where there is only straight-line transmission of light without considering the multi-path scattering. This simplification along with radiance of light R is expressed as;$$R\left(r\right)=R\left(0\right){e}^{-ar},$$$$a\left(\lambda \right)=l\left(\lambda \right)+m\left(\lambda \right).$$
- Monte-Carlo simulations are used for the Tx modeling, where the initial position of the Tx is $(x,y,z)$ with moving directional cosines of the photons $({v}_{x},{v}_{y},{v}_{z})$. At the Tx end, both polar angles $\theta $ and radial angles $\varphi $ must be set precisely to obtain the initial track. The $\theta $ gets updated in each scattering event during the transmission phase along the path of propagation and is calculated recursively. The variations in $\theta $ and $\varphi $ for both the Tx and Rx are depicted in Figure 3. It should be noted that $\varphi $ is taken as a random variable in the range of $[0,2\pi ]$.
- The most important part is to measure the antecedent position of each and every photon of the considered Gaussian beam [54,55]. To analyze the overall distribution of the Gaussian beam, it is of greater importance to first plot the probability density function (PDF) and cumulative distribution function (CDF). Hence, the PDF and CDF for the considered radial position ${d}_{s}$ are expressed as$$p\left({d}_{s}\right)=\frac{{e}^{\left(\frac{{-{d}_{s}}^{2}}{{\gamma}^{2}}\right)}}{{\gamma}^{2}}\times 2{d}_{s},$$$$P\left({d}_{s}\right)=1-{e}^{\frac{{-{d}_{s}}^{2}}{{\gamma}^{2}}},$$$${d}_{s}=\gamma \sqrt{(-\mathrm{ln}(1-\rho \left)\right)},$$$$({v}_{x},{v}_{y},{v}_{z})=(\mathrm{sin}\theta \mathrm{cos}\varphi ,\mathrm{sin}\theta \mathrm{sin}\varphi ,\mathrm{cos}\theta ).$$$$p\left({d}_{t}\right)=\frac{2\pi {d}_{t}}{\pi {i}^{2}},$$$${d}_{t}=i\sqrt{\rho}$$$$({v}_{x},{v}_{y},{v}_{z})=(0,0,1).$$$$p\left(\theta \right)=2\pi J\left(\theta \right)\mathrm{sin}\theta ,$$$$P\left(\theta \right)={\int}_{0}^{\theta}2\pi J\mathrm{sin}\theta d\theta ,$$
- The photons traveling in an underwater environment usually deviate from the defined direction after striking with water particles. In the initial state, the weights of these photons are made equal to unity. These initial state weights will further be reduced by water albedo at each scattering event. The albedo of water is termed as the ratio of coefficient of scattering and coefficient of attenuation as ${\psi}_{o}\left(\lambda \right)=m\left(\lambda \right)/a\left(\lambda \right)$. It basically defines the percentage drop in weights of the photons caused by the absorption occurred as a result of interaction with different particles present in water. During this interaction, the path followed by these photons can be properly traced by three random parameters such as $\Delta n$, $\theta $, and $\varphi $ directly associated with the trajectory. Among these parameters, $\Delta n$ is the distance between two consecutive interactions and is expressed as follows$$\Delta n=\frac{-1}{a\left(\lambda \right)}\mathrm{ln}\left(\rho \right),$$$${p}_{HG}(\theta ,\varphi )=\frac{1-{s}^{2}}{4\pi {(1+{s}^{2}-2s\mathrm{cos}\theta )}^{\frac{3}{2}}},$$$$\theta ={\mathrm{cos}}^{-1}\left(\right)open="("\; close=")">\frac{1}{2s}[1+{s}^{2}-{(\frac{1-{s}^{2}}{1+s-2s\rho})}^{2}]$$
- On the Rx side, only those photons are received which are in the limits of FOV and aperture of the Rx. Furthermore, the weights of photons at different axis, and the distance traveled are recorded for calculation of various quantities such as effect on link misalignment, MALO, and BER performance.

## 4. Bit Error Rate Analysis for Link Misalignment

## 5. Results and Discussions

#### 5.1. Impact on Link Misalignment

#### 5.2. Maximum Acceptable Literal Offset (MALO) for Rx

#### 5.3. BER Calculation

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 4.**(

**a**) Normalized received power (${P}_{r}$) for plane, Gaussian, and spherical beams in clean water; (

**b**) Normalized received power (${P}_{r}$) for plane, Gaussian, and spherical beams in turbid water.

**Figure 5.**(

**a**) Normalized received power (${P}_{r}$) vs. angle of divergence for various beams in 25 m clean water; (

**b**) Normalized received power (${P}_{r}$) vs. angle of divergence for various beams in 10 m turbid water.

**Figure 6.**(

**a**) MALO on x-direction vs. the angle of divergence for various Power levels in 25 m clean water; (

**b**) MALO on x-direction vs. the angle of divergence for various Power levels in 10 m turbid water.

UWOC Channel | Merits | Shortcomings | References |
---|---|---|---|

Beer Lambert’s law | Simple to implement | Less accurate | [34,35,36] |

Chlorophyl Monte-Carlo | Accurate in simulation environment | Less efficient for errors | [37,38] |

Analytical Radiative Transfer Equation (RTE) | Provide accurate results | Offer difficulty in solving | [39,40] |

Analytical stochastic | Efficient for performance analysis | Difficult derivation with limited assumptions | [41,42] |

Numerical RTE | Easy to program, providing accurate results | Efficiency is low in case of error | [43,44] |

NLOS technique | NLOS technique for UWOC | Less accurate in case of surface reflection | [45,46] |

Turbulence model | Turbulence technique for errors in UWOC | Less accurate in case of turbulence | [47,48] |

Parameters | Value |
---|---|

Number of Photons | $5\times {10}^{7}$ |

s | 0.924 |

wavelength $\lambda $ | 520 nm |

Tx beam width ${\psi}_{0}$ | 1 mm |

Rx aperture diameter | 0.18 m |

Rx NEP | ${10}^{-15}W\sqrt{Hz}$ |

Rx aperture FOV | ${180}^{\xb0}$ |

Link span (clean water) | 0–25 m |

Link span (turbid water) | 0–10 m |

Albedo (clean water) | 0.247 |

Albedo (turbid water) | 0.8329 |

$l\left(\lambda \right)$, $m\left(\lambda \right)$, $a\left(\lambda \right)$ (clean water) | 0.114, 0.037, 0.151 |

$l\left(\lambda \right)$, $m\left(\lambda \right)$, $a\left(\lambda \right)$ (turbid water) | 0.366, 1.824, 2.19 |

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## Share and Cite

**MDPI and ACS Style**

Khalil, R.A.; Babar, M.I.; Saeed, N.; Jan, T.; Cho, H.-S.
Effect of Link Misalignment in the Optical-Internet of Underwater Things. *Electronics* **2020**, *9*, 646.
https://doi.org/10.3390/electronics9040646

**AMA Style**

Khalil RA, Babar MI, Saeed N, Jan T, Cho H-S.
Effect of Link Misalignment in the Optical-Internet of Underwater Things. *Electronics*. 2020; 9(4):646.
https://doi.org/10.3390/electronics9040646

**Chicago/Turabian Style**

Khalil, Ruhul Amin, Mohammad Inayatullah Babar, Nasir Saeed, Tariqullah Jan, and Ho-Shin Cho.
2020. "Effect of Link Misalignment in the Optical-Internet of Underwater Things" *Electronics* 9, no. 4: 646.
https://doi.org/10.3390/electronics9040646