# Link Connectivity and Coverage of Underwater Cognitive Acoustic Networks under Spectrum Constraint

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- We develop a novel analytical model to investigate the link connectivity and the coverage probability of SUs in UCANs. We find that the link connectivity and coverage of SUs depends on both the spectrum availability and the topological connectivity, while the spectrum availability has been ignored in most existing works.
- We conduct extensive simulations to verify the accuracy of our proposed model. The simulation results match the analytical results, implying that our proposed model is fairly accurate.
- We observe that the probability of connectivity and the probability of coverage are affected by acoustic signal frequency, various ambient factors (spreading factor and wind speed), and the activity of PUs. Our results also offer some useful insights in designing QoS-aware UCANs.

## 2. Related Works

## 3. System Model

#### 3.1. Problem Definition

_{5}cannot establish a communication link with SU

_{6}due to the possible interference to PU

_{3}, as PU

_{3}is in close proximity to SU

_{5}. Similarly, SU

_{1}and SU

_{2}cannot connect with each other successfully because of the existence of PU

_{2}, which is close to both SU

_{1}and SU

_{2}. As illustrated in this typical UCAN, we observe that the link connectivity of SU pairs is more difficult to ensure that of PUs, and consequently SU pairs have a lower probability of coverage. Therefore, we aim to investigate the link connectivity and the probability of coverage of SUs in UCANs in this paper.

#### 3.2. Network Model

#### 3.3. Channel Model

## 4. Analysis of Link Connectivity and Probability of Coverage

**Definition**

**1.**

- (1)
- Both of the SUs can connect topologically;
- (2)
- Both of the SUs have the spectrum.

#### 4.1. Topological Connection Condition

#### 4.2. Spectrum Availability

_{1}and SU

_{2}). As shown in Figure 3, the detection region of each SU is a circle with a radius of detection range ${r}_{d}$. We observe that a pair of SUs can have the spectrum if both of the following conditions are satisfied:

- (1)
- No PUs in the detection region of SU
_{1}; - (2)
- No PUs in the detection region of SU
_{2}.

#### 4.3. Link Connectivity

#### 4.4. Probability of Coverage

## 5. Simulations

#### 5.1. Simulation Method

^{2}. Figure 4 shows a random topology of a simulation snapshot, where red circles denote PUs, and blue triangles denote SUs (the distance between a pair of SUs is r). Then, the probability of connectivity ${p}_{con}^{s}$ of simulations can be acquired by

#### 5.2. Probability of Connection

#### 5.2.1. Impacts of Ambient Environment

#### 5.2.2. Impacts of PUs

#### 5.3. Probability of Coverage

#### 5.4. Discussion and Future Works

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A. Attenuation

## Appendix B. Ambient Noise

## References

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**Figure 2.**Maximum communication distance ${r}_{max}$ (km) with different spreading factor k and wind speed w (m/s) when $s=1$, ${P}_{s}=100$ dB, and ${\delta}_{s}=20$ dB. (

**a**) $k=1$; (

**b**) $k=2$.

**Figure 4.**Random topology of a simulation snapshot of underwater cognitive acoustic sensor networks (UCANs), where red circles denote PUs and blue triangles denote SUs.

**Figure 5.**Probability of connection ${p}_{con}$ versus distance r with different spreading factor k and wind speed w. System parameters are set as ${P}_{p}=110$ dB, ${P}_{s}=100$ dB, ${\lambda}_{p}=0.003$, $s=1$, ${\delta}_{s}=20$ dB, and ${\delta}_{d}=20$ dB. (

**a**) $k=1,w=0$ m/s; (

**b**) $k=2,w=0$ m/s; (

**c**) $k=1,w=10$ m/s; (

**d**) $k=2,w=10$ m/s; (

**e**) $k=1,w=20$ m/s; (

**f**) $k=2,w=20$ m/s.

**Figure 6.**Probability of connection ${p}_{con}$ versus distance r with different intensity of PUs ${\lambda}_{p}$. System parameters are set as $k=1$, $w=10$ m/s, $f=30$ kHz, ${P}_{p}=110$ dB, ${P}_{s}=100$ dB, $s=1$, ${\delta}_{s}=20$ dB and ${\delta}_{d}=20$ dB.

**Figure 7.**Probability of connection ${p}_{con}$ versus distance r with different transmission power of PUs ${P}_{p}$. System parameters are set as $k=1$, $w=10$ m/s, ${\lambda}_{p}=0.005$, $f=30$ kHz, ${P}_{s}=100$ dB, $s=1$, ${\delta}_{s}=20$ dB, and ${\delta}_{d}=20$ dB.

**Figure 8.**Coverage ${p}_{cov}$ versus frequency f with different spreading factor k and wind speed w. System parameters are set as ${R}_{d}=12$ km, ${P}_{p}=110$ dB, ${P}_{s}=100$ dB, ${\lambda}_{p}=0.003$, $s=1$, ${\delta}_{s}=20$ dB, and ${\delta}_{d}=20$ dB.

**Figure 9.**Coverage ${p}_{cov}$ versus frequency f with different ${\lambda}_{p}$. System parameters are set as ${R}_{d}=12$ km, ${P}_{p}=110$ dB, ${P}_{s}=100$ dB, $s=1$, $k=1$, $w=10$ m/s, ${\delta}_{s}=20$ dB, and ${\delta}_{d}=20$ dB.

**Figure 10.**Coverage ${p}_{cov}$ versus frequency f with different power of PUs ${P}_{p}$. System parameters are set as ${R}_{d}=12$ km, ${P}_{s}=100$ dB, ${\lambda}_{p}=0.003$, $k=1$, $w=10$ m/s, $s=1$, ${\delta}_{s}=20$ dB, and ${\delta}_{d}=20$ dB.

**Table 1.**Deviation of ${p}_{con}^{s}$ between simulation results (with different values of $\Omega $) and analytical results. System parameters are set as $f=20$ kHz, ${P}_{p}=110$ dB, ${P}_{s}=100$ dB, ${\lambda}_{p}=0.003$, $k=1$, $w=0$ m/s, $s=1$, ${\delta}_{s}=20$ dB, and ${\delta}_{d}=20$ dB.

Analytical Value | Simulation Value with Ω = 500 | Simulation Value with Ω = 20,000 | |
---|---|---|---|

r = 1 km | 0.1758 | 0.1520 (13.53%) | 0.1726 (0.18%) |

r = 2 km | 0.1624 | 0.1640 (0.99%) | 0.1612 (0.74%) |

r = 3 km | 0.1500 | 0.1560 (4.00%) | 0.1454 (3.07%) |

r = 4 km | 0.1386 | 0.1180 (14.86%) | 0.1417 (2.24%) |

Average deviation | 8.35% | 1.56% |

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**MDPI and ACS Style**

Wang, Q.; Dai, H.-N.; Cheang, C.F.; Wang, H.
Link Connectivity and Coverage of Underwater Cognitive Acoustic Networks under Spectrum Constraint. *Sensors* **2017**, *17*, 2839.
https://doi.org/10.3390/s17122839

**AMA Style**

Wang Q, Dai H-N, Cheang CF, Wang H.
Link Connectivity and Coverage of Underwater Cognitive Acoustic Networks under Spectrum Constraint. *Sensors*. 2017; 17(12):2839.
https://doi.org/10.3390/s17122839

**Chicago/Turabian Style**

Wang, Qiu, Hong-Ning Dai, Chak Fong Cheang, and Hao Wang.
2017. "Link Connectivity and Coverage of Underwater Cognitive Acoustic Networks under Spectrum Constraint" *Sensors* 17, no. 12: 2839.
https://doi.org/10.3390/s17122839