Researching | Performance characterization of two-way multi-hop underwater networks in turbulent channels [Invited]

Journals >Chinese Optics Letters >Volume 17 >Issue 10 >Page 100005 > Article

Chinese Optics Letters
Vol. 17, Issue 10, 100005 (2019)

Performance characterization of two-way multi-hop underwater networks in turbulent channels [Invited]

Fangyuan Xing, Hongxi Yin^*, and Lianyou Jing

Author Affiliations

School of Information and Communication Engineering, Dalian University of Technology, Dalian 116023, China

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DOI: 10.3788/COL201917.100005 Cite this Article Set citation alerts

Fangyuan Xing, Hongxi Yin, Lianyou Jing. Performance characterization of two-way multi-hop underwater networks in turbulent channels [Invited][J]. Chinese Optics Letters, 2019, 17(10): 100005 Copy Citation Text

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Abstract

This Letter investigates the performance of the two-way multi-hop system for underwater optical wireless communications. With the decode-and-forward (DF) relaying, the two-way multi-hop system is modeled, where the effects of absorption, scattering, and oceanic turbulence are all taken into account. An exact closed-form expression for outage probability is derived under the assumption that the oceanic turbulence obeys a log-normal distribution. Numerical results demonstrate the impacts of various parameters on the outage performance and indicate that the two-way multi-hop system significantly improves the performance in comparison to both the one-way multi-hop system and the two-way two-hop system.

H_{i j} = α_{i j}^{2} h_{i j},

(1)

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h_{i j} = \frac{η_{t} η_{r} A_{r} \cos θ}{2 π d_{i j}^{2} (1 - \cos θ_{0})} \exp [- c (λ) d_{i j}],

(2)

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f (α_{i j}) = \frac{1}{α_{i j} \sqrt{2 π σ_{X_{i j}}^{2}}} \exp [- \frac{{(\ln α_{i j} - μ_{X_{i j}})}^{2}}{2 σ_{X_{i j}}^{2}}],

(3)

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σ_{X_{i j}}^{2} = \frac{1}{4} \ln (σ_{I_{i j}}^{2} + 1) .

(4)

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y_{0, 1} = ρ P_{0, 1} H_{0, 1} x_{A} + n_{0, 1},

(5)

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y_{k + 1, k} = ρ P_{k + 1, k} H_{k + 1, k} x_{B} + n_{k + 1, k},

(6)

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y_{1, 2} = ρ P_{1, 2} H_{1, 2} x_{A} + n_{1, 2},

(7)

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y_{k, k - 1} = ρ P_{k, k - 1} H_{k, k - 1} x_{B} + n_{k, k - 1},

(8)

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y_{1, 0} = ρ P_{1, 0} H_{1, 0} x_{B} + n_{1, 0},

(9)

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y_{k, k + 1} = ρ P_{k, k + 1} H_{k, k + 1} x_{A} + n_{k, k + 1},

(10)

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γ_{A B} = \min {γ_{0, 1}, \dots, γ_{i, i + 1}, \dots, γ_{k, k + 1}}, i = 0, 1, \dots, k,

(11)

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γ_{B A} = \min {γ_{k + 1, k}, \dots, γ_{j, j - 1}, \dots, γ_{1, 0}}, j = 1, 2, \dots, k + 1,

(12)

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γ_{i, i + 1} = \frac{{(ρ P_{i, i + 1} H_{i, i + 1})}^{2}}{σ_{f, i + 1}^{2}}, γ_{j, j - 1} = \frac{{(ρ P_{j, j - 1} H_{j, j - 1})}^{2}}{σ_{b, j - 1}^{2}},

(13)

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P_{out} = \Pr (\min {γ_{A B}, γ_{B A}} \leq γ_{th}) = 1 - \Pr (γ_{A B} > γ_{th}) \Pr (γ_{B A} > γ_{th}),

(14)

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P_{out} = 1 - \prod_{i = 0}^{k} \Pr (γ_{i, i + 1} > γ_{th}) \prod_{j = 1}^{k + 1} \Pr (γ_{j, j - 1} > γ_{th}) .

(15)

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P_{out} = 1 - \prod_{i = 0}^{k} \Pr (α_{i, i + 1}^{2} > \frac{\sqrt{γ_{th} σ_{f, i + 1}^{2}}}{ρ P_{i, i + 1} h_{i, i + 1}}) \prod_{j = 1}^{k + 1} \Pr (α_{j, j - 1}^{2} > \frac{\sqrt{γ_{th} σ_{b, j - 1}^{2}}}{ρ P_{j, j - 1} h_{j, j - 1}}) .

(16)

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P_{out} = 1 - \prod_{i = 0}^{k} Q {\frac{\ln [γ_{th} σ_{f, i + 1}^{2} / {(ρ P_{i, i + 1} h_{i, i + 1})}^{2}] - 4 μ_{X_{i, i + 1}}}{4 σ_{X_{i, i + 1}}}} \times \prod_{j = 1}^{k + 1} Q {\frac{\ln [γ_{th} σ_{b, j - 1}^{2} / {(ρ P_{j, j - 1} h_{j, j - 1})}^{2}] - 4 μ_{X_{j, j - 1}}}{4 σ_{X_{j, j - 1}}}},

(17)

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Q (x) = \frac{1}{\sqrt{2 π}} \int_{x}^{\infty} \exp (\frac{- η^{2}}{2}) d η .

(18)

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Fangyuan Xing, Hongxi Yin, Lianyou Jing. Performance characterization of two-way multi-hop underwater networks in turbulent channels [Invited][J]. Chinese Optics Letters, 2019, 17(10): 100005

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