US-BSF: a unified simplification of BSF model with different scattering phase functions for underwater wireless optical communication

Fan Yang; Ruiheng Zhong; Guanyu Cao

doi:10.1364/OL.499112

Optics Letters
Vol. 48,
Issue 17,
pp. 4524-4527
(2023)
•https://doi.org/10.1364/OL.499112

US-BSF: a unified simplification of BSF model with different scattering phase functions for underwater wireless optical communication

Fan Yang, Ruiheng Zhong, and Guanyu Cao

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Fan Yang, Ruiheng Zhong, and Guanyu Cao, "US-BSF: a unified simplification of BSF model with different scattering phase functions for underwater wireless optical communication," Opt. Lett. 48, 4524-4527 (2023)

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Table of Contents Category
- Fiber Optics and Optical Communications
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About this Article
History
- Original Manuscript: June 29, 2023
- Revised Manuscript: July 26, 2023
- Manuscript Accepted: July 28, 2023
- Published: August 21, 2023

Abstract

Underwater wireless optical communications (UWOCs) use beam shaping techniques such as the Beer–Lambert (BL) law which describes how light interacts with matter. The BL model ignores the scattering effect of UWOC, while the beam spread function (BSF) can characterize the combined effect of absorption and scattering of UWOC more accurately. The original triple-integral beam spread function (OTI-BSF) involves the Bessel function, which is very time-consuming to calculate. In addition, different seawater environments may require different scattering phase functions (SPFs) to obtain accurate modeling results compared with Henyey–Greenstein SPF (HG-SPF). So far, the BSF-based channel data generation and performance analysis in complex water environments have been time-consuming. We propose a unified simplification of BSF (US-BSF) channel based on the Gaussian mixture model, which is suitable for three commonly used SPFs. From the point of view of time consumption, our proposed US-BSF only requires an order of O(10⁻⁴) s to calculate a value on average, while the OTI-BSF requires an order of O(10²) s.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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	$p_{H G}^{U S} (v)$	$p_{F F}^{U S} (v)$	$p_{T T}^{U S} (v)$
$A_{1}$	$3.658 \times 10^{0}$	$2.080 \times 10^{12}$	$7.242 \times 10^{- 4}$
$B_{1}$	$- 5.163 \times 10^{1}$	$- 5.730 \times 10^{2}$	$1.067 \times 10^{1}$
$C_{1}$	$3.427 \times 10^{1}$	$1.065 \times 10^{2}$	$1.953 \times 10^{0}$
$A_{2}$	$- 4.359 \times 10^{- 5}$	$1.250 \times 10^{- 2}$	$6.016 \times 10^{0}$
$B_{2}$	$2.110 \times 10^{1}$	$1.666 \times 10^{1}$	$- 2.124 \times 10^{2}$
$C_{2}$	$8.838 \times 10^{- 2}$	$3.778 \times 10^{0}$	$1.174 \times 10^{2}$
$A_{3}$	$3.443 \times 10^{2}$	$9.764 \times 10^{2}$	$5.492 \times 10^{1}$
$B_{3}$	$- 2.068 \times 10^{2}$	$- 1.742 \times 10^{3}$	$- 5.479 \times 10^{2}$
$C_{3}$	$8.212 \times 10^{1}$	$6.294 \times 10^{2}$	$2.650 \times 10^{2}$

	$p_{H G}^{U S} (v)$	$p_{F F}^{U S} (v)$	$p_{T T}^{U S} (v)$
$A_{1}$	$3.658 \times 10^{0}$	$2.080 \times 10^{12}$	$7.242 \times 10^{- 4}$
$B_{1}$	$- 5.163 \times 10^{1}$	$- 5.730 \times 10^{2}$	$1.067 \times 10^{1}$
$C_{1}$	$3.427 \times 10^{1}$	$1.065 \times 10^{2}$	$1.953 \times 10^{0}$
$A_{2}$	$- 4.359 \times 10^{- 5}$	$1.250 \times 10^{- 2}$	$6.016 \times 10^{0}$
$B_{2}$	$2.110 \times 10^{1}$	$1.666 \times 10^{1}$	$- 2.124 \times 10^{2}$
$C_{2}$	$8.838 \times 10^{- 2}$	$3.778 \times 10^{0}$	$1.174 \times 10^{2}$
$A_{3}$	$3.443 \times 10^{2}$	$9.764 \times 10^{2}$	$5.492 \times 10^{1}$
$B_{3}$	$- 2.068 \times 10^{2}$	$- 1.742 \times 10^{3}$	$- 5.479 \times 10^{2}$
$C_{3}$	$8.212 \times 10^{1}$	$6.294 \times 10^{2}$	$2.650 \times 10^{2}$

Abstract

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