Secure turbulence-resistant coherent free-space optical communications via chaotic region-optimized probabilistic constellation shaping

Tingwei Wu; Tingwei Wu; Tingwei Wu; Wei Zeng; Wei Zeng; Yejun Liu; Yejun Liu; Song Song; Song Song; Lun Zhao; Lun Zhao; Chen Chen; Chongfu Zhang; Lei Guo; Lei Guo

doi:10.1364/OL.480981

Optics Letters
Vol. 48,
Issue 3,
pp. 684-687
(2023)
•https://doi.org/10.1364/OL.480981

Secure turbulence-resistant coherent free-space optical communications via chaotic region-optimized probabilistic constellation shaping

Tingwei Wu, Wei Zeng, Yejun Liu, Song Song, Lun Zhao, Chen Chen, Chongfu Zhang, and Lei Guo

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Tingwei Wu, Wei Zeng, Yejun Liu, Song Song, Lun Zhao, Chen Chen, Chongfu Zhang, and Lei Guo, "Secure turbulence-resistant coherent free-space optical communications via chaotic region-optimized probabilistic constellation shaping," Opt. Lett. 48, 684-687 (2023)

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Table of Contents Category
- Fiber Optics and Optical Communications
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About this Article
History
- Original Manuscript: November 15, 2022
- Revised Manuscript: December 17, 2022
- Manuscript Accepted: December 29, 2022
- Published: January 24, 2023

Abstract

We propose a chaotic region-optimized probabilistic constellation shaping (CRPCS) scheme to enhance the security and the resistance to turbulence for free-space optical (FSO) communications. For this approach, a four-dimensional hyperchaotic system generates a pseudorandom sequence to rotate and encrypt the constellation. Constellation distribution of short pseudorandom sequences behaves as the law of a non-uniform character. Grouping long pseudorandom sequences and counting the characteristics of constellation distribution can realize probabilistic constellation shaping with low and fixed redundant information. We demonstrate a 56 Gbyte/s coherent FSO communication system based on log-normal and Gamma–Gamma turbulence models with a key space of 10⁷⁵. The results show that the optical receiver sensitivity is improved by 0.3–1.1 dB, and the transmission distance is also improved by 3.2%–7.0% in different shaping cases.

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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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Size Relationship	Method
$S_{1} > S_{2} > S_{3} > S_{4}$ , $S_{1} > S_{3} > S_{2} > S_{4}$	None
$S_{1} > S_{2} > S_{4} > S_{3}$ , $S_{1} > S_{4} > S_{2} > S_{3}$	$a_{4} \leftrightarrow$ $a_{3}$
$S_{1} > S_{3} > S_{4} > S_{2}$ , $S_{1} > S_{4} > S_{3} > S_{2}$	$a_{4} \leftrightarrow$ $a_{2}$
$S_{2} > S_{1} > S_{3} > S_{4}$ , $S_{2} > S_{3} > S_{1} > S_{4}$	$a_{2} \leftrightarrow a_{1}$
$S_{2} > S_{1} > S_{4} > S_{3}$ , $S_{2} > S_{4} > S_{1} > S_{3}$	$a_{4} \leftrightarrow$ $a_{3}$ , $a_{2} \leftrightarrow$ $a_{1}$
$S_{3} > S_{1} > S_{2} > S_{4}$ , $S_{3} > S_{2} > S_{1} > S_{4}$	$a_{3} \leftrightarrow$ $a_{1}$
$S_{4} > S_{1} > S_{2} > S_{3}$ , $S_{4} > S_{2} > S_{1} > S_{3}$	$a_{4} \leftrightarrow$ $a_{3}$ , $a_{3} \leftrightarrow$ $a_{1}$
$S_{3} > S_{1} > S_{4} > S_{2}$ , $S_{3} > S_{4} > S_{1} > S_{2}$	$a_{4} \leftrightarrow$ $a_{2}$ , $a_{3} \leftrightarrow$ $a_{1}$
$S_{4} > S_{1} > S_{3} > S_{2}$	$a_{4} \leftrightarrow$ $a_{1}$ , $a_{4} \leftrightarrow$ $a_{2}$
$S_{4} > S_{3} > S_{1} > S_{2}$	$a_{4} \leftrightarrow$ $a_{2}$ , $a_{2} \leftrightarrow$ $a_{1}$
$S_{2} > S_{3} > S_{4} > S_{1}$ , $S_{2} > S_{4} > S_{3} > S_{1}$	$a_{2} \leftrightarrow$ $a_{1}$ , $a_{4} \leftrightarrow$ $a_{2}$
$S_{3} > S_{2} > S_{4} > S_{1}$ , $S_{3} > S_{4} > S_{2} > S_{1}$	$a_{3} \leftrightarrow$ $a_{1}$ , $a_{4} \leftrightarrow$ $a_{3}$
$S_{4} > S_{2} > S_{3} > S_{1}$ , $S_{4} > S_{3} > S_{2} > S_{1}$	$a_{4} \leftrightarrow$ $a_{1}$

Shaping Case	$R$	$\bar{P}$	$\bar{ρ}$
Origin	1.000	10.00	2.000
$N = 16$	0.800	8.21	2.434
$N = 32$	0.889	8.50	2.352
$N = 48$	0.924	8.70	2.300
$N = 64$	0.941	8.85	2.262
$N = 80$	0.952	8.96	2.234
$N = 96$	0.975	9.04	2.212

Parameter	Value
Wavelength	1550 nm
Beam divergence	2 mrad
Transmitter aperture diameter	5 cm
Receiver aperture diameter	20 cm
Attenuation	5–15 dB/km
Transmission power	$- 0.3$ – $16.9$ dBm
Scintillation model	Log-normal, Gamma–Gamma
Refractive index structure constant	$10^{- 16}$ – $10^{- 14} m^{- 2 / 3}$

Size Relationship	Method
$S_{1} > S_{2} > S_{3} > S_{4}$ , $S_{1} > S_{3} > S_{2} > S_{4}$	None
$S_{1} > S_{2} > S_{4} > S_{3}$ , $S_{1} > S_{4} > S_{2} > S_{3}$	$a_{4} \leftrightarrow$ $a_{3}$
$S_{1} > S_{3} > S_{4} > S_{2}$ , $S_{1} > S_{4} > S_{3} > S_{2}$	$a_{4} \leftrightarrow$ $a_{2}$
$S_{2} > S_{1} > S_{3} > S_{4}$ , $S_{2} > S_{3} > S_{1} > S_{4}$	$a_{2} \leftrightarrow a_{1}$
$S_{2} > S_{1} > S_{4} > S_{3}$ , $S_{2} > S_{4} > S_{1} > S_{3}$	$a_{4} \leftrightarrow$ $a_{3}$ , $a_{2} \leftrightarrow$ $a_{1}$
$S_{3} > S_{1} > S_{2} > S_{4}$ , $S_{3} > S_{2} > S_{1} > S_{4}$	$a_{3} \leftrightarrow$ $a_{1}$
$S_{4} > S_{1} > S_{2} > S_{3}$ , $S_{4} > S_{2} > S_{1} > S_{3}$	$a_{4} \leftrightarrow$ $a_{3}$ , $a_{3} \leftrightarrow$ $a_{1}$
$S_{3} > S_{1} > S_{4} > S_{2}$ , $S_{3} > S_{4} > S_{1} > S_{2}$	$a_{4} \leftrightarrow$ $a_{2}$ , $a_{3} \leftrightarrow$ $a_{1}$
$S_{4} > S_{1} > S_{3} > S_{2}$	$a_{4} \leftrightarrow$ $a_{1}$ , $a_{4} \leftrightarrow$ $a_{2}$
$S_{4} > S_{3} > S_{1} > S_{2}$	$a_{4} \leftrightarrow$ $a_{2}$ , $a_{2} \leftrightarrow$ $a_{1}$
$S_{2} > S_{3} > S_{4} > S_{1}$ , $S_{2} > S_{4} > S_{3} > S_{1}$	$a_{2} \leftrightarrow$ $a_{1}$ , $a_{4} \leftrightarrow$ $a_{2}$
$S_{3} > S_{2} > S_{4} > S_{1}$ , $S_{3} > S_{4} > S_{2} > S_{1}$	$a_{3} \leftrightarrow$ $a_{1}$ , $a_{4} \leftrightarrow$ $a_{3}$
$S_{4} > S_{2} > S_{3} > S_{1}$ , $S_{4} > S_{3} > S_{2} > S_{1}$	$a_{4} \leftrightarrow$ $a_{1}$

Shaping Case	$R$	$\bar{P}$	$\bar{ρ}$
Origin	1.000	10.00	2.000
$N = 16$	0.800	8.21	2.434
$N = 32$	0.889	8.50	2.352
$N = 48$	0.924	8.70	2.300
$N = 64$	0.941	8.85	2.262
$N = 80$	0.952	8.96	2.234
$N = 96$	0.975	9.04	2.212

Abstract

Data availability

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Tables (3)

Equations (9)

Optics Letters