16QAM Adaptive Probability Shaping Under Combined Influence of Turbulence and Phase Noise

Dan Chen; Feier Ai; Rui Wang; Peiyan Zhao

doi:10.3788/AOS231210

Acta Optica Sinica, Volume. 43, Issue 24, 2406004(2023)

16QAM Adaptive Probability Shaping Under Combined Influence of Turbulence and Phase Noise

Dan Chen^*, Feier Ai, Rui Wang, and Peiyan Zhao

School of Automation and Information Engineering, Xi'an Key Laboratory of Wireless Optical Communication and Network Research, Xi'an University of Technology, Xi'an 710048, Shaanxi , China

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Figures & Tables(9)

Fig. 1. Block diagram of adaptive probabilistic shaping system based on free-space optical communication model

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Fig. 2. Using heuristic optimization algorithm to traverse the search for PMF under different signal-to-noise ratio conditions, the optimal $R_{B M D}$ is obtained. (a) Optimal $R_{B M D}$ considering only the influence of turbulence; (b) optimal $R_{B M D}$ under the influence of different phase noise ( $σ_{I}^{2} = 0.4$ ); (c) optimal $R_{B M D}$ under the influence of different turbulence intensities ( $σ_{φ}^{2} = 0.01$ )

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Fig. 3. $R_{B M D}$ of PS distribution and uniform distribution under different turbulence intensities and phase noise. (a) BMD rate curves under weak turbulence $σ_{I}^{2} = 0.4$ ; (b) BMD rate curves under moderate turbulence $σ_{I}^{2} = 1.0$ ; (c) BMD rate curves under weak turbulence $σ_{I}^{2} = 0.4$ and phase noise $σ_{φ}^{2} = 0.01$ ; (d) BMD rate curves under weak turbulence $σ_{I}^{2} = 0.4$ and phase noise $σ_{φ}^{2} = 0.12$

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Fig. 4. NGMI values of PS-16QAM under different channel conditions. (a) NGMI under influence of turbulence; (b) NGMI under combined influence of turbulence and phase noise

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Fig. 5. BER of PS-16QAM on Gamma-Gamma channel. (a) Pre-FEC BER under influence of turbulence; (b) pre-FEC BER under influence of turbulence and phase noise

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Fig. 6. Probability distributions of three-dimensional constellation points obtained using particle swarm optimization algorithm when only considering weak turbulence. (a)-(c) 3D constellation distributions at 2 dB, 8 dB, and 15 dB filtered under weak turbulence ( $σ_{I}^{2} = 0.4$ ); (d)-(f) 3D constellation distributions at 2 dB, 8 dB, and 15 dB filtered under moderate turbulence ( $σ_{I}^{2} = 1.0$ )

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Fig. 7. Probability distributions of source 3D constellation points under different SNRs for probabilistic shaping particle swarm optimization algorithm with different phase noise. (a)-(c) 3D constellation distributions at 2 dB, 8 dB, and 15 dB filtered out under $σ_{φ}^{2} = 0.01$ and $σ_{I}^{2} = 0.4$ ; (d)-(f) 3D constellation distributions at 2 dB, 8 dB, and 15 dB filtered out under $σ_{φ}^{2} = 0.12$ and $σ_{I}^{2} = 0.4$

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Table 1. $P_{X}$ of input PMFs corresponding to different SNR ranges when only considering turbulence effect

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Table 1. $P_{X}$ of input PMFs corresponding to different SNR ranges when only considering turbulence effect

Turbulence intensity	Channel SNR range /dB	$P_{X} (1 D)$ （one-sided 1D PMF）
$σ_{I}^{2} = 0.4$	2-8	［0.0114 0.0420 0.0114 0.0420 0.0420 0.1546 0.0420 0.1546］
	8-15	［0.0150 0.0463 0.0150 0.0463 0.0463 0.1424 0.0463 0.1424］
	15-18	［0.0370 0.0592 0.0370 0.0592 0.0592 0.0946 0.0592 0.0946］
	18-20	［0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625］
$σ_{I}^{2} = 1.0$	2-8	［0.0087 0.0380 0.0087 0.0380 0.0380 0.1653 0.0380 0.1653］
	8-15	［0.0144 0.0456 0.0144 0.0456 0.0456 0.1444 0.0456 0.1444］
	15-18	［0.0336 0.0581 0.0336 0.0581 0.0581 0.1002 0.0581 0.1002］
	18-20	［0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625］

Table 2. $P_{X}$ of input PMFs corresponding to different SNR ranges when considering combined effect of turbulence and phase noise

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Table 2. $P_{X}$ of input PMFs corresponding to different SNR ranges when considering combined effect of turbulence and phase noise

Condition	Channel SNR range /dB	$P_{X} (1 D)$ （one-sided 1D PMF）
$σ_{I}^{2} = 0.4$ $σ_{φ}^{2} = 0.01$	2-8	［0.0101 0.0402 0.0101 0.0402 0.0402 0.1595 0.0402 0.1595］
	8-15	［0.0138 0.0449 0.0138 0.0449 0.0449 0.1464 0.0449 0.1464］
	15-18	［0.0268 0.0551 0.0268 0.0551 0.0551 0.1130 0.0551 0.1130］
	18-20	［0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625］
$σ_{I}^{2} = 0.4$ $σ_{φ}^{2} = 0.12$	2-8	［0.0067 0.0342 0.0067 0.0342 0.0342 0.1749 0.0342 0.1749］
	8-15	［0.0112 0.0417 0.0112 0.0417 0.0417 0.1554 0.0417 0.1554］
	15-18	［0.0242 0.0536 0.0242 0.0536 0.0536 0.1186 0.0536 0.1186］
	18-20	［0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625］

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Dan Chen, Feier Ai, Rui Wang, Peiyan Zhao. 16QAM Adaptive Probability Shaping Under Combined Influence of Turbulence and Phase Noise[J]. Acta Optica Sinica, 2023, 43(24): 2406004

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Paper Information

Category: Fiber Optics and Optical Communications

Received: Jul. 3, 2023

Accepted: Oct. 7, 2023

Published Online: Dec. 15, 2023

The Author Email: Chen Dan (chdh@xaut.edu.cn)

DOI:10.3788/AOS231210

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. PX of input PMFs corresponding to different SNR ranges when only considering turbulence effect

Table 1. PX of input PMFs corresponding to different SNR ranges when only considering turbulence effect

Table 2. PX of input PMFs corresponding to different SNR ranges when considering combined effect of turbulence and phase noise

Table 2. PX of input PMFs corresponding to different SNR ranges when considering combined effect of turbulence and phase noise

Table 1. $P_{X}$ of input PMFs corresponding to different SNR ranges when only considering turbulence effect

Table 1. $P_{X}$ of input PMFs corresponding to different SNR ranges when only considering turbulence effect

Table 2. $P_{X}$ of input PMFs corresponding to different SNR ranges when considering combined effect of turbulence and phase noise

Table 2. $P_{X}$ of input PMFs corresponding to different SNR ranges when considering combined effect of turbulence and phase noise