Improved modulation format identification based on Stokes parameters using combination of fuzzy c-means and hierarchical clustering in coherent optical communication system

Longxue Cheng; Lixia Xi; Donghe Zhao; Xianfeng Tang; Wenbo Zhang; Xiaoguang Zhang

doi:10.3788/COL201513.100604

Journals >Chinese Optics Letters >Volume 13 >Issue 10 >Page 100604 > Article

Chinese Optics Letters
Vol. 13, Issue 10, 100604 (2015)

Improved modulation format identification based on Stokes parameters using combination of fuzzy c-means and hierarchical clustering in coherent optical communication system

Longxue Cheng¹, Lixia Xi^1、*, Donghe Zhao¹, Xianfeng Tang¹, Wenbo Zhang², and Xiaoguang Zhang¹

Author Affiliations

¹State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China

²School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

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DOI: 10.3788/COL201513.100604 Cite this Article Set citation alerts

Longxue Cheng, Lixia Xi, Donghe Zhao, Xianfeng Tang, Wenbo Zhang, Xiaoguang Zhang. Improved modulation format identification based on Stokes parameters using combination of fuzzy c-means and hierarchical clustering in coherent optical communication system[J]. Chinese Optics Letters, 2015, 13(10): 100604 Copy Citation Text

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Fig. 1. Stokes cluster inside the Poincaré sphere. (a) PM-BPSK, (b) PM-QPSK, (c) PM-8PSK, (d) PM-16-QAM, and (e) PM-32-QAM.

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Fig. 2. Constellation diagram of 16-QAM.

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Fig. 3. Stokes cluster with nonnegative coordinate values inside the Poincaré sphere. (a) PM-16-QAM and (b) PM-32-QAM.

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Fig. 4. Simulation setup and decision flowchart.

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Fig. 5. γmax versus OSNR for various modulation formats.

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Fig. 6. Probability of correct identification versus OSNR.

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Fig. 7. Probability of correct identification versus DGD.

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Amplitude ( $A_{x}$ or $A_{y}$ )	Phase ( $φ_{x}$ or $φ_{y}$ )
$\sqrt{2}$	$\pm \frac{π}{4}, \pm \frac{3 π}{4}$
$\sqrt{10}$	$\pm \frac{π}{10}, \pm \frac{4 π}{10}, \pm \frac{6 π}{10}, \pm \frac{9 π}{10}$
$3 \sqrt{2}$	$\pm \frac{π}{4}, \pm \frac{3 π}{4}$

Table 1. Amplitude and Phase of 16-QAM

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$(A_{x}, A_{y})$	$δ$	$(s_{1}, s_{2}, s_{3})$
$(\sqrt{2}, \sqrt{2})$	$0, \pm \frac{π}{2}, π$	$(0, 0, \pm 4), (0, \pm 4, 0)$ .
$(\sqrt{10}, \sqrt{10})$	$0, \pm \frac{2 π}{10}, \pm \frac{3 π}{10}, \pm \frac{5 π}{10}, \pm \frac{7 π}{10}, \pm \frac{8 π}{10}, π$	$(0, 0, \pm 20), (0, \pm 20, 0)$ , $(0, \pm 20 \cos \frac{2 π}{10}, \pm 20 \sin \frac{2 π}{10})$ , $(0, \pm 20 \cos \frac{3 π}{10}, \pm 20 \sin \frac{3 π}{10})$ .
$(3 \sqrt{2}, 3 \sqrt{2})$	$0, \pm \frac{π}{2}, π$	$(0, 0, \pm 36), (0, \pm 36, 0)$ .
$(\sqrt{2}, \sqrt{10})$	$\pm \frac{3 π}{20}, \pm \frac{7 π}{20}, \pm \frac{13 π}{20}, \pm \frac{17 π}{20}$	$(\pm 8, \pm 2 \sqrt{20} \cos \frac{3 π}{20}, \pm 2 \sqrt{20} \sin \frac{3 π}{20})$ , $(\pm 8, \pm 2 \sqrt{20} \cos \frac{7 π}{20}, \pm 2 \sqrt{20} \sin \frac{7 π}{20})$ .
$(\sqrt{2}, 3 \sqrt{2})$	$0, \pm \frac{π}{2}, π$	$(\pm 16, 0, \pm 12), (\pm 16, \pm 12, 0)$ .
$(\sqrt{10}, 3 \sqrt{2})$	$\pm \frac{3 π}{20}, \pm \frac{7 π}{20}, \pm \frac{13 π}{20}, \pm \frac{17 π}{20}$	$(\pm 8, \pm 6 \sqrt{20} \cos \frac{3 π}{20}, \pm 6 \sqrt{20} \sin \frac{3 π}{20})$ , $(\pm 8, \pm 6 \sqrt{20} \cos \frac{7 π}{20}, \pm 6 \sqrt{20} \sin \frac{7 π}{20})$ .