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

Chinese Optics Letters, Volume. 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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Figures & Tables(10)

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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Table 1. Amplitude and Phase of 16-QAM
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Table 1. Amplitude and Phase of 16-QAM
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 2. Possible Values of (s1,s2,s3)

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Table 2. Possible Values of (s1,s2,s3)

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

Table 3. Optimal Cluster Number
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Table 3. Optimal Cluster Number
BPSK QPSK 8PSK 16-QAM 32-QAM
Theoretical Value 2 4 8 14 43
Decision Metric [1,2] [4,5] [7,11] [12,28] [29,51]

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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

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