Abstract

A novel weighted K-means scheme for a probabilistic-shaped (PS) 64 quadrature amplitude modulation (QAM) signal is proposed in order to locate the decision points more accurately and enhance the robustness of clustering algorithm. By using a weighting factor following the reciprocal of Maxwell-Boltzmann distribution, the proposed algorithm can combine the advantages of PS and K-means robustly while reducing the overall computational complexity of the clustering process. Experimental verification of the proposed clustering technique was demonstrated in a 120-Gb/s probabilistic-shaped 64QAM coherent optical communication system. The results show that the proposed algorithm has outperformed K-means with respect to bit error rate (BER), clustering robustness and iteration times in both back-to-back and 375km transmission scenarios. For the back-to-back situation, the proposed algorithm is capable of achieving about 0.6dB and 1.8dB OSNR gain over K-means clustered signals and unclustered signals. For the case of transmission, the proposed clustering procedure can robustly locate the optimal decision points with launched signal power ranging from −5dBm to 5dBm, while the working range for K-means procedure is only −4dBm to 2dBm. In addition, the proposed weighted algorithm takes less iteration times than K-means to converge, especially when the signal impairments caused by fiber Kerr nonlinearity is severe.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (7)

K. Wang, Y. Wei, M. Zhao, W. Zhou, and J. Yu, “140-Gb/s PS-256-QAM Transmission in an OFDM System Using Kramers–Kronig Detection,” IEEE Photonics Technol. Lett. 31(17), 1405–1408 (2019).
[Crossref]

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[Crossref]

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[Crossref]

M. Kong, X. Li, J. Zhang, K. Wang, X. Xin, F. Zhao, and J. Yu, “High Spectral Efficiency 400 Gb/s Transmission by Different Modulation Formats and Advanced DSP,” J. Lightwave Technol. 37(20), 5317–5325 (2019).
[Crossref]

J. Ren, B. Liu, X. Xu, L. Zhang, Y. Mao, X. Wu, Y. Zhang, L. Jiang, and X. Xin, “A probabilistically shaped star-CAP-16/32 modulation based on constellation design with honeycomb-like decision regions,” Opt. Express 27(3), 2732–2746 (2019).
[Crossref]

H. Zhou, Y. Li, D. Lu, L. Yue, C. Gao, Y. Liu, R. Hao, Z. Zhao, W. Li, J. Qiu, X. Hong, H. Guo, Y. Zuo, and J. Wu, “Joint clock recovery and feed-forward equalization for PAM4 transmission,” Opt. Express 27(8), 11385–11395 (2019).
[Crossref]

J. Lin, H. Sepehrian, L. A. Rusch, and W. Shi, “Single-carrier 72 GBaud 32QAM and 84 GBaud 16QAM transmission using a SiP IQ modulator with joint digital-optical pre-compensation,” Opt. Express 27(4), 5610–5619 (2019).
[Crossref]

2018 (3)

2017 (4)

J. Zhang, W. Chen, M. Gao, and G. Shen, “K-means-clustering-based fiber nonlinearity equalization techniques for 64-QAM coherent optical communication system,” Opt. Express 25(22), 27570–27580 (2017).
[Crossref]

B. Liu, Y. Zhang, K. Wang, M. Kong, L. Zhang, Q. Zhang, Q. Tian, and X. Xin, “Performance Comparison of PS Star-16QAM and PS Square-Shaped 16QAM (Square-16QAM),” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

F. Li, J. Yu, Z. Cao, J. Zhang, M. Chen, and X. Li, “Experimental Demonstration of Four-Channel WDM 560 Gbit/s 128QAM-DMT Using IM/DD for 2-km Optical Interconnect,” J. Lightwave Technol. 35(4), 941–948 (2017).
[Crossref]

J. Yu, “Photonics-Assisted Millimeter-Wave Wireless Communication,” IEEE J. Quantum Electron. 53(6), 1–17 (2017).
[Crossref]

2016 (3)

2015 (1)

2014 (1)

2013 (1)

X. Zhou, L. E. Nelson, and P. Magill, “Rate-adaptable optics for next generation long-haul transport networks,” IEEE Commun. Mag. 51(3), 41–49 (2013).
[Crossref]

2010 (1)

N. G. Gonzalez, D. Zibar, A. Caballero, and I. T. Monroy, “Experimental 2.5-Gb/s QPSK WDM Phase-Modulated Radio-Over-Fiber Link With Digital Demodulation by a K-means Algorithm,” IEEE Photonics Technol. Lett. 22(5), 335–337 (2010).
[Crossref]

2006 (1)

Z. Tong, A. Nehorai, and B. Porat, “K-means clustering-based data detection and symbol-timing recovery for burst-mode optical receiver,” IEEE T. Commun. 54(8), 1492–1501 (2006).
[Crossref]

2004 (1)

1982 (1)

S. Lloyd, “Least squares quantization in PCM,” IEEE Trans. Inf. Theory 28(2), 129–137 (1982).
[Crossref]

Agrell, E.

Alvarado, A.

Bayvel, P.

Biondini, G.

Bocherer, G.

Buchali, F.

Caballero, A.

N. G. Gonzalez, D. Zibar, A. Caballero, and I. T. Monroy, “Experimental 2.5-Gb/s QPSK WDM Phase-Modulated Radio-Over-Fiber Link With Digital Demodulation by a K-means Algorithm,” IEEE Photonics Technol. Lett. 22(5), 335–337 (2010).
[Crossref]

Cai, Y.

H.-C. Chien, J. Yu, Y. Cai, B. Zhu, X. Xiao, Y. Xia, X. Wei, T. Wang, and Y. Chen, “Approaching Terabits Per Carrier Metro-Regional Transmission Using Beyond-100GBd Coherent Optics With Probabilistically Shaped DP-64QAM Modulation,” J. Lightwave Technol. 37(8), 1751–1755 (2019).
[Crossref]

H. Chien, J. Yu, B. Zhu, J. Shi, Y. Cai, X. Xiao, Y. Xia, X. Wei, and Y. Chen, “Probabilistically Shaped DP-64QAM Coherent Optics at 105 GBd Achieving 900 Gbps Net Bit Rate per Carrier over 800 km Transmission,” in 2018 European Conference on Optical Communication (ECOC), (2018), 1–3.

H. Chien, J. Zhang, J. Yu, and Y. Cai, “Single-carrier 400G PM-256QAM generation at 34 GBaud trading off bandwidth constraints and coding overheads,” in Proc. OFC 2017, paper W1J.3.

J. Yu, K. Wang, J. Zhang, B. Zhu, S. Dzioba, X. Li, H.-C. Chien, X. Xiao, Y. Cai, J. Shi, Y. Chen, S. Shi, and Y. Xia, “8×506-Gb/s 16QAM WDM Signal Coherent Transmission over 6000-km Enabled by PS and HB-CDM,” in Proc. OFC 2019, paper M2C.3.

Cao, Z.

Che, D.

Chen, M.

Chen, W.

Chen, Y.

H.-C. Chien, J. Yu, Y. Cai, B. Zhu, X. Xiao, Y. Xia, X. Wei, T. Wang, and Y. Chen, “Approaching Terabits Per Carrier Metro-Regional Transmission Using Beyond-100GBd Coherent Optics With Probabilistically Shaped DP-64QAM Modulation,” J. Lightwave Technol. 37(8), 1751–1755 (2019).
[Crossref]

H. Chien, J. Yu, B. Zhu, J. Shi, Y. Cai, X. Xiao, Y. Xia, X. Wei, and Y. Chen, “Probabilistically Shaped DP-64QAM Coherent Optics at 105 GBd Achieving 900 Gbps Net Bit Rate per Carrier over 800 km Transmission,” in 2018 European Conference on Optical Communication (ECOC), (2018), 1–3.

M. Kong, J. Yu, H. Chien, K. Wang, X. Li, J. Shi, L. Zhao, B. Zhu, X. Pan, X. Xin, B. Ye, Y. Xia, T. Wang, and Y. Chen, “WDM Transmission of 600G Carriers Over 5,600 km with Probabilistically Shaped 16QAM at 106 Gbaud,” in Proc. OFC 2018, paper M4I.3.

J. Yu, M. Kong, H. Chien, K. Wang, J. Shi, X. Li, X. Pan, X. Xin, Y. Xia, B. Ye, X. Wei, T. Wang, and Y. Chen, “400G/Channel 50-GHz WDM Coherent Transmission: PS 64QAM Versus Hybrid 32/64QAM,” in Proc. OFC 2019, paper Th3G.3.

J. Yu, K. Wang, H. Chien, B. Zhu, X. Li, J. Zhang, J. Shi, Y. Zhang, S. Shi, C. Ge, Y. Xia, and Y. Chen, “8×528Gb/s PS-64QAM Transmission over 3000 km in a Terrestrial System with an Amplifier Span of 100 km,” in 2018 European Conference on Optical Communication (ECOC), (2018), 1–3.

J. Yu, K. Wang, J. Zhang, B. Zhu, S. Dzioba, X. Li, H.-C. Chien, X. Xiao, Y. Cai, J. Shi, Y. Chen, S. Shi, and Y. Xia, “8×506-Gb/s 16QAM WDM Signal Coherent Transmission over 6000-km Enabled by PS and HB-CDM,” in Proc. OFC 2019, paper M2C.3.

Chen, Z.

Chien, H.

J. Yu, M. Kong, H. Chien, K. Wang, J. Shi, X. Li, X. Pan, X. Xin, Y. Xia, B. Ye, X. Wei, T. Wang, and Y. Chen, “400G/Channel 50-GHz WDM Coherent Transmission: PS 64QAM Versus Hybrid 32/64QAM,” in Proc. OFC 2019, paper Th3G.3.

J. Yu, K. Wang, H. Chien, B. Zhu, X. Li, J. Zhang, J. Shi, Y. Zhang, S. Shi, C. Ge, Y. Xia, and Y. Chen, “8×528Gb/s PS-64QAM Transmission over 3000 km in a Terrestrial System with an Amplifier Span of 100 km,” in 2018 European Conference on Optical Communication (ECOC), (2018), 1–3.

H. Chien, J. Yu, B. Zhu, J. Shi, Y. Cai, X. Xiao, Y. Xia, X. Wei, and Y. Chen, “Probabilistically Shaped DP-64QAM Coherent Optics at 105 GBd Achieving 900 Gbps Net Bit Rate per Carrier over 800 km Transmission,” in 2018 European Conference on Optical Communication (ECOC), (2018), 1–3.

M. Kong, J. Yu, H. Chien, K. Wang, X. Li, J. Shi, L. Zhao, B. Zhu, X. Pan, X. Xin, B. Ye, Y. Xia, T. Wang, and Y. Chen, “WDM Transmission of 600G Carriers Over 5,600 km with Probabilistically Shaped 16QAM at 106 Gbaud,” in Proc. OFC 2018, paper M4I.3.

H. Chien, J. Zhang, J. Yu, and Y. Cai, “Single-carrier 400G PM-256QAM generation at 34 GBaud trading off bandwidth constraints and coding overheads,” in Proc. OFC 2017, paper W1J.3.

Chien, H.-C.

H.-C. Chien, J. Yu, Y. Cai, B. Zhu, X. Xiao, Y. Xia, X. Wei, T. Wang, and Y. Chen, “Approaching Terabits Per Carrier Metro-Regional Transmission Using Beyond-100GBd Coherent Optics With Probabilistically Shaped DP-64QAM Modulation,” J. Lightwave Technol. 37(8), 1751–1755 (2019).
[Crossref]

J. Yu, K. Wang, J. Zhang, B. Zhu, S. Dzioba, X. Li, H.-C. Chien, X. Xiao, Y. Cai, J. Shi, Y. Chen, S. Shi, and Y. Xia, “8×506-Gb/s 16QAM WDM Signal Coherent Transmission over 6000-km Enabled by PS and HB-CDM,” in Proc. OFC 2019, paper M2C.3.

Deng, L.

Du, J.

L. Sun, J. Du, K. Xu, B. Liu, and Z. He, “K-means assisted soft decision of PAM4 to mitigate level nonlinearity and level-dependent noise for VCSEL-based 100-Gbps 100-m MMF optical interconnection,” in Proc. OFC 2019, paper M1F.5.

Dzioba, S.

J. Yu, K. Wang, J. Zhang, B. Zhu, S. Dzioba, X. Li, H.-C. Chien, X. Xiao, Y. Cai, J. Shi, Y. Chen, S. Shi, and Y. Xia, “8×506-Gb/s 16QAM WDM Signal Coherent Transmission over 6000-km Enabled by PS and HB-CDM,” in Proc. OFC 2019, paper M2C.3.

Fu, S.

Gao, C.

Gao, M.

Ge, C.

J. Yu, K. Wang, H. Chien, B. Zhu, X. Li, J. Zhang, J. Shi, Y. Zhang, S. Shi, C. Ge, Y. Xia, and Y. Chen, “8×528Gb/s PS-64QAM Transmission over 3000 km in a Terrestrial System with an Amplifier Span of 100 km,” in 2018 European Conference on Optical Communication (ECOC), (2018), 1–3.

Gonzalez, N. G.

N. G. Gonzalez, D. Zibar, A. Caballero, and I. T. Monroy, “Experimental 2.5-Gb/s QPSK WDM Phase-Modulated Radio-Over-Fiber Link With Digital Demodulation by a K-means Algorithm,” IEEE Photonics Technol. Lett. 22(5), 335–337 (2010).
[Crossref]

N. G. Gonzalez, D. Zibar, and I. T. Monroy, “Cognitive digital receiver for burst mode phase modulated radio over fiber links,” in 2010 European Conference on Optical Communication (ECOC), (2010), 1–3.

Guo, H.

Hao, R.

He, Z.

C. Xie, Z. Chen, S. Fu, W. Liu, Z. He, L. Deng, M. Tang, and D. Liu, “Achievable information rate enhancement of visible light communication using probabilistically shaped OFDM modulation,” Opt. Express 26(1), 367–375 (2018).
[Crossref]

L. Sun, J. Du, K. Xu, B. Liu, and Z. He, “K-means assisted soft decision of PAM4 to mitigate level nonlinearity and level-dependent noise for VCSEL-based 100-Gbps 100-m MMF optical interconnection,” in Proc. OFC 2019, paper M1F.5.

Hong, X.

Idler, W.

Jiang, L.

Kath, W. L.

Kong, M.

M. Kong, X. Li, J. Zhang, K. Wang, X. Xin, F. Zhao, and J. Yu, “High Spectral Efficiency 400 Gb/s Transmission by Different Modulation Formats and Advanced DSP,” J. Lightwave Technol. 37(20), 5317–5325 (2019).
[Crossref]

B. Liu, Y. Zhang, K. Wang, M. Kong, L. Zhang, Q. Zhang, Q. Tian, and X. Xin, “Performance Comparison of PS Star-16QAM and PS Square-Shaped 16QAM (Square-16QAM),” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

M. Kong, J. Yu, H. Chien, K. Wang, X. Li, J. Shi, L. Zhao, B. Zhu, X. Pan, X. Xin, B. Ye, Y. Xia, T. Wang, and Y. Chen, “WDM Transmission of 600G Carriers Over 5,600 km with Probabilistically Shaped 16QAM at 106 Gbaud,” in Proc. OFC 2018, paper M4I.3.

J. Yu, M. Kong, H. Chien, K. Wang, J. Shi, X. Li, X. Pan, X. Xin, Y. Xia, B. Ye, X. Wei, T. Wang, and Y. Chen, “400G/Channel 50-GHz WDM Coherent Transmission: PS 64QAM Versus Hybrid 32/64QAM,” in Proc. OFC 2019, paper Th3G.3.

Kschischang, F. R.

Lavery, D.

Li, F.

Li, G.

K. Wang, J. Zhang, M. Zhao, G. Li, C. Wang, and J. Yu, “A Joint Algorithm for Photonics-Aided Microwave-Communication System at K-Band,” IEEE Photonics Technol. Lett. 30(20), 1807–1810 (2018).
[Crossref]

Li, W.

Li, X.

X. Li, J. Yu, L. Zhao, K. Wang, C. Wang, M. Zhao, W. Zhou, and J. Xiao, “1-Tb/s Millimeter-Wave Signal Wireless Delivery at D-Band,” J. Lightwave Technol. 37(1), 196–204 (2019).
[Crossref]

M. Kong, X. Li, J. Zhang, K. Wang, X. Xin, F. Zhao, and J. Yu, “High Spectral Efficiency 400 Gb/s Transmission by Different Modulation Formats and Advanced DSP,” J. Lightwave Technol. 37(20), 5317–5325 (2019).
[Crossref]

F. Li, J. Yu, Z. Cao, J. Zhang, M. Chen, and X. Li, “Experimental Demonstration of Four-Channel WDM 560 Gbit/s 128QAM-DMT Using IM/DD for 2-km Optical Interconnect,” J. Lightwave Technol. 35(4), 941–948 (2017).
[Crossref]

X. Li, J. Xiao, and J. Yu, “Heterodyne detection and transmission of 60-Gbaud PDM-QPSK signal with SE of 4b/s/Hz,” Opt. Express 22(8), 9307–9313 (2014).
[Crossref]

J. Yu, K. Wang, J. Zhang, B. Zhu, S. Dzioba, X. Li, H.-C. Chien, X. Xiao, Y. Cai, J. Shi, Y. Chen, S. Shi, and Y. Xia, “8×506-Gb/s 16QAM WDM Signal Coherent Transmission over 6000-km Enabled by PS and HB-CDM,” in Proc. OFC 2019, paper M2C.3.

J. Yu, K. Wang, H. Chien, B. Zhu, X. Li, J. Zhang, J. Shi, Y. Zhang, S. Shi, C. Ge, Y. Xia, and Y. Chen, “8×528Gb/s PS-64QAM Transmission over 3000 km in a Terrestrial System with an Amplifier Span of 100 km,” in 2018 European Conference on Optical Communication (ECOC), (2018), 1–3.

J. Yu, M. Kong, H. Chien, K. Wang, J. Shi, X. Li, X. Pan, X. Xin, Y. Xia, B. Ye, X. Wei, T. Wang, and Y. Chen, “400G/Channel 50-GHz WDM Coherent Transmission: PS 64QAM Versus Hybrid 32/64QAM,” in Proc. OFC 2019, paper Th3G.3.

M. Kong, J. Yu, H. Chien, K. Wang, X. Li, J. Shi, L. Zhao, B. Zhu, X. Pan, X. Xin, B. Ye, Y. Xia, T. Wang, and Y. Chen, “WDM Transmission of 600G Carriers Over 5,600 km with Probabilistically Shaped 16QAM at 106 Gbaud,” in Proc. OFC 2018, paper M4I.3.

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J. Ren, B. Liu, X. Xu, L. Zhang, Y. Mao, X. Wu, Y. Zhang, L. Jiang, and X. Xin, “A probabilistically shaped star-CAP-16/32 modulation based on constellation design with honeycomb-like decision regions,” Opt. Express 27(3), 2732–2746 (2019).
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J. Yu, M. Kong, H. Chien, K. Wang, J. Shi, X. Li, X. Pan, X. Xin, Y. Xia, B. Ye, X. Wei, T. Wang, and Y. Chen, “400G/Channel 50-GHz WDM Coherent Transmission: PS 64QAM Versus Hybrid 32/64QAM,” in Proc. OFC 2019, paper Th3G.3.

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J. Yu, K. Wang, J. Zhang, B. Zhu, S. Dzioba, X. Li, H.-C. Chien, X. Xiao, Y. Cai, J. Shi, Y. Chen, S. Shi, and Y. Xia, “8×506-Gb/s 16QAM WDM Signal Coherent Transmission over 6000-km Enabled by PS and HB-CDM,” in Proc. OFC 2019, paper M2C.3.

J. Yu, M. Kong, H. Chien, K. Wang, J. Shi, X. Li, X. Pan, X. Xin, Y. Xia, B. Ye, X. Wei, T. Wang, and Y. Chen, “400G/Channel 50-GHz WDM Coherent Transmission: PS 64QAM Versus Hybrid 32/64QAM,” in Proc. OFC 2019, paper Th3G.3.

J. Yu, K. Wang, H. Chien, B. Zhu, X. Li, J. Zhang, J. Shi, Y. Zhang, S. Shi, C. Ge, Y. Xia, and Y. Chen, “8×528Gb/s PS-64QAM Transmission over 3000 km in a Terrestrial System with an Amplifier Span of 100 km,” in 2018 European Conference on Optical Communication (ECOC), (2018), 1–3.

M. Kong, J. Yu, H. Chien, K. Wang, X. Li, J. Shi, L. Zhao, B. Zhu, X. Pan, X. Xin, B. Ye, Y. Xia, T. Wang, and Y. Chen, “WDM Transmission of 600G Carriers Over 5,600 km with Probabilistically Shaped 16QAM at 106 Gbaud,” in Proc. OFC 2018, paper M4I.3.

H. Chien, J. Yu, B. Zhu, J. Shi, Y. Cai, X. Xiao, Y. Xia, X. Wei, and Y. Chen, “Probabilistically Shaped DP-64QAM Coherent Optics at 105 GBd Achieving 900 Gbps Net Bit Rate per Carrier over 800 km Transmission,” in 2018 European Conference on Optical Communication (ECOC), (2018), 1–3.

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J. Yu, K. Wang, H. Chien, B. Zhu, X. Li, J. Zhang, J. Shi, Y. Zhang, S. Shi, C. Ge, Y. Xia, and Y. Chen, “8×528Gb/s PS-64QAM Transmission over 3000 km in a Terrestrial System with an Amplifier Span of 100 km,” in 2018 European Conference on Optical Communication (ECOC), (2018), 1–3.

J. Yu, K. Wang, J. Zhang, B. Zhu, S. Dzioba, X. Li, H.-C. Chien, X. Xiao, Y. Cai, J. Shi, Y. Chen, S. Shi, and Y. Xia, “8×506-Gb/s 16QAM WDM Signal Coherent Transmission over 6000-km Enabled by PS and HB-CDM,” in Proc. OFC 2019, paper M2C.3.

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Shieh, W.

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Sun, C.

Sun, L.

L. Sun, J. Du, K. Xu, B. Liu, and Z. He, “K-means assisted soft decision of PAM4 to mitigate level nonlinearity and level-dependent noise for VCSEL-based 100-Gbps 100-m MMF optical interconnection,” in Proc. OFC 2019, paper M1F.5.

Tang, M.

Tian, Q.

B. Liu, Y. Zhang, K. Wang, M. Kong, L. Zhang, Q. Zhang, Q. Tian, and X. Xin, “Performance Comparison of PS Star-16QAM and PS Square-Shaped 16QAM (Square-16QAM),” IEEE Photonics J. 9(6), 1–8 (2017).
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Z. Tong, A. Nehorai, and B. Porat, “K-means clustering-based data detection and symbol-timing recovery for burst-mode optical receiver,” IEEE T. Commun. 54(8), 1492–1501 (2006).
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X. Li, J. Yu, L. Zhao, K. Wang, C. Wang, M. Zhao, W. Zhou, and J. Xiao, “1-Tb/s Millimeter-Wave Signal Wireless Delivery at D-Band,” J. Lightwave Technol. 37(1), 196–204 (2019).
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K. Wang, J. Zhang, M. Zhao, G. Li, C. Wang, and J. Yu, “A Joint Algorithm for Photonics-Aided Microwave-Communication System at K-Band,” IEEE Photonics Technol. Lett. 30(20), 1807–1810 (2018).
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X. Li, J. Yu, L. Zhao, K. Wang, C. Wang, M. Zhao, W. Zhou, and J. Xiao, “1-Tb/s Millimeter-Wave Signal Wireless Delivery at D-Band,” J. Lightwave Technol. 37(1), 196–204 (2019).
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K. Wang, Y. Wei, M. Zhao, W. Zhou, and J. Yu, “140-Gb/s PS-256-QAM Transmission in an OFDM System Using Kramers–Kronig Detection,” IEEE Photonics Technol. Lett. 31(17), 1405–1408 (2019).
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K. Wang, J. Zhang, M. Zhao, G. Li, C. Wang, and J. Yu, “A Joint Algorithm for Photonics-Aided Microwave-Communication System at K-Band,” IEEE Photonics Technol. Lett. 30(20), 1807–1810 (2018).
[Crossref]

B. Liu, Y. Zhang, K. Wang, M. Kong, L. Zhang, Q. Zhang, Q. Tian, and X. Xin, “Performance Comparison of PS Star-16QAM and PS Square-Shaped 16QAM (Square-16QAM),” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

J. Yu, K. Wang, J. Zhang, B. Zhu, S. Dzioba, X. Li, H.-C. Chien, X. Xiao, Y. Cai, J. Shi, Y. Chen, S. Shi, and Y. Xia, “8×506-Gb/s 16QAM WDM Signal Coherent Transmission over 6000-km Enabled by PS and HB-CDM,” in Proc. OFC 2019, paper M2C.3.

J. Yu, M. Kong, H. Chien, K. Wang, J. Shi, X. Li, X. Pan, X. Xin, Y. Xia, B. Ye, X. Wei, T. Wang, and Y. Chen, “400G/Channel 50-GHz WDM Coherent Transmission: PS 64QAM Versus Hybrid 32/64QAM,” in Proc. OFC 2019, paper Th3G.3.

J. Yu, K. Wang, H. Chien, B. Zhu, X. Li, J. Zhang, J. Shi, Y. Zhang, S. Shi, C. Ge, Y. Xia, and Y. Chen, “8×528Gb/s PS-64QAM Transmission over 3000 km in a Terrestrial System with an Amplifier Span of 100 km,” in 2018 European Conference on Optical Communication (ECOC), (2018), 1–3.

M. Kong, J. Yu, H. Chien, K. Wang, X. Li, J. Shi, L. Zhao, B. Zhu, X. Pan, X. Xin, B. Ye, Y. Xia, T. Wang, and Y. Chen, “WDM Transmission of 600G Carriers Over 5,600 km with Probabilistically Shaped 16QAM at 106 Gbaud,” in Proc. OFC 2018, paper M4I.3.

Wang, T.

H.-C. Chien, J. Yu, Y. Cai, B. Zhu, X. Xiao, Y. Xia, X. Wei, T. Wang, and Y. Chen, “Approaching Terabits Per Carrier Metro-Regional Transmission Using Beyond-100GBd Coherent Optics With Probabilistically Shaped DP-64QAM Modulation,” J. Lightwave Technol. 37(8), 1751–1755 (2019).
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M. Kong, J. Yu, H. Chien, K. Wang, X. Li, J. Shi, L. Zhao, B. Zhu, X. Pan, X. Xin, B. Ye, Y. Xia, T. Wang, and Y. Chen, “WDM Transmission of 600G Carriers Over 5,600 km with Probabilistically Shaped 16QAM at 106 Gbaud,” in Proc. OFC 2018, paper M4I.3.

J. Yu, M. Kong, H. Chien, K. Wang, J. Shi, X. Li, X. Pan, X. Xin, Y. Xia, B. Ye, X. Wei, T. Wang, and Y. Chen, “400G/Channel 50-GHz WDM Coherent Transmission: PS 64QAM Versus Hybrid 32/64QAM,” in Proc. OFC 2019, paper Th3G.3.

Wei, X.

H.-C. Chien, J. Yu, Y. Cai, B. Zhu, X. Xiao, Y. Xia, X. Wei, T. Wang, and Y. Chen, “Approaching Terabits Per Carrier Metro-Regional Transmission Using Beyond-100GBd Coherent Optics With Probabilistically Shaped DP-64QAM Modulation,” J. Lightwave Technol. 37(8), 1751–1755 (2019).
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J. Yu, M. Kong, H. Chien, K. Wang, J. Shi, X. Li, X. Pan, X. Xin, Y. Xia, B. Ye, X. Wei, T. Wang, and Y. Chen, “400G/Channel 50-GHz WDM Coherent Transmission: PS 64QAM Versus Hybrid 32/64QAM,” in Proc. OFC 2019, paper Th3G.3.

H. Chien, J. Yu, B. Zhu, J. Shi, Y. Cai, X. Xiao, Y. Xia, X. Wei, and Y. Chen, “Probabilistically Shaped DP-64QAM Coherent Optics at 105 GBd Achieving 900 Gbps Net Bit Rate per Carrier over 800 km Transmission,” in 2018 European Conference on Optical Communication (ECOC), (2018), 1–3.

Wei, Y.

K. Wang, Y. Wei, M. Zhao, W. Zhou, and J. Yu, “140-Gb/s PS-256-QAM Transmission in an OFDM System Using Kramers–Kronig Detection,” IEEE Photonics Technol. Lett. 31(17), 1405–1408 (2019).
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Wu, X.

Xia, Y.

H.-C. Chien, J. Yu, Y. Cai, B. Zhu, X. Xiao, Y. Xia, X. Wei, T. Wang, and Y. Chen, “Approaching Terabits Per Carrier Metro-Regional Transmission Using Beyond-100GBd Coherent Optics With Probabilistically Shaped DP-64QAM Modulation,” J. Lightwave Technol. 37(8), 1751–1755 (2019).
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H. Chien, J. Yu, B. Zhu, J. Shi, Y. Cai, X. Xiao, Y. Xia, X. Wei, and Y. Chen, “Probabilistically Shaped DP-64QAM Coherent Optics at 105 GBd Achieving 900 Gbps Net Bit Rate per Carrier over 800 km Transmission,” in 2018 European Conference on Optical Communication (ECOC), (2018), 1–3.

M. Kong, J. Yu, H. Chien, K. Wang, X. Li, J. Shi, L. Zhao, B. Zhu, X. Pan, X. Xin, B. Ye, Y. Xia, T. Wang, and Y. Chen, “WDM Transmission of 600G Carriers Over 5,600 km with Probabilistically Shaped 16QAM at 106 Gbaud,” in Proc. OFC 2018, paper M4I.3.

J. Yu, M. Kong, H. Chien, K. Wang, J. Shi, X. Li, X. Pan, X. Xin, Y. Xia, B. Ye, X. Wei, T. Wang, and Y. Chen, “400G/Channel 50-GHz WDM Coherent Transmission: PS 64QAM Versus Hybrid 32/64QAM,” in Proc. OFC 2019, paper Th3G.3.

J. Yu, K. Wang, H. Chien, B. Zhu, X. Li, J. Zhang, J. Shi, Y. Zhang, S. Shi, C. Ge, Y. Xia, and Y. Chen, “8×528Gb/s PS-64QAM Transmission over 3000 km in a Terrestrial System with an Amplifier Span of 100 km,” in 2018 European Conference on Optical Communication (ECOC), (2018), 1–3.

J. Yu, K. Wang, J. Zhang, B. Zhu, S. Dzioba, X. Li, H.-C. Chien, X. Xiao, Y. Cai, J. Shi, Y. Chen, S. Shi, and Y. Xia, “8×506-Gb/s 16QAM WDM Signal Coherent Transmission over 6000-km Enabled by PS and HB-CDM,” in Proc. OFC 2019, paper M2C.3.

Xiao, J.

Xiao, X.

H.-C. Chien, J. Yu, Y. Cai, B. Zhu, X. Xiao, Y. Xia, X. Wei, T. Wang, and Y. Chen, “Approaching Terabits Per Carrier Metro-Regional Transmission Using Beyond-100GBd Coherent Optics With Probabilistically Shaped DP-64QAM Modulation,” J. Lightwave Technol. 37(8), 1751–1755 (2019).
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H. Chien, J. Yu, B. Zhu, J. Shi, Y. Cai, X. Xiao, Y. Xia, X. Wei, and Y. Chen, “Probabilistically Shaped DP-64QAM Coherent Optics at 105 GBd Achieving 900 Gbps Net Bit Rate per Carrier over 800 km Transmission,” in 2018 European Conference on Optical Communication (ECOC), (2018), 1–3.

J. Yu, K. Wang, J. Zhang, B. Zhu, S. Dzioba, X. Li, H.-C. Chien, X. Xiao, Y. Cai, J. Shi, Y. Chen, S. Shi, and Y. Xia, “8×506-Gb/s 16QAM WDM Signal Coherent Transmission over 6000-km Enabled by PS and HB-CDM,” in Proc. OFC 2019, paper M2C.3.

Xie, C.

Xin, X.

M. Kong, X. Li, J. Zhang, K. Wang, X. Xin, F. Zhao, and J. Yu, “High Spectral Efficiency 400 Gb/s Transmission by Different Modulation Formats and Advanced DSP,” J. Lightwave Technol. 37(20), 5317–5325 (2019).
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J. Ren, B. Liu, X. Xu, L. Zhang, Y. Mao, X. Wu, Y. Zhang, L. Jiang, and X. Xin, “A probabilistically shaped star-CAP-16/32 modulation based on constellation design with honeycomb-like decision regions,” Opt. Express 27(3), 2732–2746 (2019).
[Crossref]

B. Liu, Y. Zhang, K. Wang, M. Kong, L. Zhang, Q. Zhang, Q. Tian, and X. Xin, “Performance Comparison of PS Star-16QAM and PS Square-Shaped 16QAM (Square-16QAM),” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

M. Kong, J. Yu, H. Chien, K. Wang, X. Li, J. Shi, L. Zhao, B. Zhu, X. Pan, X. Xin, B. Ye, Y. Xia, T. Wang, and Y. Chen, “WDM Transmission of 600G Carriers Over 5,600 km with Probabilistically Shaped 16QAM at 106 Gbaud,” in Proc. OFC 2018, paper M4I.3.

J. Yu, M. Kong, H. Chien, K. Wang, J. Shi, X. Li, X. Pan, X. Xin, Y. Xia, B. Ye, X. Wei, T. Wang, and Y. Chen, “400G/Channel 50-GHz WDM Coherent Transmission: PS 64QAM Versus Hybrid 32/64QAM,” in Proc. OFC 2019, paper Th3G.3.

Xu, K.

L. Sun, J. Du, K. Xu, B. Liu, and Z. He, “K-means assisted soft decision of PAM4 to mitigate level nonlinearity and level-dependent noise for VCSEL-based 100-Gbps 100-m MMF optical interconnection,” in Proc. OFC 2019, paper M1F.5.

Xu, X.

Ye, B.

J. Yu, M. Kong, H. Chien, K. Wang, J. Shi, X. Li, X. Pan, X. Xin, Y. Xia, B. Ye, X. Wei, T. Wang, and Y. Chen, “400G/Channel 50-GHz WDM Coherent Transmission: PS 64QAM Versus Hybrid 32/64QAM,” in Proc. OFC 2019, paper Th3G.3.

M. Kong, J. Yu, H. Chien, K. Wang, X. Li, J. Shi, L. Zhao, B. Zhu, X. Pan, X. Xin, B. Ye, Y. Xia, T. Wang, and Y. Chen, “WDM Transmission of 600G Carriers Over 5,600 km with Probabilistically Shaped 16QAM at 106 Gbaud,” in Proc. OFC 2018, paper M4I.3.

Yu, J.

M. Kong, X. Li, J. Zhang, K. Wang, X. Xin, F. Zhao, and J. Yu, “High Spectral Efficiency 400 Gb/s Transmission by Different Modulation Formats and Advanced DSP,” J. Lightwave Technol. 37(20), 5317–5325 (2019).
[Crossref]

H.-C. Chien, J. Yu, Y. Cai, B. Zhu, X. Xiao, Y. Xia, X. Wei, T. Wang, and Y. Chen, “Approaching Terabits Per Carrier Metro-Regional Transmission Using Beyond-100GBd Coherent Optics With Probabilistically Shaped DP-64QAM Modulation,” J. Lightwave Technol. 37(8), 1751–1755 (2019).
[Crossref]

X. Li, J. Yu, L. Zhao, K. Wang, C. Wang, M. Zhao, W. Zhou, and J. Xiao, “1-Tb/s Millimeter-Wave Signal Wireless Delivery at D-Band,” J. Lightwave Technol. 37(1), 196–204 (2019).
[Crossref]

K. Wang, Y. Wei, M. Zhao, W. Zhou, and J. Yu, “140-Gb/s PS-256-QAM Transmission in an OFDM System Using Kramers–Kronig Detection,” IEEE Photonics Technol. Lett. 31(17), 1405–1408 (2019).
[Crossref]

K. Wang, J. Zhang, M. Zhao, G. Li, C. Wang, and J. Yu, “A Joint Algorithm for Photonics-Aided Microwave-Communication System at K-Band,” IEEE Photonics Technol. Lett. 30(20), 1807–1810 (2018).
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J. Yu, K. Wang, J. Zhang, B. Zhu, S. Dzioba, X. Li, H.-C. Chien, X. Xiao, Y. Cai, J. Shi, Y. Chen, S. Shi, and Y. Xia, “8×506-Gb/s 16QAM WDM Signal Coherent Transmission over 6000-km Enabled by PS and HB-CDM,” in Proc. OFC 2019, paper M2C.3.

H. Chien, J. Zhang, J. Yu, and Y. Cai, “Single-carrier 400G PM-256QAM generation at 34 GBaud trading off bandwidth constraints and coding overheads,” in Proc. OFC 2017, paper W1J.3.

J. Yu, M. Kong, H. Chien, K. Wang, J. Shi, X. Li, X. Pan, X. Xin, Y. Xia, B. Ye, X. Wei, T. Wang, and Y. Chen, “400G/Channel 50-GHz WDM Coherent Transmission: PS 64QAM Versus Hybrid 32/64QAM,” in Proc. OFC 2019, paper Th3G.3.

J. Yu, K. Wang, H. Chien, B. Zhu, X. Li, J. Zhang, J. Shi, Y. Zhang, S. Shi, C. Ge, Y. Xia, and Y. Chen, “8×528Gb/s PS-64QAM Transmission over 3000 km in a Terrestrial System with an Amplifier Span of 100 km,” in 2018 European Conference on Optical Communication (ECOC), (2018), 1–3.

H. Chien, J. Yu, B. Zhu, J. Shi, Y. Cai, X. Xiao, Y. Xia, X. Wei, and Y. Chen, “Probabilistically Shaped DP-64QAM Coherent Optics at 105 GBd Achieving 900 Gbps Net Bit Rate per Carrier over 800 km Transmission,” in 2018 European Conference on Optical Communication (ECOC), (2018), 1–3.

M. Kong, J. Yu, H. Chien, K. Wang, X. Li, J. Shi, L. Zhao, B. Zhu, X. Pan, X. Xin, B. Ye, Y. Xia, T. Wang, and Y. Chen, “WDM Transmission of 600G Carriers Over 5,600 km with Probabilistically Shaped 16QAM at 106 Gbaud,” in Proc. OFC 2018, paper M4I.3.

Yue, L.

Zhang, J.

M. Kong, X. Li, J. Zhang, K. Wang, X. Xin, F. Zhao, and J. Yu, “High Spectral Efficiency 400 Gb/s Transmission by Different Modulation Formats and Advanced DSP,” J. Lightwave Technol. 37(20), 5317–5325 (2019).
[Crossref]

K. Wang, J. Zhang, M. Zhao, G. Li, C. Wang, and J. Yu, “A Joint Algorithm for Photonics-Aided Microwave-Communication System at K-Band,” IEEE Photonics Technol. Lett. 30(20), 1807–1810 (2018).
[Crossref]

F. Li, J. Yu, Z. Cao, J. Zhang, M. Chen, and X. Li, “Experimental Demonstration of Four-Channel WDM 560 Gbit/s 128QAM-DMT Using IM/DD for 2-km Optical Interconnect,” J. Lightwave Technol. 35(4), 941–948 (2017).
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H. Chien, J. Zhang, J. Yu, and Y. Cai, “Single-carrier 400G PM-256QAM generation at 34 GBaud trading off bandwidth constraints and coding overheads,” in Proc. OFC 2017, paper W1J.3.

J. Yu, K. Wang, J. Zhang, B. Zhu, S. Dzioba, X. Li, H.-C. Chien, X. Xiao, Y. Cai, J. Shi, Y. Chen, S. Shi, and Y. Xia, “8×506-Gb/s 16QAM WDM Signal Coherent Transmission over 6000-km Enabled by PS and HB-CDM,” in Proc. OFC 2019, paper M2C.3.

J. Yu, K. Wang, H. Chien, B. Zhu, X. Li, J. Zhang, J. Shi, Y. Zhang, S. Shi, C. Ge, Y. Xia, and Y. Chen, “8×528Gb/s PS-64QAM Transmission over 3000 km in a Terrestrial System with an Amplifier Span of 100 km,” in 2018 European Conference on Optical Communication (ECOC), (2018), 1–3.

Zhang, L.

J. Ren, B. Liu, X. Xu, L. Zhang, Y. Mao, X. Wu, Y. Zhang, L. Jiang, and X. Xin, “A probabilistically shaped star-CAP-16/32 modulation based on constellation design with honeycomb-like decision regions,” Opt. Express 27(3), 2732–2746 (2019).
[Crossref]

B. Liu, Y. Zhang, K. Wang, M. Kong, L. Zhang, Q. Zhang, Q. Tian, and X. Xin, “Performance Comparison of PS Star-16QAM and PS Square-Shaped 16QAM (Square-16QAM),” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

Zhang, Q.

B. Liu, Y. Zhang, K. Wang, M. Kong, L. Zhang, Q. Zhang, Q. Tian, and X. Xin, “Performance Comparison of PS Star-16QAM and PS Square-Shaped 16QAM (Square-16QAM),” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

Q. Zhang and C. Shu, “Performance Evaluation of K-means Clustering Assisted Common Phase Error Estimation,” in Conference on Lasers and Electro-Optics (CLEO) (2016), paper SW3O.3.

Zhang, Y.

J. Ren, B. Liu, X. Xu, L. Zhang, Y. Mao, X. Wu, Y. Zhang, L. Jiang, and X. Xin, “A probabilistically shaped star-CAP-16/32 modulation based on constellation design with honeycomb-like decision regions,” Opt. Express 27(3), 2732–2746 (2019).
[Crossref]

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N. G. Gonzalez, D. Zibar, and I. T. Monroy, “Cognitive digital receiver for burst mode phase modulated radio over fiber links,” in 2010 European Conference on Optical Communication (ECOC), (2010), 1–3.

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M. Kong, J. Yu, H. Chien, K. Wang, X. Li, J. Shi, L. Zhao, B. Zhu, X. Pan, X. Xin, B. Ye, Y. Xia, T. Wang, and Y. Chen, “WDM Transmission of 600G Carriers Over 5,600 km with Probabilistically Shaped 16QAM at 106 Gbaud,” in Proc. OFC 2018, paper M4I.3.

J. Yu, K. Wang, H. Chien, B. Zhu, X. Li, J. Zhang, J. Shi, Y. Zhang, S. Shi, C. Ge, Y. Xia, and Y. Chen, “8×528Gb/s PS-64QAM Transmission over 3000 km in a Terrestrial System with an Amplifier Span of 100 km,” in 2018 European Conference on Optical Communication (ECOC), (2018), 1–3.

H. Chien, J. Yu, B. Zhu, J. Shi, Y. Cai, X. Xiao, Y. Xia, X. Wei, and Y. Chen, “Probabilistically Shaped DP-64QAM Coherent Optics at 105 GBd Achieving 900 Gbps Net Bit Rate per Carrier over 800 km Transmission,” in 2018 European Conference on Optical Communication (ECOC), (2018), 1–3.

J. Yu, M. Kong, H. Chien, K. Wang, J. Shi, X. Li, X. Pan, X. Xin, Y. Xia, B. Ye, X. Wei, T. Wang, and Y. Chen, “400G/Channel 50-GHz WDM Coherent Transmission: PS 64QAM Versus Hybrid 32/64QAM,” in Proc. OFC 2019, paper Th3G.3.

H. Chien, J. Zhang, J. Yu, and Y. Cai, “Single-carrier 400G PM-256QAM generation at 34 GBaud trading off bandwidth constraints and coding overheads,” in Proc. OFC 2017, paper W1J.3.

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Figures (9)

Fig. 1.
Fig. 1. A schematic illustration for the PS of the 64QAM signal.
Fig. 2.
Fig. 2. Illustration of deploying clustering algorithms to PS 64QAM, when: (a) the OSNR is 19dB; (b) the OSNR is 24dB yet the nonlinear effects are not severe; (c) the OSNR is 32dB and the signal constellation is suffering from strong nonlinear effects.
Fig. 3.
Fig. 3. Experiment Setup for the 64QAM coherent optical communication system.
Fig. 4.
Fig. 4. Flow chart of the offline digital signal processing.
Fig. 5.
Fig. 5. Optical spectra of 10 GBaud Uniform 64QAM and 11.5 GBaud PS 64QAM.
Fig. 6.
Fig. 6. Measured BER curves versus OSNR in the 120-Gb/s 64 QAM coherent optical communication system for back-to-back case.
Fig. 7.
Fig. 7. Measured BER curves versus launched signal power into 375 km SMF ${P_{in}}$ (dBm) in the 120-Gb/s 64 QAM coherent optical communication system.
Fig. 8.
Fig. 8. Constellation diagrams and the clustering results of PS 64 QAM signal with the launched power at 5dBm with: (a) K-means procedure; (b) weighted K-means procedure.
Fig. 9.
Fig. 9. Iteration times and CPU running time versus launched signal power into 375 km SMF ${P_{in}}$ (dBm) in the 120-Gb/s 64 QAM coherent optical communication system.

Equations (5)

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P X ( x i ) =  exp ( ν ( Re ( x i ) 2 + Im ( x i ) 2 ) ) k = 1 M exp ( ν ( Re ( x k ) 2 + Im ( x k ) 2 ) )
H = i = 1 64 P X ( x i log 2 P X ( x i
α i  =  k = 1 M exp ( ν ( Re ( x k ) 2 + Im ( x k ) 2 ) ) exp ( ν ( Re ( X i ) 2 + Im ( X i ) 2 ) )
D ( X i , O j ) = q = 1 m ( X i q O j q ) 2   1 i N , 1 j K
O j = X i S j α i X i | S j | × X i S j α i   1 i | S j | , 1 j k

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