Abstract

An effective bit-based support vector machine (SVM) is proposed as a non-parameter nonlinear mitigation approach in the millimeter-wave radio-over-fiber (RoF) mobile fronthaul (MFH) system for various modulation formats. First, we analyze the impairments originated from nonlinearities in the millimeter-wave RoF system. Then we introduce the operation principle of the bit-based SVM detector. As a classifier, the SVM can create nonlinear decision boundaries by kernel function to mitigate the distortions caused by both linear and nonlinear noise. In our design, SVM can learn and capture the link characteristics from only a few training data without requiring the prior estimation of the system link. The bit-based SVM only needs log2M SVMs to detect the signal of M-order modulation format. Experimental results have been obtained to verify the feasibility of the proposed method. The sensitivities are improved by 1.2-dB for 16-QAM, 1.3-dB for 64-QAM, 1.8-dB for 16-APSK and 1.3-dB for 32-APSK at BER = 1E-3 with SVM detector, respectively. The proposed bit-based SVM gains a large improvement in the nonlinear system tolerance and outperforms the system employing k-means algorithm.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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2017 (4)

D. Wang, M. Zhang, Z. Li, C. Song, M. Fu, J. Li, and X. Chen, “System impairment compensation in coherent optical communications by using a bio-inspired detector based on artificial neural network and genetic algorithm,” Opt. Commun. 399, 1–12 (2017).

D. Wang, M. Zhang, J. Li, Z. Li, J. Li, C. Song, and X. Chen, “Intelligent constellation diagram analyzer using convolutional neural network-based deep learning,” Opt. Express 25(15), 17150–17166 (2017).
[PubMed]

D. Wang, M. Zhang, Z. Li, J. Li, M. Fu, Y. Cui, and X. Chen, “Modulation format recognition and OSNR estimation using CNN-based deep learning,” IEEE Photonics Technol. Lett. 29, 1667 (2017).

S. Liu, M. Xu, J. Wan, F. Lu, W. Zhang, H. Tian, and G. K. Chang, “A Multi-level Artificial Neural Network Nonlinear Equalizer for Millimeter-wave Mobile Fronthaul Systems,” J. Lightwave Technol. 35, 4406 (2017).

2016 (5)

D. Wang, M. Zhang, Z. Cai, Y. Cui, Z. Li, H. Han, and B. Luo, “Combatting nonlinear phase noise in coherent optical systems with an optimized decision processor based on machine learning,” Opt. Commun. 369, 199–208 (2016).

D. Wang, M. Zhang, M. Fu, Z. Cai, Z. Li, H. Han, Y. Cui, and B. Luo, “Nonlinearity mitigation using a machine learning detector based on k-nearest neighbors,” IEEE Photonics Technol. Lett. 28(19), 2102–2105 (2016).

P. Liu, M. Di Renzo, and A. Springer, “Line-of-sight spatial modulation for indoor mmWave communication at 60 GHz,” IEEE Trans. Wirel. Commun. 15(11), 7373–7389 (2016).

S. Liu, G. Shen, Y. Kou, and H. Tian, “Special cascade LMS equalization scheme suitable for 60-GHz RoF transmission system,” Opt. Express 24(10), 10599–10610 (2016).
[PubMed]

F. Lu, M. Xu, L. Cheng, J. Wang, J. Zhang, and G. K. Chang, “Non-orthogonal multiple access with successive interference cancellation in millimeter-wave radio-over-fiber systems,” J. Lightwave Technol. 34(17), 4179–4186 (2016).

2014 (4)

J. Wang, C. Liu, M. Zhu, A. Yi, L. Cheng, and G. K. Chang, “Investigation of data-dependent channel cross-modulation in multiband radio-over-fiber systems,” J. Lightwave Technol. 32(10), 1861–1871 (2014).

J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. Soong, and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Comm. 32(6), 1065–1082 (2014).

T. Watanabe, D. Kessler, C. Scott, M. Angstadt, and C. Sripada, “Disease prediction based on functional connectomes using a scalable and spatially-informed support vector machine,” Neuroimage 96, 183–202 (2014).
[PubMed]

Y. Han, S. Yu, M. Li, J. Yang, and W. Gu, “An SVM-based detection for coherent optical APSK systems with nonlinear phase noise,” IEEE Photonics J. 6(5), 1–10 (2014).

2013 (4)

C. Hager, A. G. Amat, A. Alvarado, and E. Agrell, “Design of APSK constellations for coherent optical channels with nonlinear phase noise,” IEEE Trans. Commun. 61(8), 3362–3373 (2013).

B. Szafraniec, T. S. Marshall, and B. Nebendahl, “Performance monitoring and measurement techniques for coherent optical systems,” J. Lightwave Technol. 31(4), 648–663 (2013).

Z. Wang, H. Yin, W. Zhang, and G. Wei, “Monobit digital receivers for QPSK: design, performance and impact of IQ imbalances,” IEEE Trans. Commun. 61(8), 3292–3303 (2013).

L. Li, G. Zhang, X. Zheng, S. Li, H. Zhang, and B. Zhou, “Phase noise suppression for single-sideband, modulation radio-over-fiber systems adopting optical spectrum processing,” IEEE Photonics Technol. Lett. 25(11), 1024–1026 (2013).

2012 (2)

M. Baldi, F. Chiaraluce, A. De Angelis, R. Marchesani, and S. Schillaci, “A comparison between APSK and QAM in wireless tactical scenarios for land mobile systems,” EURASIP J. Wirel. Commun. Netw. 2012(1), 317 (2012).

P. Du, K. Tan, and X. Xing, “A novel binary tree support vector machine for hyperspectral remote sensing image classification,” Opt. Commun. 285(13), 3054–3060 (2012).

2011 (2)

A. Mian, “Illumination invariant recognition and 3D reconstruction of faces using desktop optics,” Opt. Express 19(8), 7491–7506 (2011).
[PubMed]

Z. Liu, Q. Xie, K. Peng, and Z. Yang, “APSK constellation with Gray mapping,” IEEE Commun. Lett. 15(12), 1271–1273 (2011).

2010 (4)

S. J. Savory, “Digital coherent optical receivers: Algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).

A. Hekkala, M. Lasanen, I. Harjula, L. C. Viera, N. J. Gomes, and A. Nkansah, “Analysis of and compensation for non-ideal RoF links in DAS [coordinated and distributed MIMO],” IEEE Wirel. Commun. 17(3), 5490979 (2010).

J. James, P. Shen, A. Nkansah, X. Liang, and N. J. Gomes, “Nonlinearity and noise effects in multi-level signal millimeter-wave over fiber transmission using single and dual wavelength modulation,” IEEE Trans. Microw. Theory Tech. 58(11), 3189–3198 (2010).

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).

2006 (1)

Z. Jia, J. Yu, and G. K. Chang, “A full-duplex radio-over-fiber system based on optical carrier suppression and reuse,” IEEE Photonics Technol. Lett. 18(16), 1726–1728 (2006).

1991 (1)

D. Marcuse, A. R. Chraplyvy, and R. Tkach, “Effect of fiber nonlinearity on long-distance transmission,” J. Lightwave Technol. 9(1), 121–128 (1991).

Agrell, E.

C. Hager, A. G. Amat, A. Alvarado, and E. Agrell, “Design of APSK constellations for coherent optical channels with nonlinear phase noise,” IEEE Trans. Commun. 61(8), 3362–3373 (2013).

Alvarado, A.

C. Hager, A. G. Amat, A. Alvarado, and E. Agrell, “Design of APSK constellations for coherent optical channels with nonlinear phase noise,” IEEE Trans. Commun. 61(8), 3362–3373 (2013).

Amat, A. G.

C. Hager, A. G. Amat, A. Alvarado, and E. Agrell, “Design of APSK constellations for coherent optical channels with nonlinear phase noise,” IEEE Trans. Commun. 61(8), 3362–3373 (2013).

Andrekson, P.

N. Jiang, Y. Gong, J. Karout, H. Wymeersch, P. Johannisson, M. Karlsson, and P. Andrekson, “Stochastic backpropagation for coherent optical communications,” in European Conference and Exposition on Optical Communications, Optical Society of America, (2011).

Andrews, J. G.

J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. Soong, and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Comm. 32(6), 1065–1082 (2014).

Angstadt, M.

T. Watanabe, D. Kessler, C. Scott, M. Angstadt, and C. Sripada, “Disease prediction based on functional connectomes using a scalable and spatially-informed support vector machine,” Neuroimage 96, 183–202 (2014).
[PubMed]

Baldi, M.

M. Baldi, F. Chiaraluce, A. De Angelis, R. Marchesani, and S. Schillaci, “A comparison between APSK and QAM in wireless tactical scenarios for land mobile systems,” EURASIP J. Wirel. Commun. Netw. 2012(1), 317 (2012).

Buzzi, S.

J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. Soong, and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Comm. 32(6), 1065–1082 (2014).

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).

Cai, Z.

D. Wang, M. Zhang, M. Fu, Z. Cai, Z. Li, H. Han, Y. Cui, and B. Luo, “Nonlinearity mitigation using a machine learning detector based on k-nearest neighbors,” IEEE Photonics Technol. Lett. 28(19), 2102–2105 (2016).

D. Wang, M. Zhang, Z. Cai, Y. Cui, Z. Li, H. Han, and B. Luo, “Combatting nonlinear phase noise in coherent optical systems with an optimized decision processor based on machine learning,” Opt. Commun. 369, 199–208 (2016).

Chang, G. K.

S. Liu, M. Xu, J. Wan, F. Lu, W. Zhang, H. Tian, and G. K. Chang, “A Multi-level Artificial Neural Network Nonlinear Equalizer for Millimeter-wave Mobile Fronthaul Systems,” J. Lightwave Technol. 35, 4406 (2017).

F. Lu, M. Xu, L. Cheng, J. Wang, J. Zhang, and G. K. Chang, “Non-orthogonal multiple access with successive interference cancellation in millimeter-wave radio-over-fiber systems,” J. Lightwave Technol. 34(17), 4179–4186 (2016).

J. Wang, C. Liu, M. Zhu, A. Yi, L. Cheng, and G. K. Chang, “Investigation of data-dependent channel cross-modulation in multiband radio-over-fiber systems,” J. Lightwave Technol. 32(10), 1861–1871 (2014).

Z. Jia, J. Yu, and G. K. Chang, “A full-duplex radio-over-fiber system based on optical carrier suppression and reuse,” IEEE Photonics Technol. Lett. 18(16), 1726–1728 (2006).

L. Cheng, M. Xu, F. Lu, J. Wang, J. Zhang, X. Ma, and G. K. Chang, “Millimeter-wave cell grouping for optimized coverage based on radio-over-fiber and centralized processing,” in Optical Fiber Communication Conference, Optical Society of America (2016).

Chen, X.

D. Wang, M. Zhang, Z. Li, C. Song, M. Fu, J. Li, and X. Chen, “System impairment compensation in coherent optical communications by using a bio-inspired detector based on artificial neural network and genetic algorithm,” Opt. Commun. 399, 1–12 (2017).

D. Wang, M. Zhang, Z. Li, J. Li, M. Fu, Y. Cui, and X. Chen, “Modulation format recognition and OSNR estimation using CNN-based deep learning,” IEEE Photonics Technol. Lett. 29, 1667 (2017).

D. Wang, M. Zhang, J. Li, Z. Li, J. Li, C. Song, and X. Chen, “Intelligent constellation diagram analyzer using convolutional neural network-based deep learning,” Opt. Express 25(15), 17150–17166 (2017).
[PubMed]

Cheng, L.

Chiaraluce, F.

M. Baldi, F. Chiaraluce, A. De Angelis, R. Marchesani, and S. Schillaci, “A comparison between APSK and QAM in wireless tactical scenarios for land mobile systems,” EURASIP J. Wirel. Commun. Netw. 2012(1), 317 (2012).

Choi, W.

J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. Soong, and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Comm. 32(6), 1065–1082 (2014).

Chraplyvy, A. R.

D. Marcuse, A. R. Chraplyvy, and R. Tkach, “Effect of fiber nonlinearity on long-distance transmission,” J. Lightwave Technol. 9(1), 121–128 (1991).

Cui, Y.

D. Wang, M. Zhang, Z. Li, J. Li, M. Fu, Y. Cui, and X. Chen, “Modulation format recognition and OSNR estimation using CNN-based deep learning,” IEEE Photonics Technol. Lett. 29, 1667 (2017).

D. Wang, M. Zhang, M. Fu, Z. Cai, Z. Li, H. Han, Y. Cui, and B. Luo, “Nonlinearity mitigation using a machine learning detector based on k-nearest neighbors,” IEEE Photonics Technol. Lett. 28(19), 2102–2105 (2016).

D. Wang, M. Zhang, Z. Cai, Y. Cui, Z. Li, H. Han, and B. Luo, “Combatting nonlinear phase noise in coherent optical systems with an optimized decision processor based on machine learning,” Opt. Commun. 369, 199–208 (2016).

De Angelis, A.

M. Baldi, F. Chiaraluce, A. De Angelis, R. Marchesani, and S. Schillaci, “A comparison between APSK and QAM in wireless tactical scenarios for land mobile systems,” EURASIP J. Wirel. Commun. Netw. 2012(1), 317 (2012).

Di Renzo, M.

P. Liu, M. Di Renzo, and A. Springer, “Line-of-sight spatial modulation for indoor mmWave communication at 60 GHz,” IEEE Trans. Wirel. Commun. 15(11), 7373–7389 (2016).

Du, P.

P. Du, K. Tan, and X. Xing, “A novel binary tree support vector machine for hyperspectral remote sensing image classification,” Opt. Commun. 285(13), 3054–3060 (2012).

Fu, M.

D. Wang, M. Zhang, Z. Li, J. Li, M. Fu, Y. Cui, and X. Chen, “Modulation format recognition and OSNR estimation using CNN-based deep learning,” IEEE Photonics Technol. Lett. 29, 1667 (2017).

D. Wang, M. Zhang, Z. Li, C. Song, M. Fu, J. Li, and X. Chen, “System impairment compensation in coherent optical communications by using a bio-inspired detector based on artificial neural network and genetic algorithm,” Opt. Commun. 399, 1–12 (2017).

D. Wang, M. Zhang, M. Fu, Z. Cai, Z. Li, H. Han, Y. Cui, and B. Luo, “Nonlinearity mitigation using a machine learning detector based on k-nearest neighbors,” IEEE Photonics Technol. Lett. 28(19), 2102–2105 (2016).

Gomes, N. J.

J. James, P. Shen, A. Nkansah, X. Liang, and N. J. Gomes, “Nonlinearity and noise effects in multi-level signal millimeter-wave over fiber transmission using single and dual wavelength modulation,” IEEE Trans. Microw. Theory Tech. 58(11), 3189–3198 (2010).

A. Hekkala, M. Lasanen, I. Harjula, L. C. Viera, N. J. Gomes, and A. Nkansah, “Analysis of and compensation for non-ideal RoF links in DAS [coordinated and distributed MIMO],” IEEE Wirel. Commun. 17(3), 5490979 (2010).

A. Hekkala, M. Lasanen, L. C. Vieira, N. J. Gomes, and A. Nkansah, “Architectures for joint compensation of RoF and PA with nonideal feedback,” in Vehicular Technology Conference (IEEE, 2010).

Gong, Y.

N. Jiang, Y. Gong, J. Karout, H. Wymeersch, P. Johannisson, M. Karlsson, and P. Andrekson, “Stochastic backpropagation for coherent optical communications,” in European Conference and Exposition on Optical Communications, Optical Society of America, (2011).

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).

Gu, W.

Y. Han, S. Yu, M. Li, J. Yang, and W. Gu, “An SVM-based detection for coherent optical APSK systems with nonlinear phase noise,” IEEE Photonics J. 6(5), 1–10 (2014).

Hager, C.

C. Hager, A. G. Amat, A. Alvarado, and E. Agrell, “Design of APSK constellations for coherent optical channels with nonlinear phase noise,” IEEE Trans. Commun. 61(8), 3362–3373 (2013).

Han, H.

D. Wang, M. Zhang, M. Fu, Z. Cai, Z. Li, H. Han, Y. Cui, and B. Luo, “Nonlinearity mitigation using a machine learning detector based on k-nearest neighbors,” IEEE Photonics Technol. Lett. 28(19), 2102–2105 (2016).

D. Wang, M. Zhang, Z. Cai, Y. Cui, Z. Li, H. Han, and B. Luo, “Combatting nonlinear phase noise in coherent optical systems with an optimized decision processor based on machine learning,” Opt. Commun. 369, 199–208 (2016).

Han, Y.

Y. Han, S. Yu, M. Li, J. Yang, and W. Gu, “An SVM-based detection for coherent optical APSK systems with nonlinear phase noise,” IEEE Photonics J. 6(5), 1–10 (2014).

Hanly, S. V.

J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. Soong, and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Comm. 32(6), 1065–1082 (2014).

Harjula, I.

A. Hekkala, M. Lasanen, I. Harjula, L. C. Viera, N. J. Gomes, and A. Nkansah, “Analysis of and compensation for non-ideal RoF links in DAS [coordinated and distributed MIMO],” IEEE Wirel. Commun. 17(3), 5490979 (2010).

Hekkala, A.

A. Hekkala, M. Lasanen, I. Harjula, L. C. Viera, N. J. Gomes, and A. Nkansah, “Analysis of and compensation for non-ideal RoF links in DAS [coordinated and distributed MIMO],” IEEE Wirel. Commun. 17(3), 5490979 (2010).

A. Hekkala, M. Lasanen, L. C. Vieira, N. J. Gomes, and A. Nkansah, “Architectures for joint compensation of RoF and PA with nonideal feedback,” in Vehicular Technology Conference (IEEE, 2010).

James, J.

J. James, P. Shen, A. Nkansah, X. Liang, and N. J. Gomes, “Nonlinearity and noise effects in multi-level signal millimeter-wave over fiber transmission using single and dual wavelength modulation,” IEEE Trans. Microw. Theory Tech. 58(11), 3189–3198 (2010).

Jia, Z.

Z. Jia, J. Yu, and G. K. Chang, “A full-duplex radio-over-fiber system based on optical carrier suppression and reuse,” IEEE Photonics Technol. Lett. 18(16), 1726–1728 (2006).

Jiang, N.

N. Jiang, Y. Gong, J. Karout, H. Wymeersch, P. Johannisson, M. Karlsson, and P. Andrekson, “Stochastic backpropagation for coherent optical communications,” in European Conference and Exposition on Optical Communications, Optical Society of America, (2011).

Johannisson, P.

N. Jiang, Y. Gong, J. Karout, H. Wymeersch, P. Johannisson, M. Karlsson, and P. Andrekson, “Stochastic backpropagation for coherent optical communications,” in European Conference and Exposition on Optical Communications, Optical Society of America, (2011).

Karlsson, M.

N. Jiang, Y. Gong, J. Karout, H. Wymeersch, P. Johannisson, M. Karlsson, and P. Andrekson, “Stochastic backpropagation for coherent optical communications,” in European Conference and Exposition on Optical Communications, Optical Society of America, (2011).

Karout, J.

N. Jiang, Y. Gong, J. Karout, H. Wymeersch, P. Johannisson, M. Karlsson, and P. Andrekson, “Stochastic backpropagation for coherent optical communications,” in European Conference and Exposition on Optical Communications, Optical Society of America, (2011).

Kawanishi, T.

T. Kuri, T. Sakamoto, and T. Kawanishi, “An effect of detuning frequency in DSP-assisted offset-frequency-spaced two-tone optical coherent detection for radio-over-fiber signal,” in Photonics Conference (IPC) (2014).

Kessler, D.

T. Watanabe, D. Kessler, C. Scott, M. Angstadt, and C. Sripada, “Disease prediction based on functional connectomes using a scalable and spatially-informed support vector machine,” Neuroimage 96, 183–202 (2014).
[PubMed]

Kou, Y.

Kuri, T.

T. Kuri, T. Sakamoto, and T. Kawanishi, “An effect of detuning frequency in DSP-assisted offset-frequency-spaced two-tone optical coherent detection for radio-over-fiber signal,” in Photonics Conference (IPC) (2014).

Lasanen, M.

A. Hekkala, M. Lasanen, I. Harjula, L. C. Viera, N. J. Gomes, and A. Nkansah, “Analysis of and compensation for non-ideal RoF links in DAS [coordinated and distributed MIMO],” IEEE Wirel. Commun. 17(3), 5490979 (2010).

A. Hekkala, M. Lasanen, L. C. Vieira, N. J. Gomes, and A. Nkansah, “Architectures for joint compensation of RoF and PA with nonideal feedback,” in Vehicular Technology Conference (IEEE, 2010).

Li, J.

D. Wang, M. Zhang, Z. Li, C. Song, M. Fu, J. Li, and X. Chen, “System impairment compensation in coherent optical communications by using a bio-inspired detector based on artificial neural network and genetic algorithm,” Opt. Commun. 399, 1–12 (2017).

D. Wang, M. Zhang, Z. Li, J. Li, M. Fu, Y. Cui, and X. Chen, “Modulation format recognition and OSNR estimation using CNN-based deep learning,” IEEE Photonics Technol. Lett. 29, 1667 (2017).

D. Wang, M. Zhang, J. Li, Z. Li, J. Li, C. Song, and X. Chen, “Intelligent constellation diagram analyzer using convolutional neural network-based deep learning,” Opt. Express 25(15), 17150–17166 (2017).
[PubMed]

D. Wang, M. Zhang, J. Li, Z. Li, J. Li, C. Song, and X. Chen, “Intelligent constellation diagram analyzer using convolutional neural network-based deep learning,” Opt. Express 25(15), 17150–17166 (2017).
[PubMed]

Li, L.

L. Li, G. Zhang, X. Zheng, S. Li, H. Zhang, and B. Zhou, “Phase noise suppression for single-sideband, modulation radio-over-fiber systems adopting optical spectrum processing,” IEEE Photonics Technol. Lett. 25(11), 1024–1026 (2013).

Li, M.

Y. Han, S. Yu, M. Li, J. Yang, and W. Gu, “An SVM-based detection for coherent optical APSK systems with nonlinear phase noise,” IEEE Photonics J. 6(5), 1–10 (2014).

Li, S.

L. Li, G. Zhang, X. Zheng, S. Li, H. Zhang, and B. Zhou, “Phase noise suppression for single-sideband, modulation radio-over-fiber systems adopting optical spectrum processing,” IEEE Photonics Technol. Lett. 25(11), 1024–1026 (2013).

Li, Z.

D. Wang, M. Zhang, Z. Li, C. Song, M. Fu, J. Li, and X. Chen, “System impairment compensation in coherent optical communications by using a bio-inspired detector based on artificial neural network and genetic algorithm,” Opt. Commun. 399, 1–12 (2017).

D. Wang, M. Zhang, Z. Li, J. Li, M. Fu, Y. Cui, and X. Chen, “Modulation format recognition and OSNR estimation using CNN-based deep learning,” IEEE Photonics Technol. Lett. 29, 1667 (2017).

D. Wang, M. Zhang, J. Li, Z. Li, J. Li, C. Song, and X. Chen, “Intelligent constellation diagram analyzer using convolutional neural network-based deep learning,” Opt. Express 25(15), 17150–17166 (2017).
[PubMed]

D. Wang, M. Zhang, Z. Cai, Y. Cui, Z. Li, H. Han, and B. Luo, “Combatting nonlinear phase noise in coherent optical systems with an optimized decision processor based on machine learning,” Opt. Commun. 369, 199–208 (2016).

D. Wang, M. Zhang, M. Fu, Z. Cai, Z. Li, H. Han, Y. Cui, and B. Luo, “Nonlinearity mitigation using a machine learning detector based on k-nearest neighbors,” IEEE Photonics Technol. Lett. 28(19), 2102–2105 (2016).

Liang, X.

J. James, P. Shen, A. Nkansah, X. Liang, and N. J. Gomes, “Nonlinearity and noise effects in multi-level signal millimeter-wave over fiber transmission using single and dual wavelength modulation,” IEEE Trans. Microw. Theory Tech. 58(11), 3189–3198 (2010).

Liu, C.

Liu, P.

P. Liu, M. Di Renzo, and A. Springer, “Line-of-sight spatial modulation for indoor mmWave communication at 60 GHz,” IEEE Trans. Wirel. Commun. 15(11), 7373–7389 (2016).

Liu, S.

Liu, Z.

Z. Liu, Q. Xie, K. Peng, and Z. Yang, “APSK constellation with Gray mapping,” IEEE Commun. Lett. 15(12), 1271–1273 (2011).

Lozano, A.

J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. Soong, and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Comm. 32(6), 1065–1082 (2014).

Lu, F.

Luo, B.

D. Wang, M. Zhang, M. Fu, Z. Cai, Z. Li, H. Han, Y. Cui, and B. Luo, “Nonlinearity mitigation using a machine learning detector based on k-nearest neighbors,” IEEE Photonics Technol. Lett. 28(19), 2102–2105 (2016).

D. Wang, M. Zhang, Z. Cai, Y. Cui, Z. Li, H. Han, and B. Luo, “Combatting nonlinear phase noise in coherent optical systems with an optimized decision processor based on machine learning,” Opt. Commun. 369, 199–208 (2016).

Ma, X.

L. Cheng, M. Xu, F. Lu, J. Wang, J. Zhang, X. Ma, and G. K. Chang, “Millimeter-wave cell grouping for optimized coverage based on radio-over-fiber and centralized processing,” in Optical Fiber Communication Conference, Optical Society of America (2016).

Marchesani, R.

M. Baldi, F. Chiaraluce, A. De Angelis, R. Marchesani, and S. Schillaci, “A comparison between APSK and QAM in wireless tactical scenarios for land mobile systems,” EURASIP J. Wirel. Commun. Netw. 2012(1), 317 (2012).

Marcuse, D.

D. Marcuse, A. R. Chraplyvy, and R. Tkach, “Effect of fiber nonlinearity on long-distance transmission,” J. Lightwave Technol. 9(1), 121–128 (1991).

Marshall, T. S.

Mian, A.

Monroy, I. T.

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).

Nebendahl, B.

Nkansah, A.

J. James, P. Shen, A. Nkansah, X. Liang, and N. J. Gomes, “Nonlinearity and noise effects in multi-level signal millimeter-wave over fiber transmission using single and dual wavelength modulation,” IEEE Trans. Microw. Theory Tech. 58(11), 3189–3198 (2010).

A. Hekkala, M. Lasanen, I. Harjula, L. C. Viera, N. J. Gomes, and A. Nkansah, “Analysis of and compensation for non-ideal RoF links in DAS [coordinated and distributed MIMO],” IEEE Wirel. Commun. 17(3), 5490979 (2010).

A. Hekkala, M. Lasanen, L. C. Vieira, N. J. Gomes, and A. Nkansah, “Architectures for joint compensation of RoF and PA with nonideal feedback,” in Vehicular Technology Conference (IEEE, 2010).

Peng, K.

Z. Liu, Q. Xie, K. Peng, and Z. Yang, “APSK constellation with Gray mapping,” IEEE Commun. Lett. 15(12), 1271–1273 (2011).

Pfeiffer, T.

T. Pfeiffer, “Next generation mobile fronthaul architectures,” in Optical Fiber Communication Conference,Optical Society of America (2015).

Sakamoto, T.

T. Kuri, T. Sakamoto, and T. Kawanishi, “An effect of detuning frequency in DSP-assisted offset-frequency-spaced two-tone optical coherent detection for radio-over-fiber signal,” in Photonics Conference (IPC) (2014).

Savory, S. J.

S. J. Savory, “Digital coherent optical receivers: Algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).

Schillaci, S.

M. Baldi, F. Chiaraluce, A. De Angelis, R. Marchesani, and S. Schillaci, “A comparison between APSK and QAM in wireless tactical scenarios for land mobile systems,” EURASIP J. Wirel. Commun. Netw. 2012(1), 317 (2012).

Scott, C.

T. Watanabe, D. Kessler, C. Scott, M. Angstadt, and C. Sripada, “Disease prediction based on functional connectomes using a scalable and spatially-informed support vector machine,” Neuroimage 96, 183–202 (2014).
[PubMed]

Shen, G.

Shen, P.

J. James, P. Shen, A. Nkansah, X. Liang, and N. J. Gomes, “Nonlinearity and noise effects in multi-level signal millimeter-wave over fiber transmission using single and dual wavelength modulation,” IEEE Trans. Microw. Theory Tech. 58(11), 3189–3198 (2010).

Song, C.

D. Wang, M. Zhang, Z. Li, C. Song, M. Fu, J. Li, and X. Chen, “System impairment compensation in coherent optical communications by using a bio-inspired detector based on artificial neural network and genetic algorithm,” Opt. Commun. 399, 1–12 (2017).

D. Wang, M. Zhang, J. Li, Z. Li, J. Li, C. Song, and X. Chen, “Intelligent constellation diagram analyzer using convolutional neural network-based deep learning,” Opt. Express 25(15), 17150–17166 (2017).
[PubMed]

Soong, A. C.

J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. Soong, and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Comm. 32(6), 1065–1082 (2014).

Springer, A.

P. Liu, M. Di Renzo, and A. Springer, “Line-of-sight spatial modulation for indoor mmWave communication at 60 GHz,” IEEE Trans. Wirel. Commun. 15(11), 7373–7389 (2016).

Sripada, C.

T. Watanabe, D. Kessler, C. Scott, M. Angstadt, and C. Sripada, “Disease prediction based on functional connectomes using a scalable and spatially-informed support vector machine,” Neuroimage 96, 183–202 (2014).
[PubMed]

Szafraniec, B.

Tan, K.

P. Du, K. Tan, and X. Xing, “A novel binary tree support vector machine for hyperspectral remote sensing image classification,” Opt. Commun. 285(13), 3054–3060 (2012).

Tian, H.

Tkach, R.

D. Marcuse, A. R. Chraplyvy, and R. Tkach, “Effect of fiber nonlinearity on long-distance transmission,” J. Lightwave Technol. 9(1), 121–128 (1991).

Vieira, L. C.

A. Hekkala, M. Lasanen, L. C. Vieira, N. J. Gomes, and A. Nkansah, “Architectures for joint compensation of RoF and PA with nonideal feedback,” in Vehicular Technology Conference (IEEE, 2010).

Viera, L. C.

A. Hekkala, M. Lasanen, I. Harjula, L. C. Viera, N. J. Gomes, and A. Nkansah, “Analysis of and compensation for non-ideal RoF links in DAS [coordinated and distributed MIMO],” IEEE Wirel. Commun. 17(3), 5490979 (2010).

Wan, J.

Wang, D.

D. Wang, M. Zhang, Z. Li, C. Song, M. Fu, J. Li, and X. Chen, “System impairment compensation in coherent optical communications by using a bio-inspired detector based on artificial neural network and genetic algorithm,” Opt. Commun. 399, 1–12 (2017).

D. Wang, M. Zhang, J. Li, Z. Li, J. Li, C. Song, and X. Chen, “Intelligent constellation diagram analyzer using convolutional neural network-based deep learning,” Opt. Express 25(15), 17150–17166 (2017).
[PubMed]

D. Wang, M. Zhang, Z. Li, J. Li, M. Fu, Y. Cui, and X. Chen, “Modulation format recognition and OSNR estimation using CNN-based deep learning,” IEEE Photonics Technol. Lett. 29, 1667 (2017).

D. Wang, M. Zhang, Z. Cai, Y. Cui, Z. Li, H. Han, and B. Luo, “Combatting nonlinear phase noise in coherent optical systems with an optimized decision processor based on machine learning,” Opt. Commun. 369, 199–208 (2016).

D. Wang, M. Zhang, M. Fu, Z. Cai, Z. Li, H. Han, Y. Cui, and B. Luo, “Nonlinearity mitigation using a machine learning detector based on k-nearest neighbors,” IEEE Photonics Technol. Lett. 28(19), 2102–2105 (2016).

Wang, H.

S. Zhao, X. Zhu, H. Wang, and L. Wu, “Analysis of joint effect of phase noise, IQ imbalance and amplifier nonlinearity in OFDM system,” in 2013 International Conference on Wireless Communications & Signal Processing (IEEE, 2013).

Wang, J.

Wang, Z.

Z. Wang, H. Yin, W. Zhang, and G. Wei, “Monobit digital receivers for QPSK: design, performance and impact of IQ imbalances,” IEEE Trans. Commun. 61(8), 3292–3303 (2013).

Watanabe, T.

T. Watanabe, D. Kessler, C. Scott, M. Angstadt, and C. Sripada, “Disease prediction based on functional connectomes using a scalable and spatially-informed support vector machine,” Neuroimage 96, 183–202 (2014).
[PubMed]

Wei, G.

Z. Wang, H. Yin, W. Zhang, and G. Wei, “Monobit digital receivers for QPSK: design, performance and impact of IQ imbalances,” IEEE Trans. Commun. 61(8), 3292–3303 (2013).

Wu, L.

S. Zhao, X. Zhu, H. Wang, and L. Wu, “Analysis of joint effect of phase noise, IQ imbalance and amplifier nonlinearity in OFDM system,” in 2013 International Conference on Wireless Communications & Signal Processing (IEEE, 2013).

Wymeersch, H.

N. Jiang, Y. Gong, J. Karout, H. Wymeersch, P. Johannisson, M. Karlsson, and P. Andrekson, “Stochastic backpropagation for coherent optical communications,” in European Conference and Exposition on Optical Communications, Optical Society of America, (2011).

Xie, Q.

Z. Liu, Q. Xie, K. Peng, and Z. Yang, “APSK constellation with Gray mapping,” IEEE Commun. Lett. 15(12), 1271–1273 (2011).

Xing, X.

P. Du, K. Tan, and X. Xing, “A novel binary tree support vector machine for hyperspectral remote sensing image classification,” Opt. Commun. 285(13), 3054–3060 (2012).

Xu, M.

Yang, J.

Y. Han, S. Yu, M. Li, J. Yang, and W. Gu, “An SVM-based detection for coherent optical APSK systems with nonlinear phase noise,” IEEE Photonics J. 6(5), 1–10 (2014).

Yang, Z.

Z. Liu, Q. Xie, K. Peng, and Z. Yang, “APSK constellation with Gray mapping,” IEEE Commun. Lett. 15(12), 1271–1273 (2011).

Yi, A.

Yin, H.

Z. Wang, H. Yin, W. Zhang, and G. Wei, “Monobit digital receivers for QPSK: design, performance and impact of IQ imbalances,” IEEE Trans. Commun. 61(8), 3292–3303 (2013).

Yu, J.

Z. Jia, J. Yu, and G. K. Chang, “A full-duplex radio-over-fiber system based on optical carrier suppression and reuse,” IEEE Photonics Technol. Lett. 18(16), 1726–1728 (2006).

Yu, S.

Y. Han, S. Yu, M. Li, J. Yang, and W. Gu, “An SVM-based detection for coherent optical APSK systems with nonlinear phase noise,” IEEE Photonics J. 6(5), 1–10 (2014).

Zhang, G.

L. Li, G. Zhang, X. Zheng, S. Li, H. Zhang, and B. Zhou, “Phase noise suppression for single-sideband, modulation radio-over-fiber systems adopting optical spectrum processing,” IEEE Photonics Technol. Lett. 25(11), 1024–1026 (2013).

Zhang, H.

L. Li, G. Zhang, X. Zheng, S. Li, H. Zhang, and B. Zhou, “Phase noise suppression for single-sideband, modulation radio-over-fiber systems adopting optical spectrum processing,” IEEE Photonics Technol. Lett. 25(11), 1024–1026 (2013).

Zhang, J.

F. Lu, M. Xu, L. Cheng, J. Wang, J. Zhang, and G. K. Chang, “Non-orthogonal multiple access with successive interference cancellation in millimeter-wave radio-over-fiber systems,” J. Lightwave Technol. 34(17), 4179–4186 (2016).

L. Cheng, M. Xu, F. Lu, J. Wang, J. Zhang, X. Ma, and G. K. Chang, “Millimeter-wave cell grouping for optimized coverage based on radio-over-fiber and centralized processing,” in Optical Fiber Communication Conference, Optical Society of America (2016).

Zhang, J. C.

J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. Soong, and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Comm. 32(6), 1065–1082 (2014).

Zhang, M.

D. Wang, M. Zhang, Z. Li, C. Song, M. Fu, J. Li, and X. Chen, “System impairment compensation in coherent optical communications by using a bio-inspired detector based on artificial neural network and genetic algorithm,” Opt. Commun. 399, 1–12 (2017).

D. Wang, M. Zhang, J. Li, Z. Li, J. Li, C. Song, and X. Chen, “Intelligent constellation diagram analyzer using convolutional neural network-based deep learning,” Opt. Express 25(15), 17150–17166 (2017).
[PubMed]

D. Wang, M. Zhang, Z. Li, J. Li, M. Fu, Y. Cui, and X. Chen, “Modulation format recognition and OSNR estimation using CNN-based deep learning,” IEEE Photonics Technol. Lett. 29, 1667 (2017).

D. Wang, M. Zhang, M. Fu, Z. Cai, Z. Li, H. Han, Y. Cui, and B. Luo, “Nonlinearity mitigation using a machine learning detector based on k-nearest neighbors,” IEEE Photonics Technol. Lett. 28(19), 2102–2105 (2016).

D. Wang, M. Zhang, Z. Cai, Y. Cui, Z. Li, H. Han, and B. Luo, “Combatting nonlinear phase noise in coherent optical systems with an optimized decision processor based on machine learning,” Opt. Commun. 369, 199–208 (2016).

Zhang, W.

S. Liu, M. Xu, J. Wan, F. Lu, W. Zhang, H. Tian, and G. K. Chang, “A Multi-level Artificial Neural Network Nonlinear Equalizer for Millimeter-wave Mobile Fronthaul Systems,” J. Lightwave Technol. 35, 4406 (2017).

Z. Wang, H. Yin, W. Zhang, and G. Wei, “Monobit digital receivers for QPSK: design, performance and impact of IQ imbalances,” IEEE Trans. Commun. 61(8), 3292–3303 (2013).

Zhao, S.

S. Zhao, X. Zhu, H. Wang, and L. Wu, “Analysis of joint effect of phase noise, IQ imbalance and amplifier nonlinearity in OFDM system,” in 2013 International Conference on Wireless Communications & Signal Processing (IEEE, 2013).

Zheng, X.

L. Li, G. Zhang, X. Zheng, S. Li, H. Zhang, and B. Zhou, “Phase noise suppression for single-sideband, modulation radio-over-fiber systems adopting optical spectrum processing,” IEEE Photonics Technol. Lett. 25(11), 1024–1026 (2013).

Zhou, B.

L. Li, G. Zhang, X. Zheng, S. Li, H. Zhang, and B. Zhou, “Phase noise suppression for single-sideband, modulation radio-over-fiber systems adopting optical spectrum processing,” IEEE Photonics Technol. Lett. 25(11), 1024–1026 (2013).

Zhu, M.

Zhu, X.

S. Zhao, X. Zhu, H. Wang, and L. Wu, “Analysis of joint effect of phase noise, IQ imbalance and amplifier nonlinearity in OFDM system,” in 2013 International Conference on Wireless Communications & Signal Processing (IEEE, 2013).

Zibar, D.

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).

EURASIP J. Wirel. Commun. Netw. (1)

M. Baldi, F. Chiaraluce, A. De Angelis, R. Marchesani, and S. Schillaci, “A comparison between APSK and QAM in wireless tactical scenarios for land mobile systems,” EURASIP J. Wirel. Commun. Netw. 2012(1), 317 (2012).

IEEE Commun. Lett. (1)

Z. Liu, Q. Xie, K. Peng, and Z. Yang, “APSK constellation with Gray mapping,” IEEE Commun. Lett. 15(12), 1271–1273 (2011).

IEEE J. Sel. Areas Comm. (1)

J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. Soong, and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Comm. 32(6), 1065–1082 (2014).

IEEE J. Sel. Top. Quantum Electron. (1)

S. J. Savory, “Digital coherent optical receivers: Algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).

IEEE Photonics J. (1)

Y. Han, S. Yu, M. Li, J. Yang, and W. Gu, “An SVM-based detection for coherent optical APSK systems with nonlinear phase noise,” IEEE Photonics J. 6(5), 1–10 (2014).

IEEE Photonics Technol. Lett. (5)

L. Li, G. Zhang, X. Zheng, S. Li, H. Zhang, and B. Zhou, “Phase noise suppression for single-sideband, modulation radio-over-fiber systems adopting optical spectrum processing,” IEEE Photonics Technol. Lett. 25(11), 1024–1026 (2013).

Z. Jia, J. Yu, and G. K. Chang, “A full-duplex radio-over-fiber system based on optical carrier suppression and reuse,” IEEE Photonics Technol. Lett. 18(16), 1726–1728 (2006).

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).

D. Wang, M. Zhang, M. Fu, Z. Cai, Z. Li, H. Han, Y. Cui, and B. Luo, “Nonlinearity mitigation using a machine learning detector based on k-nearest neighbors,” IEEE Photonics Technol. Lett. 28(19), 2102–2105 (2016).

D. Wang, M. Zhang, Z. Li, J. Li, M. Fu, Y. Cui, and X. Chen, “Modulation format recognition and OSNR estimation using CNN-based deep learning,” IEEE Photonics Technol. Lett. 29, 1667 (2017).

IEEE Trans. Commun. (2)

Z. Wang, H. Yin, W. Zhang, and G. Wei, “Monobit digital receivers for QPSK: design, performance and impact of IQ imbalances,” IEEE Trans. Commun. 61(8), 3292–3303 (2013).

C. Hager, A. G. Amat, A. Alvarado, and E. Agrell, “Design of APSK constellations for coherent optical channels with nonlinear phase noise,” IEEE Trans. Commun. 61(8), 3362–3373 (2013).

IEEE Trans. Microw. Theory Tech. (1)

J. James, P. Shen, A. Nkansah, X. Liang, and N. J. Gomes, “Nonlinearity and noise effects in multi-level signal millimeter-wave over fiber transmission using single and dual wavelength modulation,” IEEE Trans. Microw. Theory Tech. 58(11), 3189–3198 (2010).

IEEE Trans. Wirel. Commun. (1)

P. Liu, M. Di Renzo, and A. Springer, “Line-of-sight spatial modulation for indoor mmWave communication at 60 GHz,” IEEE Trans. Wirel. Commun. 15(11), 7373–7389 (2016).

IEEE Wirel. Commun. (1)

A. Hekkala, M. Lasanen, I. Harjula, L. C. Viera, N. J. Gomes, and A. Nkansah, “Analysis of and compensation for non-ideal RoF links in DAS [coordinated and distributed MIMO],” IEEE Wirel. Commun. 17(3), 5490979 (2010).

J. Lightwave Technol. (5)

Neuroimage (1)

T. Watanabe, D. Kessler, C. Scott, M. Angstadt, and C. Sripada, “Disease prediction based on functional connectomes using a scalable and spatially-informed support vector machine,” Neuroimage 96, 183–202 (2014).
[PubMed]

Opt. Commun. (3)

P. Du, K. Tan, and X. Xing, “A novel binary tree support vector machine for hyperspectral remote sensing image classification,” Opt. Commun. 285(13), 3054–3060 (2012).

D. Wang, M. Zhang, Z. Li, C. Song, M. Fu, J. Li, and X. Chen, “System impairment compensation in coherent optical communications by using a bio-inspired detector based on artificial neural network and genetic algorithm,” Opt. Commun. 399, 1–12 (2017).

D. Wang, M. Zhang, Z. Cai, Y. Cui, Z. Li, H. Han, and B. Luo, “Combatting nonlinear phase noise in coherent optical systems with an optimized decision processor based on machine learning,” Opt. Commun. 369, 199–208 (2016).

Opt. Express (3)

Other (15)

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Figures (15)

Fig. 1
Fig. 1

mm-wave RoF based fiber-wireless transmission system.

Fig. 2
Fig. 2

Example of binary SVM.

Fig. 3
Fig. 3

(a) Classification strategy for16-QAM; (b) Classification strategy for 64-QAM.

Fig. 4
Fig. 4

(a) Classification strategy for16-APSK; (b) Classification strategy for 32-APSK.

Fig. 5
Fig. 5

Experimental setup of the mm-wave RoF system. BBU: baseband unit. RRH: remote radio head. DFB: distributed feedback laser. MZM: Mach-Zehnder modulator. AWG: arbitrary waveform generator. EDFA: Erbium doped fiber amplifier. SMF: single-mode fiber. PD: photo-detector. EA: electrical amplifier. DSO: digital oscilloscope.

Fig. 6
Fig. 6

Optical spectra of OCS in the first MZM.

Fig. 7
Fig. 7

(a) Measured BER as a function of the Vin for 16-QAM; (b) Measured BER as a function of received optical power for 16-QAM.

Fig. 8
Fig. 8

The classification results of bit-based SVM decision processor for 16-QAM signal.

Fig. 9
Fig. 9

(a) Measured BER as a function of the Vin for 64-QAM; (b) Measured BER as a function of received optical power of 64-QAM.

Fig. 10
Fig. 10

The classification results of bit-based SVM decision processor for 64-QAM signal.

Fig. 11
Fig. 11

BER as a function of the Vin for 16-QAM and 16-APSK.

Fig. 12
Fig. 12

(a) Measured BER as a function of the Vin for 16-APSK; (b) Measured BER as a function of received optical power of 16-APSK.

Fig. 13
Fig. 13

The classification results of bit-based SVM decision processor for 16-APSK signal.

Fig. 14
Fig. 14

(a) Measured BER as a function of the Vin for 32-APSK; (b) Measured BER as a function of received optical power of 32-APSK.

Fig. 15
Fig. 15

The classification results of bit-based SVM decision processor for 32-APSK signal.

Equations (5)

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f(x)= w t +b
C ^ =sign[f(x)]=sign[ w t +b]
κ( x i , x j )=exp( x i x j 2 2 σ 2 )
C + =sign[f(x)]>0 l + =+1"1"
C =sign[f(x)]<0 l =1"0"